Characterization of the Brillouin loss of single mode fibers by use of very short (10ns) pulses

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Flooding Stress-Induced Glycine-Rich

Mol. Cells OT, 47-54DOI/10.1007/s10059-009-0004-4Flooding Stress-Induced Glycine-RichRNA-Binding Protein from Nicotiana tabacum Mi-Ok Lee1, Keun Pill Kim1,3, Byung-gee Kim2, Ji-Sook Hahn2, and Choo Bong Hong1,*A cDNA clone for a transcript preferentially expressed during an early phase of flooding was isolated from káÅçJ íá~å~=í~Ä~Åìã. Nucleotide sequencing of the cDNA clone identified an open reading frame that has high homology to the previously reported glycine-rich RNA-binding pro-teins. The open reading frame consists of 157 amino acids with an N-terminal RNA-recognition motif and a C-terminal glycine-rich domain, and thus the cDNA clone was desig-nated as káÅçíá~å~=í~Ä~ÅÅìãglycine-rich RNA-binding protein-1 (kídomN). Expression of kídomN was upregu-lated under flooding stress and also increased, but at much lower levels, under conditions of cold, drought, heat, high salt content, and abscisic acid treatment. RNA homopolymer-binding assay showed that NtGRP1 binds to all the RNA homopolymers tested with a higher affinity to poly r(G) and poly r(A) than to poly r(U) and poly r(C). Nu-cleic acid-binding assays showed that NtGRP1 binds to ssDNA, dsDNA, and mRNA. NtGRP1 suppressed expres-sion of the fire luciferase gene áå=îáíêç, and the suppres-sion of luciferase gene expression could be rescued by addition of oligonucleotides. Collectively, the data suggest NtGRP1 as a negative modulator of gene expression by binding to DNA or RNA in bulk that could be advantageous for plants in a stress condition like flooding.INTRODUCTIONFlooding often causes severe damage to crops and this is es-pecially important in about 16% of the production area world-wide (Boyer, 1962). Although this problem occurs mainly in tropical rainforests, plants can also undergo such stress in cooler regions during much of the year when soil water remains saturated due to bad drainage and slow evaporation. Occa-sional heavy rainfalls also affect crops in temperate zones. Although there are plants that can cope with prolonged flooding conditions, most plants are tolerant to flooding in a very re-stricted level (Drew et al., 2000). When plants susceptible to flooding stress are subjected to submergence, most genes are silenced while some genes are newly induced. The proteins that are specifically up-regulated when this type of stress oc-curs are referred to as anaerobic proteins, and the proteins most studied so far mainly comprised metabolic pathway en-zymes (Dat et al., 2004; Dennis et al., 2000). However, much more diverse genes are induced when plants become sub-merged. These include putative transcription factor genes, signal transduction pathway component genes, and some without predicted functions (Agarwal and Grover, 2005; Klok et al., 2002). Among the flooding stress-induced proteins, we were interested in studying the GRPs that have been reported to function in posttranscriptional gene regulation. Regulation of gene expression at the posttranscriptional level is one major regulatory domain that influences and controls growth, development, and differentiation of organisms that often relate to stress response. Posttranscriptional gene regula-tion includes pre-mRNA splicing, capping and poly adenylation, mRNA transport, mRNA stability, and translation of the func-tional mRNA (Higgins, 1991; Simpson and Filipowicz, 1996). In these processes, regulation is mainly achieved either directly by the RNA-binding proteins (RBPs), or indirectly by the RBPs modulating function of other regulatory factors. RBPs that con-tain one or more RNA recognition motifs (RRMs) at the N-terminus and a variety of auxiliary motifs at the C-terminus, such as glycine-rich, arginine-rich, SR-repeat, RD-repeat, and acidic domain, have been identified (Alb and Pages, 1998; Bove et al., 2008; Fukami-Kobayashi et al., 1993; Fusaro et al., 2007; Kenan et al., 1991; Mousavi and Hotta, 2005; Nakami-nami et al., 2006; Palusa et al., 2007). The RRM contains two essential motifs, designated ribonucleoprotein (RNP)-1, posi-tioned centrally, and RNP-2, positioned toward the N-terminus (Query et al., 1989).Posttranscriptional regulatory functions of RBPs in plants have not been studied as much as those in other eukaryotes (Fedoroff, 2002). Although it has been shown that ^ê~ÄáÇçéëáëgenome encodes more than 200 putative RNA-binding proteins, only a few RBPs in plants have been studied for their function (Lorkovic and Barta, 2002; Rochaix, 2001). A gene encoding a protein containing RRMs at the N-terminus and glycine-rich region at the C-terminus (glycine-rich RNA-binding protein, GRP) was first isolated from maize (Gomez et al., 1988), following which, cDNAs encoding homologous proteins have been identified from various plant species (Carpenter et al.,MoleculesandCells©2009 KSMCB1School of Biological Sciences and Institute of Molecular Biology and Genetics, Seoul National University, Seoul 151-742, Korea, 2School of Chemical and Biological Engineering, Seoul National University, Seoul 151-742, Korea, 3Present address: Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA02138, USA*Correspondence: hcb@snu.ac.krReceived July 11, 2008; revised October 7, 2008; accepted October 17, 2008; published online February 5, 2009Keywords: flooding, glycine-rich RNA-binding protein, negative modulator I=NtGRP1, tobacco48 Flooding-Induced Glycine-Rich RNA-Binding Protein1994; Condit et al., 1990; Gendra et al., 2004; Hirose et al., 1993; Horvath and Olson, 1998; Masaki et al., 2008; Moriguchi et al., 1997; Shinozuka et al., 2006; van Nocker and Vierstra, 1993). Given their possible role in RNA recognition and proc-essing, plant GRPs with RNA-binding capacity may have im-portant roles in plant cell physiology, and their involvement in the stress responses of plants has been indicated by several expression analyses. The GRP mRNA accumulation levels were shown to be modified following exposure to stresses such as wounding, salt, and dehydration (Kim et al., 2005; Sachetto-Martins et al., 2000). The involvement of plant GRPs during cold acclimation has also been implicated by the fact that GRP transcription was significantly induced by low temperatures (Dunn et al., 1996; Stephen et al., 2003). Although the functions of the plant GRPs remain elusive, affinity of the GRPs for vari-ous types of nucleic acids has been reported. In riboho-mopolymer-binding assays, GRP proteins from maize, barley, and ^ê~ÄáÇçéëáë show higher affinity to poly r(U) and poly r(G) than to poly r(C) and poly r(A) (Dunn et al., 1996; Karlson et al., 2002; Kim et al., 2005; Ludevid et al., 1992). GRPs bind not only to double stranded DNA but also to single stranded DNA (Hirose et al., 1993; Karlson et al., 2002).As a step toward understanding the biological role of GRPs in plants under flooding stress condition, a cDNA clone for a GRP was isolated from tobacco (káÅçíá~å~=í~Ä~Åìã) under a flooding stress condition, and designated kídomN. Here we report experimental evidences for NtGRP1 that support its func-tion as a comprehensive negative modulator of gene expres-sion. It probably suggests that down regulation of expression of a wide range of genes in plants under stress conditions would be one mechanism to adapt to unfavorable conditions like flooding.MATERIALS AND METHODSPlant material and stress treatmentsTobacco (káÅçíá~å~=í~Ä~Åìã=cv W38) plants were grown in soil in a growth room (16-h photoperiod, 23°C, 60% relative humid-ity, and 200 μE m-2 s-1 from fluorescent lamps), and 6-weeks old plants with 4 to 6 leaves were used as the source of plant tis-sue for all experiments, unless otherwise mentioned. Flooding stress was applied by fully immersing the pots in tap water for 2 or 4 h. For low-temperature treatment, the plants were placed at 4°C for 12, 24, or 48 h. For drought treatment, plants were placed on a filter paper and maintained for 12, 24, or 48 h. For salinity treatment, the root was immersed in 0.5 or 1 M NaCl solution for 12 h, and for ABA treatment, the root was im-mersed in 10 μM ABA solution for 12 or 24 h.cDNA cloning for a GRPA tobacco flooding-stressed cDNA library (Lee et al., 2007) was screened using 32P-labeled single-stranded cDNA probes that were synthesized from poly(A)+ RNA isolated from either flood-ing-stressed or unstressed tobacco plants. The cDNA clones showing induction under flooding stress were isolated, one-path nucleotide sequenced, and the sequences were analyzed based on the existing annotation for non-redundant databases at the NCBI () using BLASTX (Alt-schul et al., 1997; Lee et al., 2008). Among the cDNA clones analyzed, a clone encoding GRP was isolated. Since the clone did not carry the 5′-terminus, PCR was carried out with a de-generative forward primer, GRP-dF (5′-ATGGC(A/T)GAAGT (T/A)GAATAC(A/C)G(G/T)TGC-3′), based on the highly con-served sequence among the most closely related GRP se-quences and a reverse primer based on the nucleotide se-quence in the partial cDNA clone, GRP-R (5′-TGAAGGAAG-CTGGAGGAGTTAA-3′). The PCR products were cloned into the pCR-Blunt II-TOPO vector (Invitrogen, USA), and the nu-cleotide sequencing of the insert confirmed that the PCR prod-uct covers the full ORF. The clone was named kídomN=(káÅçJ íá~å~=í~Ä~Åìã glycine-rich RNA-binding protein 1).RNA blot hybridizationTotal RNA was isolated from tobacco according to the method of Sambrook et al. (1989) with minor modifications (Lee et al., 2007). Briefly, tissues were ground in liquid nitrogen with a mortar, and extracted with homogenization buffer (50 mM LiCl, 25 mM Tris-Cl pH 7.5, 35 mM EDTA, 35 mM EGTA, and 0.5% SDS) and then with phenol:chloroform:isoamylalcohol (25:24:1) mixture. The aqueous phase was separated by centrifugation, and extracted with chloroform:isoamylalcohol (1:1) mixture. RNA was precipitated by adding 4 M LiCl, and collected by centrifugation. Twenty μg of total RNA was loaded in each lane and subjected to electrophoresis on a 1.2% formaldehyde gel. RNA was then transferred onto a membrane (Hybond N; Am-ersham Bioscience, USA), and the membrane was pre-hybridized and hybridized with 32P-labeled kídomN cDNA clone at 65°C in a solution of 0.5 M sodium phosphate (pH 7.2), 7% (w/v) SDS, and 1 mM EDTA (pH 7.0). The membrane was washed and exposed to X-ray film.Production and purification of recombinant NtGRP1 proteins from bK=ÅçäáThree recombinant constructs of kídomN were made with the N-terminal His6-fusion in the pBAD NH vector (Cho et al., 2005). The full ORF of NtGRP1 was prepared by PCR using primers of GRP F27 (5′-GGGGAGCTCATGGCTGAAGTTGAATACAG-3′) and GRP R28 (5′-GGGCATGCTTAACTCCTCCAGCTTCCT- 3′). The cDNA containing the N-terminal region (from 1 to 85 amino acid of NtGRP1, designated as NtGRP11-85) was pre- pared using GRP F27 and GRP R39 (5′-GGGCATGCTTA-GACAGACTGGGCTTCGT-3′), and the cDNA containing the C-terminal region (from 47 to 156 amino acid of NtGRP1, des-ignated as NtGRP147-156) was produced by primers of GRP F40 (5′- GGGAGCTCAGAGGATTTGGATTTGTTACC-3′) and GRP R28. The six underlined nucleotides are p~ÅI and péÜI restric-tion sites. Amplified PCR products were digested with p~ÅI and péÜI and ligated into the pBADNH vector. All DNA manipula-tions were performed according to the methods of Sambrook et al. (1989), and all constructs were confirmed by DNA sequenc-ing. The resulting constructs were transformed into bK=Åçäá=strain MC1061. Expression of H6NtGRP1 and its truncated forms was induced by adding 0.1% L(+)-arabinose and incubating for 6 h at 37°C; the proteins were subsequently purified using an Ni-NTA agarose column (Qiagen, USA). Eluates were concen-trated in Centricon spin columns (Milllipore, USA). Concen-trated samples were spectrophotometrically quantified with the RC DC protein assay system (Bio-Rad Laboratories, USA). Antibody production and protein blot analysisThe purified H6NtGRP1 of 100 μg was intravenously injected into a rabbit to raise a polyclonal antibody. After the first injec-tion, three additional injections of H6NtGRP1 followed every 2 weeks. A week after the last injection, sera were collected and stored at 4°C in 50 mM phosphate buffered saline containing 30% glycerol at a concentration of 1 mg of IgG per ml (Sam-brook et al., 1989). Protein blot analyses basically followed Sambrook et al. (1989). Briefly, proteins were separated on SDS-PAGE gel and blotted onto nitrocellulose membrane (Am-ersham Bioscience). The membrane was incubated with eitherMi-Ok Lee et al. 49polyclonal anti-H6NtGRP1 antibody or anti-luciferase antibody (Promega, USA). After three washes, the membrane was hy-bridized to the horseradish peroxidase-conjugated goat anti-rabbit secondary antibody and visualized using the enhanced chemiluminescence kit (Amersham Bioscience).Binding assay on DNAGel-retardation assay for the binding activity of NtGRP1 onto ssDNA and dsDNA substrates was carried out as described previously (Nakaminami et al., 2006) with minor modifications. Briefly, 150 ng of either ssDNA (M13mp8) or dsDNA (pSPT18) were incubated with purified H6NtGRP1in a binding buffer (10 mM Tris-Cl pH 7.5). The protein was added in the following amounts: 0, 50, 100, 200, 300, and 500 ng. To test the binding affinity of NtGRP1 to ssDNA and dsDNA, 400 ng of H6NtGRP1 was added to 150 ng of DNA in the binding buffer with variable concentrations of KCl (0, 100, 200, 400, and 800 mM). The mix-tures were maintained on ice for 10 min before being subjected to agarose gel electrophoresis and visualization by ethidium bro-mide staining. The reaction volume was kept at 15 μl.Binding assay on RNAH6NtGRP1, H6NtGRP11-85, and H6NtGRP147-156proteins (300 μM each) were separated by SDS-PAGE and transferred to a nitrocellulose membrane. The membrane was washed with tris-buffered saline solution (20 mM Tris-Cl pH 7.5, 150 mM NaCl) for 20 min and prehybridized overnight at 4°C in a renaturation buffer (50 mM Tris-Cl pH 7.6, 50 mM NaCl, 1 mM EDTA, 1 mM DTT, and 1% BSA). It was then incubated for 2 h at 23°C in Northwestern binding buffer (10 mM Tris-Cl pH 7.6, 50 mM NaCl, 1 mM EDTA, and 1 mM DTT) with 32P-labeled riboho-mopolymers of 25 nucleotides. After washing four times with the northwestern binding buffer containing NaCl up to 500 mM at 23°C, the membranes were exposed to X-ray film. For the binding assay to luciferase mRNA (Promega), it was processed as the case of binding to DNA except additional RNase inhibitor RNasin (Promega) used and the incubation time kept at 15 min. Multiple bands observed in Fig. 3E for luciferase mRNA were due to the shorter and longer than expected transcripts of luciferase mRNA from the áå=îáíêçtranscription process of luciferase gene (Promega). The mRNA and protein complexes were subjected to agarose gel electrophoresis and visualized by ethidium bromide staining.Coupled áå=îáíêç transcription/translationT N T Coupled Reticulocyte Lysate System (Promega) was used for coupled áå=îáíêçtranscription/translation reaction. Briefly, plasmid T7-luciferase DNA was mixed with T7 RNA poly-merase, 0.02 mM amino acid mixture, RNase inhibitor, T N T Coupled Reticulocyte Lysate, and H6NtGRP1 (0-300 μM), and incubated at 30°C for 90 min. The amount of synthesized luciferase protein was quantified either by protein blot analysis as described above or by chemiluminescence assay. For the chemilumiscence assay, 5 μl of the 1/10 diluted áå=îáíêç transla-tion product was mixed with 20 μl of luciferase assay reagent (Promega), and chemiluminescence was measured for 2 s using a luminometer (Turner design, USA).Oligonucleotide competition assayDNA oligomer (10-500 μM; TTTTTTTTTTTTTTTTTTTTGGA-TCC) or RNA oligomer (100-500 μM; 25 mer of rU) was added to the coupled áå=îáíêç transcription/translation reaction mixture with 100 μM H6NtGRP1. The result was quantified by measur-ing chemiluminiscence from the luciferase activity as described above. RESULTSIsolation and structural characterization of NtGRP1 cDNA cloneWe constructed a cDNA library representing mRNAs from to-bacco plants exposed to a short-term flooding (Lee et al., 2007). From a differential screening of the cDNA library, we isolated cDNA clones with apparently increased expression under flood-ing. Nucleotide sequencing of the cDNA clones and homology search on the public database isolated a cDNA clone that showed high homology to the previously reported clones en-coding GRPs. The cDNA clone was named káÅçíá~å~=í~Ä~Åìãglycine-rich RNA-binding protein-1 (kídomN). This clone con-tained an incomplete open reading frame (ORF) of 418 nucleo-tides and a 3′-untranslated region of 189 nucleotides that lacked a poly(A)-tail. The missing 5′-terminus of the ORF was obtained by degenerative polymerase chain reaction (PCR); the resulting ORF was initiated with ATG and was extended for 474 nucleotides, encoding a protein of 157 amino acids with a calculated molecular mass of 17.27 kDa. RNA-binding proteins commonly feature RRMs. RRMs, in turn, usually contain two highly conserved RNP motifs: RNP-1, which consists of eight amino acid residues (K/R)G(F/Y)(G/A)RVX(F/Y), and RNP-2, which contains six amino acid residues (L/I)(F/Y)(V/I)(G/K) (G/N)L (Hanano et al., 1996). NtGRP1 has a single RRM at the N-terminus that contains RNP-1 (RGFGFVTF) and RNP-2 (CFVGGL) sequences and a glycine-rich domain at the C-terminus. About 60% of the glycine residues in the glycine-rich domain are contiguous, and tyrosine residues and charged amino acid stretches (such as RRE or RRD) are inserted be-tween the glycine stretches (Fig. 1A). Multiple alignment of NtGRP1 with other plant GRPs showed more than 70% identi-ties toward the N-terminal region in the RRM (Fig. 1B). DNA blot hybridization for kídomN on kK=í~Ä~Åìã=genomic DNA showed a single band from two restriction digests that indicates kídomN as a single copy gene in the tobacco genome (Fig. 1C).Effect of various stresses and ABA treatment on the expression of=kídomNEffect of various stresses such as flooding, cold, drought, heat and salinity, and abscisic acid (ABA) treatment on the transcript level of kídomN in tobacco plants was examined by RNA blot analyses. As shown in Fig. 2, only minor level of kídomN=tran-script was detected in the unstressed-tobacco plants. Expres-sion of kídomN was markedly induced within an hour of flood-ing, increased till the 24-h time point, and then decreased. Ex-pression of kídomN was also induced by low temperature, drought, salinity, and heat, but at much lower levels. Slight in-crease in the transcript level was also observed under the ABA treatment (Fig. 2).Nucleic acid-binding activity of NtGRP1For the analysis of NtGRP1 activity, NtGRP1 was expressed in bëÅÜÉêáÅÜá~=Åçäá as a His6-fused form (H6NtGRP1) and purified using Ni-NTA column chromatography (Fig. 3A). H6NtGRP1 showed strong binding activity to all four types of homoribonu-cleotide polymers at a lower salt concentration. At a higher salt concentration, H6NtGRP1 bound more preferentially to poly r(A) and poly r(G) than to poly r(U) and poly r(C) (Fig. 3B). When the truncated NtGRP1 proteins were subjected to the homori-boguanine polymer binding at an NaCl concentration of 250 mM, both truncated forms, i.e. H6NtGRP11J85 and H6NtGRP147-156, showed drastically reduced binding activity to poly r(G) (Figs. 3C and 3D). Gel-retardation assay on the incubation mixture of50 Flooding-Induced Glycine-Rich RNA-Binding ProteinA BCFig. 1. cDNA clone for a flooding stress-induced GRP from kK=í~Ä~Åìã. (A) Nucleotide and deduced amino acid sequences of kídomN.The RRM motif is in a grey-box, and the RNP-1 and RNP-2 sequences are underlined (RNP-2 is placed at the N-terminus). The glycine-rich region is indicated by a dashed underline. Numbers on the left indicate the position of nucleotide, and numbers on the right indicate the position of amino acid. (B) Multiple alignment of amino acid sequences of NtGRP1 and other plant GRPs in plants. The RNP-1 and RNP-2 motifs are indicated in grey. Amino acids common to all the aligned sequences are indicated by asterisks. The aligned sequences belong to the GRPs from ^ê~ÄáÇçéëáë=íÜ~äá~å~ (Z14987), páå~éëáë=~äÄ~ (L31374), pçä~åìã=íìÄÉêçëìã (Z49197), wÉ~=ã~óë (AF496726), lêóò~=ë~íáî~ (AJ302060), and däóÅáåÉ=ã~ñ (AF169205). (C) DNA blot hybridization analysis of tobacco genome for kídomN. Genomic DNA of tobacco was digested with bÅçRI or bÅçRV and subjected to DNA blot hybridization to the 32P-labeled kídomN cDNA. The nucleotide sequence reported in this article has been submitted to NCBI under the accession number EU569289.H6NtGRP1 and luciferase mRNA showed shifting of mRNA band positions in case of the luciferase mRNA and H6NtGRP1 mixture but not from the luciferase mRNA and BSA mixture (Fig. 3E). Binding activity of NtGRP1 was again tested on M13mp8 phage ssDNA and pSPT18 dsDNA. Gel mobility shift assays showed that NtGRP1 bound both ssDNA and dsDNA, but with different affinities. With the increasing amount of H6NtGRP1, shifting of the DNA band was much more evident from the ssDNA than from the dsDNA. On the other hand, BSA did not affect the mobility of both forms of DNA (Fig. 3F). Binding affin-ity of NtGRP1 onto the ssDNA was not affected by salt concen-tration up to 800 mM, and in the case of the dsDNA, a slight increase in the binding was apparent as the salt concentration increased (Fig. 3G).Effect of NtGRP1 on the coupled transcription/translation To test NtGRP1 activity on the expression of genes, H6NtGRP1 in different concentrations was added to the coupled áå=îáíêçtranscription/translation system using the firefly luciferase gene as the reporter to monitor the concentration-dependent effect of NtGRP1 on gene expression. Protein blot analysis of the luciferase protein showed that addition of H6NtGRP1 to the cou-pled áå=îáíêç transcription/translation mixture lowered the amount of luciferase protein produced from the luciferase gene in the mixture in a concentration-dependent manner (Fig. 4A). Sup-pression activity of NtGRP1 on the expression of luciferase gene was again confirmed by quantifying the activity of luciferase in the reaction mixture. The luminescence of luciferase decreased with the increase in the amount of NtGRP1 added (Fig. 4B).Oligomer DNA and RNA recover expression of the reporter gene that was suppressed by NtGRP1We hypothesized that the suppression effect of NtGRP1 on the expression of luciferase gene is due to the binding of NtGRP1 to DNA and RNA that interferes with transcription and translation of the luciferase gene. However, other possible mechanisms, such as interaction of NtGRP1 with other proteins functioning in tran-scription and/or translation, are possible that can bring about the inhibition of transcription and/or translation. To further define the suppression activity of NtGRP1, we added small deoxyoligonu-cleotide to the coupled áå=îáíêç transcription/translation mixture. If addition of this deoxyoligonucleotide to the mixture can lower the suppression activity of NtGRP1 on the expression of luciferase gene in the coupled áå=îáíêç transcription/translation mixture, it is likely to be due to competition between the deoxyoligonucleotide and the luciferase DNA for binding to NtGRP1. When the de-oxyoligonucleotide was added to the coupled áå=îáíêçtranscrip-tion/translation mixture with the luciferase gene and NtGRP1,Mi-Ok Lee et al. 51Fig. 2. Effects of ABA and various stresses on the level of kídomN transcript. Total RNA was isolated from tobacco plants that had been exposed to flooding, low temperature, drought, heat, salinity, and ABA. Each lane was loaded with 20 μg of total RNA. The num-ber above each lane indicates the number of hours that the plant had been treated for, except salinity where the number indicates molarity of NaCl.luminescence by luciferase was recovered from the suppressed level in a concentration-dependent manner up to 200 μM of the deoxyoligonucleotide in the mixture with 100 μM NtGRP1. Above this concentration, the luminescence was again suppressed (Fig. 5A). The suppression activity of NtGRP1 by binding to the tran-script of luciferase was similarly evaluated. When an RNA oli-gomer instead of the deoxyoligonucleotide was used as a com-petitor, recovery from the suppressed level of luminescence by the luciferase gene in the coupled mixture was apparent for up to 200 μM of the RNA oligomer (Fig. 5B).DISCUSSIONA cDNA clone for a glycine-rich RNA-binding protein (kídomN) was isolated from a cDNA library of flooding-stressed tobacco (Lee et al., 2007). Biological roles of GRPs in response to envi-ronmental stresses have been implicated based on the expres-sion analysis of GRPs in plants exposed to various biotic and abiotic stresses including low temperature, drought stress, and viral infection (Kwak et al., 2005; Palusa et al., 2007; Raab et al., 2006; Stephen et al., 2003). In this study, we showed that kídomN expression is strongly induced by flooding stress (Fig.2). This is the first report of a GRP being strongly induced un-der a flooding stress condition and expands the role of GRP related to flooding stress.The N-terminal RRM domain of GRPs is highly conserved but the C-terminal glycine-rich region shows substantial diver-sity (Lorkovic and Barta, 2002). NtGRP1, which is comprised of 157 amino acids, is one of the smallest among the GRPs. The size difference among the GRPs is mainly from the difference in the glycine-rich region, and NtGRP1 has a shorter glycine-rich region compared to other GRPs. NtGRP1 has a significant number of arginine residues in the glycine-rich region (Fig. 1B) that are probably responsible for the interaction with nucleic acids as shown in Fig. 3. The N-terminal RRM domain interacts with nucleic acids (Fusaro et al., 2007; Maris et al., 2005), and the C-terminal glycine-rich region is known to interact with other proteins and distinguish substrate nucleic acids (Mousavi and Hotta, 2005). Previously, GRPs from other plant species showed preferential affinity to poly r(U) and poly r(G) (Dunn et al., 1996; Kim et al., 2005; Ludevid et al., 1992; Nomata et al., 2004). On the other hand, NtGRP1 showed higher affinity to poly r(A) and poly r(G) than to poly r(U) and poly r(C). At pre-sent, no experimental evidence is available to link the structural difference observed in the glycine-rich regions of NtGRP1 and other reported GRPs: however, higher proportion of arginine residues in the region compared with other GRPs attracted our attention associated with the differences in substrate affinity. Genomic DNA blot analysis for kídomN suggests the pres-ence of a single copy of the gene in the tobacco genome (Fig. 1C). RNA blot analyses for kídomN showed strong induction of kídomN transcript under the flooding condition, and under other abiotic stress conditions, the induction was marginal (Fig.2). Signal transduction pathways involved in abiotic stresses are well known to be crosslinked, and thus a gene whose ex-pression is induced under one abiotic stress condition is often induced by other abiotic stress conditions (Knight and Knight, 2001; Mahajan and Tuteja, 2005). However, the RNA blot analysis results shown in Fig. 2 demonstrate that kídomN is a directly flooding-stress-inducible GRP gene that is drastically induced under the flooding stress condition but not under other abiotic stress conditions. Signal transduction pathways induced under abiotic stress conditions are often described as ABA-dependent or ABA-independent (Knight and Knight, 2001; Ma-hajan and Tuteja, 2005). kídomN transcript level was slightly increased upon treatment with ABA (Fig. 2); this probably does not imply strong involvement of ABA related to NtGRP1 under flooding condition.As mentioned earlier, NtGRP1 binds more preferentially to r(G) and r(A) than to r(U) and r(C) (Fig. 3B) that differentiates NtGRP1 from the previously reported binding affinity of GRPs to homoribonucleotide polymers (Dunn et al., 1996; Kim et al., 2005; Ludevid et al., 1992; Nomata et al., 2004). The histine tag attached at the N-terminus of NtGRP1 probably does not inter-fere with the binding activity of NtGRP1 to the nucleic acids at least at a high salt concentration such as 250 mM used in most buffers for the binding assays in this study. The truncated forms of NtGRP1 lost most of the binding activity (Figs. 3C and 3D). It probably indicates that NtGRP1 cannot accommodate signifi-cant deletion to carry out binding to nucleic acids. NtGRP1 binds not only to the homoribonucleotide polymers but also to mRNA (Fig. 3E); this proves its binding capacity to various types of RNAs probably in áå=îáîç. The extent of NtGRP1 bind-ing to single stranded form of DNA is strong, while its binding to double stranded form of DNA is significantly weaker (Figs. 3F and 3G). This differential affinity of NtGRP1 between ssDNA and dsDNA probably indicates that NtGRP1 is able to bind DNA much more preferentially either in the replication or tran-scription processes.If NtGRP1 binds to RNA and ssDNA, what would be the con-sequence?To test the NtGRP1 function as a gene expression regulator, we used an áå=îáíêç gene expression system with luciferase as a quantifiable reporter. We applied different concentrations of NtGRP1 on each experiment and found a dramatic decrease in expression of the luciferase gene as the amount of NtGRP1 increased (Fig. 4). Competition experiments using oligomer DNA and RNA supported the notion that NtGRP1 can bind to。

The Pik-p resistance to Magnaporthe oryzae in rice is mediated by a pair of closely

Theor Appl Genet (2011) 122:1017–1028DOI 10.1007/s00122-010-1506-3ORIGINAL PAPERThe Pik-p resistance to Magnaporthe oryzae in rice is mediated by a pair of closely linked CC-NBS-LRR genesBin Yuan · Chun Zhai · Wenjuan Wang ·Xiaoshan Zeng · Xiaoke Xu · Hanqiao Hu ·Fei Lin · Ling Wang · Qinghua PanReceived: 14 August 2010 / Accepted: 22 November 2010 / Published online: 12 December 2010© Springer-Verlag 2010Abstract The blast resistance gene Pik-p, mapping to the Pik locus on the long arm of rice chromosome 11, was iso-lated by map-based in silico cloning. Four NBS-LRR genes are present in the target region of cv. Nipponbare, and a presence/absence analysis in the Pik-p carrier cv. K60 excluded two of these as candidates for Pik-p. The other two candidates (KP3 and KP4) were expressed in cv. K60.A loss-of-function experiment by RNAi showed that both KP3 and KP4 are required for Pik-p function, while a gain-of-function experiment by complementation test revealed that neither KP3 nor KP4 on their own can impart resis-tance, but that resistance was expressed when both were introduced simultaneously. Both Pikp-1 (KP3) and Pikp-2 (KP4) encode coiled-coil NBS-LRR proteins and share, respectively, 95 and 99% peptide identity with the two alle-les, Pikm1-TS and Pikm2-TS. The Pikp-1 and Pikp-2 sequences share only limited homology. Their sequence allowed Pik-p to be distinguished from Pik, Pik-s, Pik-m and Pik-h.Both Pikp-1 and Pikp-2 were constitutively expressed in cv. K60 and only marginally induced by blast infection.IntroductionPlants have developed a multifarious defense system against their various viral, bacterial, fungal, nematode and insect pathogens. The W rst line of their defense is raised by pattern recognition receptors, which respond to pathogen-associated molecular patterns by initiating a basal defense response (Nurnberger et al. 2004; Zipfel and Felix 2005). This response is generally able to prevent infection by non-host pathogens. Some pathogens have evolved e V ector pro-teins and/or toxins, which inhibit this basal defense response, allowing the pathogen to colonize the plant (Jones and Dangl 2006; Zipfel 2008). Their second line of defense is activated by resistance (R)genes, which encode R proteins able to recognize speci W c e V ector molecules produced by the pathogen and then trigger a response within the plant cell (Da Cunha et al. 2006; Jones and Dangl 2006), R proteins typically confer race-speci W c resis-tance, and their expression is frequently associated with a hypersensitive response. Pathogen e V ectors able toCommunicated by B. Keller.B. Yuan andC. Zhai contributed equally to this work.Electronic supplementary material The online version of this article (doi:10.1007/s00122-010-1506-3) contains supplementary material, which is available to authorized users.B. Yuan ·C. Zhai · W. Wang · X. Zeng · X. Xu · H. Hu · F. Lin · L. Wang · Q. Pan (&)Laboratory of Plant Resistance and Genetics,College of Resources and Environmental Sciences,South China Agricultural University,Guangzhou 510642, Chinae-mail: panqh@Present Address:B. YuanHubei Academy of Agricultural Science,Wuhan 430064, ChinaPresent Address:X. XuGuangdong Institute of Microbiology,Guangzhou 510070, ChinaPresent Address:H. HuGuangdong Ocean University,Zhanjinag 524088, Guangdong, Chinasuppress this response are the products of avirulence (Avr) genes. Numerous R genes have been isolated from a range of plant species (Fu et al. 2009; Krattinger et al. 2009; Liu et al. 2007a; Martin et al. 1993), and their analysis has shown that they fall into several well-de W ned classes. The nucleotide-binding site leucine-rich repeat proteins (NBS-LRR) is the largest of these (McHale et al. 2006). Their N termini comprises either a Toll-interleukin receptor (TIR)-like domain or a coiled-coil (CC) structure, so allowing for the recognition of the TIR-NBS-LRR and the CC-NBS-LRR subtypes. The Arabidopsis thaliana genome includes 159 NBS-LRR genes (both the TIR and the CC type are represented), while the rice genome includes 535 exclusively CC-NBS-LRR genes (Meyers et al. 2003; Zhou et al. 2004). In both rice and A. thaliana, most of the NBS-LRR genes occur in clusters and some in tandem arrays. Some clusters feature a heterogeneous population of genes, while others contain groups of highly homologous sequences (Leister 2004; Richly et al. 2002). In a few cases, functionality requires the simultaneous presence of two R genes (Ashikawa et al. 2008; Lee et al. 2009; Loutre et al. 2009; Sinapidou et al. 2004).Rice blast (causative pathogen Magnaporthe oryzae) is one of the most devastating diseases of rice (Ou 1985). Over 80 genes encoding resistance to various combina-tions of blast races have been documented (Ballini et al. 2008; Yang et al. 2009) and so far 13 have been isolated and characterized. Except for two (Pi-d2 and pi21), all are of the NBS-LRR type. Pi36 and Pid3 are single copy genes (Liu et al. 2007b; Shang et al. 2009), while Pita, Pib, Pi37 and Pit are members of a gene family (Bryan et al. 2000; Hayashi and Yoshida 2009; Lin et al. 2007; Wang et al. 1999). Pi9, Pi2 and Piz-t map to a single locus, but the Pi9 sequence is only weakly related to that of the allelic pair Pi2/Piz-t(Qu et al. 2006; Zhou et al. 2006). Rice chromosome 11 carries a large number of R genes, with 106 containing the protein kinase domain and 102 the NB-ARC domain (Rice Chromosomes 11 and 12 Sequencing Consortia 2005). Speci W cally, the chromosome carries the blast resistance genes Pik, Pik-p, Pik-s, Pik-g, Pik-h and Pik-m, along with the bacterial blight resistance genes Xa4 and Xa26 (Ashikawa et al. 2008; Kiyosawa 1987; Pan et al. 1998; Sun et al. 2003, 2004; Wang et al. 2009; Xu et al. 2008; Yang et al. 2003). Pik, Pik-p and Pik-m are probably allelic (Hayashi et al. 2006). The resistance spectrum of Pik-m is broader than those of Pik, Pik-p or Pik-s among Japanese, but not necessarily among Chinese pathogen populations (Kiyosawa 1987; Wang et al. 2009). The objective of the present study was to isolate and charac-terize Pik-p, which confers stable and strong resistance against both Japanese and Chinese isolates (Wang et al. 2009).Materials and methodsCandidate gene identi W cationPik-p has been mapped within a 126-kb interval of rice chromosome 11 plus a contig gap (Wang et al. 2009). The gene content in the equivalent interval of cv. Nipponbare was predicted using GENESCAN (/ GENSCAN.html) and FGENESH (http://www.softberry. com). DNA sequence comparisons were performed by pair-wise BLAST (/BLAST/bl2seq/ bl2.html) and protein sequence similarities obtained by BLASTP (Altschul et al. 1997). Transcripts of the genes present in the critical interval were sought in both the GenBank (/blast) and the rice full-length cDNA database (http://cdna01.dna.affrc.go.jp/cDNA). The presence/ absence of candidate genes was established by PCR, wherever there was a large insertion/deletion in the target region between the reference (cv. Nipponbare) and the donor (cv. K60) genomes (Figs.1 and S1).RNAi constructs and transformationTwo Pikp-1 cDNA fragments (1,246–1,730 bp from the start codon, within the NBS domain, and 2,526–3,275 bp corresponding to the LRR domain, see Fig.3a) and three cDNA Pikp-2 fragments (89–833 bp, corresponding to the CC domain, 1,163–1,748 bp, corresponding to NBS domain, and 2,546–3,061 bp, corresponding to LRR domain, see Fig.4a) were ampli W ed using primer sets, KP3i2 F/R, KP3i1 F/R, KP4i1 F/R, KP4i2 F/R and KP4i F/R, respectively (see Table S1). The W rst four of these fragments were ligated into the pDS1301 vector (Chu et al. 2006) and the W fth into the pANDA vector (Miki and Shimamoto 2004). The constructs were introduced into Agrobacterium tumefaciens strain EHA105 by electroporation (GenePulser Xcell, Bio-Rad, Hercules, CA) and then transformed into the Pik-p carrier cv. K60, as described by Lin and Zhang (2005). T0 and T1 plants were inoculated with blast isolate CHL381, and dis-ease reactions were scored as described by Pan et al. (2003). RT–PCR was used to verify that Pik-p expression was absent in susceptible T0 plants. The T1 progeny segregated as one resistant to three susceptibles and were randomly sampled to establish the correlation between disease pheno-type and the presence of the transgene (Fig.2a, b). Statisti-cal testing of the silencing e Y ciency achieved by the various RNAi fragments was carried out using a z test with Excel (Table1; Microsoft Corp., Redmond, WA).Candidate gene cloning and transformationFour overlapping fragments (3.5, 6.5, 5.7 and 6.4 kb; see Fig.S2) were ampli W ed using Phusion, a high-W delityTaq polymerase (NEB, England). After an A-tailing procedure, the 3.5-kb product was ligated into pMD20-T (TaKaRa, Dalian, China), and the other three were digested with Asc I and inserted into the pCAM-BIA1301AscI vector. The sequences of the four resulting recombinant plasmids (KP3-3.5, KP3-6.5, KP34-5.7 and KP4-6.4) were assembled by DNAStar software (http:// ). The Kpn I-Mlu I KP3-3.5, Mlu I-Sal I KP3-6.5 and Sal I-Asc I KP34-5.7 fragments were intro-duced in tandem into pCAMBIA1301AscI to form a full-length Pikp-1 insert of length 12,432 bp (Fig. S2). The full-length Pikp-2 insert (10,459 bp) comprised a combi-nation of KP34-5.7 and KP4-6.4 (Fig. S2). The 16,919 bp KP3+4 construct was built from the Kpn I–Bam HI (KP3), Bam HI–Sal I (KP3), Sal I–Bsp HI (KP4) and Bsp HI–Asc I (KP4) fragments ligated into pCAMBIA1301AscI (Fig.S2). The three constructs were independently trans-formed into the blast-susceptible cv. Q1063 as above. All T0plants were tested for their reaction to blast infection using isolates CHL381 and CHL346. The selected T0 plants were then tested for the presence of both right and left border markers. T1 progeny segregating as three resis-tant to one susceptible were randomly sampled and subjected to co-segregation analysis.Analysis of full-length cDNA and predicted protein sequencesThe cDNA 5Ј end sequences were obtained by RACE-PCR, using a SMART RACE cDNA ampli W cation kit (Clontech, Mountain View, CA), following the manufacturer’s instructions. The KP3 and KP45Ј RACE products were ampli W ed using nested PCR [W rst reaction using primers KP3-5RACE1 and KP4-5RACE1 with the universal primer A mix provided by the kit; the second PCR using KP3-5RACE2 and KP4-5RACE2 primers and the nested univer-sal primer A (NUP) from the same kit (see Table S1; Fig. S2)]. The 3Ј end sequences of KP3 and KP4 were obtained using a GeneRacerTM kit (Invitrogen, Groningen, The Netherlands) as described by Lin et al. (2007). Intermediate RT–PCR fragments were obtained using primer sets KP3ORF F/R and KP4ORF F/R for, respectively, KP3 and KP4, which overlap the 5Ј RACE and 3Ј RACE fragments of each gene. The RACE and intermediate RT–PCR prod-ucts were all cloned into pMD-20 (TaKaRa) for sequenc-ing. Sequence data of Pik-p gene has been deposited in GenBank as accession HM035360.The compute pI/Mw tool (http://www.expasy.ch/ tools/pi_tool.html; Gasteiger et al. 2005) was used topredict the isoelectric point (pI) and molecular weight of each translation product. CC structure was predicted using either COILS (/software/COILS_form.html ; Lupas et al. 1991) or Paircoil2 (/cb/paircoil2; McDonnell et al. 2006)software.Single nucleotide polymorphism (SNP) assayThe coding sequences of the susceptible cv. Q1063 and the Pik -m carrier cv. Tsuyuake, and the Pik -p carrier cv. K60were aligned using Multalin (http://bioinfo.genotoul.fr/multalin/multalin.html ) software. To validate the resulting putative SNP sites, primers were designed to create dCAPS markers able to distinguish Pik -p from Pik , Pik -m , Pik -s and Pik -h .Characterization of the race speci W city of the transgenic linesThe resistance of four T 2 lines carrying the construct KP3+4 was tested for race speci W city. Five reference lines,each carrying one of Pik , Pik -s , Pik -m , Pik -h or Pik -p (Kobayashi et al. 2007), as well as the susceptible recipient cv. Q1063, were used as a control. Eight blast isolates were selected for the test (Table 2). Blast inoculation and disease evaluation were carried out according to Pan et al.(2003).Gene expressionTwo-week-old seedlings of cv. K60 (Pik -p )and cv. Tsu-yuake (Pik -m )were inoculated with isolate CHL381 andPhenot yp eRR S S S S S S S H 2O DNA 2 4 11 15 18K60M 5 17 18 21 23nSR Pikp-1n1 2 3 5 25 5 9 10 11 13H 2ODNAK60M Phenot yp eRSSRSSR SSSSPikp-2M H 2O V213456R S S MS S Sp M H 2O V213456Phenot yp e R R S S S S S 7M H 2O V2134567RRSSSSSRRPhenot yp eSSSSSp 2134567M V Q 1063 1 2 3 4 5 6 7 8 910 MM V Q 1063 1 2 3 4 5 6 1 2 34 5 6 MPhenot yp e R R S R R R S R RSPhenot yp e R S R R R R R S S R R Rheld in the dark at 25°C with 100% relative humidity for 20h in an inoculation incubator. Inoculated leaves were sampled at the time of inoculation and then at 12, 24 and 72h post-inoculation. Total RNA was isolated from leaves using the TRIzol reagent (Invitrogen, Carlsbad, CA),following the manufacturer’s instructions. Quantitative reverse transcription PCR (qRT-PCR) was performed in two steps: W rst, »1 g total RNA was treated with RNase-freeTable 1Characterization of the coupled genes of Pik-p through loss and gain of function analyses **Signi W cant di V erences (at the =0.01 level) in the silencing e Y ciency among constructs containing di V erent fragments of the coupled genes for a 2aAbbreviations for candidates/constructs are KP3, Pikp -1; KP4, Pikp -2; KP3+4, Pikp -1+Pikp -2; RNAi, RNA interference. The detailed informa-tion on the constructs are shown in Figs.3, 4, S2bLoss-of-function-constructs were transformed into the Pik -p carrier cultivar K60, and gain-of-function-constructs were transformed into the highly susceptible cultivar Q1063c The detailed information on the primer sequences and restriction sites for constructing each vector is shown in Table S1d T 0 plants derived from each construct were inoculated with the Pik -p -avirulent isolate, CHL381 and CHL346. R resistant, MR moderately resistant, MS moderately susceptible, S susceptible eThe ratios for loss- and gain-of-function analyses were calculated as (MS +S)/(R +MR +MS +S) and (R +MR)/(R +MR +MS +S),respectivelyCandidate/construct a Recipient cultivar bExpected size (bp)Vector cReaction of T 0 plants d Success ratio (%)eRMRMSSLoss of function KP3 RNAi1K60485pDS130125*********.5**KP3 RNAi2K60750pDS130134123455822.0KP4 RNAi K60745pANDA 1274368147.2**KP4 RNAi1K60585pDS13011707255932.2KP4 RNAi2K60516pDS130131428322915.1Gain of function KP3Q106312,432pCAMBIA1301AscI 0011360KP4Q106310,459pCAMBIA1301AscI 0011080KP3+4Q106316,919pCAMBIA1301AscI7752230120.2Table 2Reactions of the W ve reference lines, each carrying one of the Pik alleles and four transgenic T 2 plants derived from the construct KP3+4,as well as the susceptible recipient cultivar Q1063 to eight isolates of Magnaporthe oryzae S susceptible, R resistant, MS moderately susceptible, MR moderately resistant, ND not determinedHostGeneM. oryzae isolates CHL22CHL346CHL42CHL272CHL446CHL503CHL508CHL995Reference lines IRBLk-Ka Pik S R S S S R ND S IRBLks-S Pik -s S S S S MS S R S IRBLkm-Ts Pik -m R R R S MR R R S IRBLkh-K3Pik -h R R R S R R R S IRBLkp-K60Pik -pRRSSSSSSTransgenic lines KP34-21-2Pikp -1+Pikp -2R R S S S S S S KP34-29-8Pikp -1+Pikp -2R R S S S S S S KP34-33-9Pikp -1+Pikp -2R R S S S S S S KP34-51-7Pikp -1+Pikp -2RRSSSSSSThe recipient cv.Q1063NoneSSSSSSSSDNase I (Promega, Madison, WI) and reverse transcribed by M-MLV (Promega, Madison, WI). Then, a 1- l aliquot of the reaction was used as the template for a qRT-PCR. The primer sets, RRT5 and RRT17 (Ashikawa et al. 2008; see Table S1), were employed to detect Pikp-1 and Pikp-2 expression. Rice Actin1 and the pathogenesis-related probe-nazole-inducible PBZ1 gene were used as internal controls (Ryu et al. 2006; Table S1). The qRT-PCR analysis was performed on a Bio-RAD CFX96 Real-Time PCR Detec-tion System device, using SYBR Premix EX TaqTM (TaKaRa, Dalian, China).ResultsIdenti W cation of candidates for Pik-pThe location of Pik-p has been placed within the genetic interval de W ned by the markers K39 and K28 (Fig.1a). In the cv. Nipponbare genome sequence, this interval is cov-ered by the four BAC clones, OSJNBb0049B20, OSJNB a0047M04, OSJNBa0036K13 and OSJNBb0018L01 (Fig.1b), and contains 25 predicted genes. Of these, four (KP1, KP2, KP3 and KP4) are of the NBS-LRR type, and so were taken as being the most likely candidates for Pik-p(Fig.1c). No ESTs corresponding to KP1 and KP2 could be identi W ed, but the EST CA763104 matched the 3Ј region of KP3, while the full-length cDNA AK073759 matched KP4. Thus, it appeared likely that both KP3 and KP4—but neither KP1 nor KP2—were expressed in cv. Nipponbare. Both KP1 and KP2 are absent in the Pik-m carrier cv. Tsu-yuake (Ashikawa et al. 2008). Ampli W cation of cv. K60 genomic DNA using PCR primer pairs targeted at KP1 and KP2 (sequences based on the cv. Nipponbare sequence, see Fig.1 and Table S1) showed that neither is present in cv. K60 either, leaving KP3 and KP4 as the two strongest can-didates for Pik-p(Figs.1c, d, S1). A number of PCR primer pairs were then designed to amplify both KP3 and KP4 from cv. K60, but the only successful ampli W cation was a 2.6-kb KP4 fragment. Extension of this sequence to »5.2kb was achieved using hi-TAIL PCR (Liu and Chen 2007), and this sequence proved to be 96% homologous to Pikm2-TS, but only 48% to Pikm6-NP (both are alleles of Pikp-2; see Figs.1, S6). Using the sequence of cv. Tsuyuake as the basis for primer design (rather than cv.Nipponbare) led to the successful ampli W cation of both the KP3 and KP4 sequences from cv. K60 (see Table S1 and below).Loss- and gain-of-function analyses for the candidate genes To determine whether KP3 or KP4 (or neither) was Pik-p, RNAi was applied to both candidates. All W ve RNAi constructs were properly expressed and abolished KP3 and KP4 expression in T0 plants (Table1; Figs.2a, S3a, S3b). The presence of the transgene and the response to pathogen infection were fully correlated among the T1 progeny (Fig.2b). The most e V ective RNAi fragment was derived from the 3Ј region of the gene, within its LRR domain (Table1; Figs.3a, 4a). Thus, both KP3 and KP4 appear to be required for Pik-p function.The three constructs KP3, KP4 and KP3+4 (Fig. S2) were then transformed into the highly susceptible japonica cv. Q1063 (Lin et al. 2007) to con W rm Pik-p function by forward complementation. A total of, respectively, 137, 109 and 406 independent T0 plants were generated. When challenged with blast isolates, CHL381 and CHL346 (avir-ulent on cv. K60), all the single gene transformants remained fully susceptible, but 83 of the 406 double gene transformants were resistant. This con W rmed that the pres-ence of both genes is needed to specify Pik-p resistance (Table1; Fig.S4). To test the correlation between pres-ence/absence of both genes and resistance/susceptibility, 53 of the 406 T0 plants were scored for the presence/absence of the right and left border markers (see Table S2; Fig. S2). Of these, 39 resistant and 11 susceptible plants carried both border markers, and two susceptible ones carried one or other of the markers; only one susceptible plant lacked both markers, indicating that the majority of the T0 plants carry-ing the complete construct (KP3+4) did not express any resistance in the recipient cultivar background when driven by their native promoters. On the other hand, the presence of the transgene and the response to pathogen infection were also fully correlated among the T1 progeny (Fig.2c). Molecular characterization of Pik-pFull-length Pikp-1 (KP3) and Pikp-2 (KP4) cDNAs were obtained by a combination of RT- and RACE-PCR (Fig. S2), and compared to their coding sequences. Pikp-1 con-tains an 83-bp 5Ј and a 163-bp 3Ј untranslated region (UTR) and two introns (150 and 2,772 bp) within its open reading frame (ORF) (Fig.3a). It encodes a 1,142-residue polypeptide with an estimated molecular weight of 126.7 kDa and a pI of 6.1. Four characteristic NBS family motifs are present: GLPGGGKTTVAR (beginning at residue 290), KKYLIVIDDIW (beginning at residue 376), DLG-GRIIMTTRLNSI (beginning at residue 402) and EDNPCY DIVNMCYGMPLALIW (beginning at residue 461), which correspond, respectively, to kinase 1a (P-loop), kinase 2, kinase 3a and motif3 (GLPL) (Fig.3b). COILS and Pair-coil2 analyses suggested the presence of a CC domain (P=0.9) between residues 146 and 177. The C-terminal region includes 16 imperfect LRR repeats, composed of »14% leucine, while the remaining 103 residues represent the C-terminal non-LRR (CtNL) region.Pikp-2 contains a 264-bp 5Ј-UTR and a 283-bp 3Ј-UTR, with two introns; the W rst is of length 882 bp and lies within the 5ЈUTR, ending 109 bp upstream of the ATG start codon, while the second is 164-bp long, and interrupts the ORF (Fig.4a). Its predicted gene product is a 1,021-residue polypeptide of molecular weight 114.6 kDa and a pI of 8.6. Its NBS domain contains six conserved motifs: kinase 1a (VLSIVGFGGVGKTTIA: beginning at residue 206), kinase 2 (LEQLLAEKSYILLIDDIW, beginning at residue 323), kinase 3a (GGRIIVTTRFQAV, beginning at residue 358), GLPL (EQVPEEIWKICGGLPLAIV, beginning at residue 415), RNBS-D (CLLYLSIFPKGWK, beginning at residue 488) and MHDV (KTFQVHDMVLEYI, beginning at residue 553) (Fig.4b). Paircoil2, but not COILS,predicted the presence of a CC domain between residues 27 and 57. The C-terminal region of the protein consists of 13 imperfect LRR repeats composed of »17% leucine.The levels of peptide sequence identity between Pikp-1 and Pikm1-TS and Pikm5-NP were 95 and 59%, respec-tively (Fig. S5), while those between Pikp-2 and Pikm2-Ts and Pikm6-NP were 99 and 76%, respectively (Fig. S6). The peptide sequences of Pikp-1 and Pikp-2 could not be aligned, as their level of similarity was lower than 23%. A comparison with the equivalent cDNA sequences ampli W ed from the susceptible cv. Q1063 and the Pik-m carrier cv. Tsuyuake revealed four potential SNPs in Pikp-1 (A222V, V230E, P251D and K261N) and three in Pikp-2 (E230D, S434T and V627M). To determine which of these weregenuinely allele speci W c, a set of reference lines, which are known carriers of Pik, Pik-p, Pik-m, Pik-s and Pik-h, as well as of Pia, Pii, Piz-t and Pita, were genotyped. The out-come was that Pik-p could be distinguished from all the above R genes using a combination of the two SNPs assays, T1-783A/G at Pikp-1 and A2-1879G at Pikp-2 (see Figs.3, 4, 5, S5, S6).Race speci W city of resistance in the transgenic linesThe W ve reference lines for the Pik alleles, Pik, Pik-s, Pik-m, Pik-h and Pik-p, reacted di V erentially to infection by the eight blast isolates (Table2). This showed that these iso-lates were able to successfully distinguish between the vari-ous Pik alleles. Since the disease reaction of the four T2lines carrying both Pikp-1 and Pikp-2 was identical to that of IRBLkp-K60 (Pik-p), the presence of Pikp-1 and Pikp-2 clearly imparts the same phenotype as that of Pik-p.Pikp-1 and Pikp-2 expression in cv. K60The transcription level of both genes was assessed in cv. K60 at four time points after blast inoculation. Both Pikp-1 and Pikp-2 transcripts were detected prior to exposure to the pathogen (Fig.6). The e V ects of mock- and pathogen inoculation were to reduce the transcription level over the W rst 24h, implying a response to stresses resulting from both inoculation and incubation in a humidity chamber (Fig.6). Expression of Pikp-1 and Pikp-2 appeared to increase only marginally during the 72h following eithermock or genuine inoculation. The expression patterns of both Pikm1-TS and Pikm2-TS (the alleles present in cv.Tsuyuake) were similar to those in cv. K60, but in contrast that of the pathogen-inducible gene, PBZ1 (Ryu et al.2006), in cv. Tsuyuake di V ered in several respects (Fig.6).DiscussionTwenty-one R genes have been mapped to date onto rice chromosome 11, including the six rice blast resistance genes Pik , Pik -s , Pik -m , Pik -p , Pik -h and Pik -g , all of which have been shown by classical genetic analysis to be allelic to one another (Ballini et al. 2008; Yang et al. 2009). With regard to the race speci W cities and/or resistance spectra of those alleles, Kiyosawa (1987) found that there are “stair-type” resistances among the alleles in the Japanese blast pathogen population, and ranked the strength of these alle-les in the order Pik -m >Pik >Pik -p >Pik -s .This, in turn,indicated that Pik , Pik -p and Pik -s all form part of the larger or stronger allele, Pik -m (Kiyosawa 1987). Among Chinese isolates, the same ranking was found in Fujian,Yunnan, Jiangsu and Heilongjiang, but not in Guandong,Fig.5Pik -p -speci W c SNP assay. SNP assay for a T1-783A/G and b T2-1879G. Lane 1 cv. K60 (Pik -p ), lane 2 IRBLkp-K60 (Pik -p reference line), lane 3 IRBLkm-Ts (Pik -m reference line), lane 4 IR-BLk-Ka (Pik reference line), lane 5 IRBLks-S (Pik -s reference line),lane 6 IRBLkh-K3 (Pik -h reference line), lane 7 IRBLa-A (Pia refer-ence line), lane 8 IRBLi-F5 (Pii reference line), lane 9 IRBLzt-T (Piz -t reference line) and lane 10 IRBLta-K1 (Pita reference line). M Size marker DL200012345678910MM abExpression analysis of Pik alleles. Transcription of Pik -m in cv. Tsuyuake and Pik -p in cv. K60 as compared by qRT-PCR. Leaf RNA was sampled before inoculation and then at 12, 24 and 72h after inoculation with either blast isolate CHL381 or water. The speci W cRNA content of each sample was estimated from the mean of three rep-licate qRT-PCRs. Outcomes of mock inoculations are shown as black bars and those of pathogen inoculations as hatched ones0 h12 h24 h72 h0 h12 h24 h72 h0 h 12 h 24 h 72 hPikp-1Pikp-2PBZ10 h 12 h 24 h 72 h0 h 12 h 24 h 72 h0 h 12 h 24 h 72 hHunan, Guizhou, Sichuan, Jiangsu, Liaoning or Jiling. In the latter regions, many isolates that were virulent against Pik-m were avirulent against Pik and Pik-p, which has been taken to indicate that the Pik alleles Pik-m, Pik and Pik-p (and perhaps other Pik alleles as well) are, indeed, indepen-dent R genes able to condition di V erential reactions against various isolates (Wang et al. 2009). The isolation of Pik-m and Pik-p has revealed that they are allelic and indepen-dent. They can be distinguished from one another on the basis of both their gene structure and their sequence. Thus, Pikp-1 and Pikm1-TS di V er from one another with respect to the length of their introns and a three base pair indel (Fig.3), while Pikp-2 carries an intron in its 5Ј UTR, which is not present in Pikm2-TS (Fig.4). Furthermore, Pik-p could be distinguished from other alleles, as well as from R genes at other loci with a combination of two SNP assays (Fig.5).Pikp-1 and Pikp-2 are closely linked to one another, but their sequence and structure are quite distinct. The presence of a CC domain in the Pikp-1 product was identi W ed by both COILS and Paircoil2 software, but this was less certain for the Pikp-2 protein. Secondly, the Pikp-2 NBS domain car-ries the motifs RNBS-D and MHDV, which are absent in Pikp-1. Thirdly, the Pikp-1 protein has a CtNL region, which Pikp-2 lacks. Fourthly, although in common with most rice NBS-LRR genes, both Pikp-1 and Pikp-2 contain an intron in their NBS kinase 2 motif (see Figs.3, 4; Bai et al. 2002), and a gene-speci W c intron is present in the Pikp-1 CC domain (Fig.3) and in the Pikp-25ЈUTR (Fig.4). Thus these two genes, although physically closely linked with one another, may well be functionally di V erent and certainly are evolutionarily distant from one another (Ashikawa et al. 2008; Bai et al. 2002; Sinapidou et al. 2004). The Pikp-1 alleles appear to be more polymorphic than the Pikp-2 ones (Figs. S5, S6), suggesting that Pikp-1 may be under greater pathogen selection pressure than Pikp-2. As the CC and NBS regions of Pik-p and Pik-m are so divergent (unlike their LRR region) (Figs. S5, S6), the indication is that race speci W city is probably determined at the CC and/or NBS, rather than at the LRR, a situation which is reproduced at the wheat Lr10 gene (Loutre et al. 2009).The reverse genetics approach RNAi has been widely used to test for loss of function (Chu et al. 2006; Miki et al. 2005; Peart et al. 2005; Peng et al. 2009). To work success-fully, it is necessary for the RNAi sequence to both e V ec-tively and speci W cally inhibit the expression of the target gene. A major e V ect on silencing e Y ciency has been shown by a range of sequences directed at various sites along a single mRNA, but the 3Ј mRNA cleavage acts as the most e V ective siRNAs (Holen et al. 2002). Here, we tested two Pikp-1 and three Pikp-2 fragments for their e Y cacy as RNAi sequences (Figs.3, 4). The most e V ective fragment in each gene was also identi W ed at the 3’ ORF region, cor-responding to the LRR domain (Table1; Figs.3, 4). These results are of general interest in furthering the understand-ing of the function and speci W city of the NBS-LRR R genes.Already, W ve R genes have turned out to be in fact a cou-pled pair. An e V ective allele of the A. thaliana RPP2 gene requires the presence of both RPP2A and RPP2B, separated from one another by »5kb and arrayed in the same orienta-tion (Sinapidou et al. 2004). RPP2A is unusual in that it has only a short LRR domain at its C-terminus, preceded by two incomplete TIR-NBS domains, whereas RPP2B has all the components expected for a full TIR-NBS-LRR class R gene. In both tetraploid and hexaploid wheat, the presence of the two adjacent, but distinct, CC-NBS-LRR genes Lr10 and RGA2 is required to confer leaf rust resistance (Loutre et al. 2009). Whereas Lr10 is a normal CC-NBS-LRR gene show-ing a measurable degree of sequence diversity in its CC domains, RGA2 is similar with RPP2A in its possession of two NBS domains and relative paucity of sequence diversity In rice, Pi5-1 and Pi5-2 are both necessary to confer race-speci W c blast resistance in the line RIL260 (Lee et al. 2009). They are arrayed in opposite orientations, separated from one another by some 15 kb of sequence, and their sequences are highly divergent from one another. The last two examples relate to Pikm1-TS/Pikm2-TS and Pikp-1/Pikp-2, where, in both cases, the pair is arrayed in opposite orientation and sep-arated by only »1kb. This small separation suggests that both genes may be under the control of a common, bidirec-tional promoter, such as the one driving A. thaliana cab1 and cab2 (Mitra et al. 2009). The evidence, such as it is from a small number of examples, is that coupled R genes consist of sequences that are divergent from one another, although both may well belong to the NBS-LRR class. It appears unlikely that these gene pairs can have evolved from one another fol-lowing an initial duplication event (Sinapidou et al. 2004).The allelism of Pik-p with Pik-m raises a number of questions regarding the Pik locus. Are Pik, Pik-h also alle-lic to Pik-p/Pik-m? Do they, like Pik-p/Pik-m, consist of a pair of coupled genes? How do these coupled genes evolve, particularly with respect to generating their allele-speci W c resistance? And how do they interact with one another, and then with their equivalent pathogen Avr genes? Acknowledgments We are grateful to Dr K. Shimamoto for his provision of the panda vector. Financial support was provided by the National 973 project and the National Transgenic Research Projects.ReferencesAltschul SF, Madden TL, Scha V er AA, Zhang J, Zhang Z, Miller W, Lipman DJ (1997) Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res 25:3389–3402。

A review of heat treatment on polyacrylonitrile fiber

Review articleA review of heat treatment on polyacrylonitrile ﬁberM.S.A.Rahaman,A.F.Ismail *,A.MustafaMembrane Research Unit (MRU),Faculty of Chemical and Natural Resources Engineering,Universiti Teknologi Malaysia,Skudai 81310,Johor,MalaysiaReceived 23January 2007;accepted 23March 2007Available online 14April 2007AbstractDeveloping carbon ﬁber from polyacrylonitrile (PAN)based ﬁber is generally subjected to three processes namely stabilization,carboniza-tion,and graphitization under controlled conditions.The PAN ﬁber is ﬁrst stretched and simultaneously oxidized in a temperature range of 200e 300 C.This treatment converts thermoplastic PAN to a non-plastic cyclic or a ladder compound.After oxidation,the ﬁbers are carbonized at about 1000 C in inert atmosphere which is usually nitrogen.Then,in order to improve the ordering and orientation of the crystallites in the direction of the ﬁber axis,the ﬁber must be heated at about 1500e 3000 C until the polymer contains 92e 100%.High temperature process generally leads to higher modulus ﬁbers which expel impurities in the chain as volatile by-products.During heating treatment,the ﬁber shrinks in diameter,builds the structure into a large structure and upgrades the strength by removing the initial nitrogen content of PAN precursor and the timing of nitrogen.With better-controlled condition,the strength of the ﬁber can achieve up to 400GPa after this pyrolysis process.Ó2007Published by Elsevier Ltd.Keywords:Polyacrylonitrile;Heat treatment;Stabilization;Carbonization;Carbon ﬁber1.IntroductionIt has been documented that the majority of all carbon ﬁ-bers used today are made from PAN precursor,which is a form of acrylic ﬁber.PAN which is a polymer with a chain of carbon connected to one another (Fig.1)is hard,horny,rel-atively insoluble,and a high-melting material [1].It has been established that PAN-based carbon ﬁber is stronger than other type of precursor-based carbon ﬁber [2].PAN-based ﬁbers also have been found to be the most suitable precursors for produc-ing high performance carbon ﬁbers (compared to pitch,rayon,etc.)generally because of its higher melting point and greater carbon yield (>50%of the original precursor mass)[3e 7].Although carbon ﬁber can be from pitch precursor,the pro-cessing and purifying it to the ﬁber form is very expensive and generally,they are more expensive than PAN-based ﬁbers [8].PAN with molecular formula [C 3H 3N]n can produce car-bon ﬁber of relatively high carbon yield giving rise toa thermally stable,extremely oriented molecular structure when subjected to a low temperature treatment [9].PAN ﬁber was also preferred to be the precursor because of its fast rate in pyrolysis without changing its basic structure [9].Optimizing the pyrolysis of PAN precursor ﬁber would ideally result in en-hanced performance of the resulting carbon ﬁber.Recent study has established that PAN ﬁbers were used on a large scale in textile industry and one of the most suitable and widely applied for making high performance carbon ﬁbers [10e 13].Most PAN-based carbon ﬁbers extensively applied in last two decades were used in the composite technology [14].They are highly desirable for high performance composites for automotive and aerospace technologies due to their enhanced physical and mechanical characteristics [9].Fitzer [15]and Chen and Harrison [16]believed that the optimization of PAN ﬁber would ideally result in high performance for use in aerospace application.Hence PAN-based ﬁber that leads to a good balance in properties can be used in structural appli-cations and provide high strength [2].Year by year there will be an improvement on performance as well as strength and modulus of PAN-based carbon ﬁber*Corresponding author.Tel.:þ6075535592;fax:þ6075581463.E-mail address:afauzi@utm.my (A.F.Ismail).0141-3910/$-see front matter Ó2007Published by Elsevier Ltd.doi:10.1016/j.polymdegradstab.2007.03.023Polymer Degradation and Stability 92(2007)1421e1432[17].Traceski[18]stated that the total worldwide production of PAN-based carbonﬁber was19million lbs per year for 1989and increased up to26million lbs per year.In addition, the worldwide outlook for the demand of PAN carbonﬁbers is currently amounting to a nearly$6billion pound per year worldwide effort[19,20].So,the wide availability of PAN pre-cursor had triggered the production of carbonﬁber.1.1.Heat treatmentHeat treatment is a process that converts the PANﬁber pre-cursor to carbonﬁber.Currently90%of all commercial carbon or graphiteﬁbers are produced by the thermal conversion of a PAN precursor,which is a form of acrylicﬁber.The successful conversion of PAN to high strength,high modulusﬁbers depend in part upon the understanding of the oxidative and thermal treatment.Liu et al.[21]listed the three steps for the conversion of precursor of PAN-basedﬁber to carbon,which are as follows.i.Oxidative stabilization,which forms ladder structure toenable them to undergo processing at higher temperatures. ii.High temperature carbonization,(1600 C)to keep out noncarbon atoms and yield a turbostatic structure.iii.Further heat up to2000 C to improve the orientation of the basal planes and the stiffness ofﬁbers,which is called graphitization.2.Precursor stabilizationAmong the conversion processes shown in Fig.2,an essen-tial and time-consuming step in the conversion of PANﬁbers to high performance carbonﬁber is the oxidative stabilization step[7].This can be explained by chemical reactions that are involved in this process,which are cyclization,dehydrogena-tion,aromatization,oxidation and crosslinking which can re-sult in the formation of the conjugated ladder structure [22,23].The oxidative stabilization stage is one of the most complicated stages,since different chemical reactions take place and the structure of the carbonﬁber is set in this stage.Stabilization process,which is done in atmosphere can change chemical structure of theﬁber and cause them to become thermally stable and so melting will not reoccur[24].Recently, the stabilization process is found to play an important role in converting PANﬁber to an infusible stable ladder polymer that converts C^N bonds to C]N bonds[25]and to develop crosslink between molecules of PAN[26]which tend to operate at high temperatures,with minimum volatilization of carbona-ceous material.The thermal stability of the stabilizedﬁber is at-tributed to the formation of the ladder structure due to cyclization of the nitrile groups in acrylic molecule.Setnescu et al.[27]observed that CH2and CN groups disappeared com-pletely due to elimination,cyclization and aromatization reac-tions and formed C]C,C]N and]C e H groups.Typically, during the course of stabilization,the PAN-based precursorﬁber undergoes a change in colour from white through shades of yel-low and browns to ultimately a black stabilizedﬁber.The mech-anism for colouration is not fully understood.However,the appearance of black colour is believed to be due to the formation of ladder ring structure[28,29].In this process,the required temperature is the important factor that would affect the heating treatment of PANﬁber. Heat treatment involved in stabilization of PANﬁber is carried out usually at the region of180e300 C[24,30].When tem-perature exceeds180 C,the molecular chains will unfold and move around.But some researchers found that heating temperature within200e300 C are usually used to stabilize theﬁber[7,23,25,31e34].Fitzer et al.[35]suggested that in producing best performance carbonﬁber,the best stabilized temperature is270 C.However,other researchers[36e38] found that heating treatment needs higher than300 C to com-plete the stabilization.Mathur et al.[39]also proposed that PANﬁber does not get preferred stability at270 C but needs higher temperature up to400 C.It was known that PANﬁber with optimum stabilization condition can produce higher mod-ulus carbonﬁber than unstablizedﬁber or thanﬁber which is prepared at high temperature stabilization process[31].If the temperature is too high,theﬁbers can overheat and fuse or even burn.However,if the temperature is too low,the reac-tions are slow and incomplete stabilization can be resulted, yielding poor carbonﬁberproperties.Previously two important reactions occur during stabiliza-tion process which can change the chemistry of PAN structure [40].They are dehydrogenation and cyclization reactions as illustrated in Fig.3.Both are important to form ladder polymer structure which was thermally stable and might be able to withstand high temperature during pyrolysis process.In addi-tion,stabilization process also could be present in oxidation reaction which gives an insight about diffusion of oxygen through the reacting polymer [41].2.1.Oxidation reactionThe oxidation reaction during PAN-based precursor stabili-zation is the least reaction and is the step which most precur-sors mercially,stabilization of PAN ﬁber is done in an ‘oxidizing’medium which is typically air.The reaction exotherm when PAN is stabilized in air is partly due to reac-tion with oxygen.Although stabilization could be done in an inert atmosphere,a polymer back-bone containing oxygen-bearing groups that evolves in PAN ladder structure (Fig.4)provides greater stability to sustain high temperature carbon-ization treatment [42].Fitzer and Muller [43]have concluded that the activation energy and the frequency factor were greater in air than in ni-trogen (inert gas).This indicates that oxygen is an initiator for the formation of activated center for cyclization because of the increase in the activation energy.Consequently,various struc-tures of oxidized PAN that account for the presence of oxygen have been proposed including those containing bridging ether links,those containing carbonyl groups,and those in which each nitrogen atom donates its lone pair of electron to an oxygen (as shown in Fig.5)[5,44].2.2.Dehydrogenation processDehydrogenation is the formation of double bonds that sta-bilizes carbon chain and cyclization is the process by whichthe rings are formed.The dehydrogenation reactions have at least two elementary steps,with oxidation in the ﬁrst step and elimination of water in the second.Studies have shown that either the original PAN polymer or cyclized ladder poly-mer can undergo dehydrogenation [43].As a conclusion from Fig.3,the reactions are usually written in the form of Fig.6.Since oxygen is required for the reaction to proceed,dehydro-genation does not occur in inert atmosphere.This is different from the cyclization reaction.The double bond or unsaturated bond that formed in the reaction improves the polymer’s ther-mal stability and reduces chain scission during carbonization [45].2.3.Cyclization reactionThe last reaction that would be discussed is cyclization which is the most important reaction in the stabilization of PAN ﬁber.Cyclization is the reaction of the nitrile groups in the precursor polymer with adjacent groups to form a stable,ladder polymer and could be described by ﬁrst order kinetic equation [43].Cyclization is the most important reaction in stabilization process.The cyclization of the nitrile groups is an exothermic reaction and that the evolution of gaseous prod-ucts accompanies this reaction [46].The reaction is necessary to hold molecules in ﬁber together and increases the stiffness [47e 50].In addition,the idea of cyclization was conceivedbyHoutz [51]in 1950from his observation that PAN stabilization led to change in colouration.During the stabilization process,the PAN structure un-dergoes cyclization reaction and converts the triple bond struc-ture (e.g.C ^N)to double bond structure (e.g.C ]N),resulting in a six-membered cyclic pyridine ring proposed by Houtz [51]as illustrated in Fig.7and changes the aliphatic to cyclic structure prior to the formation of ladder polymer.Referring to this ﬁgure (Fig.7),cyclization reactions can pro-ceed in either an inert atmosphere or in the presence of oxy-gen.In other words,oxygen is not involved in the reaction mechanism of cyclization.When the temperature rises up to 600 C,the cyclized structure undergoes dehydrogenation and links up in lateral direction,producing a graphite-likelayer or ribbon structure (shown in Fig.8)consisting of three hexagons in the lateral direction and bounded by nitrogen atom [52].The initiation of the cyclization reaction has been attributed to several sources:(1)impurities such as catalyst fragments,re-sidual polymerization products,inhibitors,etc.[53](2)the chain end groups;[54](3)random initiation by hydrogen atoms a to the nitrile;[55](4)transformation of a nitrile to an azomethine;[56];(5)the presence of a ketonitrile formed by hydrolysis dur-ing polymerization;[28]and (6)hydrolysis of nitriles to acids during polymerization [57].In addition,due to their reaction,cyclization reactions can proceed in either an inert atmosphere or in the presence of oxygen.In other words,oxygen is not in-volved in the reaction mechanism of cyclization.2.4.Miscellaneous types of stabilization processAlthough a wide variety of stabilization processes are described,they have several design objectives in common.1.Runaway reactions from heat must be prevented.2.Stabilization must be completed throughout the ﬁber.3.The shrinkage must be completed throughout the ﬁbers.4.The reactions are slow and accelerations are helpful.When the production volume increased speciﬁc methods of stabilizing the ﬁber were patented.The patents deal with three major areas:batch process,continuous process,and accelera-tion of stabilization reactions.This section provides general example from each of these areas that illustrates common de-sign objectives described above.2.4.1.Batch processThree examples of batch processes are shown in Figs.9e 11.The ﬁrst process blows hot air through a spool precursor loosely wound on a porous core.The air permits heatremovaland provides a source of oxygen.Shrinkage is controlled by the ﬁber itself as it is wound and spool.However,since the air ﬂow is not uniform and the ﬁbers are in contact with one another,a batch process with a method to move the yarn and improve the uniformity was developed as in Fig.10.The ends are tied and the rollers turned to minimize thecontact of the yarn with the rollers.And the shrinkage is con-trolled by adjusting the tension applied to the rack.The ﬁnal process in Fig.11is a step toward continuous process and probably is more expensive to operate than the two processes (Figs.9and 10)described before.The initial stages of stabili-zation are performed continuously in a multiphase oven with the ﬁber restrained from shrinkage by the oven roller.The more stable ﬁnal stages are completed in batch oven where the yarn is wrapped into loose skeins.However,the process is limited in its ability to produce since the yarn in contact with the support will differ from that surrounded by air,and the tension is not uniform in the skein.2.4.2.Continuous processThe continuous processes for stabilizing PAN are all based on the idea of pulling tows through heated boxes.The ﬁrst sketch in Fig.12illustrates the basic heated box with multiple passes.The tow may be oriented horizontally or vertically in the oven and the air in the oven is circulated to control heat and mass transfers.It also patented by Toho Company [61],where the ﬁber passes through the oven,turns on a roller,and re-enters the oven.In addition,the heat is controlled by the yarn moving outside the hot oven every few minutes.Meanwhile Cour-taulds (Fig.13)has patented a stabilization oven which con-tains a number of different temperature zones in a single oven [62].The yarn is wound on long rollers which pass through a series of bufﬂed oven zones.This concept of multi-ple zones with a stage temperature is probably used in all com-mercial processes.An interesting continuous process is shown by the ﬂuidized bed process (Fig.14)[63].Here the ﬁbersareFig.9.Batch stabilization of polyacrylonitrile yarn on the tube [58].Fig.10.Moving rack process by atomic energy authority [59].1425M.S.A.Rahaman et al./Polymer Degradation and Stability 92(2007)1421e 1432passed through a bed of ﬂuidized hollow balls,signiﬁcantly improving the heat and mass transfer rates.This design could allow the use of higher temperatures and still avoid runaway reaction and should allow more rapid dehydrogenation and oxidation.2.4.3.Accelerator processMost accelerators serve as initiators for the cyclization re-actions.An example of this is the introduction of acidic groups like itaconic acids which was claimed by the US patent 4,079,122[64].This monomer contains two acid groups which provide two initiation sites,leaving fewer uncyclized links for later carbonization.Besides,the US patent 4,397,831[61]claimed that by passing the ﬁbers through a bath which con-tains a water-soluble zinc compound and then washes the ﬁber with the water,could result in Lewis acid served to initiate the cyclization reaction.Other than that,an example for accelera-tor process by modifying the stabilization gas is given by the US patent 3,954,947[65].An atmosphere of oxygen and hy-drogen chloride is used,resulting in shorter times for complete stabilization.3.CarbonizationCarbonization was an aromatic growth and polymerization,in which the ﬁber would undergo heating process at a hightemperature up to 800e 3000 C,typically to a 95%carbon content [31].Carbonization at 1000 C will produce carbon ﬁ-ber in low modulus type and intermediate modulus or type II carbon ﬁber will produce at up to 1500 C [13,16,31,66].Trin-quecoste and group [67],also observed that heating process around 1000 C produced high tensile strength ﬁber,and for high modulus ﬁber,higher temperature treatment is needed.Thus,it would change the PAN structure as illustrated Fig.15[68]and Fig.16[69].A few researchers had put in effort to understand the car-bonization step especially in continuous model [21].However,whatever be the technique,the process only occurs in inert at-mosphere condition and usually involves heating the polymer in a nitrogen rich environment (Fig.17)[70].In addition,ten-sile and modulus have shown signiﬁcant increase with carbon-ization treatment under N 2[71].But some researchers proved that argon also can act as inert gas in carbonization process [72e 76].Whereas,carbonizing the stabilized PAN ﬁber in an atmosphere of HCl vapors could enhance the carbon ﬁber yield,subsequently decreasing the amount of hydrogen cya-nide (HCN)by eliminating nitrogen as ammonia.However,Fig.13.Courtaulds furnace for oxidation,carbonization and graphitization [62].1426M.S.A.Rahaman et al./Polymer Degradation and Stability 92(2007)1421e 1432the consumption of argon and HCl was very costly and HCl could make the equipment corrosive[76,77].In carbonization process,there are two steps wherein,the ﬁrst step involves in carbonization process and is the thermal pyrolysis up to600 C.Low heating rate as low as5 C/min was used which could lower the mass transfer because of in-ability of the structure[35].In the second stage,high heating rate for highﬁnal temperature is needed.Unlike theﬁrst stage,the high heating rate had been used in the second stage because of lesser possibility of damage to the structure due to stability of PAN structure[38].Thus,the pro-cess requires only less than10min for the second stage[78]. However,previous study claimed that too high heating rate could cause higher amount of shrinkage[16,35].Some studies stated that PANﬁber that stabilized at temperature fewer than 250 C could not withstand at high heating rate beyond 1700 C and produced a brittleﬁber[38].Hence,the optimum carbonization was required in order to form better properties ofﬁnal carbonﬁber.3.1.Stretching during pyrolysisStretching during pyrolysis process helps to develop high tensile modulus and improvesﬁber strength upon subsequent heat treatment.Some study indicated that the strength of the ﬁber had been restored and could be improved when the high temperatures were accompanied by reasonable degree of stretching[79].Tsai and Lin[80]and Edie[33]also stated that with the requirement of the stretching in this step,ade-quate modulus and strength of carbonﬁber could be produced.Other than that stretching could attenuate amount of shrink-age,which was caused by high heating rate[70].Therefore,if no stretching was applied in the early stage of pyrolysis,then the length shrinkage and the loss of preferred orientation occur and hence deteriorate the mechanical properties of carbon ﬁber[80].4.GraphitizationFor further improvement on the performance,carbonizedﬁ-ber must undergo graphitization process.Graphitization is the transformation of carbon structure into graphite structure by heat treatment as well as thermal decomposition at high tem-perature processing.Actually,the process of production of both carbonﬁber and graphiteﬁber was essentially the same either in carbonization or in graphitization.During graphitiza-tion the temperature does not only rise until1600 C,but ex-ceeds up to3000 C[38,77,81].In other words,graphitization process was a carbonization process at high heating tempera-ture.At this stage,up to99%of PAN polymer was converted to carbon structure.Carbonﬁber which was produced in this condition was in very high modulusﬁber or can be classiﬁed as type I carbonﬁber.5.Functionality gaseousGenerally,carbonizedﬁber can be found when the temper-ature reaches1200 C and above in inert atmosphere[76]. Through the heating process,theﬁber could expel impurities as volatile by-products such as methane(CH4),hydrogen (H2),hydrogen cyanide(HCN),water(H2O),CO2,NH3and various gases[25,33,35,82].Among that gases,HCN,NH3 and CO are the toxic compounds that evolved during pyrolysis [83].But,HCN and NH3are the major toxic gases that evolved from decomposition of PAN.Data pertaining to evo-lution of gases during the carbonization process,from Donnet and Bahl[84],are shown in Fig.18.The other factor that promoted excessively volatile compo-nent was high stabilization temperature.High stabilization temperature promotes over absorption of oxygen in stabilized ﬁber and might form excessive e C]O ually,the ox-ygen in these bonds escapes as water vapor[25].It is known that the decrease of oxygen as water vapor is due to evolution of H2O in the early stages of carbonization in the range be-tween300e500 C.The evolution of H2O results from the crosslinking condensation reactions between two monomer units of the adjacent ladder polymeric molecular chains which is illustrated in Fig.19[85].When the temperature increased up to800 C,hydrogen cyanide and ammonia were the side gases which also evolved and released with water[68].Watt [86]stated that reaction involving chain termination have been stated as the reason for the formation of ammonia. This could be either by the formation of ammonia from active chain ends,or by the end-to-end joining of two ladder struc-ture(Fig.20A).While,the mechanisms for evolution of hy-drogen cyanide by the same author are shown in Fig.20A,B.Meanwhile,the formation of N2has been found to start early at720 C[68]and more nitrogen was eliminated from the bulk than from the surface during this heating process [69].Evolution of nitrogen and hydrogen was explained by Watt[86]with the scheme in Fig.21.This results in nitrogen atoms substituted in the hexagonal lattice of aromatized car-bon,and explains the presence of large amounts of nitrogen in the carbonizedﬁber.Graphitization at higher temperatures reduces the concentration of residual nitrogen to very small levels.An alternate scheme for dehydrogenation and denitro-genation has been proposed by Zhu et al.[68]and is shown in Fig.15.In addition,there is also elimination of CH4,CO2 and CO that occurs at temperature higher than800 C[87].As a result,the gases were removed until theﬁber contains up to50%carbon content and above[9,88,89].Sometimes, when the temperature increased up to1300 C,the carbonized PANﬁber could achieve96%carbon content[31].The in-crease in the carbon would decrease the nitrogen,hydrogen and oxygen content[25,31,69].Table1shows the percentage of nitrogen and hydrogen which was released from theﬁber and the increase of carbon content when the temperature rises. The release of the gases would result in loss in theﬁberweightwithin 55e 60wt%,and likely generate pores [33].Some stud-ies divided the decrease in the weight into two conditions,for about 32%weight loss in the range of 350e 800 C and 13%loss within 900e 1000 C [90].However,no weight loss was observed beyond 1900 C,and the ﬁber contains only carbon [91].Much of the research work has been done either to improve mechanical properties or to decrease the manufacturing cost of carbon ﬁber [4,35,92].The manufacturing of carbon ﬁber is not an easy task due to their strict procedure.The ﬁber also tends to brittle without proper control on optimization process.Therefore,a comprehensive study should be done to ﬁnd the optimum condition for the production of carbon ﬁber with excellent performance that used in advanced materials and becoming worldwide application.6.Effect of heating treatment on PAN-based carbon ﬁber propertiesThe characteristics of PAN-based carbon ﬁber could be measured through infrared spectra.The infrared spectrum would identify whether the PAN ﬁber was stabilized and car-bonized or not.Sometimes the characteristic was measured by physical properties as well as the diameter and the density of the ﬁber.There was a relationship between diameter,densityand performance of carbon ﬁber.Mittal et al.[38]observed that generally when the diameter decreased,the density would be increased.In general,reducing the PAN ﬁber diameter and increasing ﬁber density could make the ﬁber denser and hence improved the performance of carbon ﬁber.The improvement could be done by introducing proper treatment especially heat treatment.6.1.Infrared (IR)characteristicsInfrared (IR)spectra can be used to analyze the chemical structure that exists in the ﬁber.According to IR analyzes,PAN ﬁber showed prominent peaks at 2940cm À1(e CH stretch),2240cm À1(C ^N stretch)and 1452cm À1(e CH 2bend)and for SAF with 1%IA and 6%MA,the carbonyl stretch of comonomer units appeared at 1730cm À1[23].Conley and Beron [93]stated that two dominant peaks,which are at 2940cm À1and 2240cm À1start decreasing at 180 C due to the formation of cyclization reaction.However,Colemen and coworkers [94e 99]suggested thatthedisappearance of 2240cm À1band for the nitrile began as early as 160 C under vacuum.Setnescu et al.[27]observed,through pyrolysis process,that two peaks almost completely disappeared and new peaks appeared around 800cm À1and 1600cm À1.The change in peaks are due to the formation of C ]C,C ]N and ]C e H and results in the formation of car-bon ﬁber structure.6.2.DiameterLarge diameter is one of the limitations of ﬁber strength.As mentioned before,to give uniformity in heat treatment,ﬁbers must have a small diameter.Chen and Harrison [16],stated that small diameter can reduce any gradient temperature across the ﬁber to form uniformity of heat treatment.Commercial PAN ﬁber like Dralon T (DT)and Special Acrylic Fiber (SAF)have diameter in the range of 8e 20m m [23].As stated before,plasticizer is applied in post-spinning modiﬁcation to reduce ﬁber diameter prior to heat treatment.When heat treatment has been applied as well as the rise in the temperature,the diameter of the ﬁber would shrink againand produced small ﬁber diameter.Sometimes a diameter with ten times lower than human hair could be produced [16].The signiﬁcant reduction in diameter has been observed within the carbonization temperature (below 1000 C)[38].Similar trend of the reduction of ﬁber diameter has been found by Liu et al.[21].In other words,the diameter diminished throughout the carbonization treatment.6.3.DensityVarious studies indicated that a signiﬁcant change in the ﬁ-ber density occurred below carbonization temperature [31,81,100].Within the carbonization temperature (300e 1200 C),the changes in the density of the ﬁbers take place up to 800 C [38].Sometimes,it could rapidly change up to 1000 C [31].The density could be changed due to the com-paction of the structure taking place during the early stages of carbonization.It is also due to the presence of the noncar-bon elements in the ﬁber and the ladder polymer structures in-terconnecting with one another [100].However,the density increase was followed by a sharp drop at 1000 C which is due to the conversion of open pores to closed pores [31].As a consequence,the air would be trapped inside the ﬁbers and hence results in low density which could limit the tensile strength of the ﬁnal carbon ﬁber [25].How-ever,Ozbek and Isaac [79]and Sauder et al.[101]observed that heating temperature (HTT),which increases up to 3000 C,can eliminate the effect of open and closed pores.This is because,in this region high heating rate and high tem-perature were used which made the vibrations ofmoleculesTable 1Chemical composition of some pyrolyzed PAN samples found by elemental analysis [27]Pyrolysis temperature ( C)Element content Carbon (%)Nitrogen (%)Hydrogen (%)Initial 66.3326.00 5.4760068.5111.93 3.6990075.466.281.461430M.S.A.Rahaman et al./Polymer Degradation and Stability 92(2007)1421e 1432。

Algebraic Structure of a Master Equation with Generalized Lindblad Form

(4)
where κ is a complex constant satisfying the condition µν ≥ |κ|2 which ensures the positivity. See for example [7]1 . Then we examine an algebraic structure related to the Lie algebras su(1, 1) and su(2), and construct interesting approximate solutions by use of it. In order to solve the equation we use the method in [1] once more. For that we review a matrix representation of a and a† on the usual Fock space F = VectC {|0 , |1 , |2 , |3 , · · · }; like 0 0 1 √ 1 0 0 2 √ √ † −iθ iθ , a = e a=e 3 2 0 0 √ .. . 0 3 0 .. .. .. . . . 0 1 † N =aa= 2 3 .. . (5) (a† )n |n = √ |0 n!

X = (xij ) −→ X = (x11 , x12 , x13 , · · · ; x21 , x22 , x23 , · · · ; x31 , x32 , x33 , · · · ; · · · · · · )T where T means the transpose. The following formula AXB = (A ⊗ B T )X holds for A, B, X ∈ M (F ). Then (4) is transformed into ∂ ρ(t) = H ρ(t) ∂t where H = −iω (N ⊗ 1 − 1 ⊗ N ) =⇒ ρ(t) = etH ρ(0)

Example-based metonymy recognition for proper nouns

Example-Based Metonymy Recognition for Proper NounsYves PeirsmanQuantitative Lexicology and Variational LinguisticsUniversity of Leuven,Belgiumyves.peirsman@arts.kuleuven.beAbstractMetonymy recognition is generally ap-proached with complex algorithms thatrely heavily on the manual annotation oftraining and test data.This paper will re-lieve this complexity in two ways.First,it will show that the results of the cur-rent learning algorithms can be replicatedby the‘lazy’algorithm of Memory-BasedLearning.This approach simply stores alltraining instances to its memory and clas-siﬁes a test instance by comparing it to alltraining examples.Second,this paper willargue that the number of labelled trainingexamples that is currently used in the lit-erature can be reduced drastically.Thisﬁnding can help relieve the knowledge ac-quisition bottleneck in metonymy recog-nition,and allow the algorithms to be ap-plied on a wider scale.1IntroductionMetonymy is aﬁgure of speech that uses“one en-tity to refer to another that is related to it”(Lakoff and Johnson,1980,p.35).In example(1),for in-stance,China and Taiwan stand for the govern-ments of the respective countries:(1)China has always threatened to use forceif Taiwan declared independence.(BNC) Metonymy resolution is the task of automatically recognizing these words and determining their ref-erent.It is therefore generally split up into two phases:metonymy recognition and metonymy in-terpretation(Fass,1997).The earliest approaches to metonymy recogni-tion identify a word as metonymical when it vio-lates selectional restrictions(Pustejovsky,1995).Indeed,in example(1),China and Taiwan both violate the restriction that threaten and declare require an animate subject,and thus have to be interpreted metonymically.However,it is clear that many metonymies escape this characteriza-tion.Nixon in example(2)does not violate the se-lectional restrictions of the verb to bomb,and yet, it metonymically refers to the army under Nixon’s command.(2)Nixon bombed Hanoi.This example shows that metonymy recognition should not be based on rigid rules,but rather on statistical information about the semantic and grammatical context in which the target word oc-curs.This statistical dependency between the read-ing of a word and its grammatical and seman-tic context was investigated by Markert and Nis-sim(2002a)and Nissim and Markert(2003; 2005).The key to their approach was the in-sight that metonymy recognition is basically a sub-problem of Word Sense Disambiguation(WSD). Possibly metonymical words are polysemous,and they generally belong to one of a number of pre-deﬁned metonymical categories.Hence,like WSD, metonymy recognition boils down to the auto-matic assignment of a sense label to a polysemous word.This insight thus implied that all machine learning approaches to WSD can also be applied to metonymy recognition.There are,however,two differences between metonymy recognition and WSD.First,theo-retically speaking,the set of possible readings of a metonymical word is open-ended(Nunberg, 1978).In practice,however,metonymies tend to stick to a small number of patterns,and their la-bels can thus be deﬁned a priori.Second,classic 71WSD algorithms take training instances of one par-ticular word as their input and then disambiguate test instances of the same word.By contrast,since all words of the same semantic class may undergo the same metonymical shifts,metonymy recogni-tion systems can be built for an entire semantic class instead of one particular word(Markert and Nissim,2002a).To this goal,Markert and Nissim extracted from the BNC a corpus of possibly metonymical words from two categories:country names (Markert and Nissim,2002b)and organization names(Nissim and Markert,2005).All these words were annotated with a semantic label —either literal or the metonymical cate-gory they belonged to.For the country names, Markert and Nissim distinguished between place-for-people,place-for-event and place-for-product.For the organi-zation names,the most frequent metonymies are organization-for-members and organization-for-product.In addition, Markert and Nissim used a label mixed for examples that had two readings,and othermet for examples that did not belong to any of the pre-deﬁned metonymical patterns.For both categories,the results were promis-ing.The best algorithms returned an accuracy of 87%for the countries and of76%for the orga-nizations.Grammatical features,which gave the function of a possibly metonymical word and its head,proved indispensable for the accurate recog-nition of metonymies,but led to extremely low recall values,due to data sparseness.Therefore Nissim and Markert(2003)developed an algo-rithm that also relied on semantic information,and tested it on the mixed country data.This algo-rithm used Dekang Lin’s(1998)thesaurus of se-mantically similar words in order to search the training data for instances whose head was sim-ilar,and not just identical,to the test instances. Nissim and Markert(2003)showed that a combi-nation of semantic and grammatical information gave the most promising results(87%). However,Nissim and Markert’s(2003)ap-proach has two major disadvantages.Theﬁrst of these is its complexity:the best-performing al-gorithm requires smoothing,backing-off to gram-matical roles,iterative searches through clusters of semantically similar words,etc.In section2,I will therefore investigate if a metonymy recognition al-gorithm needs to be that computationally demand-ing.In particular,I will try and replicate Nissim and Markert’s results with the‘lazy’algorithm of Memory-Based Learning.The second disadvantage of Nissim and Mark-ert’s(2003)algorithms is their supervised nature. Because they rely so heavily on the manual an-notation of training and test data,an extension of the classiﬁers to more metonymical patterns is ex-tremely problematic.Yet,such an extension is es-sential for many tasks throughout theﬁeld of Nat-ural Language Processing,particularly Machine Translation.This knowledge acquisition bottle-neck is a well-known problem in NLP,and many approaches have been developed to address it.One of these is active learning,or sample selection,a strategy that makes it possible to selectively an-notate those examples that are most helpful to the classiﬁer.It has previously been applied to NLP tasks such as parsing(Hwa,2002;Osborne and Baldridge,2004)and Word Sense Disambiguation (Fujii et al.,1998).In section3,I will introduce active learning into theﬁeld of metonymy recog-nition.2Example-based metonymy recognition As I have argued,Nissim and Markert’s(2003) approach to metonymy recognition is quite com-plex.I therefore wanted to see if this complexity can be dispensed with,and if it can be replaced with the much more simple algorithm of Memory-Based Learning.The advantages of Memory-Based Learning(MBL),which is implemented in the T i MBL classiﬁer(Daelemans et al.,2004)1,are twofold.First,it is based on a plausible psycho-logical hypothesis of human learning.It holds that people interpret new examples of a phenom-enon by comparing them to“stored representa-tions of earlier experiences”(Daelemans et al., 2004,p.19).This contrasts to many other classi-ﬁcation algorithms,such as Naive Bayes,whose psychological validity is an object of heavy de-bate.Second,as a result of this learning hypothe-sis,an MBL classiﬁer such as T i MBL eschews the formulation of complex rules or the computation of probabilities during its training phase.Instead it stores all training vectors to its memory,together with their labels.In the test phase,it computes the distance between the test vector and all these train-ing vectors,and simply returns the most frequentlabel of the most similar training examples.One of the most important challenges inMemory-Based Learning is adapting the algorithmto one’s data.This includesﬁnding a represen-tative seed set as well as determining the rightdistance measures.For my purposes,however, T i MBL’s default settings proved more than satis-factory.T i MBL implements the IB1and IB2algo-rithms that were presented in Aha et al.(1991),butadds a broad choice of distance measures.Its de-fault implementation of the IB1algorithm,whichis called IB1-IG in full(Daelemans and Van denBosch,1992),proved most successful in my ex-periments.It computes the distance between twovectors X and Y by adding up the weighted dis-tancesδbetween their corresponding feature val-ues x i and y i:∆(X,Y)=ni=1w iδ(x i,y i)(3)The most important element in this equation is theweight that is given to each feature.In IB1-IG,features are weighted by their Gain Ratio(equa-tion4),the division of the feature’s InformationGain by its split rmation Gain,the nu-merator in equation(4),“measures how much in-formation it[feature i]contributes to our knowl-edge of the correct class label[...]by comput-ing the difference in uncertainty(i.e.entropy)be-tween the situations without and with knowledgeof the value of that feature”(Daelemans et al.,2004,p.20).In order not“to overestimate the rel-evance of features with large numbers of values”(Daelemans et al.,2004,p.21),this InformationGain is then divided by the split info,the entropyof the feature values(equation5).In the followingequations,C is the set of class labels,H(C)is theentropy of that set,and V i is the set of values forfeature i.w i=H(C)− v∈V i P(v)×H(C|v)2This data is publicly available and can be downloadedfrom /mnissim/mascara.73P F86.6%49.5%N&M81.4%62.7%Table1:Results for the mixed country data.T i MBL:my T i MBL resultsN&M:Nissim and Markert’s(2003)results simple learning phase,T i MBL is able to replicate the results from Nissim and Markert(2003;2005). As table1shows,accuracy for the mixed coun-try data is almost identical to Nissim and Mark-ert’sﬁgure,and precision,recall and F-score for the metonymical class lie only slightly lower.3 T i MBL’s results for the Hungary data were simi-lar,and equally comparable to Markert and Nis-sim’s(Katja Markert,personal communication). Note,moreover,that these results were reached with grammatical information only,whereas Nis-sim and Markert’s(2003)algorithm relied on se-mantics as well.Next,table2indicates that T i MBL’s accuracy for the mixed organization data lies about1.5%be-low Nissim and Markert’s(2005)ﬁgure.This re-sult should be treated with caution,however.First, Nissim and Markert’s available organization data had not yet been annotated for grammatical fea-tures,and my annotation may slightly differ from theirs.Second,Nissim and Markert used several feature vectors for instances with more than one grammatical role andﬁltered all mixed instances from the training set.A test instance was treated as mixed only when its several feature vectors were classiﬁed differently.My experiments,in contrast, were similar to those for the location data,in that each instance corresponded to one vector.Hence, the slightly lower performance of T i MBL is prob-ably due to differences between the two experi-ments.Theseﬁrst experiments thus demonstrate that Memory-Based Learning can give state-of-the-art performance in metonymy recognition.In this re-spect,it is important to stress that the results for the country data were reached without any se-mantic information,whereas Nissim and Mark-ert’s(2003)algorithm used Dekang Lin’s(1998) clusters of semantically similar words in order to deal with data sparseness.This fact,togetherAcc RT i MBL78.65%65.10%76.0%—Figure1:Accuracy learning curves for the mixed country data with and without semantic informa-tion.in more detail.4Asﬁgure1indicates,with re-spect to overall accuracy,semantic features have a negative inﬂuence:the learning curve with both features climbs much more slowly than that with only grammatical features.Hence,contrary to my expectations,grammatical features seem to allow a better generalization from a limited number of training instances.With respect to the F-score on the metonymical category inﬁgure2,the differ-ences are much less outspoken.Both features give similar learning curves,but semantic features lead to a higherﬁnal F-score.In particular,the use of semantic features results in a lower precisionﬁg-ure,but a higher recall score.Semantic features thus cause the classiﬁer to slightly overgeneralize from the metonymic training examples.There are two possible reasons for this inabil-ity of semantic information to improve the clas-siﬁer’s performance.First,WordNet’s synsets do not always map well to one of our semantic la-bels:many are rather broad and allow for several readings of the target word,while others are too speciﬁc to make generalization possible.Second, there is the predominance of prepositional phrases in our data.With their closed set of heads,the number of examples that beneﬁts from semantic information about its head is actually rather small. Nevertheless,myﬁrst round of experiments has indicated that Memory-Based Learning is a sim-ple but robust approach to metonymy recogni-tion.It is able to replace current approaches that need smoothing or iterative searches through a the-saurus,with a simple,distance-based algorithm.Figure3:Accuracy learning curves for the coun-try data with random and maximum-distance se-lection of training examples.over all possible labels.The algorithm then picks those instances with the lowest conﬁdence,since these will contain valuable information about the training set(and hopefully also the test set)that is still unknown to the system.One problem with Memory-Based Learning al-gorithms is that they do not directly output prob-abilities.Since they are example-based,they can only give the distances between the unlabelled in-stance and all labelled training instances.Never-theless,these distances can be used as a measure of certainty,too:we can assume that the system is most certain about the classiﬁcation of test in-stances that lie very close to one or more of its training instances,and less certain about those that are further away.Therefore the selection function that minimizes the probability of the most likely label can intuitively be replaced by one that max-imizes the distance from the labelled training in-stances.However,ﬁgure3shows that for the mixed country instances,this function is not an option. Both learning curves give the results of an algo-rithm that starts withﬁfty random instances,and then iteratively adds ten new training instances to this initial seed set.The algorithm behind the solid curve chooses these instances randomly,whereas the one behind the dotted line selects those that are most distant from the labelled training exam-ples.In theﬁrst half of the learning process,both functions are equally successful;in the second the distance-based function performs better,but only slightly so.There are two reasons for this bad initial per-formance of the active learning function.First,it is not able to distinguish between informativeandFigure4:Accuracy learning curves for the coun-try data with random and maximum/minimum-distance selection of training examples. unusual training instances.This is because a large distance from the seed set simply means that the particular instance’s feature values are relatively unknown.This does not necessarily imply that the instance is informative to the classiﬁer,how-ever.After all,it may be so unusual and so badly representative of the training(and test)set that the algorithm had better exclude it—something that is impossible on the basis of distances only.This bias towards outliers is a well-known disadvantage of many simple active learning algorithms.A sec-ond type of bias is due to the fact that the data has been annotated with a few features only.More par-ticularly,the present algorithm will keep adding instances whose head is not yet represented in the training set.This entails that it will put off adding instances whose function is pp,simply because other functions(subj,gen,...)have a wider variety in heads.Again,the result is a labelled set that is not very representative of the entire training set.There are,however,a few easy ways to increase the number of prototypical examples in the train-ing set.In a second run of experiments,I used an active learning function that added not only those instances that were most distant from the labelled training set,but also those that were closest to it. After a few test runs,I decided to add six distant and four close instances on each iteration.Figure4 shows that such a function is indeed fairly success-ful.Because it builds a labelled training set that is more representative of the test set,this algorithm clearly reduces the number of annotated instances that is needed to reach a given performance.Despite its success,this function is obviously not yet a sophisticated way of selecting good train-76Figure5:Accuracy learning curves for the organi-zation data with random and distance-based(AL) selection of training examples with a random seed set.ing examples.The selection of the initial seed set in particular can be improved upon:ideally,this seed set should take into account the overall dis-tribution of the training examples.Currently,the seeds are chosen randomly.Thisﬂaw in the al-gorithm becomes clear if it is applied to another data set:ﬁgure5shows that it does not outper-form random selection on the organization data, for instance.As I suggested,the selection of prototypical or representative instances as seeds can be used to make the present algorithm more robust.Again,it is possible to use distance measures to do this:be-fore the selection of seed instances,the algorithm can calculate for each unlabelled instance its dis-tance from each of the other unlabelled instances. In this way,it can build a prototypical seed set by selecting those instances with the smallest dis-tance on average.Figure6indicates that such an algorithm indeed outperforms random sample se-lection on the mixed organization data.For the calculation of the initial distances,each feature re-ceived the same weight.The algorithm then se-lected50random samples from the‘most proto-typical’half of the training set.5The other settings were the same as above.With the present small number of features,how-ever,such a prototypical seed set is not yet always as advantageous as it could be.A few experiments indicated that it did not lead to better performance on the mixed country data,for instance.However, as soon as a wider variety of features is taken into account(as with the organization data),the advan-pling can help choose those instances that are most helpful to the classiﬁer.A few distance-based al-gorithms were able to drastically reduce the num-ber of training instances that is needed for a given accuracy,both for the country and the organization names.If current metonymy recognition algorithms are to be used in a system that can recognize all pos-sible metonymical patterns across a broad variety of semantic classes,it is crucial that the required number of labelled training examples be reduced. This paper has taken theﬁrst steps along this path and has set out some interesting questions for fu-ture research.This research should include the investigation of new features that can make clas-siﬁers more robust and allow us to measure their conﬁdence more reliably.This conﬁdence mea-surement can then also be used in semi-supervised learning algorithms,for instance,where the clas-siﬁer itself labels the majority of training exam-ples.Only with techniques such as selective sam-pling and semi-supervised learning can the knowl-edge acquisition bottleneck in metonymy recogni-tion be addressed.AcknowledgementsI would like to thank Mirella Lapata,Dirk Geer-aerts and Dirk Speelman for their feedback on this project.I am also very grateful to Katja Markert and Malvina Nissim for their helpful information about their research.ReferencesD.W.Aha, D.Kibler,and M.K.Albert.1991.Instance-based learning algorithms.Machine Learning,6:37–66.W.Daelemans and A.Van den Bosch.1992.Generali-sation performance of backpropagation learning on a syllabiﬁcation task.In M.F.J.Drossaers and A.Ni-jholt,editors,Proceedings of TWLT3:Connection-ism and Natural Language Processing,pages27–37, Enschede,The Netherlands.W.Daelemans,J.Zavrel,K.Van der Sloot,andA.Van den Bosch.2004.TiMBL:Tilburg Memory-Based Learner.Technical report,Induction of Linguistic Knowledge,Computational Linguistics, Tilburg University.D.Fass.1997.Processing Metaphor and Metonymy.Stanford,CA:Ablex.A.Fujii,K.Inui,T.Tokunaga,and H.Tanaka.1998.Selective sampling for example-based wordsense putational Linguistics, 24(4):573–597.R.Hwa.2002.Sample selection for statistical parsing.Computational Linguistics,30(3):253–276.koff and M.Johnson.1980.Metaphors We LiveBy.London:The University of Chicago Press.D.Lin.1998.An information-theoretic definition ofsimilarity.In Proceedings of the International Con-ference on Machine Learning,Madison,USA.K.Markert and M.Nissim.2002a.Metonymy res-olution as a classification task.In Proceedings of the Conference on Empirical Methods in Natural Language Processing(EMNLP2002),Philadelphia, USA.K.Markert and M.Nissim.2002b.Towards a cor-pus annotated for metonymies:the case of location names.In Proceedings of the Third International Conference on Language Resources and Evaluation (LREC2002),Las Palmas,Spain.M.Nissim and K.Markert.2003.Syntactic features and word similarity for supervised metonymy res-olution.In Proceedings of the41st Annual Meet-ing of the Association for Computational Linguistics (ACL-03),Sapporo,Japan.M.Nissim and K.Markert.2005.Learning to buy a Renault and talk to BMW:A supervised approach to conventional metonymy.In H.Bunt,editor,Pro-ceedings of the6th International Workshop on Com-putational Semantics,Tilburg,The Netherlands. G.Nunberg.1978.The Pragmatics of Reference.Ph.D.thesis,City University of New York.M.Osborne and J.Baldridge.2004.Ensemble-based active learning for parse selection.In Proceedings of the Human Language Technology Conference of the North American Chapter of the Association for Computational Linguistics(HLT-NAACL).Boston, USA.J.Pustejovsky.1995.The Generative Lexicon.Cam-bridge,MA:MIT Press.78。

Unnatural L0 Sparse Representation for Natural Image Deblurring

(e) our x ˜
Hale Waihona Puke (f) ﬁnal restored image
Figure 1. Intermediate unnatural image representation exists in many state-of-the-art approaches.
1.1. Analysis
Prior MAP-based approaches can be roughly categorized into two groups, i.e., methods with explicit edge prediction 1
taining salient image edges. These maps are vital to make motion deblurring accomplishable in different MAP-variant frameworks. Implicit Regularization Shan et al. [20] adopted a sparse image prior. This method, in the ﬁrst a few iterations, uses a large regularization weight to suppress insigniﬁcant structures and preserve strong ones, creating crisp-edge image results, as exempliﬁed in Fig. 1(b). This scheme is useful to remove harmful subtle image structures, making kernel estimation generally follow correct directions in iterations. Krishnan et al. [16] used an L1 /L2 regularization scheme. The main feature is to adapt L1 -norm regularization by treating the L2 -norm of image gradients as a weight in iterations. One intermediate result from this method is shown in Fig. 1(c). The main difference between this form and that of [20] is on the way to adapt regularization strength in iterations. Note both of them suppress details in the early stage during optimization. Explicit Filter and Selection In [19, 3], shock ﬁlter is introduced to create a sharpened reference map for kernel estimation. Cho and Lee [3] performed bilateral ﬁlter and edge thresholding in each iteration to remove small- and medium-amplitude structures (illustrated in Fig. 1(d)), also avoiding the trivial solution. Xu and Jia [25] proposed a texture-removal strategy, explained and extended in [28], to guide edge selection and detect large-scale structures. The resulting edge map in each step is also a small-edge-subdued version from the natural input. These two schemes have been extensively validated in motion deblurring. Unnatural Representation The above techniques enable several successful MAP frameworks in motion deblurring. All of them have their intermediate image results or edge maps different from a natural one, as shown in Fig. 1, due to only containing high-contrast and step-like structures while suppressing others. We generally call them unnatural representation, which is the key to robust kernel estimation in motion deblurring.

氟化钙_氟化钡混晶制备与光学性能表征

关珮雯等：铒铥共掺碲酸盐光纤的近红外宽带发射光谱· 1599 ·第41卷第11期DOI：10.7521/j.issn.0454–5648.2013.11.23 氟化钙–氟化钡混晶制备与光学性能表征谷亮1，曾繁明1，李春1，林海1，张莹2，刘禹1，刘景和1(1. 长春理工大学材料科学与工程学院，长春 130022；2. 中国科学院长春光学精密机械与物理研究所，长春 130033 )摘要：通过直接沉淀法制备氟化钙–氟化钡(CaF2-BaF2)混晶多晶料。

采用坩埚下降法，通过设计合理的工艺条件(真空度：10–3 Pa，下降速率：0.2～1mm/h；轴向温度梯度：40～70/cm℃；径向温度梯度：50～70/cm℃，降温速率：25/h℃)，生长出不同原料配比的CaF2-BaF2混晶。

用X射线衍射仪、双折射率仪、红外分光光度计对CaF2-BaF2混晶性能进行表征，并研究其光学性能。

结果表明：CaF2-BaF2混晶尺寸为φ20mm×(175～180)mm，晶体透过率为70%～80%，其本征双折射率略低于CaF2单晶。

关键词：氟化钙；氟化钡；混晶原料纯度；双折射；透过率中图分类号：TU502.4 文献标志码：A 文章编号：0454–5648(2013)11–1599–04网络出版时间：2013–10–28 15:40:49 网络出版地址：/kcms/detail/11.2310.TQ.20131028.1540.023.htmlPreparation and Optical Characterization of Calcium Fluoride-Barium Fluoride Mixed CrystalGU Liang1，ZENG Fanming1，LI Chun1，LIN Hai1，ZHANG Ying2，LIU Yu1，LIU Jinghe1(1. School of Material Science and Engineering, Changchun University of Science and Technology, Changchun 130022, China;2. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China) Abstract: The polycrystalline materials of calcium fluoride-barium fluoride (CaF2–BaF2) were prepared by a direct precipitation method. The CaF2-BaF2 mixed crystals at different ratios of raw materials were grown by the Bridgman method. The parameters of the growth used were the vacuum degree of 10–3 Pa, the decline rate of 0.2–1mm/h, the axial temperature gradient of 40–70/cm℃, the radial temperature gradient of 50–70/cm℃, and the cooling rate of 25/h℃. The performance of the CaF2-BaF2 materials was characterized by X-ray diffraction, birefringence analysis and Fourier transform infrared spectroscopy, respectively. The optical prop-erties of the CaF2-BaF2 mixed crystal were also analyzed. The results show that the size of the CaF2-BaF2 is φ20mm in diameter and 175–180mm in length. The transmittance of the mixed crystals is 70%–80%. The intrinsic birefringence of the mixed crystals is less than that of CaF2 single crystal.Key words: calcium fluoride; barium fluoride; mixed crystals; purity of raw materials; birefringence; transmission1 IntroductionThe stages of developing integrated circuits (ICs) are divided by small-scale, large-scale, and even great-scale. The ICs can be applied in various fields such as aero-space engineering, defense engineering, etc.[1]Lithography as one of the most mature methods to prepare ICs has undergone four stages, g line (436nm), i line (365nm), far ultraviolet (UV)(248nm, KrF laser), and deep ultraviolet (DUV) (193nm, ArF laser).[2–3] The wavelength reduction at each stage represents the de-velopment of the ICs, the lithography range of DUV laser is from 193nm to 121nm now[4]. The CaF2 crys-tals are widely used as optical medium materials and important lithography lens elements due to its remark-able properties such as high and stable transmission at the ultraviolet region, broad transmittance range (from far UV to mid-IR), high laser damage threshold, low refractive index, low stress birefringence, and corrosion resistance.[5–7]As the lens of the lithography system, the lens surface of the two polarizations has different refractive indices,收稿日期：2013–02–18。

Abstract

Hyper-Polynomial Hierarchies and the NP-JumpStephen Fenner University of Southern MaineSteven HomerBoston UniversityRandall PruimBoston UniversityCalvin CollegeMarcus SchaeferUniversity of ChicagoDecember19,1997AbstractAssuming that the polynomial hierarchy()does not collapse,we show the existence of ascending sequences of ptime Turing degrees of lengthall of which are in and uniformly hard for,such that succes-sors are-jumps of their predecessors.This is analgous to the hyperarith-metic hierarchy,which is deﬁned similarly but with the(computable)Turing degrees.The lack of uniform least upper bounds for ascending sequences of ptime degrees causes the limit levels of our hyper-polynomial hierarchy to be inherently non-canonical.This problem is investigated in depth,and various possible structures for hyper-polynomial hierarchies are explicated,as are properties of the-jump operator on the languages which are inbut not in.1IntroductionSince its deﬁnition in1976,[Sto77]the polynomial hierarchy has been used to classify and measure the complexity of infeasible combinatorial problems.It has been hugely successful in this capacity,providing the main framework for com-plexity classes above polynomial time within which most subsequent complexity theory has taken place.The classes in this hierarchy,particularly in theﬁrst few levels of the hierarchy,have been studied extensively and their structure carefully examined.In this paper we consider extensions of the polynomial hierarchy into extended hierarchies,all lying within.Our aim is to provide tools for a further understanding of many complex and interesting problems which lie just outside as well as to gain further understanding of the intricacies of ptime reductions,degrees and the-jump operator.The-jump has provento be a fundamental and useful tool in complexity theory.It is the central concept in the deﬁnition of the high and low hierarchies.Its properties have recently been explored by Fenner[Fen95].The polynomial time hierarchy was deﬁned and motivated in analogy with the arithmetic hierarchyﬁrst studied by Stephen Kleene.The structure and many key properties of the classes in the polynomial hierarchy are similar to those in the arithmetic hierarchy.Furthermore various concepts and deﬁnitions originating in the arithmetic hierarchy have been important in illuminating interesting aspects of the complexity theory of problems in the resource bounded setting.For example, the alternating quantiﬁer characterizations of the levels of both the arithmetic and polynomial hierarchies provides a simple and useful method for placing problems within levels of these hierarchies.One of the deepest and most elegant develop-ments in this area of mathematical logic was the extension of the arithmetic hier-archy to the hyperarithmetic hierarchy by transﬁnite iteration of the Turing jump operator and the subsequent development by Kleene,Spector and others of the properties of this hierarchy.(See,for example,[Sac90],[Rog67].)Our work here intends to develop an analogous resource bounded framework for problems lying within and above.In this work we deﬁne and(under reasonable as-sumptions)prove the existence of hyper-polynomial hierarchies formed by transﬁ-nite iteration of the-jump operator and study their properties and the properties of the-jump operator in the realm between and.Assuming the polynomial hierarchy is inﬁnite,Ambos-Spies[AS89]has shown the existence of a rich,inﬁnite partial order of degrees in above.In this paper we extend his techniques to deﬁne inﬁnite,NP-jump-respecting hierar-chies of length(theﬁrst nonconstructive ordinal)in above, which naturally extend the polynomial hierarchy.This shows that if does not collapse then not only is there a rich and complex structure to the degrees in1,but that is in some sense“very far”from,since not even many-jumps sufﬁce to get from to.We are hopeful that the classes of problems hard for levels of these hierarchies will also provide a new classiﬁcation scheme for interesting hard combinatorial problems,such as the -complete languages,which lie in but above.The major technical obstacle encountered in proving the existence of an ex-tended polynomial hierarchy is the lack of uniform least upper bounds for ascend-ing sequences of ptime degrees.This fact was noted by Ambos-Spies[AS89],and makes the deﬁnition of our hierarchies non-canonical at limit levels,giving rise to several possibilities for the properties of the extended hierarchy.This situation is explored in depth here and various possible structures for the hyper-polynomial hierarchy are explicated.For example,under reasonable assumptions about the structure of uniformly hard sets for,we prove that there is a problem which is a uniform upper bound for but is not such a bound for any ptime non-constant alternation class.Such a problem would lie“just above”,and a careful ex-amination of the proof of Toda's Theorem[Tod91]indicates that the-complete languages mayﬁt this description.Outline.After providing the necessary background on constructive ordinals and uniform upper bounds in Section2,we constuct in Section3an inﬁnite hi-erarchy of languages of length in above.This hierarchy is proper provided that doesn't collapse.In Sections4and5we investigate the extent to which such a hierarchy is or is not canonical by asking where within such a hierarchy can be placed.This investigation leads to the differentiation between two types of uniform upper bounds,slow and fast.Finally, in Section6we present some directions for further investigation.2PreliminariesWe identify,the natural numbers,with,the set of all binary strings,via the usual dyadic representation.We let be the empty string and denote bya standard ptime-computable,ptime-invertible bijection such that,and for all.Weﬁx a standard,acceptable enumeration of nondeterminis-tic oracle TMs,and a standard enumeration of deterministic ptime oracle TMs,where for each,enumerates the set of all oracle com-putations running in time for all oracles and inputs of length.Often we will abuse notation and associate with a set(language)its characteristic function. Thus if and only if.We write if and accesses the oracle only in a manner allowed by the2reduction type.For the most part we are interested in-and-reductions. As usual,is a standard acceptable enumeration of the computable partial functions(as in[Soa87]).Deﬁnition2.1For any set,we deﬁne,in the spirit of Balc´a zar,et al. [BDG88],has an acceptingpath of lengthWe call the-jump of.It is complete for under(unrelativized) -reductions.It is easy to check that lifts to a well-deﬁned operator on the degrees. We denote by the-fold iteration of.Let be a ptime alternating oracle Turing machine such that for all and,,the canonical -complete set,and write for.We assume without loss of generality that has been chosen so that for any oracle,only makes oracle queries of length.2.1Kleene'sHere we give a brief deﬁnition of Kleene's partial order,,of all notations for constructive ordinals.Here and is a binary relation on.The information in this section comes chieﬂy from Sacks[Sac90],but see also[Rog67]. Our development is slightly different from,but entirely isomorphic to,Kleene's original deﬁnition.Deﬁne and.We deﬁne by transﬁnite induction.It is the least partial order such that the following hold for all :1..2.If,then and.3.If is total,,and,then and for all.4.is transitive.It can be shown that is well-founded,and hence functions with domain can be deﬁned by transﬁnite recursion.For all we deﬁne,the unique ordinal for which is a notation,in this way:1..32.If,then.3.If,then.Each element of is the notation for a constructive ordinal,and each constructive ordinal has at least one(but usually more than one)notation.Also,if,then ,but not conversely.The set of all constructive ordinals is,which is the least non-constructive ordinal,and is countable.The structure of is a tree,where(inﬁnite)branching occurs at every limit level.Some branches(maximal linearly ordered subsets)peter out well be-fore reaching height(in fact,there are branches of height only),but some branches do reach height.The most important fact about is that one can construct objects via“effective transﬁnite recursion”up to by using notations from.We will do just that in Section3,where we deﬁne sets in for all such that implies,and.(This last inequality assumes that is inﬁnite.)This mirrors the classical construction of the hyperarithmetic hierarchy.2.2Uniform Upper Bounds and Padding ArraysIn computability theory,it is a simple matter to deﬁne a canonical join of a uni-vormly enumerable sequence of sets which is the least uniform-upper bound (in fact,the least uniform-upper bound)for the sequence.In complexity the-ory this is not possible,since there is no least uniform-upper bound[AS89], [Lad75].Furthermore,the most natural join operator has the unfortunate(for our purposes)property that the join of a collection consisting of a complete language for each level of is-complete.In our case we are interested in un-derstanding the problems which lie between and and we would like the join to be as close to as possible.Therefore,we must work instead with uniform upper bounds,deﬁned below,which correspond to possible choices for a nicely behaved join operator.Deﬁnition2.2Given a countable collection of languages,a uniform-upper bound for is a language such that there is a computable function with the property that for all,.We are primarily interested in uniform upper bounds for and similar classes.A uniform upper bound for is a uniform upper bound for. Since for any,is computably enumerable in,it also makes sense to talk about uniform upper bounds for.4Deﬁnition2.3For any computable function and any countable collection of languages,the padding array for via is the language deﬁned byTwo types of padding arrays are of special interest.1.If for every,is monotone non-decreasing and is ptimecomputable,and for every is monotone non-decreasing,then we say that is a ptime padding array via.2.If in addition,there are constants and such that for all,then we say that is a ptime padding array of degree via.A ptime padding array for is a ptime padding array for.As the following lemma shows,padding arrays are particularly nice uniform upper bounds.Lemma2.4If is a ptime padding array for via then is a uniform-upper bound for.Proof.The map is a many-one reduction from to.As a partial converse to the result above we have the following lemma.Deﬁnition2.5A function is nice if is monotone non-decreasing,unbounded, and can be computed in steps.Lemma2.6Let be a uniform-upper bound for via.If is the ptime padding array for via,and is a nice function such that for all halts in fewer than steps,then.Proof.We describe a reduction from to.On input:1.If,then.This can be determined in polynomial timebecause is nice.2.If,then compute.Since is greater thanthe number of steps required to compute,this can also be done in polynomial time.5Thus,in particular,every ptime padding array is a uniform-upper bound for,and every set which is a uniform-upper bound for is-above some ptime padding array for.3A Hyper-Polynomial HierarchyWe now come to the construction of an extended polynomial hierarchy.We show how to“embed”into in such a way that successors correspond to-jumps and limits to uniform upper bounds.We will call such an embedding a hyper-polynomial hierarchy,or-.More formally,we construct a set such that if denotes,then satisﬁes the following properties.(P1).(P2).(P3)for all.(P4)For any with,is a uniform upper bound for.(P5)If is inﬁnite,then for any,. Although is deﬁned here for all,we are really only interested in when.will be constructed by transﬁnite induction over.We will say that is universal for this hyper-polynomial hierarchy.To ensure the last two properties,we build so that is inﬁnite. At the same time,we must code into all for.We do the latter by making a uniform upper bound of,which we do by making a ptime padding array for.Now to get to separate over we delay coding each into until we notice that some designated-reduction fails to reduce some-level of the hierarchy over to the previous level(say,the st to the th).If we can do this for all and,we are done.Assuming by transﬁnite induction that separates for all,this can be accomplished by delayed diagonalization.We are guaranteed to kill off ourreduction just by waiting long enough before coding each level:will “look like”and since,will eventually make a mistake.The particular“delayed diagonalization”strategy employed here is simi-lar to those used by Ambos-Spies[AS89],which in turn are based on well-known techniques of Ladner[Lad75].We now deﬁne formally by simultaneous transﬁnite induction over and length-decreasing recursion.In what follows,are arbitrary and is a ﬁxed ptime alternating oracle Turing machine such that for all and,,the canonical-complete set.We write for and assume without loss of generality that has been chosen so that for any oracle,only makes oracle queries of length.The limit case is as explained above.We need to perform the diagonalization via a look-back technique in order to keep in—this explains the stringent bounds on ,,and in3(b).1.(thus).2.(thus).3.,unless is of the form,where is least(if it exists)such that(a)all halt in a combined total of steps,and(b)there is“sufﬁcient evidence”thatWe will say there is sufﬁcient evidence ifsuch thatIf such a least exists and for some,then we letIn this way,will be a padded version of.It is important to observe that the value of is3(b)above only depends on and not on.7Theorem3.1The set satisﬁes properties(P1)–(P5)listed above.Proof.It is not too difﬁcult to see that:the recursive aspects of the deﬁnition are all length-decreasing—due to the stringent bounds on,,and in3(b)—and the rest of the algorithm clearly needs no more than a polynomialamount of space.Properties(P2)and(P3)are also clearly satisﬁed.We prove properties(P4)and(P5)simultaneously by induction over. Actually,we need to prove a stronger property than(P5),namely:(P5a)If is inﬁnite,then is inﬁnite.Choose an arbitrary and assume that properties(P4)and(P5a)hold for all with.There are three cases:Case1:.Property(P4)holds vacuously.Since,property(P5a) holds.Case2:.Again,property(P4)holds vacuously for.Since is inﬁnite and,clearly is inﬁnite as well.Case3:.Note that is total.For property(P4),we will only show that is a uniform upper bound for.This sufﬁces,be-cause for any,there is a such that and henceand one could furthermoreﬁnd such a reduction effectively in and, using certain basic facts about.Weﬁrst show that for every,the mentioned in case(3)of the deﬁnition ofmust always exist.Assuming otherwise,let be least such that no such corresponding exists.Then for all and all, so we never code into.This makes,or if then.Now by our inductive hypothesis,is inﬁnite,so in particular,for all,there is a such thatand hence must exist by case3(b)in the deﬁnition of.The fact that exists for all immediately implies thatis inﬁnite,via an argument similar to the one just given,and8for all,a padded version of is coded into,and thusvia the mapping,where is the corresponding to.This concludes the proof.4Uniform Upper Bounds forIn this section and the next we investigate the extent to which the construction of extended hierarchies in Section3is canonical.Since uniform upper bounds can be thought of as non-canonical joins,it is inevitable that,at least level by level,such a hierarchy cannot be canonically deﬁned.As we shall see,the fact that we were able to use ptime padding arrays of bounded degree(in fact,degree0)for all of the uniform upper bounds in our construction allows for considerable manipulation of the structure of our extended hierarchies.4.1Quick Uniform Upper BoundsThe observation that all of the uniform upper bounds in our construction in the previous section were actually ptime padding arrays of degree0prompts the fol-lowing deﬁnition.We will call a uniform-upper bound forquick if there is a polynomial such that for each there is a-reduction which runs in time.A uniform-upper bound which is not quick is slow.All ptime padding arrays of bounded degree are quick uniform upper bounds.Quick uniform upper bounds for can also be characterized in terms of alternating time,as deﬁned in[CKS81].For this we deﬁne the class to consist of all languages accepted by an alternating Turing machine in polynomial time and at most alternations,beginning in an existencial state.(Note that this really is alternations and not.)Lemma4.1A set is a quick uniform-upper bound for if and only if it is -hard for for some nice.Proof.If is a quick uniform-upper bound for,then there is a com-putable function and a polynomial such that in time. Let be the largest such that all of can be computed in less than steps.Then fulﬁlls the conditions.9For the other direction let be-hard for for some as above.Con-sider the set for some., so.On the other hand via a reduction that can be found effectively.The following theorem says that quick uniform upper bounds for cannot be“just above”.Theorem4.2If is a quick uniform upper bound for,then there is a ptime padding array(hence also a uniform upper bound for)such that.The proof of Theorem4.2makes use of the following lemma.Lemma4.3If and are ptime padding arrays for via nice functions and respectively and there is some polynomial such thatthen.Note that for any,is a polynomial in of the same degree as.So to satisfy the requirements of the lemma,must be a ptime padding array of bounded degree.Thus,we have the theorem only for quick uniform upper bounds for.It remains open if there are slow uniform upper bounds for which cannot compute the jump of any other(necessarily slow)uniform upper bound for.Before proceeding to the proofs of Theorem4.2and Lemma4.3,we give a couple of examples.1.If is a padding array for via or,where is a constant,then,so is aﬁxed point of the-jump.2.If is a bounded degree ptime padding array for via,then the ptimepadding array for via satisﬁes. Proof of Theorem4.2.If is a quick uniform upper bound for then there is a bounded degree ptime padding array for,such that.By the Lemma4.3there is another ptime padding array for,,such that .10Proof of Lemma4.3.We describe an algorithm for a reduction. Remember that accepts in steps.For this proof we will use the fact that-QBF is a true formula. WLOG we can assume that,the encoding of the formula as a binary string satisﬁes.Algorithm for:1.On input,ﬁrst determine,,and such that.If none suchexist,then,so can be chosen to be someﬁxed element of .2.We need toﬁnd a QBF,such that accepts if and only if is true.Furthermore,we must in time polynomial in be able to produce a string where is coded into.For this we need the following observations about the queries made during the computation(along any path)..Therefore,if makes queries to any strings,then.If does not have the form,where is a formula and,then we know that,so we could modify so that it answers such queries“internally”(via a syntax check)without actuallyquerying the oracle.If,then we will say that is a query of typeabout.Note that,since.Let be the query of type such that is maximal among thequeries.Then all of the queries in the simulation of not handledby the syntax check above are about formulas with codes of length .ing the observations above,we see that determining whether ac-cepts is equivalent to a formula of the formwhere codes a path in the non-deterministic computation tree,codes a sequence of queries to B,codes answer bits to those queries,and is a polynomial time predicate which checks that along path,makes queries to if the answers(to previous queries)are and halts in an accept-ing conﬁguration after at most steps.11By the comments above,each predicate is,so that -QBF accepts.4.Finally,.Notice that and that,since there was a query of type.So,where is the degree of.Therefore,can be computed in time polynomial in.4.2Slow Uniform Upper BoundsWe will now construct a set which is a slow uniform upper bound for,i.e. it is an upper bound for,but there is no uniform time bound on the reductions from each level of the hierarchy to.For this proof we need to assume more than that separates.We present one hypothesis which is sufﬁcient;modiﬁcations are possible.This hypothesis is expressed in terms of a notion of subexponential advice and says roughly that no level of can be computed from a previous level,even with the additional aid of polynomial time reductions with subexponential advice.By increasing the padding,we can modify our construction of a-to include slow uniform upper bounds,if they exist.We begin by deﬁning what we mean by subexponential advice.For this,we use deﬁnitions of advice classes and reductions which are based on oracle access to the advice string.This deﬁnition is equivalent to the usual one for deﬁning common classes such as,,etc.The motivation for our deﬁnition comes from the observation that,in deﬁning for some function class such that,the usual deﬁnition in terms of languages(see[BDG88])allows the accepting machine not only to get advice from the advice string,but may also provide it with greater resource bounds,since the length of the advice string counts toward the length of the input.Thus,for example,an advice string consisting solely of a super-polynomially long sequence of0's becomes potentially useful, not because it contains any information,but simply because of its length.Our deﬁnition avoids this problem.Deﬁnition4.4(Superpolynomial advice)Let be a class of functions.For any string,let be the smallestﬁnite set for which is an initial segment of the characteristic sequence i.e.,.12We write if there is a an oracle Turing machine which runs in polynomial time regardless of oracle and a function in such thatacceptsand write if.This is equivalent to saying that access to the advice comes by querying bits of the advice string,.Similar notions could be deﬁned for other classes of Turing machines as well.For,letThe classesandhave their usual meanings,since using the advice oracle,one can calculate the ad-vice string as a preprocess,and using the advice string one can simulate the queries to the advice oracle by checking bits of the advice string.Similar statements can be made whenever the machines are capable of querying the entire advice oracle bit by bit.Also note that is the class of all languages,since we can use bits to code the membership of all the strings of length.We can now state a hypothesis sufﬁcient to demonstrate the existence of slow uniform upper bounds for.Hypothesis.The polynomial hierarchy does not collapse under polynomial time reductions with subexponential advice in the following sense:Notice that Hypothesis is(a priori)slightly stronger than the statement that whereand13Theorem4.5If is nice,then contains a slow uniform-upper bound for ,unless fails.Corollary4.6If is nice,then contains a uniform-upper bound for that is not hard for any(with nice),unless fails.Proof.We deﬁne and verify the properties.From the deﬁnition of it is clear that is a uniform-upper bound for.If were quick,then we would haveWe show that this contradicts Hypothesis.So suppose is quick,andﬁx.LetSo we can use the oracle to decide.14Thus,can be simulated making use only of and.Furthermore,since implies that and,we can code the information about into a string of length.So from our assumption that is quick it follows thatand therefore that fails.To this point we have not concerned ourselves with the complexity of.The proof just given can,however,be improved to get the upper bound required by the statement of the theorem.Given any nice,we can obtain a slow uniform upper bound for which is in as follows.Let be the smallest for which .We will use for additional padding:Then if is a string of length in,we know that,and hence.Hence lies in.The rest of the proof needs only minor adjustments.This yields the result as stated.4.3Fixed Points of the NP-jumpIn constructing a-we must avoidﬁxed points of the-jump.We show that everyﬁxed point of the-jump is a uniform upper bound for and that ﬁxed points exist which are very unlikely(even more unlikely than the examples after Lemma4.3)to be-complete.Thus it really is necessary to actively avoid them in our construction.Lemma4.7If then is a uniform-upper bound for(in fact for).Proof.Fix the reduction from to i.e..We assume that our enumeration of nondeterministic OTMs is nice in that the jump and composition of machines is effective,i.e.,that there are two computable functions and such thatif via,then via,andif via and via,then via.15Now by deﬁnition say via.Then we can prove by induction thating we can deﬁne a computable function such that via which proves that is a uniform upper bound of.Starting with instead of will yield the same result for(without making any additional assumptions).Remarks.1.If we start with the stronger assumption that,then will bea uniform upper bound for with regard to-reductions.The necessaryadjustments in the proof are straightforward.2.If is witnessed by a reduction which runs in linear time,thenthe uniformity in the above proof,together with the fact that andare also computable in linear time,yields that is hard foroperator and upper bounds,and(assuming is inﬁnite)has no-jumpﬁxed points.Furthermore,it is evident from our construction of that is a quick uniform upper bound for every with.Section4showed how every quick uniform upper bound can compute the jump of another quick uniform upper bining these results it is possible to give further evidence of the richness of the quick uniform upper bounds with respect to the-jump.We iterate our construction in Section4to construct a proper,“upside-down”image of in the quick uniform upper bounds below any given quick uniform upper bound. That is,Theorem5.1Given any which is a quick uniform-upper bound for,there is a such that(letting)1.for all,is a quick uniform upper bound for and if sepa-rates,then separates,2.,3.for all,via a reduction found effectively in,4.for all such that,is a uniform lower bound for,and5.if is inﬁnite,then for all,,so the embedding is properin the ptime degrees.Within this upside-down-,it is also possible to place a(right-side up) -starting with any and completely below all the for. Proof Sketch.We deﬁne a hierarchy of padding functions so that successor func-tions satisfy the conditions in Lemma4.3with respect to their predecessors,and limit functions dominate all previous padding functions.This by itself is straight-forward,but there are a few extra wrinkles that we must smooth out.All our padding functions must be nice,to satisfy the conditions in Lemma4.3,and must give rise to good sets(i.e.,sets over which separates)to ensure a properly descending hierarchy of degrees.Let be a quick uniform upper bound for andﬁx anand a computable such that for all,.By taking a padded version of and choosing a new,we can assume that.Hence, by Lemma2.6there is a computable such that,and this fact remains true if we increase the padding.Now let be least such thatfor all.This implies that,,and,where is the function corresponding to,c.f.17。

A PCR based method for identification of bifidobacteria

A PCR-based method for identi¢cation of bi¢dobacteria fromthe human alimentary tract at the species levelKoen Venema Ã,Annet J.H.MaathuisTNO Nutrition and Food Research,Department of Nutritional Physiology,P.O.Box 360,3700AJ Zeist,The NetherlandsReceived 25March 2003;received in revised form 9May 2003;accepted 23May 2003First published online 19June 2003AbstractA polymerase chain reaction (PCR)-based method was developed for the identification of isolates of Bifidobacterium at the species ing two Bifidobacterium -specific primers directed against the 16S ribosomal gene (Bif164and Bif662),a PCR product was obtained from the type strainsof 12different bifidobacterial species that have been found in the human alimentary tract.After purification of the PCR products,the DNA was restricted with five different restriction enzymes.The size of the different restriction fragments was used as a fingerprint for the identification of individual bifidobacterial species.The amplified ribosomal DNA restriction analysis method was subsequently used to speciate bifidobacterial isolates from child’s feces and from an in vitro model of the large intestine.ß2003Federation of European Microbiological Societies.Published by Elsevier Science B.V.All rights reserved.Keywords:Bi¢dobacterium ;16S rDNA;Ampli¢ed ribosomal DNA restriction analysis;Alimentary tract1.IntroductionThe human intestinal tract harbors a large,active,and complex community of microbes,collectively termed intes-tinal microbiota.The intestinal microbiota plays a signi¢-cant role in the fermentation of food components that have not been digested or taken up in the small intestine and of endogenous compounds,the production of essen-tial vitamins,the modulation of the immune system,and the prevention of colonization by pathogens in the gastro-intestinal tract and therefore is involved in maintaining human health [1].Members of the genus Bi¢dobacterium are amongst the most common microorganisms in the hu-man intestinal tract [2].It has been suggested that Bi¢do-bacterium species are important in maintaining intestinal health because they contribute to a bene¢cial microbiota in the intestinal tract.It is believed that among other fac-tors the diversity and number of Bi¢dobacterium species provide a marker for the stability of the human intestinalmicrobiota.Therefore,many attempts have been made to increase the number of Bi¢dobacterium cells in the intesti-nal tract by supplying certain bi¢dobacterial strains (pro-biotics)[3,4]or food ingredients that stimulate the growth of bi¢dobacteria (prebiotics)(e.g.[5]).Bi¢dobacteria are extensively used in the food industry as health-promoting microorganisms.Hence,the distribution of bi¢dobacteria in the human intestinal microbiota is of major ing classical culture methods,it has been found that Bi¢dobacterium adolescentis and B.longum are major bi¢-dobacterial species in the adult intestinal microbiota [6^8],whereas B.infantis and B.breve are predominant species in the intestinal tracts of human infants [8,9].In addition,B.bi¢dum ,B.catenulatum ,B.pseudocatenulatum ,B.ani-malis ,B.angulatum ,B.gallicum ,B.dentium ,B.inopinatum and B.denticolens have also been reported to be human intestinal bi¢dobacteria ([9^13],our own unpublished re-sults).Classical culture methods,including isolation,iden-ti¢cation,and enumeration of these species,are labor-in-tensive and time-consuming.Moreover,identi¢cation based on phenotypic traits does not always provide clear-cut results and is sometimes unreliable.For some years,16S rRNA sequencing has been a reliable method for classi¢cation and identi¢cation of several bacterial spe-cies [14].16S rRNA-targeted hybridization probes or poly-merase chain reaction (PCR)primers enable rapid and0378-1097/03/$22.00ß2003Federation of European Microbiological Societies.Published by Elsevier Science B.V.All rights reserved.doi:10.1016/S0378-1097(03)00436-1*Corresponding author.Tel.:+31(0)306944703;Fax:+31(0)306944928.E-mail address:venema@voeding.tno.nl (K.Venema).FEMS Microbiology Letters 224(2003)143^149speci¢c detection of a wide range of bacterial species.Apart from genus-speci¢c 16S rRNA probes for Bi¢dobac-terium [15,16],several bi¢dobacterial species-speci¢c 16S rRNA probes have also been developed [17^19].Also,recently an ampli¢ed ribosomal DNA restriction analysis (ARDRA)method was developed which allowed discrim-ination of 12out of 16bi¢dobacterial species [20].This method included 11of the 14species that have been iso-lated from the human alimentary tract to date,of which nine had a unique ARDRA pro¢le.In order to extend this method,and to develop an ac-curate,convenient,and quick method for characterization of all bi¢dobacteria isolates from the intestinal microbiota,we aimed to develop a 16S rRNA gene (rDNA)-targeted PCR method for all known species of bi¢dobacteria that have been shown to inhabit the human alimentary tract.The PCR method was combined with restriction of the PCR products with ¢ve restriction enzymes and the pat-terns of DNA fragments obtained with this ARDRA method were used for identi¢cation of the species.2.Materials and methods2.1.Bacterial strains and growth conditionsThe strains used in this study were obtained from the Belgian Co-ordinated Collections of Micro-organisms or the German Collection of Microorganisms and Cell Cul-tures (Table 1).The choice of bi¢dobacterial strains was carried out according to their presence in the human (chil-dren and adults)alimentary tract.The strains were sub-cultured in MRS broth supplemented with 0.5%cysteineat 37‡C for 24^36h and maintained in the same medium with 10%glycerol at 380‡C.Material from TNO’s in vitro model of the large intestine consisted of a mixture of fecal material from 10healthy human volunteers [21].Beeren’s agar [22]was used as a selective medium for isolation of strains from fecal material of one infant or TNO’s in vitro model of the large intestine [23].The samples were serially diluted 10-fold in peptone physiological salt (Biotrading,Mijdrecht,The Netherlands),and appropriate dilutions were plated.The plates were incubated in an anaerobic cabinet (90%N 2,5%H 2,5%CO 2,IKS,Leerdam,The Netherlands)at 37‡C for 2^3days.2.2.Fructose-6-phosphate phosphoketolase (F6PPK)assay Colonies isolated from Beeren’s medium and cultured in MRS supplemented with cysteine were identi¢ed as Bi¢-dobacterium species by the F6PPK assay,essentially as described before [24],but scaled down to a volume suit-able for 1.5-ml Eppendorf tubes.2.3.DNA isolationBacterial cells were grown in 7ml MRS broth supple-mented with cysteine for 36^48h at 37‡C.A 1-ml aliquot of each culture was centrifuged at 10000U g (10min;Ep-pendorf centrifuge).Cells were then washed with 1ml water and centrifuged again.The supernatant was dis-carded and the pellet was resuspended (either immediately or after storage at 320‡C)in 0.5ml lysis solution (10mM Tris^HCl,1mMEDTA,50mMNaCl,200g l 31sucrose;pH 8.0)to which 2mg ml 31lysozyme and 15U ml 31mutanolysin were added,just prior to use.After a 30-min incubation at 55‡C 20W l proteinase K solution (20mg ml 31in 10mMTris,1mMEDTA (T 10E 1),pH 8.0)was added.After mixing carefully by inversion of the tubes,25W l of a 10%sodium dodecyl sulfate solu-tion was added,after which the mixture was incubated at 60‡C for at least 1h.DNA was extracted with phenol/chloroform/isoamyl alcohol (25:24:1),and precipitated and washed with ethanol (70%).The DNA pellet was dried on air,after which the pellet was resuspended in 20W l T 10E 1containing RNase (3mg ml 31)and stored at 320‡C.2.4.Oligonucleotide primers and DNA sequencesThe primers used in this study were Bif164and Bif662[16]and were obtained from Isogen Bioscience (Maarsen,The Netherlands).The sequences of the 16S ribosomal RNA genes of the species used in this study were retrieved from GenBank ( ).The area of the rDNA ampli¢ed by the PCR reaction was selected in silico and analyzed for the presence of restriction en-zymes that might be used to characterize the individual species.Table 1Strains used in this study Species Culture collection number a GenBank accession number B.adolescentis LMG 10502M58729B.angulatum LMG 10503M84775B.animalis LMG 10508X70971B.bi¢dum LMG 11041M84777B.breveLMG 11042M58731B.catenulatum LMG 11043M58732B.denticolens DSM10105D89331B.dentium LMG 11045U10434B.gallicum b DSM20093D86189B.infantis LMG 8811X70974B.inopinatum DSM10107AB029087B.longumLMG 13197M58739B.pseudocatenulatum LMG 10505M84785B.scardovii c^AJ307005aLMG:Belgian Co-ordinated Collections of Micro-organisms;DSM:German Collection of Microorganisms and Cell Cultures.bB.gallicum was only used in silico,because the strain could not be grown.cB.scardovii was only used in silico,because the species is relatively new [38]and had not been isolated at the time of performing these ex-periments.K.Venema,A.J.H.Maathuis /FEMS Microbiology Letters 224(2003)143^1491442.5.PCR conditions and analysis of PCR products Ampli¢cation was carried out in the thermal cycler Hy-baid Omnigene(Biozym,Landgraaf,The Netherlands). The reaction mixture(50W l)contained approximately 25pmol of each primer,0.2mMof each deoxyribonucleo-tide triphosphate(Roche,Mannheim,Germany),1W l PCR bu¡er without MgCl2(Roche),1W l of the isolated bacterial DNA and 2.5U of Taq DNA polymerase (Roche).DNA fragments were ampli¢ed as follows:initial denaturation at94‡C for5min,followed by¢ve cycles consisting of denaturation at94‡C for60s,annealing at 55‡C for30s,extension at72‡C for60s,followed by 35cycles consisting of denaturation at91‡C for30s,an-nealing at55‡C for30s,extension at72‡C for60s,and a 7-min¢nal extension step at72‡C.The products were stored at320‡C until analysis.Aliquots(5W l)of the ampli¢ed products were subjected to electrophoresis in2%agarose gels in TAE bu¡er (40mMTris acetate,1mMEDTA,pH8.2).G els were stained with ethidium bromide(5W g ml31)and visualized under UV light.A100-bp DNA ladder(Roche)was used as a molecular mass marker.2.6.Puri¢cation and restriction of PCR products,andanalysis of the restriction fragmentsPCR products were puri¢ed using the QIAquick PCR puri¢cation kit(Westburg,Leusden,The Netherlands)ac-cording to the instruction of the manufacturer except that the DNA was eluted in25W l water.Puri¢ed PCR prod-ucts were restricted with Sau3A,Taq I,Rsa I,Alu I(all from Roche)or Sau96I(Westburg)in the bu¡ers supplied by the manufacturers,and incubated at37‡C(or65‡C for Taq I)for1^1.5h.The DNA fragments were separated on a6%polyacrylamide(acrylamide:bisacrylamide 37.5:1)gel at75V for45min.Gels were stained with ethidium bromide(5W g ml31)and visualized under UV light.A100-bp DNA ladder was used as a molecular mass marker.2.7.Development of a software program that allowed quickspeciationA simple software program was developed in Microsoft Excel which allowed entering the approximate size of the DNA fragments after restriction with the¢ve di¡erent restriction enzymes.The bi¢dobacterial isolate to which the DNA fragments corresponded was then automatically speciated.3.Results and discussion3.1.In silico analysis of the DNA fragment of the16SrDNA gene between nucleotides164and662The genes encoding the16S ribosomal RNA were ob-tained from GenBank(see Table1).The fragments(rang-ing from511to525bp;Table2)corresponding to the DNA that would be ampli¢ed by the PCR primers used in this study(between nucleotides164and662;Escheri-chia coli numbering)were restricted in silico with di¡erent restriction enzymes.From the di¡erent restrictions,¢ve enzymes were chosen that allowed discrimination of the 14Bi¢dobacterium species that have been found in the human alimentary tract.These were Sau3A,Taq I,Rsa I, Alu I and Sau96I.Table2shows the sizes of the fragments that were predicted by the in silico restriction analysis with the di¡erent enzymes for14of these strains.Only the two largest fragments were used for ctis (GenBank accession number X89513)gave the same re-striction pattern as B.animalis.For these two species,it has been proposed that they represent the same species [25],and more recently it has been proposed to taxonomi-cally reclassify ctis as a B.animalis subspecies[26],Table2Size of the PCR products and restriction fragments(in bp)predicted by in silico analysisPCR product size Sau3A Taq I Rsa I Alu I Sau96IB.adolescentis512512199,196,117307,155,50427,85343,103,66 B.angulatum511447,64312,199306,155,50397,114342,103,66 B.animalis524458,66322,202470,54440,84355,103,66 B.bi¢dum514421,67,26202,195,117306,155,51429,85345,169B.breve516449,67202,198,116308,155,53432,84348,102,66 B.catenulatum514278,169,67312,202306,155,53514514B.denticolens513513397,116513223,206,49345,150,18 B.dentium516278,238202,197,117308,155,53431,85347,103,66 B.gallicum a524458,66322,202470,54233,207,84355,103,66 B.infantis511418,67,26395,116458,53427,49,35343102,66B.inopinatum525525408,117317,208205,151,85275,232,18 B.longum513418,69,26395,118460,53427,86343,170B.pseudocatenulatum511278,168,65312,199306,155,50511342,103,66 B.scardovii b513447,66397,116304,155,54430,83345,150,18a B.gallicum was only used in silico,because the strain could not be grown.b B.scardovii was only used in silico,because the species is relatively new[38]and had not been isolated at the time of performing these experiments.K.Venema,A.J.H.Maathuis/FEMS Microbiology Letters224(2003)143^149145although no decision has been made by the International Committee on Systematic Bacteriology whether to contin-ue to treat the two as separate species[27].Still,the two (sub)species could be di¡erentiated with ARDRA on the basis of a sixth restriction enzyme,Nci I(data not shown). In addition,the sequences of other Bi¢dobacterium spe-cies present in GenBank were treated in silico with the same¢ve restriction enzymes: B.asteroides(GenBank accession number M58730;origin honeybee hindgut), B.boum(D86190;cattle rumen),B.choerinum(D86186; swine feces),B.coryneforme(M58733;honeybee hindgut), B.cuniculi(M58734;rabbit feces),B.gallinarum(D86191; chicken feces),B.globosum(D86194;swine feces),B.in-dicum(D86188;honeybee hindgut),B.magnum(D86193; rabbit feces), B.merycicum(D86188;bovine rumen), B.minimum(AY174103;sewage), B.pseudolongum (D86195;swine feces),B.pullorum(D86196;chicken fe-ces),B.ruminantium(D86197;bovine rumen),B.saeculare (D89328;rabbit feces),B.subtile(D89379;sewage),B.suis(M58743;swine feces),and B.thermophilum(U10151; swine feces). B.thermacidophilum was not taken along, since the few sequences deposited in GenBank di¡er sub-stantially from each other.Furthermore,this species can be easily distinguished from the other bi¢dobacterial spe-cies since the(in silico)PCR product with the primers Bif164and Bif662is only449bp long compared to511^ 525bp for the other species(data not shown).Not all the additional species could be discriminated on the basis of the¢ve restriction enzymes(data not shown).B.meryci-cum gave the same pattern as the human species B.angu-latum(however,the two species could be discriminated on the basis of a sixth restriction enzyme:Stu I),B.coryne-forme had the same pattern as B.indicum(discrimination by Sal I),B.minimum the same as B.subtile(discrimination by Stu I),and B.gallinarum the same as B.pullorum and B.saeculare(discrimination by Stu I and Tsp509I).How-ever,none of the additionally tested species has been found in the human gastrointestinal tract,and therefore misidenti¢cation of human isolates is unlikely.For four of the non-human species(B.asteroides, B.coryneforme, B.cuniculi,and B.suis)the presence of unknown bases in the sequence(‘n’)prevented precise conclusions about their restriction patterns.However,even when it was as-sumed that the unknown bases would create a restriction site for the¢ve chosen enzymes,the patterns were still unique to these species(or,as in the case of B.coryne-forme,the two largest fragments used for identi¢cation did not di¡er in size,resulting in the same in silico ARDRA pattern).3.2.PCR reaction and DNA restrictions of the type strainsof bi¢dobacterial species found in the humangastrointestinal tractWith all12type strains tested the expected PCR frag-ment was obtained(data not shown),and after DNA re-striction of the puri¢ed PCR product,DNA fragments of the expected size(based on the in silico analyses)were found after polyacrylamide gel electrophoresis(in Fig.1 shown for B.animalis).3.3.Identi¢cation of isolates from child’s feces and an invitro model of the large intestineChild’s feces was serially diluted and plated on Beeren’s medium.In addition,samples from TNO’s in vitro model of the large intestine[23],containing a complex microbiota of healthy human adults[21],were diluted and plated as described above.The experiments in the in vitro model from which the samples originated will be described in detail elsewhere(van Nuenen et al.,submitted).In short, the model was run for4days with addition of10g day31 inulin.Samples were taken at the start of the experiments and4days after inulin feeding.Isolated colonies were picked and grown in MRS containing cysteine.To con¢rm that the isolates were of the genus Bi¢dobacterium,the F6PPK assay was performed as described in Section2. Twenty-three of the43isolated colonies(53%)were shown to contain the F6PPK enzyme(data not shown).Table3 shows the DNA fragments obtained after restriction of the puri¢ed PCR products.In addition,the species classi¢ca-tion based on the in silico analysis is given.In all cases,the estimated fragment size corresponded well with the frag-ment size obtained from in silico analysis.The majority of the isolates were B.animalis,especially those isolated after 4days inulin feeding in the in vitro model of the large intestine(isolates09^23).In contrast,at the start of the experiment in the in vitro model the microbiota contained a number of di¡erent bi¢dobacterial species:three isolates of B.infantis,two of B.animalis,one of B.longum and one of B.adolescentis.At this moment it is unclear whether one particular strain of B.animalis selectively ex-panded upon addition of inulin,or whether severalstrains Fig. 1.Polyacrylamide gel electrophoresis of restricted DNA of the PCR fragment from nes1and5:100-bp ladder(from bottom on upwards,100bp,200bp,300bp,400bp,500bp(more in-tense band),etc.);lane2:Sau3A digest(in silico predicted fragments 457bp,67bp);lane3:Sau96I digest(355bp,102bp,67bp);lane4: Alu I digest(440bp,84bp);lane6:Rsa I digest(471bp,53bp);and lane7:Taq I digest(322bp,202bp).K.Venema,A.J.H.Maathuis/FEMS Microbiology Letters224(2003)143^149 146of B.animalis used inulin as a substrate and therefore increased in number more rapidly relative to the other bi¢dobacterial isolates that were present at the start of the experiment.Pulse¢eld gel electrophoresis might be able to discriminate between these options.Several strategies have been designed to speci¢cally identify bi¢dobacterial species from the human alimentary tract of dairy e has been made of genus-spe-ci¢c16S rRNA probes[15,16],species-speci¢c16S rRNA probes[17^19,28],in combination with either PCR or hy-bridization.Other(partial)genes used for speciation have been rec A[29]and hsp60[30].(On the basis of hsp60, B.inopinatum and B.denticolens have been proposed to be transferred to two new genera as Scardovia inopinata gen.nov.,comb.nov.,and Parascardovia denticolens gen. nov.,comb.nov.,respectively[31]).Even randomly cloned fragments have been used to identify strains of a speci¢c species[32,33].In addition,ribosomal RNA polymor-phism was studied to demonstrate intra-and interspecies di¡erentiation by digestion of chromosomal DNA and hy-bridization with the23S rRNA probe[34^36].Moreover, the intergenetic16S^23S spacer region allowed analysis at the subspecies and strain levels[26,37].The studies cited above were all performed with a limited set of bi¢dobac-terial species,or even with the intention to discriminate only one or a few species from the rest.The ARDRA method designed in this paper allows discrimination and identi¢cation to the species level of all32hitherto de-scribed bi¢dobacterial species,except B.thermacidophilum, for which several deposited sequences in GenBank with major nucleotide sequence di¡erences exist.The method extends that of Ventura et al.[20],where16species were used for discrimination with ARDRA on the basis of two restriction enzymes(Sau3A and Bam HI).Of those16spe-cies,only B.suis and B.longum could not be discriminated using those two enzymes.In addition, B.animalis and ctis showed the same restriction fragment length poly-morphism pattern with both enzymes,but the same au-thors have recently proposed these two species to be con-sidered subspecies of the B.animalis species[26].As they do not consider ctis and B.animalis to be di¡erent species,they did not conclude in their paper that the two species could not be discriminated.In this study,almost the complete16S rRNA gene was ampli¢ed.In the present study,only the region between the bi¢dobacterial-speci¢c primers Bif164and Bif662was used,and no PCR ampli-con was obtained in non-Bi¢dobacterium isolates(data not shown).In addition,in the present study B.suis and B.longum could be discriminated,and the same applies for B.animalis and ctis,whether they are considered to be subspecies or not.Moreover,more bi¢dobacterial species were tested in the present study.The Ventura studyTable3Characterization of bi¢dobacterial isolatesClone isolate Approximate fragment sizes estimated after gel electrophoresis(in bp)Strain identi¢cation Sau3A Taq I Rsa I Alu I Sau96I01(CF a)450,70320,200470,50440,80350,100,70 B.animalis02420,70,(20)b400,120460,50430,50,(30)340,100,70 B.infantis03420,70,(20)400,120460,50430,90340,170 B.longum04450,70320,200470,50440,80350,100,70 B.animalis 05510200c,190c,110310,150,50430,90340,100,70 B.adolescentis 06420,70,(20)400,120460,50430,50,(30)340,100,70 B.infantis07420,70,(20)400,120460,50430,50,(30)340,100,70 B.infantis08450,70320,200470,50440,80350,100,70 B.animalis09450,70320,200470,50440,80350,100,70 B.animalis10450,70320,200470,50440,80350,100,70 B.animalis11450,70320,200470,50440,80350,100,70 B.animalis12450,70320,200470,50440,80350,100,70 B.animalis13450,70320,200470,50440,80350,100,70 B.animalis14450,70320,200470,50440,80350,100,70 B.animalis15450,70320,200470,50440,80350,100,70 B.animalis16450,70320,200470,50440,80350,100,70 B.animalis17450,70320,200470,50440,80350,100,70 B.animalis18450,70320,200470,50440,80350,100,70 B.animalis19450,70320,200470,50440,80350,100,70 B.animalis20450,70320,200470,50440,80350,100,70 B.animalis21450,70320,200470,50440,80350,100,70 B.animalis22450,70320,200470,50440,80350,100,70 B.animalis23450,70320,200470,50440,80350,100,70 B.animalisa CF=child’s feces.All other tested isolates were obtained from the in vitro model of the large intestine.b Fragments between parentheses were not observed in the polyacrylamide gel,because the intensity of staining with ethidium bromide was too low. They were predicted based on the total PCR fragment size.However,as described in Section2,identi¢cation of the species was done with the two larg-est fragments.c Bands co-migrated.Based on intensity of the bands,the upper of the two bands that were visible was considered to consist of two bands.This was con¢rmed by electrophoresis of the same sample on a1%agarose gel(data not shown).K.Venema,A.J.H.Maathuis/FEMS Microbiology Letters224(2003)143^149147allows a more high-throughput screening of isolates,since it only uses one(Sau3A)or two(Sau3A and Bam HI)re-striction enzymes for identi¢cation,compared to¢ve en-zymes in our study for human alimentary tract isolates,or at most six enzymes when all bi¢dobacterial species are considered.Moreover,as more and more species are dis-covered,restriction patterns based on¢ve enzymes will be more discriminative than those based on two enzymes.For the strain isolated from infant’s feces characterization was con¢rmed by previous16S rDNA sequencing(data not shown).In conclusion,we have developed an ARDRA method,based on the sequences of the type strains of all 14bi¢dobacterial species that have been found in the hu-man alimentary tract,which allowed discrimination of these14isolates to the species level.Moreover,when the method was subsequently tested(in silico)against18more species,it proved to be able to discriminate almost all of these species as well.References[1]Fuller,R.(1989)Probiotics in man and animals.J.Appl.Bacteriol.66,365^378.[2]Scardovi,V.(1984)Genus Bi¢dobacterium Orla-Jensen,1924.In:Bergey’s Manual of Systematic Bacteriology,Vol.1(Krieg,N.R.and Holt,J.G.,Eds.),pp.1418^1434.Williams and Wilkins,Balti-more,MD.[3]Kok,R.,De Waal,A.,Schut,F.,Welling,G.W.,Weenk,G.andHellingwerf,K.J.(1996)Speci¢c detection and analysis of a probiotic Bi¢dobacterium strain in infant feces.Appl.Environ.Microbiol.62, 3668^3672.[4]Vaughn,E.E.and Mollet,B.(1999)Probiotics in the new millen-nium.Nahrung43,148^153.[5]Gibson,G.R.and 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cuniculi,Bi¢dobacterium choerinum,Bi¢dobacterium boum,and Bi¢dobacterium pseudocatenulatum:four new species and their deoxyribonucleic acid homology relationships.Int.J.Syst.Bac-teriol.29,291^311.[12]Lauer,E.(1990)Bi¢dobacterium gallicum,new species isolated fromhuman feces.Int.J.Syst.Bacteriol.40,100^102.[13]Crociani,F.,Biavati,B.,Alessandrini,A.,Chiarini,C.and Scardovi,V.(1996)Bi¢dobacterium inopinatum sp.nov.and Bi¢dobacteriumdenticolens sp.nov.,two new species isolated from human dental caries.Int.J.Syst.Bacteriol.46,564^571.[14]Woese, C.R.(1987)Bacterial evolution.Microbiol.Rev.51,221^271.[15]Kaufmann,P.,Pfe¡erkorn, A.,Teuber,M.and Meile,L.(1997)[16]G.R.,Wilkinson,M.H.F.and Welling,G.W.(1995)Quantitative£uorescence in situ hybridization of Bi¢dobacterium spp.with ge-nus-speci¢c16S rRNA targeted probes and its application in fecal samples.Appl.Environ.Microbiol.61,3069^3075.[17]Matsuki,T.,Watanabe,K.,Tanaka,R.and Oyaizu,H.(1998)Rapididenti¢cation of human intestinal bi¢dobacteria by16S rRNA-tar-geted species and group-speci¢c primers.FEMS Microbiol.Lett.167,113^121.[18]Matsuki,T.,Watanabe,K.,Tanaka,R.,Fukuda,M.and Oyaizu,H.(1999)Distribution of bi¢dobacterial species in human intestinal mi-cro£ora examined with16S rRNA-gene-targeted species-speci¢c primers.Appl.Environ.Microbiol.65,4506^4512.[19]Yamamoto,T.,Morotomi,M.and Tanaka,R.(1992)Species-speci¢coligonucleotide probes for¢ve Bi¢dobacterium species detected in human intestinal micro£ora.Appl.Environ.Microbiol.58,4076^ 4079.[20]Ventura,M.,Elli,M.,Reniero,R.and Zink,R.(2001)Molecularmicrobial analysis of Bi¢dobacterium isolates from di¡erent environ-ments by the species-speci¢c ampli¢ed ribosomal DNA restriction analysis(ARDRA).FEMS Microbiol.Ecol.36,113^121.[21]Venema,K.,Van Nuenen,H.M.C.,Smeets-Peeters,M.J.E.,Minekus,M.and Havenaar,R.(2000)TNO’s in vitro large intestinal model: an excellent screening tool for functional food and pharmaceutical research.Erna«hrung/Nutrition24,558^564.[22]Beerens,H.(1991)Detection of bi¢dobacteria by using propionicacid as a selective agent.Appl.Environ.Microbiol.57,2418^2419.[23]Minekus,M.,Smeets-Peeters,M.J.E.,Bernalier,A.,Marol-Bonnin,S.,Havenaar,R.,Marteau,P.,Alric,M.,Fonty,G.and Huis in’t Veld,J.H.J.(1999)A computer-controlled system to simulate condi-tions of the large intestine with peristaltic mixing,water absorption and absorption of fermentation products.Appl.Microb.Biotechnol.53,108^114.[24]Grill,J.-P.,Crociani,J.and Ballongue,J.(1995)Characterization offructose6phosphate phosphoketolases puri¢ed from bi¢dobacteria species.Curr.Microbiol.31,49^54.[25]Cai,Y.,Matsumoto,M.and Benno,Y.(2000)Bi¢dobacterium lactisMeile et al.,1997is a subjective synonym of Bi¢dobacterium animalis (Mitsuoka1969)Scardovi and Trovatelli1974.Microbiol.Immunol.44,815^820.[26]Ventura,M.and Zink,R.(2002)Rapid identi¢cation,di¡erentiation,and proposed new taxonomic classi¢cation of Bi¢dobacterium lactis.Appl.Environ.Microbiol.68,6429^6434.[27]Seventh International Committee on Systematic Bacteriology(2001)Minutes of the meetings,22and23September1999,Veldhoven,The Netherlands.Int.J.Syst.Evol.Microbiol.51,259^261.[28]Ventura,M.,Reniero,R.and Zink,R.(2001)Speci¢c identi¢cationand targeted characterization of Bi¢dobacterium lactis from di¡erent environmental isolates by a combined multiplex-PCR approach.Appl.Environ.Microbiol.67,2760^2765.[29]Kullen,M.J.,Brady,L.J.and O’Sullivan,D.J.(1997)Evaluation ofusing a short region of the rec A gene for rapid and sensitive speci-ation of dominant bi¢dobacteria in the human large intestine.FEMS Microbiol.Lett.154,377^383.[30]Jian,W.,Zhu,L.and Dong,X.(2001)New approach to phyloge-netic analysis of the genus Bi¢dobacterium based on partial HSP60 gene sequences.Int.J.Syst.Evol.Microbiol.51,1633^1638. [31]Jian,W.and Dong,X.(2002)Transfer of Bi¢dobacterium inopinatumand Bi¢dobacterium denticolens to Scardovia inopinata gen.nov.,K.Venema,A.J.H.Maathuis/FEMS Microbiology Letters224(2003)143^149 148。

高岭土红外分析

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ห้องสมุดไป่ตู้
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BALAN ET AL.: AB INITIO INFRARED SPECTRUM OF KAOLINITE
ing disorder in kaolinite group minerals has been the subject of numerous studies (Giese 1988). In addition, IR and Raman spectroscopy have been used to investigate hydroxyl groups and hydrogen bonding patterns in kaolinite (Farmer 1974; Prost et al. 1989; Johnston et al. 1990; Frost and Van der Gaast 1997; Farmer 1998). However, recent attempts to calculate the IR spectrum of kaolinite from structural data alone provided only a limited agreement between calculation and experiment (Bougeard et al. 2000).
1
ABSTRACT
The theoretical infrared spectrum of kaolinite [Al2Si2O5(OH)4, triclinic] was computed using ab initio quantum mechanical calculations. Calculations were performed using the Density Functional Theory and the generalized gradient approximation. The low-frequency dielectric tensor of kaolinite was determined as a function of the light frequency using linear response theory. The IR spectrum was then calculated using a model that takes into account the shape and size of kaolinite particles. A remarkable agreement was obtained between theory and experiment, especially on the position of the stretching bands of OH groups. This agreement provides a firm basis for the interpretation of the IR spectrum of kaolinite in terms of structural parameters.

Construction of Hilbert Transform Pairs of Wavelet

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 9, SEPTEMBER 20093411Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like TransformsKunal Narayan Chaudhury, Student Member, IEEE, and Michael Unser, Fellow, IEEEAbstract—We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions—the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal by relating the corresponding wavelet ﬁlwavelet bases of ters via a discrete form of the continuous HT ﬁlter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a speciﬁc ﬂavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufﬁciently large orders. Analytic wavelets, derived from the complexiﬁcation of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable , we then discuss a methodbiorthogonal wavelet bases of ology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT—the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efﬁcient fast Fourier transform (FFT)-based ﬁlterbank algorithm for implementing the associated complex wavelet transform. Index Terms—Analytic signal, biorthogonal wavelet basis, B-spline multiresolution, directional Hilbert transform, dual-tree complex wavelet transform, Gabor function, Hilbert transform, time-frequency localization.transform, besides improving on the shift-invariance of the 2-D DWT, exhibits better direction selectivity as well. There is now good evidence that the transform tends to perform better than its real counterpart in a variety of applications such as such as deconvolution [3], denoising [4], and texture analysis [5]. The crucial observation that the dual-tree wavelets involved in Kingsbury’s construction form an approximate HT pair was made by Selesnick [6], [7]. He also demonstrated that a particular phase relation between the lowpass (reﬁnement) ﬁlters of the two channels resulted in the desired HT correspondence. This link consequently transposed the problem of designing different ﬂavors of dual-tree wavelets to that of identifying new HT pairs of wavelets. Indeed, following this remarkable connection, several new paradigms and extensions have been proposed: design of HT pairs of biorthogonal wavelet bases [8], alternative frameworks for complex nonredundant transforms [9], and the M-band extension [10], to name a few. A. Motivation The deployment of complex signal representations for the determination of instantaneous amplitude and frequency is classical [11], [12]. Gabor and Ville [11], [13] proposed to unambiguously deﬁne them using the concept of the analytic signal—a unique complex-valued signal representation speciﬁed using the HT. Speciﬁcally, the analytic signal corresponding to a real-valued ( denotes the HT operator) was used to stipsignal ulate the instantaneous amplitude and phase via the polar . In particular, this reprerepresentation sentation allows one to retrieve the time-varying amplitude and frequency of an AM–FM signal of the form via the estimates and , assuming to be slowly-varying compared to . The analytic signal has become an important complex-valued representation in signal processing, especially in applications such as phase and frequency modulation, speech recognition and processing of seismic data. These concepts have also been transposed to the multidimensional setting: the local frequency has been used as a measure of local signal scale; structures such as lines and edges have been distinguished using the local phase; and the local amplitude and phase have been used for edge detection and for texture and ﬁngerprint analysis [14]. The advantage of viewing the dual-tree wavelets as a HT pair is that we can make a direct connection with the formalism of analytic signals. Indeed, if we transpose the above concept to the wavelet domain and consider the input signal to be locally of the AM–FM form, we obtain a response where the local energy of the signal is encoded in the magnitude of the waveletI. INTRODUCTIONTHE dual-tree complex wavelet transform (DT- WT) is a recent enhancement of the conventional discrete wavelet transform (DWT) that has gained increasing popularity as a signal processing tool. The transform was originally introduced by Kingsbury [1], [2] to circumvent the shift-variance of the decimated DWT, and involved two DWT channels in parallel with the corresponding wavelets forming a quadrature pair. In particular, Kingsbury realized the quadrature relation by interpolating the lowpass ﬁlters of one DWT “mid-way” between the lowpass ﬁlters of the other DWT. Moreover, based on appropriate combinations of separable wavelets, he extended the dualtree construction to two-dimensions, where the correspondingManuscript received May 23, 2008; accepted March 14, 2009. First published April 10, 2009; current version published August 12, 2009. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Patrick Flandrin. This work was supported by the Swiss National Science Foundation under Grant 200020-109415. The authors are with the Biomedical Imaging Group, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne VD, Switzerland (e-mail: kunal.chaudhury@epﬂ.ch; michael.unser@epﬂ.ch). Color versions of one or more of the ﬁgures in this paper are available online at . Digital Object Identiﬁer 10.1109/TSP.2009.20207671053-587X/$26.00 © 2009 IEEEAuthorized licensed use limited to: EPFL LAUSANNE. Downloaded on August 19, 2009 at 08:46 from IEEE Xplore. Restrictions apply.3412IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 9, SEPTEMBER 2009coefﬁcients, while the relative displacement is captured by the phase. In fact, this turns out to be the fundamental reason for the superiority of the DT- WT over conventional real-valued transforms whose response is necessarily oscillating. B. Our Contribution In this contribution, we invoke the B-spline factorization theorem [15]—a fundamental spectral factorization result—along with certain fractional B-spline calculus [16], to construct HT pairs of biorthogonal wavelets from well-localized scaling functions. In particular, we do so by relating the corresponding wavelets ﬁlters via a discrete version of the continuous HT ﬁlter. Next, we identify a family of analytic spline wavelets, of increasing vanishing moments and regularity, that asymptotically converge to Gabor-like functions [11]. As far as the implementation is concerned, unlike Kingsbury’s scheme that uses different ﬁlters for different stages (often with ﬁlter-swapping between the dual-trees), our implementation uses the same set of ﬁlters at all stages of the ﬁlterbank decomposition. Notably, we use an appropriate pair of projection ﬁlters for coherent signal analysis which, in turn, allows us to identify a discrete counterpart of the analytic wavelet—the so-called analytic wavelet ﬁlter that exhibits a one-sided spectrum. The construction is then extended to two-dimensions through appropriate tensor-products of the one-dimensional analytic wavelets. In particular, we construct a family of directional complex wavelets that resemble the directional Gabor functions proposed by Daugman [17] for sufﬁciently large orders. Moreover, we also relate the real and imaginary components of the complex wavelets using the directional HT—a multidimensional extension of the HT—that provides further insight into the directional-selectivity of the dual-tree wavelets. C. Organization of the Paper We begin by recalling certain fundamental deﬁnitions and properties pertaining to the HT and the fractional B-splines in Section II. We characterize the action of the HT operator on B-splines in Section III, which, along with the B-spline factorization theorem, is used to propose a formalism for constructing HT pairs of biorthogonal wavelet bases in Section IV. The implementation aspects are discussed in Section V. As a concrete application, we construct the Gabor-like wavelets in Section VI. In Section VII, directional complex wavelets are constructed by appropriately combining the wavelets corresponding to certain separable multiresolution analyses; the highlight of this section is the construction of 2-D Gabor-like spline wavelets. The implementation aspects of the corresponding 2-D Gabor-like transform are provided in Section VIII, before concluding with Section IX. II. PRELIMINARIES We begin by introducing speciﬁc operators and functions that play a major role in the sequel followed by a discussion of their relevant properties. In what follows, we use to denote the Fourier transformon , with being the usual of a function . We also frequently use the notations inner-product on and , corresponding to some in and , to denote the function obtained by translating (respectively, dilating) by (respectively, ). We denote the Kronecker-delta sequence by : its value is 1 at , and is zero at all other integers. A. Hilbert Transform and Wavelets The Hilbert transform, that generalizes the notion of the beyond pure quadrature transformation sinusoids [18], forms the cornerstone of this paper. From a signal-processing perspective, the HT can be interpreted as a ﬁltering operation in which the amplitude of the frequency components is left unchanged, while their phase is altered by depending on the sign of the frequency. Mathematically, the HT of a sufﬁciently well-behaved function is deﬁned using a singular integral transform [19], [20]. However, in the context of ﬁnite-energy signals, it admits a particularly straightforward formulation based on the Fourier trans. In particular, the Hilbert transform on is form on characterized by the equivalence (1) where the multiplier is deﬁned as for nonzero , and as zero at . Based on the above deﬁnition,1 and the properties of the , the following properties of the HT Fourier transform on can be readily derived. • Linearity and Translation-Invariance: It is a linear and translation-invariant operator; that is, it acts as a convolution operator. • Dilation-Invariance: It commutes with dilations: for all . • Anti-Symmetry: It anti-commutes with the ﬂip operation , so that ; thus the HT of a symmetric function is necessarily anti-symmetric. • Unitary (Isometric) Nature: It acts as a unitary operator on , so that for all and , where denotes the usual inner-product on . Equivalently, this means that the inverse HT operator is given by its adjoint: . It is well-known that HT of a wavelet is also a wavelet. The implication of the simultaneous invariance to dilations and translations is that the HT of a dilated-translated wavelet is a wavelet, dilated and translated by the same amount: . Moreover, an immediate consequence of the unitary property is that the HT operator form a (Riesz) wavelet basis maps a basis into a basis: if of , then so does . It even preserves biorthogonal : if and form a biorthogwavelet bases of , satisfying the duality criteria onal wavelet basis of1The deﬁnition can also be extended to tempered distributions such as the Dirac delta and the sinusoid [19, Sec. 2.5].Authorized licensed use limited to: EPFL LAUSANNE. Downloaded on August 19, 2009 at 08:46 from IEEE Xplore. Restrictions apply.CHAUDHURY AND UNSER: CONSTRUCTION OF HILBERT TRANSFORM PAIRS3413, then using the same unitary property, we have (2) so that and form a biorthogonal wavelet basis as well. It is exactly the above invariance properties of that make the construction of HT pair of wavelet bases of feasible. Unfortunately, the HT exhibits certain inherent pathologies in the context of multiresolution analyses and wavelets. The (in the sense of impulse response of the HT, distributions), clearly indicates the nonlocal nature of the operator. This has two serious implications: i) the HT of a compactly-supported scaling function/wavelet is no longer of ﬁnite support; ii) the HT-transformed function has a -decay in general, and hence is not integrable; and iii) the (anti-symmetric) HT suppresses the dc-component of symmetric scaling functions that is essential for fulﬁlling the partition-of-unity criterion. Therefore, the HT of a scaling function is not a valid scaling function, and cannot be used to specify a multiresolution analysis in the sense of Mallat and Meyer [21], [22]. Next, we recall the notion of an analytic signal that generto alizes the phasor transformation ﬁnite-energy signals using the HT as the quadrature transformation. In general, the analytic signal associated with a is deﬁned as the complex-valued signal real-valued signalThe fundamental role played by fractional B-splines in this paper is, however, based on the fact they satisfy certain admissibility criteria [16], [23] needed to generate a valid multireso. lution of C1) The approximation space admits a stable Riesz basis. (reﬁnement C2) There exists an integrable sequence ﬁlter) such that the two-scale relationholds. In particular, the transfer function of the reﬁnement ﬁlter is speciﬁed byIn particular, when . Importantly, note that the Fourier transform of the analytic signal , so that vanishes evaluates to for all negative frequencies. It is exactly this one-sided spectrum that makes the analytic signal particularly interesting in signal processing [11]; we exploit this property for constructing directional wavelets in Section VII. B. Fractional B-Spline Multiresolution The family of fractional B-splines [23]—fractional extensions of the polynomial B-splines—will play a key role in the sequel. In particular, we recall that the fractional B-spline , corresponding to a degree and a shift , is speciﬁed by its Fourier transform (3) The parameters and control the width and the average group delay of the scaling function respectively. In particular, when , the fractional B-spline corresponds to the deﬁned in [16]. The fractional B-splines, causal B-spline in general, do not have a compact support (except for integer degrees); however, their decay ensures their inclu. Another relevant property that will be sion in invoked frequently is that the shift inﬂuences only the phase of the Fourier transform; that is, is independent of .C3) Partition of unity: The integer-translates of can reproduce the unity function. We brieﬂy discuss the signiﬁcance of these admissibility conditions. The criterion C1) ensures a stable and unique represenusing coefﬁcients from ; equivtation of functions in alently, this also signiﬁes that the transfer function of the auto, is correlation (Gram) ﬁlter, uniformly bounded from above, and away from zero [24]. On the other hand, C2) implies the inclusion of in , which, in turn, allows one to deﬁne a hierarchical embedding that is key to the multiresoof approximation spaces lution structure of the associated wavelet transform. Finally, the is technical condition C3) ensures that the multiresolution dense in : arbitrarily close approximations of functions in can be achieved using elements from . III. HILBERT TRANSFORM AND B-SPLINES It turns out that the action of the HT on B-splines can be effectively characterized in terms of certain fractional ﬁnite-difference (FD) operators. In particular, corresponding to an order and shift , we consider the operator deﬁned by onwhere . One recovers the conventional th order FD operator by setting and . Since the operator has a periodic frequency response, one can associate with it a digital ﬁlter through the correspondence . The FD operator that is especially relevant for our purpose is (henceforth, we simply dethe zeroth-order operator note it by ). The corresponding frequency response reduces2 tospecify the fractional power of a complex number by corresponding to the principal argument . holds only if On this principal branch, the identity [25, Ch. 3].2WeAuthorized licensed use limited to: EPFL LAUSANNE. Downloaded on August 19, 2009 at 08:46 from IEEE Xplore. Restrictions apply.3414IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 9, SEPTEMBER 2009signifying that coefﬁcientsis in in; the corresponding ﬁlter are then speciﬁed3 byProposition 3.2: The spline reﬁnement ﬁlters and are “half-sample” shifted versions of one another in the sense that (5) for all in . Indeed, if we consider the bandlimited function that satisﬁes the constraint , then we have, as a consequence of (5), the relation : each ﬁlter provides the bandlimited interpolation of the other midway between its samples. Finally, we make a note of the fact that the above reﬁnement ﬁlters can also be related through a conjugate-mirrored version of the FD ﬁlter: (6)Thus, similar to the HT operator, is also unitary, and the corcan be interpreted as a discrete form of responding ﬁlter . In particular, we can relate the the continuous HT ﬁlter action of the HT on the B-splines solely in terms of this ﬁlter. Indeed, it can easily be seen that the Fourier transform of the B-spline can be factorized aswhich, along with the identity , results in the equivalence IV. HT PAIR OF WAVELET BASESthat establishes the desired result as follows. Proposition 3.1: The HT of a fractional B-spline can be expressed as (4) In particular, the digital ﬁlter acts as a unitary convolution operator on when applied to functions, and as a discrete when applied to sequences. The theoretical difﬁlter on ﬁculty with the HT stems from the fact that its frequency re, which results in a poor decay sponse has a singularity at of the transformed output. The remarkable feature of (4) is that we have been able to express the slowly decaying HT as a linear combination of the better-behaved B-splines. Speciﬁcally, the decays only as , whereas desequence cays as . Thus, by expressing the HT using shifted B-splines as in (4), we have, in effect, moved the singularity onto the digital ﬁlter. In the sequel, we shall apply this ﬁlter to the wavelets where its effect around the origin. is much more innocuous since Half-Delay Filters: As remarked earlier, the shift parameter only affects the phase of the Fourier transform of the fractional B-spline and the corresponding reﬁnement ﬁlter [23]. In particular, based on the factorizationBefore stating the main results, we recall the approximation-theoretic notion of approximation order, and a fundamental spectral factorization result involving B-splines. Approximation Order: Scaling functions play a fundamental role in wavelet theory. The technical criteria for a valid scaling function was discussed earlier in the context of B-splines (cf. Section II-B). Next we recall the fundamental notion of order for a scaling function that characterizes its approximation power is said to have an approximation [15]. A scaling function order if and only if there exists a positive constant such that , of order , we for all elements of the Sobolev space have the estimatewe arrive at the following result.3Theinverse Fourier transform over the principal periodis invoked.Here denotes the projection operator from onto the approximation subspace , and denotes the (distributional) derivative of order . In other words, the approximation order provides a characterization of the rate of decay of the approximation error for sufﬁciently regular functions as a function of the scale. It turns out that, akin to their polynomial counterparts, the order of fractional B-splines is entirely controlled by their de. Equivalently, gree [16], [23]; in particular, we have can be reprothis signiﬁes that any polynomial of degree , which is crucial for capturing the duced by the set lowpass information in images is concerned. Characterization of Scaling Functions: A fundamental result in wavelet theory is that it is always possible to express a valid scaling function as a convolution between an fractional B-spline and a distribution [15]. The original result in [15] involves causal B-splines; however, the result can readily be extended to the more general fractional B-splines since the shift parameter does not inﬂuence the order of the scaling function. Indeed, note the theorem in [15] asserts that is theAuthorized licensed use limited to: EPFL LAUSANNE. Downloaded on August 19, 2009 at 08:46 from IEEE Xplore. Restrictions apply.CHAUDHURY AND UNSER: CONSTRUCTION OF HILBERT TRANSFORM PAIRS3415reﬁnement ﬁlter of a valid scaling function (cf. Section II-B) of if and only if it can be factorized as order(7) is stable: for all . where Rewriting (7) in terms of a B-spline reﬁnement ﬁlter, we then have the following equivalent representation:. Let be any arbitrary wavelet, corresponding to the , that is speciﬁed multiresolution analysis associated with . We then have the following by necessary and sufﬁcient condition for the desired HT correspon(see Section XI-A dence in terms of the discrete HT ﬁlter for a proof). and Theorem 4.2 (HT Pair of Wavelets): The wavelets have the correspondence if and only if . Moreover, the construction has the following characteristics: and have the same Riesz bounds and the • both same decay; and corresponding • the reﬁnement ﬁlters and respectively, are related as to(8) with for . is stable, with for all . Note that That is, is the reﬁnement ﬁlter of a valid scaling function if and only if it admits a stable factorization as in of order (8). We then arrives at the following extension. Theorem 4.1 (B-Spline Factorization): A valid scaling function is of order if and only if its Fourier transform can be factorized asfor all in . The equality of the Riesz bounds follows from the observation and are identical. that the autocorrelation ﬁlters of Indeed, we haveThe assertion regarding the decay is based on the observation and have the same decay. Finally, that both using (5) and (8), we can relate the transfer functions on as followsfor some , where is a function of that is bounded on every compact interval, and equals unity at the origin. In the signal domain, this corresponds to a well-deﬁned conbetween a B-spline and the temvolution pered distribution . The crux of the above result is that it is the constituent B-spline that is solely responsible for the approximation property, and other desirable features of the scaling function [15]. A. Construction of HT Pairs of Wavelets In what follows, we use the notation , corresponding to , and integers and , to denote the (normalized) a function . The HT of a wavelet dilated-translated function is also a wavelet in a well-deﬁned sense. In particular, if is a wavelet whose dilations-translations form a Riesz , then is also a valid wavelet with basis of constituting a Riesz basis of . As remarked earlier, this follows from the fundamental invariance properties of the HT. We now establish a formalism for constructing the HT of . In particular, if be the associated a given wavelet , and be the generating scaling function, say of order wavelet ﬁlter, then we have the relationFollowing Theorem 4.1, let us factorizeascorresponding to some real . Then, consider the scaling function , of the same order, speciﬁed bywhere denotes the transfer function of the ﬁlter associated with the distribution . is unique, the scaling Remark: Note that although function and the corresponding ﬁlter generating are by no means unique. For instance, the particular and is sufﬁcient to ensure choice . Moreover, if and genthat erate the wavelet such that , then so do and . Here, the ﬁlter is such that for all so that the convolutional is well-deﬁned. inverse is both necessary and The condition sufﬁcient only for our preferred choice of the scaling function . This particular choice of the scaling is justiﬁed on function against the more direct choice the following grounds. is well-localized with better decay • The function properties than ; the latter is not even integrable in general (e.g., the Harr scaling function). satisﬁes the partition-of-unity • The scaling function is not a valid scaling funcrequirement, whereas is not necessarily unity. For example, if tion since is symmetric and is integrable, then we have following the fact that is anti-symmetric.Authorized licensed use limited to: EPFL LAUSANNE. Downloaded on August 19, 2009 at 08:46 from IEEE Xplore. Restrictions apply.3416IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 9, SEPTEMBER 2009B. HT Pairs of Biorthogonal Wavelets A biorthogonal wavelet basis of dual-primal scaling function pair involves the nested multiresolution , corresponding to the of order , as, we can express the inner-productand its dual which establishes the assertion. • The lowpass ﬁlters on both the analysis and synthesis side are “half-sample” shifted versions of one another, and are related via the modulation of the discrete HT ﬁlter:where the approximation subspace (respectively, ) is generated by the translations of (respectively, ) [24]. be the wavelets associated with these multiresoluLet tions, which, along with their dilated-translated copies, encode the residual signal—the difference of the signal approximations (rein successive subspaces. In particular, the wavelet ) and its translates span the complementary spectively, space (respectively, ). The crucial aspect of the construction is that the dilated-translated and form a dual basis of , ensemble i.e., they satisfy the biorthogonality criteria . The expansion of a ﬁnite-energy signal in terms of this biorthogonal basis is then given byIn particular, the ﬁlter is “half-sample” delayed on the analysis side, whereas on the synthesis side the ﬁlter has a “half-sample” advance. • The highpass ﬁlters on both the analysis and synthesis side are related through the FD ﬁlter as• If the analysis and synthesis ﬁlters of the original biorthogonal system satisfy the PR conditions In other words, the wavelets and , interpreted as the analysis and synthesis wavelets respectively, to. gether constitute a biorthognal wavelet basis of In particular, let and be the scaling functions, of and respectively, associated with a given order biorthogonal wavelet basis, with associated waveletsthen so do the ﬁlters of the HT pair. Indeed, since , we haveNow, let and be the and . Consider the scaling respective factorizations of functions and , with associated wavelets speciﬁed bySimilarly, . Note that above properties relate to a common theme: the unitary nature of the operators and involved in the wavelet and the ﬁlterbank construction, respectively. V. 1-D IMPLEMENTATION Signal Preﬁltering: In order to implement the DT- WT, we need to employ two parallel wavelet decompositions correand . Moreover, to have a sponding to the wavelets coherent signal analysis—same input applied to both wavelet separately branches—we need to project the input signal and before applying the respective DWTs. In onto , we consider particular, given a ﬁnite-energy input signal onto the its orthogonal projection space . The -level wavelet decomposition of the signal is subsequently given byThen the following result comes as a direct consequence of Theorem (4.2). Corollary 4.3: (HT Pair of Biorthogonal Wavelets): The following are equivalent: • the primal and dual wavelets form HT pairs, and , and and together constitute a biorthogonal wavelet basis of ; and • the discrete HT correspondences hold. The above construction also exhibits the following properties. • The two biorthogonal systems have the same order and the same Riesz bounds. satisfy the biorthogonality relation, then • If the pair . Indeed, using the identity so doAuthorized licensed use limited to: EPFL LAUSANNE. Downloaded on August 19, 2009 at 08:46 from IEEE Xplore. Restrictions apply.。

MedeA-VASP优势

MedeA-VASP优势1.VASP使用PAW方法或超软赝势，因此基组尺寸非常小，描述体材料一般需要每原子不超过100个平面波，大多数情况下甚至每原子50个平面波就能得到可靠结果。

2.磁性材料最精确的计算软件。

3.在平面波程序中，某些部分代码的执行是三次标度。

在VASP中，三次标度部分的前因子足可忽略，导致关于体系尺寸的高效标度。

因此可以在实空间求解势的非局域贡献，并使正交化的次数最少。

当体系具有大约2000个电子能带时，三次标度部分与其它部分可比，因此VASP可用于直到4000个价电子的体系。

4.VASP使用传统的自洽场循环计算电子基态。

这一方案与数值方法组合会实现有效、稳定、快速的Kohn-Sham方程自洽求解方案。

程序使用的迭代矩阵对角化方案（RMM-DISS和分块Davidson）可能是目前最快的方案。

5.VASP包含全功能的对称性代码，可以自动确定任意构型的对称性。

6.对称性代码还用于设定Monkhorst-Pack特殊点，可以有效计算体材料和对称的团簇。

Brillouin区的积分使用模糊方法或四面体方法。

四面体方法可以用Blöchl校正去掉线性四面体方法的二次误差，实现更快的k点收敛速度。

MedeA 2.5版本软件将材料设计领域的应用最广的工具VASP的最新版本5.2作为计算引擎，提供了更加丰富的计算功能和更高的稳定性能：．光学性质，特别是与介电函数相关的频率虚部和实部计算。

．增加外场和粒子位置相关的线性响应机制。

．大部分二阶响应函数，如内部应力张量、压电张量、Born有效电荷和原子间应力常数。

．准确的交换混合函数（PBE0）不仅支持Γ点而且支持整个k点。

因为目前的程序是基于波函数的对称性来执行的，所以k点是指IRZ（不可约布里渊区）。

计算量将随着增加很快，增加大约两个数量级。

．屏蔽交换能，COHSEX中的GW将得到支持。

．支持优化的有效势方法中的交换能确定。

．提高全频率GW方法计算的效率，如等离子体柱模型：并行效率非常高、Si 128能带、6×6×6 k点计算用双核Opteron机器需要500-1000秒。

单模光纤参数对布里渊散射阈值的影响

单模光纤参数对布里渊散射阈值的影响王菊巍;薛乐梅【摘要】Both Spontaneous Brillouin scattering model and stimulated Brillouin scattering model are applied for the analysis of the threshold for stimulated Bdllouin scattering in short and long SMF respectively at 1550nm communication window.For short distance transmission the dependency of the threshold exponential gain on fiber numerical aperture and fiber length is studied.%应用自发布里渊散射模型和受激布里渊散射模型,在1550nm通信窗口,分别对短距离和长距离普通单模光纤中的布里渊散射阈值进行了研究.对于短距离传输,分析了自发布里渊阈值增益系数与光纤数值孔径以及有效长度的依赖关系.【期刊名称】《光通信技术》【年(卷),期】2013(037)006【总页数】4页(P56-59)【关键词】单模光纤;布里渊散射;阈值增益系数【作者】王菊巍;薛乐梅【作者单位】青海大学基础部,西宁810016;兰州理工大学理学院,兰州730050;青海大学基础部,西宁810016【正文语种】中文【中图分类】TN929.110 引言受激布里渊散射 (stimulated Brillouin scattering,SBS)过程是一种受激的非线性过程，是泵浦波、斯托克斯波与声波之间的相互作用[1]。

SBS阈值是非常低的，所以布里渊散射是光纤中主要存在的一种非线性效应。

Smith从理论上估算出了SBS阈值的方法，这种计算方法是建立在大损耗光纤当中的，而它并不适用于当今低损耗的光纤系统中。

激光等离子体不稳定性及其抑制方案研究

·惯性约束聚变物理与技术·激光等离子体不稳定性及其抑制方案研究*余诗瀚1,2，李晓锋1,2，翁苏明1,2，赵　耀3，马行行1,2，陈　民1,2，盛政明1,2（1. 上海交通大学物理与天文学院激光等离子体实验室，上海 200240； 2. 上海交通大学 IFSA 协同创新中心，上海 200240；3. 中国科学院上海光学精密机械研究所高功率激光物理联合实验室，上海 201800）摘要：受激拉曼散射、受激布里渊散射等激光等离子体不稳定性（LPI ）是激光等离子体物理领域最重要的研究课题之一。

特别是在激光驱动的惯性约束聚变中，LPI 会造成相当份额的激光能量损失，破坏辐射对称性，产生的超热电子还会预热靶丸，进而影响压缩效率和聚变能量增益。

近期，在美国国家点火装置上开展的实验表明对LPI 物理过程的充分理解和有效控制对成功实现ICF 点火至关重要。

我们对近期LPI 方面的一系列研究进展进行了简单介绍与讨论。

首先，回顾了描述LPI 过程的三波耦合理论，由此得出了LPI 在线性阶段的增长率。

接着讨论了一些复杂情景下的LPI 物理过程，譬如LPI 的非线性发展阶段、级联LPI 、多光束LPI 以及LPI 间的非线性耦合。

最后，着重介绍了一系列抑制LPI 的技术方案，包括束匀滑技术、光束时域整形、宽带激光、偏振旋转激光以及外加磁场等。

关键词：激光等离子体不稳定性；惯性约束聚变；受激拉曼散射；受激布里渊散射；宽带激光中图分类号： O534. 文献标志码： A doi : 10.11884/HPLPB202133.200125Laser plasma instabilities and their suppression strategiesYü Shihan 1,2， Li Xiaofeng 1,2， Weng Suming 1,2， Zhao Yao 3， Ma Hanghang 1,2， Chen Min 1,2， Sheng Zhengming 1,2（1. School of Physics and Astronomy , Shanghai Jiaotong University , Shanghai 200240, China ;2. Collaborative Innovation Center of IFSA , Shanghai Jiaotong University , Shanghai 200240, China ;3. Key Laboratory of High Power Laser and Physics , Shanghai Institute of Optics and Fine Mechanics , Chinese Academy of Sciences , Shanghai 201800, China ）Abstract ： The issue of laser plasma instabilities (LPIs) including stimulated Raman scattering, stimulated Brillouin scattering and so on is one of the most fascinating subjects in laser plasma physics. In particular, LPIs may cause significant laser energy loss and produce hot electrons to preheat fusion targets, which affect target compression and fusion energy gain in laser-driven inertial confinement fusion. Recent experiments carried out on the National Ignition Facility, the largest laser facility in the world for laser fusion, indicate that the understanding and the control of LPIs are essential to the realization of laser fusion. In this paper, we present a review on recent studies of LPIs.Firstly, we retrospect the classical theoretical model of LPIs, which offers a good estimation of growth rate in the linear development stage. Then, we discuss some progresses on the understanding of LPIs in more complex and real scenarios, such as LPI development in the nonlinear regions, cascaded LPIs, multi-beam LPIs, and nonlinear couplings between LPIs. Following the exploration of LPI physics, we emphasize on the strategies for the control of LPIs,including beam smoothing techniques, temporal profile shaping, broadband laser, laser polarization rotation, external magnetic field and so on.Key words ： laser plasma instabilities ； inertial confinement fusion ； stimulated Raman scattering ；stimulated Brillouin scattering ； broadband laser激光等离子体不稳定性（LPI ）是一种典型的参量不稳定性。

MedeA-VASP优势

2.磁性材料最精确的计算软件。

3.在平面波程序中，某些部分代码的执行是三次标度。

在VASP中，三次标度部分的前因子足可忽略，导致关于体系尺寸的高效标度。

因此可以在实空间求解势的非局域贡献，并使正交化的次数最少。

当体系具有大约2000个电子能带时，三次标度部分与其它部分可比，因此VASP可用于直到4000个价电子的体系。

4.VASP使用传统的自洽场循环计算电子基态。

这一方案与数值方法组合会实现有效、稳定、快速的Kohn-Sham方程自洽求解方案。

程序使用的迭代矩阵对角化方案（RMM-DISS和分块Davidson）可能是目前最快的方案。

5.VASP包含全功能的对称性代码，可以自动确定任意构型的对称性。

6.对称性代码还用于设定Monkhorst-Pack特殊点，可以有效计算体材料和对称的团簇。

Brillouin区的积分使用模糊方法或四面体方法。

四面体方法可以用Blöchl校正去掉线性四面体方法的二次误差，实现更快的k点收敛速度。

．增加外场和粒子位置相关的线性响应机制。

．大部分二阶响应函数，如内部应力张量、压电张量、Born有效电荷和原子间应力常数。

．准确的交换混合函数（PBE0）不仅支持Γ点而且支持整个k点。

因为目前的程序是基于波函数的对称性来执行的，所以k点是指IRZ（不可约布里渊区）。

计算量将随着增加很快，增加大约两个数量级。

．屏蔽交换能，COHSEX中的GW将得到支持。

．支持优化的有效势方法中的交换能确定。

．提高全频率GW方法计算的效率，如等离子体柱模型：并行效率非常高、Si 128能带、6×6×6 k点计算用双核Opteron机器需要500-1000秒。

An introduction to topological insulators

C.R.Physique 14(2013)779–815Contents lists available at ScienceDirectComptes Rendus PhysiqueTopological insulators/IsolantstopologiquesAn introduction to topological insulatorsIntroduction aux isolants topologiquesMichel Fruchart,David Carpentier ∗Laboratoire de physique,École normale supérieure de Lyon (UMR CNRS 5672),46,allée d’Italie,69007Lyon,Francea r t i c l e i n f o ab s t r ac tArticle history:Available online 21October 2013Keywords:Topological insulator Topological band theory Quantum anomalous Hall effect Quantum spin Hall effect Chern insulator Kane–Mele insulator Mots-clés :Isolant topologiqueThéorie des bandes topologiqueEffet Hall quantique anomalEffet Hall quantique de spinIsolant de ChernIsolant de Kane–Mele Electronic bands in crystals are described by an ensemble of Bloch wave functionsindexed by momenta deﬁned in the ﬁrst Brillouin Zone,and their associated energies.In an insulator,an energy gap around the chemical potential separates valence bandsfrom conduction bands.The ensemble of valence bands is then a well deﬁned object,which can possess nontrivial or twisted topological properties.In the case of a twistedtopology,the insulator is called a topological insulator.We introduce this notion oftopological order in insulators as an obstruction to deﬁne the Bloch wave functions overthe whole Brillouin Zone using a single phase convention.Several simple historical modelsdisplaying a topological order in dimension two are considered.Various expressions of thecorresponding topological index are ﬁnally discussed.©2013Académie des sciences.Published by Elsevier Masson SAS.All rights reserved.r és u m éLes bandes électroniques dans un cristal sont déﬁnies par un ensemble de fonctions d’onde de Bloch dépendant du moment déﬁni dans la première zone de Brillouin,ainsi quedes énergies associées.Dans un isolant,les bandes de valence sont séparées des bandesde conduction par un gap en énergie.L’ensemble des bandes de valence est alors unobjet bien déﬁni,qui peut en particulier posséder une topologie non triviale.Lorsquecela se produit,l’isolant correspondant est appeléisolant topologique.Nous introduisonscette notion d’ordre topologique d’une bande comme une obstruction àla déﬁnition desfonctions d’ondes de Bloch àl’aide d’une convention de phase unique.Plusieurs modèlessimples d’isolants topologiques en dimension deux sont considérés.Différentes expressionsdes indices topologiques correspondants sont ﬁnalement discutées.©2013Académie des sciences.Published by Elsevier Masson SAS.All rights reserved.1.IntroductionTopological insulators are phases of matter characterized by an order of a new kind,which is not ﬁt into the standard symmetry breaking paradigm.Instead these new phases are described by a global quantity which does not depend on the details of the system –a so-called topological order.More precisely,their ensemble of valence bands possess a non-standard topological property.A band insulator is a material which has a well-deﬁned set of valence bands separated by an energy gap from a well-deﬁned set of conduction bands.The object of interest in the study of topological order in insulators is the *Corresponding author.E-mail addresses:michel.fruchart@ens-lyon.fr (M.Fruchart),david.carpentier@ens-lyon.fr (D.Carpentier).1631-0705/$–see front matter ©2013Académie des sciences.Published by Elsevier Masson SAS.All rights reserved./10.1016/j.crhy.2013.09.013780M.Fruchart,D.Carpentier/C.R.Physique14(2013)779–815ensemble of valence bands,which is unambiguously well deﬁned for an insulator.The question underlying the topological classiﬁcation of insulators is whether all insulating phases are equivalent to each other,i.e.whether their ensemble of va-lence bands can be continuously transformed into each other without closing the gap.Topological insulators correspond to insulating materials whose valence bands possess non-standard topological properties.Related to their classiﬁcation is the determination of topological indices which will differentiate standard insulators from the different types of topological insulators.A canonical example of such a topological index is the Euler–Poincarécharacteristic of a two-dimensional mani-fold[1].This index counts the number of“holes”in the manifold.Two manifolds with the same Euler characteristic can be continuously deformed into each other,which is not possible for manifolds with different Euler characteristics.The existence of topological order in an insulator induces unique characteristic experimental signatures.The most uni-versal and remarkable consequence of a nontrivial bulk topology is the existence of gapless edge or surface states;in other words,the surface of the topological insulator is necessarily metallic.An informal argument explaining those surface states is as follows.The vacuum as well as most conventional insulating crystals are topologically trivial.At the interface between such a standard insulator and a topological insulator,it is not possible for the“band structure”to interpolate continuously between a topological insulator and the vacuum without closing the gap.This forces the gap to close at this interface leading to metallic states of topological origin.This kind of topological phase orderingﬁrst arose in condensed matter in the context of the integer quantum Hall effect. This phase,discovered in1980by Klaus von Klitzing et al.[2],is reached when electrons trapped in a two-dimensional interface between semi-conductors are submitted to a strong transverse magneticﬁeld.Quantized plateaux appear for the Hall conductivity while the longitudinal resistance simultaneously vanishes[3].In the bulk of the sample,the electronic states are distributed in Landau levels with a large gap between them.The quantization of the Hall conductivity can be attributed within standard linear response theory to a topological property of these bulk Landau levels,the so-calledﬁrst Chern number of the bands located below the chemical potential[4].From this point of view the robustness of the phase manifested in the high precision of the Hall conductivity plateau is an expression of the topological nature of the related order,which by deﬁnition is insensitive to perturbations.The existence of robust edge states is another manifestation of this topological ordering.The quantized Hall conductivity can be alternatively accounted for by the ballistic transport properties of the edge states.Note that in the initial work of Thouless et al.[4],this topological ordering was described as a property of electronic Bloch bands of electrons on a lattice,and was only generalized later to free electrons on a planar interface.The topological property of the ensemble of Bloch states of a valence band can be inferred by the explicit determination of these Bloch states.In a nontrivial or twisted insulator,one faces an impossibility or obstruction to deﬁne electronic Bloch states over the whole band using a single phase convention:at least two different phase conventions are required,as opposed to the usual case.This obstruction is a direct manifestation of the nontrivial topology or twist of the corresponding band.It was realized in1988by D.Haldane[5]that while this type of order was speciﬁc to two-dimensional insulators,it did not require a strong magneticﬁeld,but only time reversal symmetry breaking.This author considered a model of electrons on a bipartite lattice (graphene),with time-reversal symmetry broken explicitly but without any net magneticﬂux through the lattice.The phase diagram consists then of three insulating phases,i.e.with aﬁnite gap separating the conduction from the valence bands. These insulators only differs by their topological property,quantized by a Chern number.The analogous phases of matter are now denoted Chern topological insulators,or anomalous quantum Hall effect.Such a phase was recently discovered experimentally[6].Within theﬁeld of topological characterization of insulators a breakthrough occurred with the seminal work of C.Kane and G.Mele[7,8].These authors considered the effect of a strong spin–orbit interaction on electronic bands of graphene. They discovered that in such a two-dimensional system where the spin of electrons cannot be neglected in determining the band structure,the constraints imposed by time-reversal symmetry could lead to a new topological order and associated metallic edge states of a new kind.While the quantum Hall effect arises in electronic system without any symmetry and is characterized by a Chern number,this new topological phase is possible only in presence of time-reversal symmetry, and is characterized by a new Z2index.It was called a quantum spin Hall phase.This discovery triggered a huge number of theoretical and experimental works on the topological properties of time reversal symmetric spin-dependent valence bands and the associated surface states and physical signatures.Soon after the initial Kane and Mele papers,A.Bernevig, T.Hughes and S.C.Zhang proposed a realistic realization of this phase in HgTe quantum wells[9].They identiﬁed a possible mechanism for the appearance of this Z2topological order through the inversion of order of bulk bands around one point in the Brillouin zone.This phase was discovered experimentally in the group of L.Molenkamp who conducted two-terminal and multi-probe transport experiments to demonstrate the existence of the edge states associated with the Z2order[10,11].In2007,three theoretical groups extended the expression of the Z2topological index to three dimensions:it was then realized that three-dimensional insulating materials and not only quasi-two-dimensional systems could display a topological order[12–14].Several classes of materials,including the Bismuth compounds BiSb,Bi2Se3and Bi2Te3,and strained HgTe were discovered to be three-dimensional topological insulators[15–17].The hallmark of the Z2topological order in d=3 is the existence of surface states with a linear dispersion and obeying the Dirac equation.The unique existence of these Dirac states as well as their associated spin polarization spinning around the Dirac point have been probed by experimental surface techniques including Angle-Resolved PhotoEmission(ARPES)and Scanning Tunneling Microscopy(STM).Their pres-ence in several materials has been conﬁrmed by numerous studies,while a clear signature of their existence on transport experiments has proven to be more diﬃcult to obtain.Note that such Dirac dispersion relations for topological surface statesM.Fruchart,D.Carpentier/C.R.Physique14(2013)779–815781Fig.1.Schematic view of the open covering(U N,U S)of S1,with the intersections V E and V W of the open sets.(Color online.)Fig.2.A cylinder(left)is a trivial bundle(with no twist),whereas a Möbius strip(right)is a nontrivial bundle(with twist).Here,we have used the typical ﬁber F=[−1,1]instead of R to get a compact manifold that is easier to draw.(Color online.)arise around a single(or an odd number of)Dirac points in the Brillouin zone,as opposed to real two-dimensional materials like graphene where these Dirac points can only occur in pairs.The purpose of the present paper is to introduce pedagogically the notion of topological order in insulators as a bulk property,i.e.as a property of the ensemble of Bloch wave functions of the valence bands.For the sake of clarity we will discuss simple examples in dimension d=2only,instead of focusing on generals deﬁnitions.As a consequence of this pedagogical choice,we will omit a discussion of the physical consequences of this topological order,most notably the physical properties of Dirac surface states of interest experimentally,as well as other kind topological order in,e.g., superconductors.The reader interested by these aspects can turn towards existing reviews[15–18].Note that a different notion of topological order was introduced in e.g.[19],which differs from the property of topological insulators discussed in this review.In the part which follows,we will deﬁne more precisely the object of study.In a following part(Section3),we will describe the simplest model of a Chern insulator,i.e.in a two-bands system.This will give us an excuse to deﬁne the Berry curvature and the Chern number,and to comprehend the nontrivial topology as an“obstruction”to properly deﬁne electronic wavefunctions.As the understanding of the more recent and subtle Z2topological order was carved by its discov-erers in a strong analogy with the Chern topological order,these concepts will equip us for the third part(Section4),where we will develop simple models to understand the Z2insulators as well as the different expressions of the Z2invariant characterizing them.2.Bloch bundles and topologyThe aim of thisﬁrst part is to deﬁne more precisely the object of this paper,namely the notion of topological order of an ensemble of valence bands in an insulator.We willﬁrst review a very simple example of nontrivial bundle:the Möbius strip,before deﬁning the notion of valence Bloch bundle in an insulator.2.1.The simplest twisted bundle:a Möbius stripA vector bundleπ:E→B is speciﬁed by a projectionπfrom the bundle space E to the base space B.Theﬁber F x=π−1(x)above each point of the base x∈B is assumed to be isomorphic to aﬁxed typicalﬁber F.Theﬁbers F x and∼=F.Hence,the vector bundle E F possesses a vector space structure assumed to be preserved by the isomorphism F xindeed looks locally like the Cartesian product B×F.The bundle is called trivial if this also holds globally,i.e.E and B×F are isomorphic.When it is not the case,the vector bundle is said to be nontrivial,or twisted(see[20,1]for details).As a consequence,a n-dimensional vector bundle is trivial iff it has a basis of never-vanishing global sections i.e.iff it has a set of n global sections which at each point form a basis of theﬁber[21].On the contrary,the obstruction to deﬁne a basis of never-vanishing global sections(or basis of theﬁbers)will signal a twisted topology of a vector bundle.In the following, we will rely on this property to identify a nontrivial topology of a vector bundle when studying simple models.To provide an intuitive picture of nontrivial bundles,we will consider a simple example:the Möbius bundle[1].Let us consider as the base manifold the circle S1,and let U N=(0− ,π+ )and U S=(−π− ,0+ )with >0be an open covering of S1 [0,2π],parameterized by the angleθ∈S1(see Fig.1).Take the typicalﬁber to be the line F=R, parameterized by t∈F,and take as a structure group the two-elements group Z2={−1,1}.To construct aﬁber bundle782M.Fruchart,D.Carpentier/C.R.Physique14(2013)779–815Fig.3.Schematic band structures of an insulator(left)and a metal(right).The variable k corresponds to the coordinate on some generic curve on the Brillouin torus.π:E→S1over S1,we have to glue together the products U N×F and U S×F.The intersection of the two open sets of the covering is U N∩U S=V E∪V W with V E=(− , )and V W=(π− ,π+ ).The transition functions t N S(θ)can be either t→t or t→−t.If we choose both transition functions equal:t N S(θ∈V E):t→t and t N S(θ∈V W):t→t(1) the bundleπ:E→S1is a trivial(nontwisted)bundle,which is a cylinder(Fig.2,left).However,is we choose different transition functions on each side:t N S(θ∈V E):t→t and t N S(θ∈V W):t→−t(2) the bundle is not trivial(it is twisted),and is the Möbius bundle(Fig.2,right).This illustrates the relation between the triviality of the bundle and the choice of the transition function t N S.When the bundle can be continuously deformed such that the transition functions be always the identity function the bundle will be trivial.Let us illustrate on this example another property of a twisted bundle:the obstruction to deﬁne a basis of never-vanishing global sections in a twisted bundle.First,notice that as R is a one-dimensional vector space,the Möbius bundle is a one-dimensional(line)real vector bundle.Let s be a global section of the Möbius bundle.After one full turn from a generic positionθ,we have crossed one transition function t→t and one transition function t→−t so we have s(θ+2π)=−s(θ). Hence s=0everywhere:the only global section on the Möbius bundle is the zero section.There is no global section of the Möbius bundle(except the zero section),so this bundle is indeed nontrivial.2.2.Bloch bundlesWe consider a d-dimensional crystal in a tight-binding approach.We will describe its electronic properties using a single electron Hamiltonian,i.e.neglecting interaction effects.Hence,from now on,we only focus onﬁrst-quantized one-particle Hamiltonians.The discrete real space lattice periodicity of this Hamiltonian reﬂects itself into the nature of its eigenstates, which are Bloch wavefunctions indexed by a quasi-momentum k.This quasi-momentum k is restricted to theﬁrst Brillouin zone of the initial lattice:it is deﬁned up to a reciprocal lattice vector G.Hence this Brillouin zone has the topology of a d-dimensional torus T d,which we call the Brillouin torus.From the initial Hamiltonian,we deduce for each value of this quasi-momentum k a“Bloch Hamiltonian”H(k)acting on a2n-dimensional Hilbert space,which accounts for the2n electronic degrees of freedom in the unit cell(e.g.sites,orbitals,or spin).Associated with this Bloch Hamiltonian are its Bloch eigenstates and eigen-energies Eα(k),α=1,...,2n.The evolution of each Eα(k)as k evolves in the Brillouin torus deﬁnes a band.An insulator corresponds to the situation where a gap in energy separates the empty bands above the gap, from theﬁlled bands or valence bands below the gap(see Fig.3).In this situation,when the chemical potential lies inside the gap,electronic states of the crystal cannot be excited by a small perturbation such as the application of the difference of potential:no current can be created.The ground state of such an insulator is determined from the ensemble of single particle eigenstates corresponding to theﬁlled bands.These eigenstates are deﬁned for each valence band,and for each point k of the Brillouin torus,up to a phase.The correspondingﬁber bundle over the Brillouin zone deﬁned from the eigenstates of the valence bands is the object of study in the present paper.Bloch Hamiltonians H(k)deﬁne for each k Hermitian operators on the effective Hilbert space H k∼=C2n at k.The col-lection of spaces H k forms a vector bundle on the base space T d.This vector bundle happens to be always trivial,hence isomorphic to T d×C2n,at least for low dimensions of space d 3(this is due to the vanishing of the total Berry curvature, see[22,23]).This means that we may assume that the Bloch Hamiltonians H(k)are k-dependent Hermitian2n×2n matri-ces deﬁned so that H(k)=H(k+G)for G in the reciprocal lattice(note that this does not always correspond to common conventions in particular on multi-partite lattices,see e.g.[24])In an insulator,there are at least two well-deﬁned subbundles of this complete trivial bundle:the valence bands bundle, which corresponds to all theﬁlled bands,under the energy gap,and the conduction bands bundle,which corresponds to all the empty bands,over the energy gap.In the context of topological insulators,we want to characterize the topology of the valence bands bundle,which underlies the ground state properties of the insulators.In a topological insulator this valence bands subbundle possesses a twisted topology while the complete bundle is trivial.M.Fruchart,D.Carpentier /C.R.Physique 14(2013)779–815783In the following,we will discuss two different kinds of topological orders.In the ﬁrst one,we will discuss Chern in-sulators (Section 3):no symmetry constraints are imposed on the Bloch bundle,and in particular time-reversal invariance is broken.In the second part,we will discuss Z 2insulators (Section 4):here,time-reversal invariance is preserved.In a time-reversal invariant system,the bundle of ﬁlled bands and the bundle of empty bands happen to be separately trivial.However,the time-reversal invariance adds additional constraints on the bundle:even if the ﬁlled bands bundle is always trivial as a vector bundle when time-reversal invariance is present,it is not always trivial in a way which preserves a structure compatible with the time-reversal operator.3.Chern topological insulators3.1.IntroductionThe ﬁrst example of a topological insulator is the quantum Hall effect (QHE)discovered in 1980by von Klitzing et al.[2].Two years later,Thouless,Kohmoto,Nightingale,and de Nijs (TKNN)[4]showed that QHE in a two-dimensional electron gas in a strong magnetic ﬁeld is related to a topological property of the ﬁlled band (see also [22,25]).Namely,the Hall conductance is quantized,and proportional to a topological invariant of the ﬁlled band named Chern number (hence the name Chern insulator).Haldane [5]has generalized this argument to a system with time-reversal breaking without a net magnetic ﬂux,hence without Landau levels.This kind of Chern insulator,which has recently been observed experimentally[6],is called quantum anomalous Hall effect.Chern insulators,with or without a net magnetic ﬂux,only exist in two dimensions.3.2.The simplest model:a two-bands insulatorThe simplest insulator possesses two bands,one above and one below the band gap.Such an insulator can generically be described as a two-level system,which corresponds to a two-dimensional Hilbert space H k C 2at each point of the Brillouin torus,on which acts a Bloch Hamiltonian continuously deﬁned on the Brillouin torus.Hence H (k )can be written as a 2×2Hermitian matrix,parameterized by the real functions h μ(z ):H (k )=h 0+h zh x −i h y h x +i h y h 0−h z (3)which can re rewritten on the basis of Pauli matrices 1plus the identity matrix σ0=1as:H (k )=h μ(k )σμ=h 0(k )1+ h(k )· σ(4)In the following,we always assumed that the coeﬃcients h μare well deﬁned on Brillouin torus,i.e.are periodic.The spec-tral theorem ensures that H (k )has two orthogonal normalized eigenvectors u ±(k )with eigenvalues ±(k ),which satisfy:H (k )u ±(k )= ±(k )u ±(k ).(5)Using Tr (H )=2h 0and det (H )=h 20−h 2with h (k )= h (k ) = h 2x (k )+h 2y (k )+h 2z (k )we obtain the energy eigenvalues:±(k )=h 0(k )±h (k )(6)The corresponding normalized eigenvectors are,up to a phase:u ±(k )=1+h z + 2±h 2x +h 2y −1 ±x +i h y 1 (7)The energy shift of both energies has no effect on topological properties,provided the system remains insulating.To simplify the discussion,let us take h 0=0.Therefore,the system is insulating provided h (k )never vanishes on the whole Brillouin torus,which we enforce in the following.As we focus only on the topological behavior of the ﬁlled band,which is now well-deﬁned,we only consider the ﬁlled eigenvector u −(k )in the following.3.3.An obstruction to continuously deﬁne the eigenstatesThe ﬁlled band of the two-bands insulator is described by a map that assigns a ﬁlled eigenvector u −(k )to each point of the Brillouin torus:it deﬁnes a one-dimensional complex vector bundle on the torus.When this vector bundle is trivial,this map can be chosen to be continuous on the whole Brillouin torus:this corresponds to the standard situation where a 1We use the usual convention that a Greek index starts at 0whereas a Latin index starts at 1.784M.Fruchart,D.Carpentier /C.R.Physique 14(2013)779–815Fig.4.Open covering (U N ,U S )of the sphere S 2.The intersection C of the open sets is topologically a circle S 1and can be viewed as the boundary of either of the open sets.choice of phase for the Bloch eigenstate at a given point k 0of the Brillouin torus can be continuously extrapolated to the whole torus.When it is not trivial,there is an obstruction to do so.To clarify this notion of obstruction,let us ﬁrst notice that the Hamiltonian (4)is parameterized by a three-dimensional real vector h.The energy shift h 0does not affect the topological properties of the system and has been discarded.In spherical coordinates,this vector reads:h =hsin θcos ϕsin θsin ϕcos θ (8)With these coordinates,we rewrite the ﬁlled eigenvector (7)as:u −( h )= −sin θ2e i ϕcos θ2 (9)We notice that the norm h = hof the parameter vector h does not affect the eigenvector.Therefore,the parameter space is a 2-sphere S 2.We will ﬁrst see in the following that there is always an obstruction to deﬁne a continuous eigenvec-tor u −( h /h )on the sphere,or in other words,that the corresponding vector bundle on the sphere S 2is not trivial.Hence,we will realize that the original vector bundle on Brillouin torus (the pullback bundle by h of the bundle on the sphere)is only nontrivial when the map k → h(k )covers the whole sphere.In the limit θ→0,the eigenvector (9)is not well deﬁned because it has an ill-deﬁned phase.We could change our phase convention and,e.g.,multiply the eigenvector (9)by e i ϕ,but this would only move the ill-deﬁned limit to θ→π.It turns out that it is not possible to get rid of this singularity and deﬁne a continuous eigenvector on the whole sphere.This behavior unveils the nontrivial topology of a vector bundle on the sphere,discovered by Dirac and Hopf in 1931[26]:at least two local trivializations are needed to describe a vector bundle on the sphere [27,1].Let us choose an open covering (U N ,U S )of the sphere,the two open sets being the north hemisphere U N and the south hemisphere U S ,chosen so that they have a nonzero intersection homotopy equivalent to the equator circle (Fig.4).We deﬁne local trivializations of the ﬁlled band bundle byu S −( h )= −sin θ2e i ϕcos θand u N −( h )= −e −i ϕsin θ2cos θ(10)Indeed,u N −is correctly deﬁned on U N (resp.u S −on U S ),but neither are well deﬁned on the whole sphere.The intersectionC =U N ∩U S can be reduced to a circle,and can be viewed as the boundary e.g.of U N ,i.e.C =∂U N S 1.The transition function from the trivialization on U N to the trivialization on U S is phase change on the equator,i.e.a map t N S :C →U (1)t N S =e i ϕ(11)Now let us recall that the Bloch electronic states are described by a bundle on the Brillouin torus.If the map h/h from the Brillouin torus to the parameter manifold does not completely cover the sphere (taking into account the orientations,see below),there will be no obstruction to globally deﬁne eigenstates of the Bloch Hamiltonian,by smoothly deforming the pulled-back transition function h t N S =t N S ◦h to the identity.On the contrary,if h/h does completely cover the sphere,the topology of the Bloch bundle is not trivial:it is never possible to deform the transition function to the identity.Those statements are indeed made quantitative through the introduction of the notion of Chern number.3.4.Berry curvature and Chern numberAs the complete Bloch bundle (with ﬁlled and empty bands)is always trivial (see Section 2.2),we can indifferently study the topological properties of the ﬁlled band or of the empty one:the topology of the ﬁlled band will reﬂect the topological properties of the empty one.In the context of Bloch bundles,topological properties of the ﬁlled band are characterized by its Chern class (see [27,Ch.2]as well as [1,Ch.10]for a general introduction to the Berry phase,connection and curvature).The Chern classes are an intrinsic characterization of the considered bundle,and do not depend on a speciﬁc connection。

Statistical mechanics of permanent random atomic and molecular networks Structure and heter

Statistical mechanics of permanent random atomic and molecular networks: Structure and heterogeneity of the amorphous solid state
Konstantin A. Shakhnovich and Paul M. Goldbart
Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, U.S.A. (January 18, 1999) Under suﬃcient permanent random covalent bonding, a ﬂuid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order parameter, resulting from a statistical-mechanical approach, captures information concerning this heterogeneity via a certain joint probability distribution. This joint probability distribution describes the variations in the positional and orientational localization of the particles, reﬂecting the random environments experienced by them, as well as further information characterizing the thermal motion of particles. A complete solution, valid in the vicinity of the amorphous solidiﬁcation transition, is constructed essentially analytically for the amorphous solid order parameter, in the context of the random network model and approach introduced by Goldbart and Zippelius [Europhys. Lett. 27, 599 (1994)]. Knowledge of this order parameter allows us to draw certain conclusions about the stucture and heterogeneity of randomly covalently bonded atomic or molecular network solids in the vicinity of the amorphous solidiﬁcation transition. Inter alia , the positional aspects of particle localization are established to have precisely the structure obtained perviously in the context of vulcanized media, and results are found for the analogue of the spin glass order parameter describing the orientational freezing of the bonds between particles. 61.43.-j, 82.70.Gg, 61.43.Dq

固体物理专业术语

弹性应变张量 Elastic strain tensor 弹性劲度常数 Elastic stiffness constant 弹性顺度常数 Elastic compliance constant
弹性模量 Elastic module 弹性动力学方程 Elastic-dynamics equation
玻尔兹曼方程 Boltzman equation 点群 Point groups
迪. 哈斯－范. 阿耳芬效应 De Hass－Van Alphen effect
胡克定律 Hooke’s law 氢键 Hydrogen bond
亲合势 Affinity 重迭排斥能 Overlap repulsive energy
能带的扩展能区图式
Extended zone scheme of energy band 配分函数 Partition function 准粒子 Quasi- particle 准动量 Quasi- momentum 准自由电子近似
Nearly free electron approximation
空间群 Space group 空位 Vacancy
范德瓦耳斯相互作用 Van der Waals interaction
金属性结合 Metallic binding 单斜晶系 Monoclinic system 单电子近似 Single-erection approximation 极化声子 Polarization phonon 拉曼散射 Raman scattering
对称操作 Symmetry operation 对称群 Symmetric group
正交化平面波 Orthogonalized plane wave 电子-晶格相互作用 Electron-lattice interaction