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梯度理论的发展及其意义

梯度理论的发展及其意义一、本文概述梯度理论，作为一种深入探究自然现象和社会现象空间分布及其动态变化的理论工具，自其诞生以来就在科学研究中占据了举足轻重的地位。

本文旨在全面梳理梯度理论的发展历程，深入探讨其理论内涵，并阐述其在多个领域中的广泛应用及其深远意义。

文章首先将对梯度理论的基本概念进行界定，阐述其起源与发展脉络，接着分析梯度理论在地理学、经济学、生态学等多个学科领域中的具体应用案例，最后总结梯度理论对于推动学科交叉融合、深化人类对自然和社会现象认识的重要作用，并展望其未来的发展趋势和潜在应用前景。

通过对梯度理论的深入研究，我们不仅能够更好地理解自然和社会现象的空间分布规律，还能够为政策制定、资源配置和可持续发展等实践问题提供科学的理论支撑。

二、梯度理论的起源与发展梯度理论，作为一种重要的空间分析框架，起源于经济学领域，尤其是在区域经济学和发展经济学中占据重要地位。

其起源可追溯至20世纪中叶，当时的经济学家们开始关注到空间因素在经济发展中的重要性，梯度理论应运而生。

梯度理论最初由美国经济学家埃德加·胡佛（Edgar Hoover）在20世纪50年代提出，他观察到在区域经济发展过程中，存在着一种由中心城市向外围地区扩散的经济活动梯度。

胡佛认为，这种梯度是由于资源、技术、信息等生产要素在空间中的不均匀分布所导致的。

随着研究的深入，梯度理论逐渐发展成为一种系统的空间经济理论。

其中，最具代表性的学者是瑞典经济学家冈纳·缪尔达尔（Gunnar Myrdal）。

他在其著作《经济理论与不发达地区》中，详细阐述了梯度理论的内涵和机制。

缪尔达尔认为，梯度现象是由经济发展的累积循环因果效应所导致的，富裕地区通过累积优势不断吸引资源和要素，形成经济发展的高地，而贫困地区则由于资源流失和要素不足而陷入低水平均衡陷阱。

此后，梯度理论不断得到完善和发展。

20世纪60年代，美国经济学家弗里德曼（John Friedmann）提出了著名的“核心-边缘”理论，进一步丰富了梯度理论的内容。

BAG a graph theoretic sequence clustering algorithm

1 BAG:A Graph Theoretic Sequence Clustering Algorithm(An Extended Abstract)Sun KimSchool of InformaticsCenter for Genomics and BioinformaticsIndiana University–Bloomingtonsunkim@AbstractRecently developed sequence clustering algorithms based on graph theory have been successful in clustering a large number of sequences into families of sequences of speciﬁc categories.In this paper,we present a new sequence clustering algorithm BAG based on graph theory.Our algorithm clusterssequences using two properties of graph,biconnected component and articulation point.As computationof biconnected components and articulation points is eﬃcient,linear in relation to the number of verticesand edges,our algorithms are well suited for comparing a large number of proteins from multiple genomes.Our experiments with protein sequences from multiple genomes show that our algorithms generatefamilies of high quality.For example,our algorithm correctly classiﬁed3,306predicted proteins from E.coli and H.inﬂuenzae into1,427families without human intervention.We also dicuss the importanceof large scale sequence comparisons from our experience in clustering many diﬀerent genomes,includingArabidopsis thaliana.1IntroductionAs more and more complete genome sequences become available,we can understand better the content of genomes by comparing multiple genomes.By comparing multiple genomes,potential protein-protein interaction[6],regulatory regions[14],or sytenic regions[17,11]can be predicted.In addition,more accurate sequence relationship can be established through the comparative analysis of genomes.However, comparing multiple genomes is a lot more complicated than standard sequence database searches.Well developed computational tools can facilitate multiple genome comparisons and also help us to deduce more reliable conclusions.One of the most important class of computational tools for genome comparison is the sequence clustering algorithm.Recently developed clustering algorithms[7,21,12,13]were successful in clustering a large number of sequences simultaneously,e.g.,whole sets of proteins from multiple organisms.In this paper we present our sequence clustering algorithm BAG based on graph theory.2Pairwise Sequence Comparison to Genome ComparisonMost sequence clustering algorithms are based on the pairwise sequence comparison.There are many pairwise sequence alignment algorithms[1,19,20].These pairwise alignment algorithms are eﬀective in detecting homology among sequences especially when similarity between sequences are relatively high.The most challenging task is to detect remotely related–distant in terms of sequence similarity–sequences. One eﬀective method to detect remote homology is to use intermediate sequences[18].For example,a relationship between two sequences,s i and s j,may be detected via another sequence s k even when the sequence similarity between s i and s j cannot be detected by the pairwise alignment method.This can be seen as building a transitive relationship among the three sequences,i.e.,s i→s k→s j.Building the transitive relationships raises two important issues:what should be intermediate sequences?and how far can we build the trasitive relationships?Clustering algorithms use structures of sequence relationships to classify a set of sequences into families of sequences,F={F1,F2,...,F n}.While generating F,the remote homology detection issue and the transitivity bounding issue are systematically addressed with the structures of sequence relationships used by the clustering algorithm.Any two sequence,s i and s j in the same family F l={...,s i,s j,s k,..}are related by intermediate sequences,say s k,even when there is no observable relationship between s i and s j,thus remote homology detection issue is addressed.The sequences s i and s m in two diﬀerent familiescould be related through intermediate sequences s m1,...,s mlbut such chaining of sequence relationshipsare blocked if the structure of sequence relationships used in the clustering algorithm classify s i and s m into two diﬀerent families.Thus the transitivity issue is addressed.Recently developed sequence clustering algorithms were successful in clustering a large number of sequences into sequence families of highly speciﬁc categories[7,21,12,13].These clustering algorithms used graph theory explicitly or implicitly.In the following sections,we present our graph theoretic clustering sequence algorithm.3A New Graph Theoretic Sequence Clustering Algorithm3.1PreliminariesThe connected component of a graph is a subgraph where any two vertices in the subgraph are reachable from each other.An articulation point of G is a vertex whose removal disconnects G.For example,in Figure1the removal of a vertex s5disconnects G.A biconnected graph is a graph where there are at lest two disjoint paths for any pair of vertices.A biconnected component of G is a maximal biconnected subgraph.In Figure1,a subraph G1induced by vertices{s2,s3,s4}is a biconnected graph but it is not maximal since another subgraph G2induced by vertices{s1,s2,s3,s4,s5}is biconnected and G1is a subgraph of G2.There are two biconnected components,{s1,s2,s3,s4,s5}and{s5,s6,s7,s8,s9}of G in Figure1.3.2The basic algorithmWe present a new graph theoretic sequence clustering algorithm that explicitly uses two graph properties: biconnected components and articulation points(see Figure1).A biconnected component(BCC in short) corresponds to a family of sequences and an articulation point corresponds to a multidomian protein.As an articulation point is the only vertex that connects multiple biconnected components,i.e.,multiple families, it is intuitive to consider each articulation point as a candidate for multidomain sequence.Figure1:Biconnected components and articulation points.The vertex s5is an articulation point since removing the vertex results in separating the graph.A simple version of our algorithm works as follows.Given a set of sequences S={s1,s2,...,s n},pute similarities(s i,s j)for all1≤i,j≤n and i=j.2.Build a sequence graph G from the pairwise matches above a preset cutoﬀthreshold.3.Generate a set of subgraphs,{G1,G2,...,G m},each of which G i is a biconnected component.4.Then a set of vertices in each subgraph G i forms a family of sequences and each articulation pointbecomes a candidate for multidomain sequence.To reduce computation time in Step1,we can use well accepted approximation algorithms such as FASTA[19]or BLAST[1,2].We simply choose FASTA for the pairwise computation,and the computation is FASTA(s i,S)for all1≤i≤n.All pairwise comparisons can be computed once and saved for later use,especially for completely sequenced genomes.Indeed,there are several databases for precomputed all pairwise comparisons,e.g.,[16,5].From the precomputed pairwise comparison databases,we can retrieve pairwise comparisons for selected genomes for clustering analysis.Our algorithm is well suited for this type of comparative clustering analysis for an arbitrary set of genomes due to the computational eﬃciency,i.e,linear time complexity in relation to the number of edges.3.3Result from application of the basic algorithmWe performed a clustering analysis of all5,998predicted protein sequences from E.coli(GenBank ac-cession number U00096,4289proteins)and H.inﬂuenzae(GenBank accession number L42023,1709 proteins)with Zscore cutoﬀof400.1426families of3431sequences were clustered excluding families ofa single sequence(these families are uninformative).Most of the resulting families are clustered correctly with high precision according to the current annotation.However,there are cases where we cannot easily verify the correctness of the clustering result from the annotation.For example,it was not obvious that Family285is clustered correctly from the annotations in the heading as shown below.>gi|1573256|gb|AAC21953.1|L-serine deaminase(sdaA)[Haemophilus influenzae Rd]>gi|1788116|gb|AAC74884.1|L-serine deaminase[Escherichia coli K12]>gi|1789161|gb|AAC75839.1|L-serine dehydratase(deaminase),L-SD2[Escherichia coli K12] >gi|1789498|gb|AAC76146.1|putative L-serine dehydratase[Escherichia coli K12]>gi|1789500|gb|AAC76147.1|putative L-serine dehydratase[Escherichia coli K12](Hinf, SDH_A & B)1573256(Ecoli, SDH_B)1789500(Ecoli, SDH_A)1789498(Ecoli, SDH_A & B)(Ecoli, SDH_A & B)2552153857223752401166416275886101788116 1789161Figure 2:Sequence graphs with the Zscore cutoﬀthreshold of 400.The numbers on the edges denote the Zscores between two sequences.SDH αand SDH βand were detected by Pfam search.To verify the clustering result,we performed protein domain search using Pfam [3]7.0and found that there are two diﬀerent domains,SDH αand SDH βin the family as shown in Figure 2.The family begin to separate into two families at a stricter cutoﬀvalue of 600as shown in Figure 3,i.e.,two BCCs,{1788116,1789161,1789498,1573256}and {1788116,1789500}1,and an articulation point,1788116.However,the question is how do we know the cutoﬀthreshold value 600apriori?.In addition,diﬀerent families are characterized at diﬀerent cutoﬀvalues in general.This fundamental issue will be eﬀectively addressed in the extended version of our algorithm in the following section.4Bag :The Extended Clustering AlgorithmThe basic algorithm in Section 3.2is extended and called Biconnected components and Articulation points based Grouping of Sequences (Bag ).4.1Issues with the basic algorithmSeveral features of the basic algorithm presented in the previous section need attention:1.The cutoﬀthreshold setting issue :as shown with the example of SDH αand SDH βdomain proteins,we do not know the cutoﬀthreshold apriori ,Zscore 600for the example.2.Merging families :given a cutoﬀthreshold,several families may need to be tested for merging since the cutoﬀvalue may be too stringent so that sequences with the same domains are separated into multiple families.3.Spitting a family ;given a cutoﬀthreshold,a family may need to be tested for splitting into several ones.For example,sequences with SDH αand SDH βdomains in Figure 2.1The family {1788116,1789500}will be extended to include the two sequences,1573256and 1789161,that have the SDH βdomain,while the family is considered for merging through an articulation point,1788116(See the next section).(Hinf, SDH_A & B)1573256(Ecoli, SDH_A & B)(Ecoli, SDH_A & B)1788116 17891611789498(Ecoli, SDH_A)(Ecoli, SDH_B)1789500Figure 3:Sequence graphs with the Zscore cutoﬀthreshold of 600.The graph has two BCCs,{1788116,1789161,1789498,1573256}and {1788116,1789500},and an articulation point,1788116.4.Multidomain protein :how do we know an articulation point truly corresponds to a multidomain protein?Each of these features will be explored in the following subsections.4.2Setting the cutoﬀthresholdWe performed a series of clustering analyses with Zscore cutoﬀthresholds ranging from 100to 1000at 50increment intervals for the pairwise comparisons from E.coli and H.inﬂuenzae .The plot on the left side in Figure 4is the distribution of the number of biconnected components vs.the Zscore cutoﬀthreshold.We will call this plot the BCC plot .As we can observe in the ﬁgure,the number of biconnected components increases up to a certain value,150for Zscore,and then continue to decrease.The increase in the number of biconnected components is intuitive as a higher cutoﬀvalue will remove more false positives,thereby families of large size due to false positives being separated into several families.The decrease in the number of biconnected components is also intuitive as a higher cutoﬀvalue will remove more true positives,thereby more vertices become singletons,i.e.,vertices without incident edges;note that singletons are not counted.We would expect that there exists a peak in the BCC plot if the scoring method like Zscore eﬀectively models the pairwise sequence relationship.This observation is consistent with non-statistical scores like Smith-Waterman score [10].Note that the basic clustering algorithm runs linear time in relation to the number of pairwise matches above a preset cutoﬀthreshold after computing pairwise matches from a set of sequences.The series of clustering analysis with Zscore in Figure 4took less than 6seconds on a Pentium IV 1.7GHz processor machine running Linux.This computational eﬃciency makes it possible to eﬃciently conduct the series of clustering analyses with varying cutoﬀthresholds to ﬁnd the cutoﬀthreshold,C maxbiconn ,that generates the maximum number of biconnected components.However,we need to consider the number of articulation points since articulation points are candidates for multidomain proteins.The right plot in Figure 4shows the number of articulation points with respect to varying Zscore cutoﬀthresholds.The articulation points become candidates for multidomain proteins and need to be tested for having multidomain proteins:the0500100015002000020*******8001000N o o f b i c o n n e c t e d c o m p o n e n t s Zscore cutoff value E.coli + Hinf 05010015020025030035040002004006008001000N o o f a r t i c u l a t i o n p o i n t s Zscore cutoff value E.coli + Hinf Figure 4:The distribution of the number of biconnected components vs.the Zscore cutoﬀthreshold (left plot)and the distribution of the number of articulation points vs.the Zscore cutoﬀthreshold (right).test method will be brieﬂy described in the following sections.We would avoid selecting the cutoﬀthreshold with too many articulation points.Let NAP C the number of articulation points at score C .One way to select the cutoﬀvalue is to use a ratio r =NAP C +I NAP C where I is the interval of the score for the series of clustering analysis.4.3The overview of the extended algorithmWe will describe the overview of the extended algorithm due to the space limitation of the paper.Details of the algorithm can be found in [10].Our algorithm BAG works as follows:1.Build a graph G from all pairwise comparisons result.2.Run the basic algorithm with cutoﬀscores ranging from C 1to C 2at each interval I and select a score,C maxbiconn ,where the number of biconnected components is the largest,and another score,C arti ,where the number of articulation points begin to decrease at a ratio r ≥∆.3.Select a cutoﬀscore C arti and generate biconnected components,G 1,G 2,...,G n with a set of articu-lation points {A 1,A 2,...,A m }.4.Iteratively split a biconnected components into several ones with more stringent cutoﬀscores until there is no candidate component for splitting.5.Iteratively merge a set of biconnected components into one with relaxing the cutoﬀscore to C maxbiconn until there is no candidate component for merging.When merging two biconnected components fails,consider a partial merging by relaxing cutoﬀscore to C maxbiconn (see the case in Figure 3).The overall procedure can be summarized in two steps:(1)generation of candidate families and (2)reﬁnement of the families by merging and splitting.The fundamental question is which biconnected components need to be reﬁned,i.e.,splitting (Step 3)and merging (Step 4).For this purpose,we propose two tests as below.: TonB_boxC domainFigure5:The region shared among gi1573631,gi1573714,gi3212198,and gi3212230can be computedby chaining pairwise overlaps.All four sequences share domains,that are not present in the Pfam database,and they are annotated to share the hemoglobin binding domain.The three sequences,gi1573631,gi1573714,and gi3212198,share the TonB boxC domain in the Pfam database.This clustering result demonstrates that our algorithm correctly cluster sequences even when multiple domains are involved.1.AP-TEST tests an articulation point for having potential multidomains.2.RANGE-TEST tests each biconnected component for being a single family.These two tests are to see if there are common shared regions among the sequences.For example,Figure5shows that four sequences share common subsequence regions.Depending on the test result,splitting and merging operations are performed in a greedy fashion,i.e.,a resulting subgraph from a splitting or merging operation is not considered for further splitting or merging.5Clustering Two Bacterial GenomesIn this section,we will discuss the application of our clustering algorithm to clustering entire protein se-quences from complete genomes.With the current prototype implemented in C++with the LEDA[15] package,we were able to compare many diﬀerent sets of genomes.An analysis of B.burgdorferi and T. pallidum can be found in[10].In this section,we describe a complete analysis of two bacterial genomes,E.coli and H.inﬂuenzae.Due to the space limitation,we cannot present a complete description.The more de-tailed clustering result will be available at /sunkim/BAG/ecoli.hinf/.As shown in Figure4,we picked150for C maxbiconn and400for C arti(see Section4.2)and the clustering analysis starts with Zscore400,i.e.,C arti,which clusters1,391families with103articulation points. Among103articulation points,18failed for AP-TEST,which implies families around these articulation points does share some domains in common,thus the families connected through the18articulation pointsare not considered for merging.Among1,391families,9failed for RANGE-TEST,which implies that each subgraph have multiple families and need to be split.We used I split=50for splitting families andI merge=50for merging families.Family Zscore Split families Sequences Common domains6145061.11573631157371432121983212230no domain detected61.215740243212230no domain detected181800181.1157308017892511790097Sulfate transp17901501790499xan ur permease181.217892501790499no domain detected 285600285.115732561788116SDH alpha17891611789498285.217891611789500SDH beta 11666001166.117863241788577178864317898161790796no domain detected1166.217886431790795no domain detected 11674501167.1178633217867441786937Usher17871721787782178842717886791789533179077223671881167.217896101788678no domain detectedTable1:The families failed for RANGE-TEST were separated into subfamilies of the same functional domains.Note that domains not common in the subfamilies are not shown.Thus,“no domain detected”means that there is no domain shared among all family members and each family member may have domains detected by Pfam search.Splitting families The list of5families among9families failed for RANGE-TEST is shown in Table??. These families are expected to have multiple domains that lead to the failure for RANGE-TEST.This can be veriﬁed either by Pfam search or by sequnece alignment with respect to the multidomain candidate(for example,aligning6sequences of the family61with repect to3212230in Table1).After splitting,there were1,427families.Among them,227families did not have any domains detected by the Pfam search. Merging families A hypergraph was formed for merging families:families from the previous step(Split-ting step)become nodes and two nodes(families)are connected if there is a sequence present in both families.All families in each biconnected component in the hypergraph are considered for merging.There were165cluster merging events.Table2shows examples of merging events.6The Importance of Large Scale Sequence ComparisonsWe performed another clustering analysis from25,545predicted protein sequences from Arabidopsis thaliana genome.4,614families with106articulation points were computed with C biconn=400and C arti=500. We are still in the process of verifying the clustering result.However,from the Pfam search result,we veriﬁed most of families with domains,that can be detected in the Pfam database,are clustered correctly.We found an interesting observation in the BCC plot of the Arabidopsis thaliana genome as shown in Figure6.Intuitively,the number of biconnected components increases as more proteins from genomes are compared since more genes(proteins)can be matched.However,what was really interesting was thatNew family Families Sequences Common domains 47-484717888541573186GATase(2),GMP synt C(2),tRNA Me trans4815731863212188GATase(2),GMP synt C,IMPDH C 77-78-797717862681790194lacI(2),Peripla BP like(2)7815744811789456lacI(2),Peripla BP like(2)79157348715738341574481lacI(2)17865401787580178790617879481788474178906817892021789846179019417903691790715111-112-113111178881117892531789606Amino oxidase,FAD binding3fer4pyr redox(2) 112178881117890672367245fer4(2)113157295015740801574621fer411317871221787749178787211317879601789370179032611323672452367345176-177-178176178651817907202-Hacid DH C,adh zinc(2) 17717877531790720adh zinc(2)178157300017877531787863adh zinc178807317884071788895179004517907181790819220-22122017892501790499xan ur permease 221157308017892511790097Sulfate transp,xan ur permease(2)17901501790499425-426-42742517893011790027no domain detected 42617884941790027PTS EIIA2(2)42715734241788494PTS EIIA2(2),PTS-HPr(2) 783-784-7857831787661178868217902813HCDH(2),3HCDH N(2),ECH 78417862201788682ECH(2)78517862201787659ECH(2)17876601789286Table2:Examples for merging events.The number in the parantheses at the end of a domain name denotes the number of occurrences of the domain.Even though several families can be merged into one, each family were initially grouped into ones of speciﬁc category.For example,families111,112,and113 can be merged into one that shares a single occurrence of the fer4domain.However,the three families were grouped correctly according to domains in the families;all members in the family111have Amino oxidase, FAD binding3,fer4,and pyr redox(2),and all members in the family112have two occurrences of the fer4 domain while all memerbs in the family113have only one occurrence of the fer4domain.The merging event also detects multidomain proteins.For example,1790027in the merging of425-426-427shares unknown domains with1789301,in addition to the PTS EIIA2domain.050010001500200025003000350040004500500001002003004005006007008009001000N o o f b i c o n n e c t e d c o m p o n e n t s Zscore cutoff value Arabidopsis 050010001500200002004006008001000N o o f b i c o n n e c t e d c o m p o n e n t s Zscore cutoff value E.coli + Hinf E.coli Hinf Figure 6:The plots of the number of biconnected components vs.Zscore cutoﬀthresholds:the left plot for Arabidopsis thaliana and the right plot for the bacterial genomes (E.coli and H.inﬂuenzae ).The number of BCCs does not decrease much as the cutoﬀincreases up to 1000in the clustering analysis of Arabidopsis thaliana ;the decreasing ratio can be measured in relation to the maximum number of BCCs.We call this the plataeu in the BCC plot,which begins to appear as a larger set of sequences are compared.the number of biconnected components did not decrease as fast as in the analysis of the two bacterial genomes.For example,the number of biconnected components at the Zscore cutoﬀof 1000was 3,587.What was happening was that many sequences in the same family have two or more separate paths –thus biconnected –through strong sequence similarities when many sequences are compared.In the Arabidopsis thaliana analysis,the numbers of BCCs vary less than 4%from the maximum BCC number at 400in the range of the cutoﬀvalues from 350to 650,which is almost ﬂat.We call the observation the plateau in the BCC plot.The plataeu can be observed in the articulation plot as well.This observation provides more conﬁdence in the clustering results since the numbers of candidates for families and multidomain proteins do not change much.The plataeu appears as larger sets of sequences are compared as shown in Figure 6:four BCC plots for two bacterial genomes (E.coli and H.inﬂuenzae )separately,two bacterial genomes combined,and Arabidopsis thaliana .The plataeu can be measured in terms of the decreasing ratio in relation to the maximum number of BCCs.This result supports the importance of large scale genome comparisons:the more genomes are compared the stronger sequence relationship,i.e.,similarity,can be used for clustering sequences,thus we can be more conﬁdent of the clustering result.More rigorous and detailed result will be reported in the forthcoming paper.7ConclusionAs more sequences become available in an exponential rate,sequence analysis on a large number of se-quences will be increasingly important.Sequence clustering algorithms are computational tools for that purpose.In this paper,we presented our clustering algorithm,BAG ,that used two graph properties,biconnected components and articulation points.Our algorithm were successful in clustering sequences into families of speciﬁc categories using the pairwise sequence comparison information only.For example,families in Figure5were clustered correctly to shares hemoglobin binding domains even when multiple domains are involved(a subset of the family share the TonB boxC domain),and families in Section3.3were separated into two families of SDHαand SDHβ.Note that these two family classiﬁcations cannot be achieved by either Pfam search(for families in Figure5)or by looking at annotations(for families in Section3.3).In addition,our algorithm can help to detect previously uncharacterized domains.For example,in the clustering analysis of E.coli and H. inﬂuenzae,227families did not have any domains detected by the Pfam search.Our algorithm utilizes the computational eﬃciency,i.e.,linear time complexity,to achieve clustering of families of very speciﬁc categories.In particular,our algorithm was successful in classifying families where the relationships among member sequences were deﬁned at diﬀerent scores;for example,Family181.1and 181.2can be separated at Zscore800but not at Zscore400where most of families were classiﬁed(see Table 1).As a result,families were clustered with highly speciﬁc precision.For example,families in Table2were separated even at the level of the number of domain occurrences;families111-112-113and176-177-178.Why can our algorithm cluster sequences into families of very speciﬁc categories?This can be explained in terms of previous work in the literature.First of all,use of intermediate sequences can detect remote homology[18].Grundy2demonstrated that a simple family pairwise search technique can classify sequences with high accuracy[9].Clustering from all pairwise comparisons incorporates these two techniques in a systematic way with structures of a graph.Thus,we would expect that clustering algorithms based on graph theory can cluster sequences into famlies of very speciﬁc categories.The future work for our algorithm includes applications of our algorithm to diﬀerent types of sequences such as DNA and EST sequences.It would also be interesting to retain the hierarchical structure of the merging procedure so that sequence relationships can be seen at diﬀerent levels.In addition,reﬁning further each family in the context of genome,i.e.,orthologs as used in COG,is an interesting topic for further research.References[1]Altschul,S.F.,Gish,W.,Miller,W.,Myers,E.W.and Lipman,D.J.(1990)“Basic local alignmentsearch tool,”Journal of Molecular Biology215403-410.[2]Altschul,S.F.,Madden,T.L.,Schﬀer,A.A.,Zhang,J.,Zhang,Z.,Miller,W.and Lipman,D.J.(1997)“Gapped BLAST and PSI-BLAST:a new generation of protein database search programs,”Nucleic Acids Research,253389-3402.[3]Bateman,A.,Birney,E.,Durbin,R.,Eddy,S.R.,Howe,K.L.,and Sonnhammer,E.L.L.,(2000)“The Pfam Protein Families Database,”Nucleic Acids Research,28263-266.[4]G.Cannarozzi,M.T.Hallett,J.Norberg,and X.Zhou(2000)“A cross-comparison of a large datasetof genes,”Bioinformatics16654-655[5]Gilbert,D.G.(2002)“euGenes:a eukaryote genome information system,”Nucleic Acids Research,30,145-148[6]Enright A.J.,Iliopoulos I.,Krypides N.,Ouzounis C.A.,(1999)’Protein interaction maps for completegenomes based on gene fusion events’Nature402,86-902The author’s name changed to William Staﬀord Noble from William Noble Grundy.。

nature method points of view -回复

nature method points of view -回复导语：在科学研究领域，Nature Method Points of View系列是一种常见的文章形式。

本文将以此为主题，简称为Points of View，探讨这个系列的特点和意义，并分析其中的一些典型文章。

I. Points of View的特点Nature Method的Points of View系列是一种科学论文的特殊形式，旨在提供一个平台，供科学家和研究者就某一特定论题或科学方法发表他们的观点和意见。

该系列通常是由Nature Method杂志的编委会或邀请专家主持编写，文章以第一人称的形式，既有科学性又有观点性，区别于传统的研究论文。

Points of View系列的特点主要包括：1. 独特的格式：文章以个人视角撰写，鼓励作者直接表达观点，并陈述其背后的科学原理和逻辑。

2. 非正式的语气：Points of View系列不要求严格的科学论证，更注重作者对特定主题的深入理解和观察。

3. 科学方法的辩论：与传统研究论文不同，Points of View系列更多地关注科学方法和技术的前沿问题，为研究者提供一个讨论、交流和添加新见解的平台。

II. Points of View的意义1. 激发创新思考：Points of View系列提供了一个自由表达观点的机会，鼓励研究者在科学领域做出新的思考和突破。

通过这种非传统的论文形式，科学家们可以分享他们对科学问题的深入见解，推动科学研究的创新发展。

2. 促进科学交流：Points of View系列为科学社区提供一个开放的平台，使科学家们能够分享自己的观点和经验。

这种交流不仅促进科学界内部的合作与互动，还有助于学术界和产业界之间的对话与合作。

3. 引导科学发展方向：Points of View系列对于科学领域的发展具有引导作用。

通过探讨和评估新的科学方法和技术，文章可以对研究方向进行引导，推动科学研究从理论向实践的转变。

格洛弗算法

格洛弗算法格洛弗算法（GloVe）是一种用于词向量表示的算法，它结合了全局词汇共现统计和局部上下文窗口的信息，能够更好地捕捉词语之间的语义关系。

本文将详细介绍格洛弗算法的原理、应用以及一些相关的优化技巧。

1. 算法原理格洛弗算法的核心思想是通过对全局词汇共现矩阵进行分解，得到每个词语的向量表示。

具体而言，算法首先构建一个全局词汇共现矩阵，其中每个元素表示两个词语在上下文窗口中共同出现的次数。

然后，通过最小化目标函数来学习每个词语的向量表示。

目标函数包括两部分：全局共现统计和局部上下文窗口。

全局共现统计通过计算每对词语之间在整个语料库中共同出现的次数来衡量它们之间的关联程度。

而局部上下文窗口则考虑了每个词语与其周围邻居词语之间的关系。

具体来说，假设我们有一个大小为V×V（V为词汇表大小）的共现矩阵X，其中第i行第j列的元素表示词语i和词语j在上下文窗口中共同出现的次数。

那么，我们可以将每个词语的向量表示表示为两个向量的乘积：词语i的词向量和词语j的词向量的转置。

为了学习这些词向量，我们需要最小化以下目标函数：(w_i%5ETw_j-b_%7Bij%7D)%5E2)其中，wi和wj分别表示词语i和词语j的词向量，Xij表示共现矩阵中第i行第j列的元素，bij是一个偏差项（用于调整不同单词之间共现次数对目标函数的影响），f是一个权重函数。

通过最小化这个目标函数，我们可以得到每个词语对应的向量表示。

这些向量捕捉了单词之间丰富而复杂的关系，并可以用于各种自然语言处理任务。

2. 算法应用格洛弗算法在自然语言处理领域有广泛的应用。

以下是一些常见的应用场景：2.1 词语相似度计算通过学习到的词向量，我们可以计算两个词语之间的相似度。

一种常见的计算方法是使用余弦相似度，即计算两个词向量之间的夹角。

相似度较高的词语往往在语义上更接近。

2.2 词语聚类通过对学习到的词向量进行聚类，我们可以将具有相似语义特征的词语分组在一起。

一族多维Copula的理论介绍与实证分析的开题报告

一族多维Copula的理论介绍与实证分析的开题报告题目：一族多维Copula的理论介绍与实证分析研究背景：Copula理论是金融风险管理领域中经常使用的方法之一。

它是用来描述两个或多个变量之间的依赖关系的概率分布函数。

在实际应用中，经常需要使用多维的Copula分布来描述资产之间的相互依赖关系。

研究内容：1. Copula理论的基本原理和概念介绍。

包括Copula的定义、性质、多元分布函数、多维Copula的构造等基本概念。

2. 多维Copula的实证分析。

对多维Copula在金融领域的实际应用进行研究，例如在风险测度、投资组合优化、市场风险分析、债券定价等方面的应用。

3. 一族多维Copula的理论研究。

研究一族多维Copula的构造方法和性质，例如经典的Gumbel Copula、Clayton Copula、Frank Copula以及更多的扩展形式。

4. 实证分析和模拟研究。

通过实证分析和模拟研究，将新构造的多维Copula应用于金融风险管理领域中的实际问题，并与传统的多维Copula方法进行比较和验证。

研究方法：1. 文献综述：对Copula理论的相关文献进行综述和分析，总结Copula相关理论及其在金融领域的应用现状。

2. 实证分析：通过实际数据样本，应用多维Copula进行实证分析。

同时，应用Monte Carlo模拟方法对模拟数据进行分析。

3. 确定一族多维Copula模型：从传统Copula模型中发掘其不足之处, 提出一族多维Copula，探究其性质和构造方法。

研究意义：本研究将有助于深入了解Copula理论及在金融风险管理领域的应用。

对于构造新的多维Copula模型，对于改进目前金融风险管理中的实际问题将具有实际的帮助和应用意义。

同时也将拓展学术界对Copula理论相关的研究领域，扩大其应用范围。

预期结果：本研究将设计出一种更为实用的多维Copula模型，并将其应用于实际金融风险管理中，提高金融风险管理的可行性和更有效的风险控制。

基于方向可控金字塔二值图像投影的图像检索

ＡＢＳＴＲＡＣＴ：Ｔｏｓｏｌｖｅｔｈｅｅｘｉｓｔｉｎｇｐｒｏｂｌｅｍｓｓｕｃｈａｓｉｎｃｏｍｐｒｅｈｅｎｓｉｖｅｉｎｔｅｘｔｕｒｅｅｘｐｒｅｓｓｉｏｎ，ｈｕｇｅｃｏｍｐｕｔａｔｉｏｎａｎｄｉｎｅｆｆｅｃｔｉｖｅｎｅｓｓｉｎｃｏｎｔｅｎｔｂａｓｅｄｉｍａｇｅｒｅｔｉｅｒｖａｌ，ｔｈｉｓｐａｐｅｒｐｒｏｐｏｓｅｄａｎｅｗｉｍａｇｅｒｅｔｉｅｒｖｌａｍｅｔｈｏｄ．Ｉｎｔｈｉｓｍｅｔｈｏｄ，
像，通过自适应阈值Ｔ进行子带图像二值化并分别在行方向和列方向上进行投影得到图像的纹理特征。在特征匹配上，采
用向量相交匹配方法。实验结果表明，上述方法运算速度快，检索效果和抗干扰性好，可以用于图像检索。关键词：方向可控金字塔；图像投影；向量相交；图像检索
ｉｆｓｔｒａｇｒａｙ－ｓｃａｌｅｉｍａｇｅｗａｓｎｏｍａｒｌｉｚｅｄｉｎｏｉｒｅｎｔａｔｉｏｎ．Ｔｈｅｎ，ｉｔｕｓｅｄｓｔｅｅｒａｂｌｅｐｙｒａｍｉｄｔｏｄｅｃｏｍｐｏｓｅｔｈｅｉｍａｇｅｉｎｔｏｓｕｂ－ｂａｎｄｉｍａｇｅｓｉｎｄｉｆｆｅｒｅｎｔｓｃａｌｅｓａｎｄｏｉｒｅｎｔａｔｉｏｎｓ．Ｔｈｅｓｅｓｕｂ－ｂａｎｄｉｍａｇｅｓｗｅｒｅｃｏｎｖｅｒｔｅｄｔｏｂｉｎａｒｙｉｍａｇｅｓｂｙｔｈｅａｄａｐｔｉｖｅｔｈｒｅｓｈｏｌｄｖｌｕａｅＴ．Ｔｈｅｂｉｎａｒｙｉｍａｇｅｓｗｅｒｅｔｈｅｎｓｕｍｍｅｄｉｎｒｏｗａｎｄｃｏｌｕｍｎｔｏｇｅｔｔｅｘｔｕｒｅｆｅａｔｕｒｅｓ．Ｖｅｃｔｏｒｉｎｔｅｒｓｅｃｔｉｏｎｍｅｔｈｏｄｗａｓｄｅｉｆｎｅｄｉｎｔｈｅｐｒｏｃｅｓｓｏｆｍａｔｃｈｉｎｇ．Ｅｘｐｅｉｍｅｒｎｔｓｓｈｏｗｔｈａｔｔｈｅｐｒｏｐｏｓｅｄｍｅｔｈｏｄｉｓｆａｓｔ．Ｉｔ

多层线性模型——原理与应用

组织环境（W）
（1）求各个组织个体成员的成就目标导向对创造力的回
归
Yij 0 j 1 j X ij rij
（2）求组织环境对 0 j 和 1j 的回归方程
0 j 00 01W j 0 j
1 j 10 11W j 1 j
一、多层线性模型简介
✓ 4、多层线性模型的优点（1）使用收缩估计的参数估计方法，使得估计结果更为
一、多层线性模型简介
✓ 5、多层线性模型的优点（1）用于类似组织管理、学校教育等具有多层数据结
构的领域研究。（ 2）用于个体重复测量数据的追踪研究。测量层面作
为第一水平，个体层面作为第二水平。（ 3）用于做文献综述，即对众多研究成果进行定量综
合。探讨不同研究中进行的处理、研究方法、被试特征和背景上的差异与效应之间的关系。
组内分析组间分析的方法较前两种方法更多的考虑到了第一层数据及第二层数据对变异产生的影响，但并无法对组内效应和组间效应做出具体的解释，也就无法解释为什么在不同的组变量间的关系存在差异。
一、多层线性模型简介
✓ 3、多层线性模型分析方法回归的回归方法 Eg：个体成就目标导向（X）
个体创造力（Y）
Level-2： 0 j 00 u0 j var(u0 j ) 00 0 j 指第j个二层单位Y的平均值； eij 反应第j个二层单位对Y的随机效应； 00 指所有二层单位的Y的总体平均数； u0 j 指第二层方程的残差（随机误差项）。
二、多层线性模型基本原理
组内相关系数 ICC 00 / ( 00 2 )
二、多层线性模型基本原理
（4）充分利用多层模型较为高级的统计估计方法来改善单层回归的估计和分析。
二、多层线性模型基本原理

网格经济学模型

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Outline
• • • • • INTRODUCTION 资源作为一种商品格经济学模型定价、计费和付费机制几个相关项目博弈论
2007-4-26
GridComputing 9-2 The Grid Economy
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Compute Power Market
• CPM 计算力市场是网格环境下基于市场机制的资源和作业调度系统，它特别是针对低端个人计算设备设计的。传送元计算环境到一个计算市场，通过闲置的资源租用计算力，存贮，和特殊服务在计算市场中解决问题。CPM主要由市场，资源消费者，资源提供者和它们的相互作用组成。它支持商品市场模型、合约模型、拍卖模型。
GridComputing 9-2 The Grid Economy
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Outline
• • • • • OVERVIEW 网格经济学模型定价、计费和付费机制几个相关项目博弈论
2007-4-26
GridComputing 9-2 The Grid Economy
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定价、计费、付费
2007-4-26
GridComputing 9-2 The Grid Economy
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拍卖模型
2007-4-26
GridComputing 9-2 The Grid Economy
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拍卖模型
• 拍卖模型 – 上升拍卖（英式拍卖） – 下降拍卖（荷兰式拍卖） – 第一价格密封拍卖 – 第二价格密封拍卖（Vickrey拍卖） – ......
2007-4-26
GridComputing 9-2 The Grid Economy
2007-4-26

the rising sea 代数几何发表

the rising sea 代数几何发表The Rising Sea: Algebraic Geometry in Modern ApplicationsIn the field of mathematics, algebraic geometry is a vibrant and rapidly growing discipline. It merges geometry and algebra, creating a powerful toolset for understanding and manipulating complex mathematical structures. The Rising Sea: Algebraic Geometry in Modern Applications is a groundbreaking textbook that delves into the depth and breadth of this fascinating field.The book opens with a discussion of the fundamental principles and building blocks of algebraic geometry. It introduces the reader to the basic concepts of polynomial rings, ideals, and varieties. The explanations are clear and accessible, laying a solid foundation for the more advanced topics that follow.The Rising Sea then delves into more advanced topics, such as abstract algebra, commutative algebra, and scheme theory. The text carefully explains these concepts, providing numerous examples and exercises to aid comprehension. It also introduces the reader to the powerful tools of homological algebra and algebraic geometry, further enriching their understanding of the subject.The book’s scope extends beyond the theoretical aspects of algebraic geometry. It also includes chapters on the applications of algebraic geometry in various fields, such as computer science, physics, and economics. These applications demonstrate the practical relevance and impact of algebraic geometry in modern society.The Rising Sea is an essential resource for students and researchers in mathematics, computer science, and related fields. Its clear and comprehensive approach makes it an excellent textbook for undergraduate and graduate courses on algebraic geometry. It will also serve as a valuable reference for professionals in industry and academia who seek a deeper understanding of this rapidly developing field.。

A Tutorial on Support Vector Machines for Pattern Recognition

CHRISTOPHER J.C. BURGES
burges@
Bell Laboratories, Lucent Technologies Editor: Usama Fayyad Abstract. The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even inﬁnite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will ﬁnd that even old material is cast in a fresh light. Keywords: support vector machines, statistical learning theory, VC dimension, pattern recognition

多维空间一般Benjamin-Bona-Mahony方程解的逐点估计

ｕ一 △Ｏｔｕ
叩是正常数，是实常向量．ｆ（ｕ）（ｆｌ（ｕ）， …，（ｕ））给定初值为
ｕＩ：０＝Ｕ０．
（２）
这里拉普拉斯算子 △ ＝ ∑ ，ｎ是空间维数．
ｊ＝ｌ
方程（１）叫做一般Ｂｅｎｊａｍｉｎ－Ｂｏｎａ－Ｍａｈｏｎｙ方程．著名的ＢＢＭ方程是由Ｂｅｎｊａｍｉｎ，Ｂｏｎａ和Ｍａｈｏｎｙ在文献『１１中提出的，该方程是作为研究非线性色散媒介里的长波传播的模型方程．在文献［２］中，郭提出并研究了多维空间里的一般ＢＢＭ方程（ＧＢＢＭ）．ＣＢＢＭ方程解的存在性和唯一性已经被多名作者证明（文献［１ — ３］）．解的衰减性也在文献［４ — ７］中被研究．但是他们所有的结果都是在范数意义下．本文中，我们给出了这个方程解的更为精确的逐点衰减估计，且这个估计是最优的．由于我们的估计首先要基于解的整体存在性，所以先把整体存在性结果列出来．定理１．１令球体
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Ｆ（，）表示函数ｌ厂的逆傅里叶变换．示通常的Ｓｏｂｏｌｅｖ空间，范数形式为是一个实向量．，（），ｍ∈ ，ＰＥ［１，＋。。］表
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Survey of clustering data mining techniques

A Survey of Clustering Data Mining TechniquesPavel BerkhinYahoo!,Inc.pberkhin@Summary.Clustering is the division of data into groups of similar objects.It dis-regards some details in exchange for data simpliﬁrmally,clustering can be viewed as data modeling concisely summarizing the data,and,therefore,it re-lates to many disciplines from statistics to numerical analysis.Clustering plays an important role in a broad range of applications,from information retrieval to CRM. Such applications usually deal with large datasets and many attributes.Exploration of such data is a subject of data mining.This survey concentrates on clustering algorithms from a data mining perspective.1IntroductionThe goal of this survey is to provide a comprehensive review of diﬀerent clus-tering techniques in data mining.Clustering is a division of data into groups of similar objects.Each group,called a cluster,consists of objects that are similar to one another and dissimilar to objects of other groups.When repre-senting data with fewer clusters necessarily loses certainﬁne details(akin to lossy data compression),but achieves simpliﬁcation.It represents many data objects by few clusters,and hence,it models data by its clusters.Data mod-eling puts clustering in a historical perspective rooted in mathematics,sta-tistics,and numerical analysis.From a machine learning perspective clusters correspond to hidden patterns,the search for clusters is unsupervised learn-ing,and the resulting system represents a data concept.Therefore,clustering is unsupervised learning of a hidden data concept.Data mining applications add to a general picture three complications:(a)large databases,(b)many attributes,(c)attributes of diﬀerent types.This imposes on a data analysis se-vere computational requirements.Data mining applications include scientiﬁc data exploration,information retrieval,text mining,spatial databases,Web analysis,CRM,marketing,medical diagnostics,computational biology,and many others.They present real challenges to classic clustering algorithms. These challenges led to the emergence of powerful broadly applicable data2Pavel Berkhinmining clustering methods developed on the foundation of classic techniques.They are subject of this survey.1.1NotationsTo ﬁx the context and clarify terminology,consider a dataset X consisting of data points (i.e.,objects ,instances ,cases ,patterns ,tuples ,transactions )x i =(x i 1,···,x id ),i =1:N ,in attribute space A ,where each component x il ∈A l ,l =1:d ,is a numerical or nominal categorical attribute (i.e.,feature ,variable ,dimension ,component ,ﬁeld ).For a discussion of attribute data types see [106].Such point-by-attribute data format conceptually corresponds to a N ×d matrix and is used by a majority of algorithms reviewed below.However,data of other formats,such as variable length sequences and heterogeneous data,are not uncommon.The simplest subset in an attribute space is a direct Cartesian product of sub-ranges C = C l ⊂A ,C l ⊂A l ,called a segment (i.e.,cube ,cell ,region ).A unit is an elementary segment whose sub-ranges consist of a single category value,or of a small numerical bin.Describing the numbers of data points per every unit represents an extreme case of clustering,a histogram .This is a very expensive representation,and not a very revealing er driven segmentation is another commonly used practice in data exploration that utilizes expert knowledge regarding the importance of certain sub-domains.Unlike segmentation,clustering is assumed to be automatic,and so it is a machine learning technique.The ultimate goal of clustering is to assign points to a ﬁnite system of k subsets (clusters).Usually (but not always)subsets do not intersect,and their union is equal to a full dataset with the possible exception of outliersX =C 1 ··· C k C outliers ,C i C j =0,i =j.1.2Clustering Bibliography at GlanceGeneral references regarding clustering include [110],[205],[116],[131],[63],[72],[165],[119],[75],[141],[107],[91].A very good introduction to contem-porary data mining clustering techniques can be found in the textbook [106].There is a close relationship between clustering and many other ﬁelds.Clustering has always been used in statistics [10]and science [158].The clas-sic introduction into pattern recognition framework is given in [64].Typical applications include speech and character recognition.Machine learning clus-tering algorithms were applied to image segmentation and computer vision[117].For statistical approaches to pattern recognition see [56]and [85].Clus-tering can be viewed as a density estimation problem.This is the subject of traditional multivariate statistical estimation [197].Clustering is also widelyA Survey of Clustering Data Mining Techniques3 used for data compression in image processing,which is also known as vec-tor quantization[89].Dataﬁtting in numerical analysis provides still another venue in data modeling[53].This survey’s emphasis is on clustering in data mining.Such clustering is characterized by large datasets with many attributes of diﬀerent types. Though we do not even try to review particular applications,many important ideas are related to the speciﬁcﬁelds.Clustering in data mining was brought to life by intense developments in information retrieval and text mining[52], [206],[58],spatial database applications,for example,GIS or astronomical data,[223],[189],[68],sequence and heterogeneous data analysis[43],Web applications[48],[111],[81],DNA analysis in computational biology[23],and many others.They resulted in a large amount of application-speciﬁc devel-opments,but also in some general techniques.These techniques and classic clustering algorithms that relate to them are surveyed below.1.3Plan of Further PresentationClassiﬁcation of clustering algorithms is neither straightforward,nor canoni-cal.In reality,diﬀerent classes of algorithms overlap.Traditionally clustering techniques are broadly divided in hierarchical and partitioning.Hierarchical clustering is further subdivided into agglomerative and divisive.The basics of hierarchical clustering include Lance-Williams formula,idea of conceptual clustering,now classic algorithms SLINK,COBWEB,as well as newer algo-rithms CURE and CHAMELEON.We survey these algorithms in the section Hierarchical Clustering.While hierarchical algorithms gradually(dis)assemble points into clusters (as crystals grow),partitioning algorithms learn clusters directly.In doing so they try to discover clusters either by iteratively relocating points between subsets,or by identifying areas heavily populated with data.Algorithms of theﬁrst kind are called Partitioning Relocation Clustering. They are further classiﬁed into probabilistic clustering(EM framework,al-gorithms SNOB,AUTOCLASS,MCLUST),k-medoids methods(algorithms PAM,CLARA,CLARANS,and its extension),and k-means methods(diﬀer-ent schemes,initialization,optimization,harmonic means,extensions).Such methods concentrate on how well pointsﬁt into their clusters and tend to build clusters of proper convex shapes.Partitioning algorithms of the second type are surveyed in the section Density-Based Partitioning.They attempt to discover dense connected com-ponents of data,which areﬂexible in terms of their shape.Density-based connectivity is used in the algorithms DBSCAN,OPTICS,DBCLASD,while the algorithm DENCLUE exploits space density functions.These algorithms are less sensitive to outliers and can discover clusters of irregular shape.They usually work with low-dimensional numerical data,known as spatial data. Spatial objects could include not only points,but also geometrically extended objects(algorithm GDBSCAN).4Pavel BerkhinSome algorithms work with data indirectly by constructing summaries of data over the attribute space subsets.They perform space segmentation and then aggregate appropriate segments.We discuss them in the section Grid-Based Methods.They frequently use hierarchical agglomeration as one phase of processing.Algorithms BANG,STING,WaveCluster,and FC are discussed in this section.Grid-based methods are fast and handle outliers well.Grid-based methodology is also used as an intermediate step in many other algorithms (for example,CLIQUE,MAFIA).Categorical data is intimately connected with transactional databases.The concept of a similarity alone is not suﬃcient for clustering such data.The idea of categorical data co-occurrence comes to the rescue.The algorithms ROCK,SNN,and CACTUS are surveyed in the section Co-Occurrence of Categorical Data.The situation gets even more aggravated with the growth of the number of items involved.To help with this problem the eﬀort is shifted from data clustering to pre-clustering of items or categorical attribute values. Development based on hyper-graph partitioning and the algorithm STIRR exemplify this approach.Many other clustering techniques are developed,primarily in machine learning,that either have theoretical signiﬁcance,are used traditionally out-side the data mining community,or do notﬁt in previously outlined categories. The boundary is blurred.In the section Other Developments we discuss the emerging direction of constraint-based clustering,the important researchﬁeld of graph partitioning,and the relationship of clustering to supervised learning, gradient descent,artiﬁcial neural networks,and evolutionary methods.Data Mining primarily works with large databases.Clustering large datasets presents scalability problems reviewed in the section Scalability and VLDB Extensions.Here we talk about algorithms like DIGNET,about BIRCH and other data squashing techniques,and about Hoﬀding or Chernoﬀbounds.Another trait of real-life data is high dimensionality.Corresponding de-velopments are surveyed in the section Clustering High Dimensional Data. The trouble comes from a decrease in metric separation when the dimension grows.One approach to dimensionality reduction uses attributes transforma-tions(DFT,PCA,wavelets).Another way to address the problem is through subspace clustering(algorithms CLIQUE,MAFIA,ENCLUS,OPTIGRID, PROCLUS,ORCLUS).Still another approach clusters attributes in groups and uses their derived proxies to cluster objects.This double clustering is known as co-clustering.Issues common to diﬀerent clustering methods are overviewed in the sec-tion General Algorithmic Issues.We talk about assessment of results,de-termination of appropriate number of clusters to build,data preprocessing, proximity measures,and handling of outliers.For reader’s convenience we provide a classiﬁcation of clustering algorithms closely followed by this survey:•Hierarchical MethodsA Survey of Clustering Data Mining Techniques5Agglomerative AlgorithmsDivisive Algorithms•Partitioning Relocation MethodsProbabilistic ClusteringK-medoids MethodsK-means Methods•Density-Based Partitioning MethodsDensity-Based Connectivity ClusteringDensity Functions Clustering•Grid-Based Methods•Methods Based on Co-Occurrence of Categorical Data•Other Clustering TechniquesConstraint-Based ClusteringGraph PartitioningClustering Algorithms and Supervised LearningClustering Algorithms in Machine Learning•Scalable Clustering Algorithms•Algorithms For High Dimensional DataSubspace ClusteringCo-Clustering Techniques1.4Important IssuesThe properties of clustering algorithms we are primarily concerned with in data mining include:•Type of attributes algorithm can handle•Scalability to large datasets•Ability to work with high dimensional data•Ability toﬁnd clusters of irregular shape•Handling outliers•Time complexity(we frequently simply use the term complexity)•Data order dependency•Labeling or assignment(hard or strict vs.soft or fuzzy)•Reliance on a priori knowledge and user deﬁned parameters •Interpretability of resultsRealistically,with every algorithm we discuss only some of these properties. The list is in no way exhaustive.For example,as appropriate,we also discuss algorithms ability to work in pre-deﬁned memory buﬀer,to restart,and to provide an intermediate solution.6Pavel Berkhin2Hierarchical ClusteringHierarchical clustering builds a cluster hierarchy or a tree of clusters,also known as a dendrogram.Every cluster node contains child clusters;sibling clusters partition the points covered by their common parent.Such an ap-proach allows exploring data on diﬀerent levels of granularity.Hierarchical clustering methods are categorized into agglomerative(bottom-up)and divi-sive(top-down)[116],[131].An agglomerative clustering starts with one-point (singleton)clusters and recursively merges two or more of the most similar clusters.A divisive clustering starts with a single cluster containing all data points and recursively splits the most appropriate cluster.The process contin-ues until a stopping criterion(frequently,the requested number k of clusters) is achieved.Advantages of hierarchical clustering include:•Flexibility regarding the level of granularity•Ease of handling any form of similarity or distance•Applicability to any attribute typesDisadvantages of hierarchical clustering are related to:•Vagueness of termination criteria•Most hierarchical algorithms do not revisit(intermediate)clusters once constructed.The classic approaches to hierarchical clustering are presented in the sub-section Linkage Metrics.Hierarchical clustering based on linkage metrics re-sults in clusters of proper(convex)shapes.Active contemporary eﬀorts to build cluster systems that incorporate our intuitive concept of clusters as con-nected components of arbitrary shape,including the algorithms CURE and CHAMELEON,are surveyed in the subsection Hierarchical Clusters of Arbi-trary Shapes.Divisive techniques based on binary taxonomies are presented in the subsection Binary Divisive Partitioning.The subsection Other Devel-opments contains information related to incremental learning,model-based clustering,and cluster reﬁnement.In hierarchical clustering our regular point-by-attribute data representa-tion frequently is of secondary importance.Instead,hierarchical clustering frequently deals with the N×N matrix of distances(dissimilarities)or sim-ilarities between training points sometimes called a connectivity matrix.So-called linkage metrics are constructed from elements of this matrix.The re-quirement of keeping a connectivity matrix in memory is unrealistic.To relax this limitation diﬀerent techniques are used to sparsify(introduce zeros into) the connectivity matrix.This can be done by omitting entries smaller than a certain threshold,by using only a certain subset of data representatives,or by keeping with each point only a certain number of its nearest neighbors(for nearest neighbor chains see[177]).Notice that the way we process the original (dis)similarity matrix and construct a linkage metric reﬂects our a priori ideas about the data model.A Survey of Clustering Data Mining Techniques7With the(sparsiﬁed)connectivity matrix we can associate the weighted connectivity graph G(X,E)whose vertices X are data points,and edges E and their weights are deﬁned by the connectivity matrix.This establishes a connection between hierarchical clustering and graph partitioning.One of the most striking developments in hierarchical clustering is the algorithm BIRCH.It is discussed in the section Scalable VLDB Extensions.Hierarchical clustering initializes a cluster system as a set of singleton clusters(agglomerative case)or a single cluster of all points(divisive case) and proceeds iteratively merging or splitting the most appropriate cluster(s) until the stopping criterion is achieved.The appropriateness of a cluster(s) for merging or splitting depends on the(dis)similarity of cluster(s)elements. This reﬂects a general presumption that clusters consist of similar points.An important example of dissimilarity between two points is the distance between them.To merge or split subsets of points rather than individual points,the dis-tance between individual points has to be generalized to the distance between subsets.Such a derived proximity measure is called a linkage metric.The type of a linkage metric signiﬁcantly aﬀects hierarchical algorithms,because it re-ﬂects a particular concept of closeness and connectivity.Major inter-cluster linkage metrics[171],[177]include single link,average link,and complete link. The underlying dissimilarity measure(usually,distance)is computed for every pair of nodes with one node in theﬁrst set and another node in the second set.A speciﬁc operation such as minimum(single link),average(average link),or maximum(complete link)is applied to pair-wise dissimilarity measures:d(C1,C2)=Op{d(x,y),x∈C1,y∈C2}Early examples include the algorithm SLINK[199],which implements single link(Op=min),Voorhees’method[215],which implements average link (Op=Avr),and the algorithm CLINK[55],which implements complete link (Op=max).It is related to the problem ofﬁnding the Euclidean minimal spanning tree[224]and has O(N2)complexity.The methods using inter-cluster distances deﬁned in terms of pairs of nodes(one in each respective cluster)are called graph methods.They do not use any cluster representation other than a set of points.This name naturally relates to the connectivity graph G(X,E)introduced above,because every data partition corresponds to a graph partition.Such methods can be augmented by so-called geometric methods in which a cluster is represented by its central point.Under the assumption of numerical attributes,the center point is deﬁned as a centroid or an average of two cluster centroids subject to agglomeration.It results in centroid,median,and minimum variance linkage metrics.All of the above linkage metrics can be derived from the Lance-Williams updating formula[145],d(C iC j,C k)=a(i)d(C i,C k)+a(j)d(C j,C k)+b·d(C i,C j)+c|d(C i,C k)−d(C j,C k)|.8Pavel BerkhinHere a,b,c are coeﬃcients corresponding to a particular linkage.This formula expresses a linkage metric between a union of the two clusters and the third cluster in terms of underlying nodes.The Lance-Williams formula is crucial to making the dis(similarity)computations feasible.Surveys of linkage metrics can be found in [170][54].When distance is used as a base measure,linkage metrics capture inter-cluster proximity.However,a similarity-based view that results in intra-cluster connectivity considerations is also used,for example,in the original average link agglomeration (Group-Average Method)[116].Under reasonable assumptions,such as reducibility condition (graph meth-ods satisfy this condition),linkage metrics methods suﬀer from O N 2 time complexity [177].Despite the unfavorable time complexity,these algorithms are widely used.As an example,the algorithm AGNES (AGlomerative NESt-ing)[131]is used in S-Plus.When the connectivity N ×N matrix is sparsiﬁed,graph methods directly dealing with the connectivity graph G can be used.In particular,hierarchical divisive MST (Minimum Spanning Tree)algorithm is based on graph parti-tioning [116].2.1Hierarchical Clusters of Arbitrary ShapesFor spatial data,linkage metrics based on Euclidean distance naturally gener-ate clusters of convex shapes.Meanwhile,visual inspection of spatial images frequently discovers clusters with curvy appearance.Guha et al.[99]introduced the hierarchical agglomerative clustering algo-rithm CURE (Clustering Using REpresentatives).This algorithm has a num-ber of novel features of general importance.It takes special steps to handle outliers and to provide labeling in assignment stage.It also uses two techniques to achieve scalability:data sampling (section 8),and data partitioning.CURE creates p partitions,so that ﬁne granularity clusters are constructed in parti-tions ﬁrst.A major feature of CURE is that it represents a cluster by a ﬁxed number,c ,of points scattered around it.The distance between two clusters used in the agglomerative process is the minimum of distances between two scattered representatives.Therefore,CURE takes a middle approach between the graph (all-points)methods and the geometric (one centroid)methods.Single and average link closeness are replaced by representatives’aggregate closeness.Selecting representatives scattered around a cluster makes it pos-sible to cover non-spherical shapes.As before,agglomeration continues until the requested number k of clusters is achieved.CURE employs one additional trick:originally selected scattered points are shrunk to the geometric centroid of the cluster by a user-speciﬁed factor α.Shrinkage suppresses the aﬀect of outliers;outliers happen to be located further from the cluster centroid than the other scattered representatives.CURE is capable of ﬁnding clusters of diﬀerent shapes and sizes,and it is insensitive to outliers.Because CURE uses sampling,estimation of its complexity is not straightforward.For low-dimensional data authors provide a complexity estimate of O (N 2sample )deﬁnedA Survey of Clustering Data Mining Techniques9 in terms of a sample size.More exact bounds depend on input parameters: shrink factorα,number of representative points c,number of partitions p,and a sample size.Figure1(a)illustrates agglomeration in CURE.Three clusters, each with three representatives,are shown before and after the merge and shrinkage.Two closest representatives are connected.While the algorithm CURE works with numerical attributes(particularly low dimensional spatial data),the algorithm ROCK developed by the same researchers[100]targets hierarchical agglomerative clustering for categorical attributes.It is reviewed in the section Co-Occurrence of Categorical Data.The hierarchical agglomerative algorithm CHAMELEON[127]uses the connectivity graph G corresponding to the K-nearest neighbor model spar-siﬁcation of the connectivity matrix:the edges of K most similar points to any given point are preserved,the rest are pruned.CHAMELEON has two stages.In theﬁrst stage small tight clusters are built to ignite the second stage.This involves a graph partitioning[129].In the second stage agglomer-ative process is performed.It utilizes measures of relative inter-connectivity RI(C i,C j)and relative closeness RC(C i,C j);both are locally normalized by internal interconnectivity and closeness of clusters C i and C j.In this sense the modeling is dynamic:it depends on data locally.Normalization involves certain non-obvious graph operations[129].CHAMELEON relies heavily on graph partitioning implemented in the library HMETIS(see the section6). Agglomerative process depends on user provided thresholds.A decision to merge is made based on the combinationRI(C i,C j)·RC(C i,C j)αof local measures.The algorithm does not depend on assumptions about the data model.It has been proven toﬁnd clusters of diﬀerent shapes,densities, and sizes in2D(two-dimensional)space.It has a complexity of O(Nm+ Nlog(N)+m2log(m),where m is the number of sub-clusters built during the ﬁrst initialization phase.Figure1(b)(analogous to the one in[127])clariﬁes the diﬀerence with CURE.It presents a choice of four clusters(a)-(d)for a merge.While CURE would merge clusters(a)and(b),CHAMELEON makes intuitively better choice of merging(c)and(d).2.2Binary Divisive PartitioningIn linguistics,information retrieval,and document clustering applications bi-nary taxonomies are very useful.Linear algebra methods,based on singular value decomposition(SVD)are used for this purpose in collaborativeﬁlter-ing and information retrieval[26].Application of SVD to hierarchical divisive clustering of document collections resulted in the PDDP(Principal Direction Divisive Partitioning)algorithm[31].In our notations,object x is a docu-ment,l th attribute corresponds to a word(index term),and a matrix X entry x il is a measure(e.g.TF-IDF)of l-term frequency in a document x.PDDP constructs SVD decomposition of the matrix10Pavel Berkhin(a)Algorithm CURE (b)Algorithm CHAMELEONFig.1.Agglomeration in Clusters of Arbitrary Shapes(X −e ¯x ),¯x =1Ni =1:N x i ,e =(1,...,1)T .This algorithm bisects data in Euclidean space by a hyperplane that passes through data centroid orthogonal to the eigenvector with the largest singular value.A k -way split is also possible if the k largest singular values are consid-ered.Bisecting is a good way to categorize documents and it yields a binary tree.When k -means (2-means)is used for bisecting,the dividing hyperplane is orthogonal to the line connecting the two centroids.The comparative study of SVD vs.k -means approaches [191]can be used for further references.Hier-archical divisive bisecting k -means was proven [206]to be preferable to PDDP for document clustering.While PDDP or 2-means are concerned with how to split a cluster,the problem of which cluster to split is also important.Simple strategies are:(1)split each node at a given level,(2)split the cluster with highest cardinality,and,(3)split the cluster with the largest intra-cluster variance.All three strategies have problems.For a more detailed analysis of this subject and better strategies,see [192].2.3Other DevelopmentsOne of early agglomerative clustering algorithms,Ward’s method [222],is based not on linkage metric,but on an objective function used in k -means.The merger decision is viewed in terms of its eﬀect on the objective function.The popular hierarchical clustering algorithm for categorical data COB-WEB [77]has two very important qualities.First,it utilizes incremental learn-ing.Instead of following divisive or agglomerative approaches,it dynamically builds a dendrogram by processing one data point at a time.Second,COB-WEB is an example of conceptual or model-based learning.This means that each cluster is considered as a model that can be described intrinsically,rather than as a collection of points assigned to it.COBWEB’s dendrogram is calleda classiﬁcation tree.Each tree node(cluster)C is associated with the condi-tional probabilities for categorical attribute-values pairs,P r(x l=νlp|C),l=1:d,p=1:|A l|.This easily can be recognized as a C-speciﬁc Na¨ıve Bayes classiﬁer.During the classiﬁcation tree construction,every new point is descended along the tree and the tree is potentially updated(by an insert/split/merge/create op-eration).Decisions are based on the category utility[49]CU{C1,...,C k}=1j=1:kCU(C j)CU(C j)=l,p(P r(x l=νlp|C j)2−(P r(x l=νlp)2.Category utility is similar to the GINI index.It rewards clusters C j for in-creases in predictability of the categorical attribute valuesνlp.Being incre-mental,COBWEB is fast with a complexity of O(tN),though it depends non-linearly on tree characteristics packed into a constant t.There is a similar incremental hierarchical algorithm for all numerical attributes called CLAS-SIT[88].CLASSIT associates normal distributions with cluster nodes.Both algorithms can result in highly unbalanced trees.Chiu et al.[47]proposed another conceptual or model-based approach to hierarchical clustering.This development contains several diﬀerent use-ful features,such as the extension of scalability preprocessing to categori-cal attributes,outliers handling,and a two-step strategy for monitoring the number of clusters including BIC(deﬁned below).A model associated with a cluster covers both numerical and categorical attributes and constitutes a blend of Gaussian and multinomial models.Denote corresponding multivari-ate parameters byθ.With every cluster C we associate a logarithm of its (classiﬁcation)likelihoodl C=x i∈Clog(p(x i|θ))The algorithm uses maximum likelihood estimates for parameterθ.The dis-tance between two clusters is deﬁned(instead of linkage metric)as a decrease in log-likelihoodd(C1,C2)=l C1+l C2−l C1∪C2caused by merging of the two clusters under consideration.The agglomerative process continues until the stopping criterion is satisﬁed.As such,determina-tion of the best k is automatic.This algorithm has the commercial implemen-tation(in SPSS Clementine).The complexity of the algorithm is linear in N for the summarization phase.Traditional hierarchical clustering does not change points membership in once assigned clusters due to its greedy approach:after a merge or a split is selected it is not reﬁned.Though COBWEB does reconsider its decisions,its。

时标上一类非线性中立型微分方程的振动性

Value Engineering1研究背景自1988年Stefan Hilger 在他的博士论文中首次提出测度链上的微分方程理论以来，测度链上时滞动力方程的研究成为目前国际上关注的一个新课题，对其研究具有重要的理论价值和实际应用价值。

而对于许多情况，只需考虑测度链的一种特殊情形———时标，时标指的是实数R 的任意一个非空闭子集，以符号表示。

详细的有关时标的理论见文献[2,5,6]。

本文考虑时标上二阶非线性中立型微分方程(x(t)+n i =1∑p i (t)x(τi (t)))ΔΔ+mj =1∑q j (t)f j (x(r j (t)))=0,t ⩾t 0>0（1）的振动性，其中p i (t)，q j (t)∈C rd ([t 0，∞)，R +），0⩽τi （t）<t ，0⩽r j (t)<t,r j (t)非减，q j (t)不最终恒为零，f j (x)/x ⩾εj >0，i=1,2,…n ，j=1,2,…m,本文中记ε=min{εj }，r(t)=min{r j （t）}，z(t)=x(t)+ni =1∑p i(t)x(τi (t))。

2主要结果引理1设x(t)为(1)的非振动解，若x(t)最终为正(负)，则最终有z Δ(t)>0(z Δ(t)<0)。

证明假设x(t)为(1)的最终正解(最终负解同样可证)，即存在充分大的t 1⩾t 0>0，当t ⩾t 1时，x(t)>0,x(τi (t))>0，x(r i (t))>0，易知z(t)=x(t)+ni =1∑p i (t)x(τi (t))⩾0且z ΔΔ(t)=-m j =1∑q j (t)f j (x(r i (t)))⩽0（2）故知z Δ(t)单调递减，且z Δ(t)>0。

若不然，则z Δ(t)⩽0，因为q j (t)不最终恒为零，故z Δ(t)不最终恒为零，故存在t 2，当t ⩾t 2⩾t 1，有z Δ(t)⩽z Δ(t 2)（3）对(3)式从t 2到t 积分，有z(t)-z(t 2)⩽t t ∫z Δ(t 2)ΔS=z Δ(t 2)(t-t 2)，当t→∞时，得z(t)→-∞。

Cheng Hao,2009,Lithos

Transitional time of oceanic to continental subduction in the Dabie orogen:Constraints from U –Pb,Lu –Hf,Sm –Nd and Ar –Ar multichronometric datingHao Cheng a ,b ,⁎,Robert L.King c ,Eizo Nakamura b ,Jeffrey D.Vervoort c ,Yong-Fei Zheng d ,Tsutomu Ota b ,Yuan-Bao Wu e ,Katsura Kobayashi b ,Zu-Yi Zhou aaState Key Laboratory of Marine Geology,Tongji University,Shanghai 200092,ChinabInstitute for Study of the Earth's Interior,Okayama University at Misasa,Tottori 682-0193,Japan cSchool of Earth and Environmental Sciences,Washington State University,Pullman,Washington 99164,USA dCAS Key Laboratory of Crust-Mantle Materials and Environments,School of Earth and Space Sciences,University of Science and Technology of China,Hefei 230026,China eState Key Laboratory of Geological Processes and Mineral Resources,Faculty of Earth Sciences,China University of Geosciences,Wuhan 430074,Chinaa b s t r a c ta r t i c l e i n f o Article history:Received 22August 2008Accepted 9January 2009Available online 8February 2009Keywords:Continental subduction Dabie EclogiteGeochronologyOceanic subduction Tectonic transitionWe investigated the oceanic-type Xiongdian high-pressure eclogites in the western part of the Dabie orogen with combined U –Pb,Lu –Hf,Sm –Nd and Ar –Ar geochronology.Three groups of weighted-mean 206Pb/238U ages at 315±5,373±4and 422±7Ma are largely consistent with previous dates.In contrast,Lu –Hf and Sm –Nd isochron dates yield identical ages of 268.9±6.9and 271.3±5.3Ma.Phengite and amphibole Ar –Ar total fusion analyses give Neoproterozoic apparent ages,which are geologically meaningless due to the presence of excess 40Ar.Plagioclase inclusions in zircon cores suggest that the Silurian ages likely represent protolith ages,whereas the Carboniferous ages correspond to prograde metamorphism,based on the compositions of garnet inclusions.Despite weakly-preserved prograde major-and trace element zoning in garnet,a combined textural and compositional study reveals that the consistent Lu –Hf and Sm –Nd ages of ca.270Ma record a later event of garnet growth and thus mark the termination of high-pressure eclogite –facies metamorphism.The new U –Pb,Lu –Hf and Sm –Nd ages suggest a model of continuous processes from oceanic to continental subduction,pointing to the onset of prograde metamorphism prior to ca.315Ma for the subduction of oceanic crust,while the peak eclogite –facies metamorphic episode is constrained to between ca.315and 270Ma.Thus,the initiation of continental subduction is not earlier than ca.270Ma.©2009Elsevier B.V.All rights reserved.1.IntroductionSubduction zones are essential to the dynamic evolution of the earth's surface due to plate tectonics.Subduction of oceanic and continental crust eventually leads to closure of backarc basins and arc-continent and continent-continent collisions (O'Brien,2001;Ernst,2005;Zheng et al.,2008),forming various types of high-pressure (HP)and ultrahigh-pressure (UHP)metamorphic rocks.Subduction of oceanic lithosphere causes a complex continuum of diagenetic and metamorphic reactions;many kilometres of oceanic lithosphere are ultimately consumed prior to the subsequent continental slab subduction and collision.Subducted continental slabs that detach from the oceanic lithosphere that was dragging them into the mantle are expected to rapidly rise to Moho depths because of their positive buoyancy.Thus,studying subducted oceanic crust in subduction zones can provide clues to the incorporation rate of supercrustal materialinto the mantle and can shed light on the initiation of successive continental subduction.Determining a geochronological framework for determining the sequence and duration of oceanic to continental subduction and HP and UHP metamorphism plays an essential role in this respect.Zircon has long been recognized as a promising geochronometer of the U –Pb decay system because of its refractory nature,commonly preserved growth zones and mineral inclusions within a single grain.Recent developments in analytical techniques allow us to unravel a wealth of information contained in zircons with respect to their growth history and thus the prograde and retrograde metamorphic evolution of the host rock (Gebauer,1996;Wu et al.,2006;Zheng et al.,2007).The Lu –Hf garnet technique has been applied to constrain the prograde and high-temperature histories of metamorphic belts (e.g.,Duchêne et al.,1997;Blichert-Toft and Frei,2001;Anczkiewicz et al.,2004,2007;Lagos et al.,2007;Kylander-Clark et al.,2007;Cheng et al.,2008a )because of its high closure temperature (Dodson,1973;Scherer et al.,2000)and the fact that garnet strongly partitions Lu over Hf,resulting in a high parent/daughter ratio (Otamendi et al.,2002).Combined with Sm –Nd age determination,the Lu –Hf garnet geochronometer can potentially be used to estimate the duration ofLithos 110(2009)327–342⁎Corresponding author.State Key Laboratory of Marine Geology,Tongji University,Shanghai 200092,China.Tel.:+862165982358;fax:+862165984906.E-mail address:chenghao@ (H.Cheng).0024-4937/$–see front matter ©2009Elsevier B.V.All rights reserved.doi:10.1016/j.lithos.2009.01.013Contents lists available at ScienceDirectLithosj ou r n a l h o m e pa g e :ww w.e l s ev i e r.c o m/l o c a t e /l i t h o sFig.1.Simpli ﬁed geologic map of the Huwan mélange area (b)in southern Dabie orogen (a),modi ﬁed after Ye et al.(1993)and Liu et al.(2004b),showing the sample localities for the Xiongdian eclogite.References:asterisk,this study;[1],Ratschbacher et al.(2006);[2],Jahn et al.(2005);[3],Liu et al.(2004a);[4],Eide et al.(1994);[5],Webb et al.(1999);[6],Xu et al.(2000);[7],Ye et al.(1993);[8],Sun et al.(2002);[9],Jian et al.(1997);[10],Jian et al.(2000);[11],Gao et al.(2002);[12],Li et al.(2001);[13],Wu et al.(2008).amp —amphibole;brs —barroisite;phen —phengite;zrn —zircon.328H.Cheng et al./Lithos 110(2009)327–342garnet growth,which either reﬂects early prograde metamorphism (Lapen et al.,2003),exhumation(Cheng et al.,2009)or a particular garnet growth stage(Skora et al.,2006).Dating the exhumation of high-pressure(HP)and ultra-high-pressure(UHP)metamorphic rocks by conventional step-heating Ar–Ar technique was largely hampered and discredited due to the presence of excess/inherited argon(Li et al.,1994;Kelley,2002).However,the Ar–Ar geochron-ometer remains irreplaceable in constraining the exhumation of HP/ UHP metamorphic rocks because of its intermediate closure tempera-ture.Nevertheless,timing must be integrated with textures and petrology in order to quantify the dynamics of geological processes, whichever geochronological method is used.During the past two decades,considerable progress has been made in constraining the prograde metamorphism and exhumation of HP/ UHP metamorphism of the Dabie–Sulu orogen by a variety of geochronological methods,indicating a Triassic collision between the South China and North China Blocks(e.g.,Eide et al.,1994;Ames et al., 1996;Rowley et al.,1997;Hacker et al.,1998;Li et al.,2000,2004; Zheng et al.,2004).The initiation of continental subduction is pinned to ca.245Ma(Hacker et al.,2006;Liu et al.,2006a;Wu et al.,2006; Cheng et al.,2008a),but the exact time is poorly constrained.On the other hand,theﬁngerprints of early continental subduction may not be preserved in continental-type metamorphic rocks due to the succes-sive high-temperature prograde and retrograde overprints.Alterna-tively,the timing of initiation of continental subduction subsequent to the termination of oceanic subduction may be registered in the HP/ UHP eclogites,whose protoliths are of oceanic origin.Currently,the only outcropping candidate is the Xiongdian HP eclogite in the western part of the Dabie orogen(Li et al.,2001;Fu et al.,2002).However,U–Pb zircon ages ranging from216±4to449±14Ma have been obtained for the Xiongdian eclogite(Jian et al.,1997;Sun et al.,2002;Gao et al., 2002);the geological signiﬁcance of this age spread is controversial. Efforts to clarify the geochronological evolution of the Xiongdian eclogite were hampered by a much older Sm–Nd garnet-whole-rock isochron of533±13Ma(Ye et al.,1993)and the fact that further Sm–Nd and Rb–Sr analyses failed to produce mineral isochrons(Li et al., 2001;Jahn et al.,2005),although oxygen isotopic equilibrium was largely attained(Jahn et al.,2005).Here,we present a combined U–Pb,Lu–Hf,Sm–Nd,Ar–Ar and oxygen multi-isotopic and mineral chemical study of the Xiongdian eclogite.The differences in these systems,in conjunction with chemical proﬁles in garnet porphyroblasts and zircons,provide a window into the time-scales of the oceanic subduction and sub-sequent exhumation.2.Geochronological background and sample descriptionsThe Qinling–Dabie–Sulu orogen in east-central China marks the junction between the North and South China Blocks(Cong,1996; Zheng et al.,2005).The western part of the Dabie orogen,usually termed the West Dabie and sometimes the Hong'an terrane,is separated from the Tongbaishan in the west by the Dawu Fault and from the East Dabie by the Shangma fault in the east(Fig.1a).It contains a progressive sequence of metamorphic zones characterized by increasing metamorphic grade,from transitional blueschist–greenschist in the south,through epidote–amphibolite and quartz eclogite,to coesite eclogite in the north(e.g.,Zhou et al.,1993;Hacker et al.,1998;Liu et al.,2004b,2006b).The Xiongdian eclogites crop out in the northwestern corner of the West Dabie,in the Xiongdian mélange within the Huwan mélange after the deﬁnition of Ratschba-cher et al.(2006),in analogy to the terms of the Sujiahe mélange(Jian et al.,1997)and Huwan shear zone(Sun et al.,2002).The Huwan mélange consists of eclogite,gabbro,amphibolite,marble,and quartzite.The eclogitic metamorphic peak for the Xiongdian eclogite is estimated at600–730°C,1.4–1.9GPa(Fu et al.,2002),550–570°C,∼2.1GPa(Liu et al.,2004b)and540–600°C,∼2.0GPa(Ratschbacher et al.,2006),followed by retrogression at530–685°C and∼0.6GPa (Fu et al.,2002).Except for the Xiongdian eclogite,consistent Triassic metamorphic ages have been obtained for other eclogites across the West Dabie (Webb et al.,1999;Sun et al.,2002;Liu et al.,2004a;Wu et al.,2008). This indicates that West Dabie is largely a coherent part of an HP–UHP belt elsewhere in the Dabie–Sulu orogenic belt.Geochronological debate is limited to the Xiongdian eclogite(Fig.1b).U–Pb zircon ages ranging from ca.216to ca.449Ma have been obtained for the Xiongdian eclogite.Jian et al.(1997)reported ca.400,ca.373and 301±0.6Ma ages by ID–TIMS method.Weighted-mean SHRIMP ages range from335±2to424±5Ma(Jian et al.,2000).The Silurian U–Pb zircon ages were interpreted as the age of the protolith,while the Carboniferous ages mark high-pressure metamorphism(Jian et al., 1997,2000).Weighted-mean206Pb/238U SHRIMP U–Pb zircons ages of 433±9,367±10and398±5Ma were interpreted as the protolith age,while323±7and312±5Ma likely date the high-pressure metamorphism(Sun et al.,2002).A Triassic age of216±4Ma together with449±14and307±14Ma weighted-mean206Pb/238U SHRIMP U–Pb zircon ages appear to argue for the involvement of the Triassic subduction in the Xiongdian eclogite(Gao et al.,2002).A garnet-whole-rock Sm–Nd isochron of533±13Ma(Ye et al.,1993)was interpreted to reﬂect the high-pressure metamorphism age.Several Table1Chemical compositions of the Xiongdian eclogite from the western Dabie.Sample number DB17DB18(Major oxides in%)SiO254.5452.45 TiO20.370.43 Al2O314.6212.35 Fe2O38.7710.15 MnO0.150.16 MgO 6.669.91 CaO10.3510.26 Na2O 2.88 2.65 K2O0.600.28 P2O50.060.05 Cr2O3⁎6601118 NiO⁎137247 L.O.I0.87 1.28 Total99.95100.11 (Trace elements in ppm)Li27.627.0 Be0.560.47 Rb9.7813.8 Sr178130Y12.612.7 Cs0.89 3.67 Ba86552.4 La 2.21 1.77 Ce 5.97 5.12 Pr0.880.80 Nd 4.35 4.10 Sm 1.25 1.26 Eu0.470.39 Gd 1.53 1.52 Tb0.280.29 Dy 1.83 1.91 Ho0.410.42 Er 1.14 1.19 Tm0.190.19 Yb 1.31 1.34 Lu0.200.20 Pb 6.44 1.85 Th0.050.07 U0.110.06 Zr28.828.2 Nb 1.19 1.77 Hf0.870.88 Ta0.050.08⁎In ppm.329H.Cheng et al./Lithos110(2009)327–342Sm –Nd and Rb –Sr analyses failed to produces isochrons (Li et al.,2001;Jahn et al.,2005),which was believed to be due to unequilibrated isotopic systems despite the fact that oxygen isotopic equilibrium was largely attained (Jahn et al.,2005).Phengite 40Ar/39Ar ages of ca.430–350Ma have been explained as the retrograde metamorphic age (Xu et al.,2000).The 310±3Ma phengite 40Ar/39Ar age (Webb et al.,1999)is likely geologically meaningless due to the concave-upward age spectrum,indicating the presence of excess argon.Collectively,existing geochronology provides an apparently con ﬂicting picture for the Xiongdian eclogites.The timing of the oceanic crust subduction and exhumation essentially remains to be resolved.The two eclogites examined in this study were selected based on their mineral assemblages,inclusion types and geological context (Fig.1).The one (DB17)from the east bank of the river to the east of Xiongdian village is a coarse-grained and strongly foliated banded eclogite,composed mainly of garnet,omphacite and phengite.A second (DB18)eclogite was sampled about 50m to the north of DB17and is strongly foliated with a similar mineralogy assemblage but smaller garnet grains.3.MethodsSample preparation,mineral separation and chemical procedures for isotope analysis,instrumentation and standard reference materials used to determine whole rock and bulk mineral compositions,in situ major and trace element analyses (Institute for Study of the Earth's Interior,Okayama University at Misasa,Japan),zircon U –Pb isotope and trace element analyses (China University of Geosciences in Wuhan),Lu –Hf and Sm –Nd isotope analyses (Washington State University),Ar –Ar isotope analyses (Guangzhou Institute of Geo-chemistry,Chinese Academy of Sciences)and oxygen isotope analyses (University of Science and Technology of China)are described in the Appendix .4.Results4.1.Bulk chemical compositionThe Xiongdian eclogites are mainly of basaltic composition,but they show a wide range of major and trace element abundances.Despite the high SiO 2(52–58%)and low TiO 2(0.32–0.43%)contents,Fig.2.Whole rock chemical analysis data.(a)Chondrite-normalized REE distribution patterns of the Xiongdian eclogites.(b)Primitive-mantle-normalized spidergrams of the Xiongdianeclogites.Fig.3.Backscattered-electron images and rim-to-rim major-element compositional zoning pro ﬁles of representative garnets in the matrix and as inclusions in zircon.Amp —amphibole;Ap —apatite;Cal —calcite;Cpx —clinopyroxene;Zo —zoisite;Phen —phengite;Omp —omphacite;Qtz —quartz;Zrn —zircon.330H.Cheng et al./Lithos 110(2009)327–342they have MgO=5.1–9.9%,Cr=430–1118ppm,Ni=88–247ppm (Table 1;Li et al.,2001;Fu et al.,2002;Jahn et al.,2005).In contrast to existing LREE-enriched chondritic REE patterns,our samples have rather ﬂat REE patterns around ten times more chondritic abundances with small,both negative and positive Eu anomalies (Fig.2a).Rubidium is depleted and Sr displays enrichment with respect to Ce.Both negative and no Nb anomalies relative to La were observed (Fig.2b).The N-MORB-normalized value of Th is around 0.5,lower than previous reported values of up to 25(Li et al.,2001).4.2.Petrography and mineral compositionThe Xiongdian eclogites occur as thin layers intercalated with dolomite –plagioclase gneiss and phengite –quartz schist (Fu et al.,2002),mainly consisting of garnet,omphacite,epidote (clinozoisite),phengite and minor amphibole,quartz and kyanite (Fig.3).Zircons were observed both as inclusions in garnet porphyroblasts and in the matrix.The samples have similar mineral assemblages,but differ in modal compositions.Omphacite (X Jd =0.46–0.48)is unzoned.Phengite has 3.30–3.32Si apfu and ∼0.4wt.%TiO 2.Garnets range in size from 0.5to 5mm in diameter,either as porphyroblasts or as coalesced polycrystals,mostly with idioblastic shapes with inclusions of quartz,calcite,apatite and omphacite (Fig.3).Garnet is largely homogeneous (Prp 24–25Alm 49–50Grs 24–25Sps 1.5–1.9),but shows a slightly Mn-enriched core (Fig.3d;Table 2).HREEs in large garnet porphyroblasts,such as Yb and Lu,display weak but continuous decreases in concentration from core to rim (Fig.4a),mimicking the MnO zoning pattern,which could be explained by their high af ﬁnity for garnet and likely arises from an overall Rayleigh distillation process during early garnet growth (Hollister,1966;Otamendi et al.,2002).However,the limited variation in MREE concentrations,such as Sm and Nd,in garnet with respect to the weak zoning in HREE (Fig.4a)might be explained by growth in an environment where MREEs are not limited and continuously supplied by the breakdown of other phases.Hafnium has a fairly ﬂat pro ﬁle (Table 3),re ﬂecting its incompatible character in garnet and absence of Hf-competing reactions involved in garnet growth.Two distinct domains can be de ﬁned in the large garnet porphyroblasts based on the chemical zoning and the abundance of inclusions.These zones are an inclusion-rich core with richer Mn and HREE and an inclusion-free rim with poorer Mn and HREE (Fig.3d).The inclusion-free rim for individual garnet has a rather similar width of 200–250μm (Fig.3).Although concentrations of Nd (0.22–0.41ppm)and Sm (0.33–0.48ppm)vary within single garnet grains,the Sm/Nd ratios (0.8–2.2)are consistentTable 2Representative major-element data of the garnets,omphacites,phengites,amphiboles and zoisites.(wt.%)Grt Omp RimCore Inclusions-in-zircon Rim Core SiO 238.6838.6438.6638.5338.6538.6637.8637.7555.9356.1256.1356.20TiO 20.050.060.050.050.050.050.050.080.120.110.110.11Al 2O 321.9221.9422.0721.9921.9921.8421.6821.8611.2611.2211.3311.26FeO ⁎22.9823.0523.0623.1623.0523.1124.4224.33 4.25 4.23 4.32 4.27MnO 0.680.720.790.880.750.680.990.930.030.020.030.02MgO 6.37 6.38 6.28 6.31 6.36 6.35 4.23 4.748.158.027.968.13CaO 9.108.949.028.929.038.9910.579.5013.2213.3613.3213.34Na 2O 0.030.030.030.030.030.030.020.01 6.65 6.41 6.39 6.42K 2O 0.000.000.000.000.000.000.000.000.000.000.000.00Total 99.8099.7799.9699.8799.9199.7199.8299.2199.6099.6099.7099.87O.N.12121212121212126666Si 2.986 2.984 2.981 2.975 2.980 2.988 2.958 2.962 1.996 2.010 2.010 2.007Al 1.994 1.997 2.006 2.001 1.999 1.990 1.997 2.0210.4740.4730.4780.474Ti 0.0030.0030.0030.0030.0030.0030.0030.0050.0030.0030.0030.003Fe 2+ 1.486 1.491 1.489 1.499 1.489 1.496 1.596 1.5990.1270.1270.1290.128Mn 0.0440.0470.0520.0580.0490.0440.0660.0620.0010.0010.0010.001Mg 0.7330.7350.7220.7260.7310.7320.4930.5540.4340.4280.4250.433Ca 0.7530.7400.7450.7380.7460.7440.8850.7980.5060.5130.5110.511Na 0.0040.0050.0050.0050.0050.0050.0030.0020.4600.4450.4430.445K0.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000Phn Amp Zo RimCore Rim Core Mantle Core SiO 248.8649.0949.3349.0147.0847.0746.7246.7539.0538.9239.0239.02TiO 20.400.410.410.400.220.220.220.220.130.130.130.12Al 2O 329.0328.6829.0129.1912.6612.8112.5812.6228.5528.2128.7328.62FeO ⁎ 1.99 1.99 2.00 1.9711.6011.4811.4611.36 6.01 6.01 6.03 6.07MnO 0.000.000.000.010.100.090.090.090.050.050.060.05MgO 2.79 2.77 2.78 2.8012.2012.4712.4412.300.070.060.070.07CaO 0.010.010.010.019.9710.0910.0710.1024.1023.8624.1324.14Na 2O 0.930.920.920.91 2.79 2.77 2.82 2.830.000.000.000.00K 2O 10.009.919.819.780.480.470.470.470.000.000.000.00Total 94.0293.7894.2894.0997.0997.4996.8896.7697.9697.2498.1698.09O.N.111111112323232312.512.512.512.5Si 3.302 3.323 3.318 3.304 6.831 6.800 6.799 6.809 3.008 3.019 3.000 3.003Al 2.313 2.288 2.300 2.319 2.164 2.182 2.158 2.167 2.592 2.579 2.603 2.596Ti 0.0200.0210.0210.0200.0240.0240.0240.0240.0070.0070.0070.007Fe 2+0.1120.1130.1130.111 1.407 1.387 1.394 1.3830.3870.3900.3880.390Mn 0.0000.0000.0000.0000.0120.0120.0120.0120.0040.0040.0040.004Mg 0.2820.2800.2790.282 2.639 2.686 2.699 2.6700.0070.0070.0070.008Ca 0.0010.0010.0010.001 1.550 1.562 1.570 1.577 1.989 1.983 1.988 1.990Na 0.1220.1210.1200.1190.7840.7770.7950.7980.0000.0000.0000.000K0.8620.8550.8420.8410.0890.0870.0880.0880.0000.0000.0000.000⁎Total iron;concentrations reported as wt.%.331H.Cheng et al./Lithos 110(2009)327–342with those obtained by ID-MC-ICPMS (1.9–2.4)within error (Fig.5a),indicating that the Nd isotopic analyses in this study are essentially unaffected by MREE-rich inclusions,likely due to ef ﬁcient mineral picking and/or concentrated H 2SO 4pre-leaching.The consistent Hf concentrations of 0.10–0.13ppm within single grains with those (0.11–0.13ppm)by ID-MC-ICPMS indicates the Hf-rich phases were essentially removed during digestion (Fig.5b).The overall Lu concentration slightly skews towards the garnet rim because of the weak zoning pattern and the spherical geometry effect,i.e.,the outershells dominate the volume of Lu (Cheng et al.,2008a ).The 0.90–0.93ppm Lu contents by ID-MC-ICPMS apparently resemble those of the garnet rim,which could be readily explained by the spherical geometry effect.However,we interpret this with caution because individual garnet porphyroblasts could have different zoning patterns and the individual Lu pro ﬁle might not be representative of the population of garnet grains,although the chemical zoning center (nucleation site)coincides with the geometric center (Fig.3d),suggesting asymmetric garnet growth.In addition,biased mineral hand-picking should be considered (Cheng et al.,2008a,b ).Moreover,since the thin-section preparation method for this study cannot ensure that the real center of the garnet was exposed,the observed zoning here likely only represents a minimum zoning of particular garnet porphyroblasts.4.3.Estimation of P –T conditionsMetamorphic peak P –T conditions of 2.2GPa and 620°C for the DB17Xiongdian eclogite (Fig.6)are evaluated on the basis of recent cali-brations of the assemblage garnet+omphacite+phengite+kyanite+quartz,according to the dataset of Holland and Powell (1998).Higher P –T values of 2.4GPa and 650°C are calculated with the calibrations of Krogh Ravna and Terry (2004).While a temperature of 620±29°C is estimated by quartz –garnet O isotope thermometer (Zheng,1993),Ti-in-zircon thermometer (Watson et al.,2006;Ferry and Watson,2007)gives similar value of 695±22°C.Zr-in-rutile thermometer (Watson et al.,2006;Ferry and Watson,2007)yields a lower value of 634–652°C and a similar temperature of 683–701°C (Fig.6)when using the pressure-dependent calibration of Tomkins et al.(2007)at 2.2GPa.Calibration 1uses updated versions of the thermodynamic dataset and activity models in the programs THERMOCALC3.26and AX (Holland,Powell,1998;latest updated dataset;Powell et al.,1998)by using an avPT calculation in the simpli ﬁed model system NCKFMASH with excess SiO 2and H 2O.Calibration 2uses thermobarometry based on the database of Holland and Powell (1998)and activity models for garnet (Ganguly et al.,1996),clinopyroxene (Holland and Powell,1990)and phengite (Holland and Powell,1998).Analyses of garnet,omphacite and phengite (Table 2)were processed according to the two calibrations.Calibration 3uses mineral O isotope compositions (Table 4)to estimate temperature based on the quartz –garnet O isotope thermometer (Zheng,1993).Calibrations 4and 5use Ti contents in zircon by LA-ICPMS and Zr concentration of rutile by SIMS (Table 5)to temperature estimations based on the Ti-in-zircon and Zr-in-rutile thermometers,respectively (Watson et al.,2006;Ferry and Watson,2007;Tomkins et al.,2007).The assemblage of garnet –omphacite –kyanite –phengite –quartz is representative of metamorphic peak conditions of theXiongdianFig.4.Chondrite-normalized REE patterns (Sun and McDonough,1989)of zircons,garnets and omphacite from Xiongdian eclogite (a)and REE distribution patterns between zircon and garnet (b).The equilibrium D REE(Zrn/Grt)values of Rubatto (2002),Whitehouse and Platt (2003)and Rubatto and Hermann (2007)are presented for comparison.Table 3SIMS Sm,Nd,Hf and Lu concentration pro ﬁles of the garnets in Figs.4and 5.(ppm)RimCore Cpx Li 0.93 1.140.880.840.890.980.750.520.990.580.690.870.670.7522.1Sr 0.100.130.120.120.100.100.100.120.110.120.130.100.110.1033.5Y 45.646.846.647.346.447.148.350.052.053.553.155.354.657.80.92Hf 0.110.130.120.120.110.110.120.120.120.100.110.100.100.100.41La 0.010.020.020.010.000.000.010.010.010.010.010.010.020.010.02Ce 0.040.050.050.060.050.040.040.040.050.030.040.040.050.030.12Pr 0.010.020.030.020.020.020.020.020.020.020.030.020.020.020.03Nd 0.390.330.280.380.350.270.220.280.340.310.270.410.280.260.36Sm 0.450.360.380.440.470.410.480.450.450.410.340.330.420.410.31Eu 0.270.270.270.280.300.240.280.280.250.300.290.240.250.220.22Gd 1.85 1.96 1.75 1.80 1.85 1.78 1.85 1.84 1.93 1.82 1.57 1.92 1.69 1.530.65Dy 5.68 5.86 5.58 6.18 5.87 5.84 5.79 6.19 6.46 6.40 5.50 6.91 6.09 6.400.26Er 3.74 4.13 4.04 4.25 4.23 4.16 3.76 4.15 4.65 4.99 4.53 4.98 4.63 5.200.06Yb 4.10 4.18 4.01 3.86 4.23 4.11 4.49 4.34 4.97 5.19 5.19 5.65 5.10 5.690.12Lu0.900.910.880.840.840.891.131.151.281.261.261.331.321.420.01332H.Cheng et al./Lithos 110(2009)327–342eclogite.A partly-calibrated thermobarometer is de ﬁned by the three reactions of 3Celadonite +1Pyrope +2Grossular =3Muscovite +6Diopside,2Kyanite+3Diopside =1Pyrope +1Grossular +2Quartz,and 3Celadonite +4Kyanite=3Muscovite +1Pyrope +4Quartz.An intersection point of 2.2GPa and 620°C is de ﬁned and therefore independent of commonly-used Fe –Mg exchange thermometers.This offers an advantage with regards to garnet –clinopyroxene,which is prone to retrograde reactions and problems stemming from ferric iron estimation of omphacite (Li et al.,2005).Results are plotted according to the calibrations mentioned above.The three reactions and intersection points are shown according to programs of calibrations 1–5in Fig.6.4.4.Oxygen isotopic dataThe O isotope compositions of minerals for the two eclogites are presented in Table 4.When paired with quartz for isotope geothermo-metry,garnet,omphacite,phengite,kyanite,zoisite and amphibole yield temperatures of 620±29,563±35,567±43,508±31,404±28and 685±39°C for eclogite DB17,respectively.Because these temperatures are concordant with rates of O diffusion and thus closure temperatures in the mineral assemblage garnet +omphacite +kyanite+phengite+quartz (Zheng and Fu,1998),representative of metamorphic peak conditions,a continuous resetting of O isotopes in the different mineral-pair systems is evident during cooling (Giletti,1986;Eiler et al.,1993;Chen et al.,2007).Quartz –garnet pairs from eclogite DB17give temperatures of 620±29°C,which are consistent with those calibrated by the THERMOCALCmethod,indicating that O isotope equilibrium was achieved and preserved during eclogite –facies recrystallization (Fig.7a).This is also evidenced by the apparent equilibrium fractionation between garnet and omphacite (Fig.7b).In contrast,equilibrium fractionation was not attained between garnets and omphacites in eclogite DB18.The calculated quartz –amphibole pair temperature of 685±39°C is distinctly higher than the 508±31°C from the quartz –zoisite pair.Because oxygen diffusion in amphibole is faster than in zoisite and kyanite (Zheng and Fu,1998),amphibole exchanges oxygen isotopes with water faster than zoisite during retrogression.Consequently,the O isotope temperature increases for the quartz –amphibole pair,whereas the quartz –zoisite temperature decreases relative to the formation temperature.In this regard,the retrograde metamorphism of amphibolite –facies should take place at a temperature between ∼685and ∼508°C.On the other hand,the low quartz –kyanite pair temperature (404±28°C)could be interpreted as a result of in ﬂuence by retrogressive metamorphism without a clear geologicalmeaning.Fig.5.Sm/Nd versus Nd and Lu/Hf versus Hf plots for garnet and whole rock.ID:data obtained by the isotope dilution method using MC-ICPMS.IMS:data obtained by ion microprobe.bombWR —whole rock by bomb-digestion,savWR —whole rock by Savillex-digestion.Error bars for both IMS and ID methods are signi ﬁcantly smaller than thesymbols.Fig.6.Peak P –T estimates of the Xiongdian eclogite.Reactions of py +2gr +3cel =6di +3mu;3di+2ky =py+gr +2q;and 3cel +4ky =py +3mu +4q and intersection points are plotted according to the calibrations of Holland and Powell (1998,latest updated dataset)in solid lines and Krogh Ravna and Terry (2004)in dashed lines.Coesite quartz equilibrium is also shown (Holland and Powell,1998).Abbreviations:alm —almandine,gr —grossular,py —pyrope,cel —celadonite,mu —muscovite,di —diopside,jd —jadeite,coe —coesite.Temperatures estimated by quartz –garnet oxygen isotope thermometry (Zheng,1993),Ti-in-zircon and Zr-in-rutile thermometries (Watson et al.,2006;Tomkins et al.,2007)are also shown.Table 4Oxygen isotope data of minerals for the Xiongdian eclogite.Sample number Mineral δ18O (‰)Pair Δ18O (‰)T 1(°C)T 2(°C)DB17Quartz 12.86,12.66Phengite 10.26,10.14Qtz –Phn 2.57567±43Garnet 8.83,8.85Qtz –Grt 3.93620±29605±22Omphacite 9.64,9.56Qtz –Omp 3.17563±35574±28Zoisite 9.31,9.43Qtz –Zo 3.40508±31494±21Amphibole 9.83,9.60Qtz –Amp 3.06685±39Kyanite 9.36,–Qtz –Ky3.41404±28WR 9.85,9.91DB18Garnet 9.74,9.59Omphacite 8.58,8.48Omp –Grt −1.14WR10.15,9.99T 1and T 2were calculated based on the theoretical calibrations of Zheng (1993)and Matthews (1994),respectively,with omphacite (Jd 45Di 55).Uncertainty on the temperature is derived from error propagation of the average reproducibility of ±15‰for δ18O (‰)values in the fractionation equations.333H.Cheng et al./Lithos 110(2009)327–342。

基于MSPA和电路理论的珠三角核心城市通风廊道构建

基于MSPA和电路理论的珠三角核心城市通风廊道构建胡娟何梓欣杨敏龙芍男林歆雨林锦耀*（广州大学地理科学与遥感学院，广东广州 510006）摘要：以珠三角核心城市为例，采用形态空间格局分析（MSPA）识别城市问题源，根据层次分析法建立阻力面，通过最短路径法构建城市通风廊道网络，基于电路理论识别通风廊道的“夹点”区域，制定优先破除策略。

结果表明，城市问题源的核心面积占研究区总面积的9.32%，且大部分面积位于城市中心，中部连接度较高，四周较稀疏；在研究区中共识别出89条通风廊道，构成廊道的主要土地利用类型为不透水面、草地绿地和水体。

MSPA方法与电路理论的结合可以更科学全面地识别各类城市问题源斑块，更合理地规划城市通风廊道。

关键词：通风廊道；珠三角核心城市；形态空间格局分析；电路理论中图分类号：TU984 文献标识码：A 文章编号：2096-1936（2023）09-0001-05DOI：10.19301/ki.zncs.2023.09.001Construction of ventilation corridors in core PRD citiesbased on MSPA and circuit theoryHU Juan HE Zi-xin YANG Min LONG Shao-nan LIN Xin-yu LIN Jin-yao Abstract：The paper takes the core city of the Pearl River Delta as an example, uses the morphological spatial pattern analysis (MSPA) to identify the source of urban problems, establishes the resistance surface according to the analytic hierarchy process, constructs the urban ventilation corridor network through the shortest path method, and finally identifies the "pinch point" area of the ventilation corridor based on the circuit theory, and develops the priority removal strategy. The results show that the core area of urban problem sources accounts for 9.32% of the total area of the study area, and most of the area is located in the urban center, with high connectivity in the middle and sparse around the periphery. A total of 89 ventilation corridors were identified in the study area, and the main land use types of the corridors were impervious water surface, grassland green space and water body. The combination of MSPA method and circuit theory can identify all kinds of urban problem source patches more scientifically and comprehensively, so that urban ventilation corridors can be planned more reasonably.Key words：ventilation corridors; core PRD cities; morphospatial pattern analysis; circuit theory伴随城市化进程加快，城市热岛效应、空气污染、人口剧增等城市问题越来越明显，对生产和生活造成较大影响[1-2]。

基于高斯混合模型的生物医学领域双语句子对齐

（ｎｏｍａｉｎＲｅｒｖｌｂｒｔｒＩｆｒｔｔｉａＬａｏａｏｙ，ＤａｉｎＵｎｖｒｉｙｏｃｎｌｇｏｅｌｉｅｓｔｆａＴｅｈｏｏｙ，Ｄａｉｎ，Ｌｉｏｉｇ１６２ｌａａｎｎ１０４，Ｃｈｎ）ｉａ
ＡｂｔａｔＡｉｉｕａｅｃｎｏｆｂｉｍｅｃｌｔｒｓｌｙｎｍｐｔｎｔｏｅｉｏｅｃｌｒｓ —ａｓｒｃ：ｂｌｎｇｌｌｘｉｏｏｄｉａｅｍｐａｓａｉｏｒａｒｌｎｂｉｍｄｉａｃｏｓｌｎｇｕｇｅｉｏｍａｉｎａｎｆｒｔｏｒｔｉｖ１ＳｅｔｎｃｉｍｅｓｔｅｆｒｔｓｅｐｔｕｉｄａｂｉｉｇｕａｅｉｏｎＴｈｅＧａｓａｉｕｒｏｌａｒｓｅｅｒｅａ．ｎｅｅａｌｇｎｎｔｉｈｉｓｔＯｂｌｌｎｌｌｘｃ．ｕｓｉｎｍｘｔｅｍｄｅｎｄｔａｎｆｒ
基于高斯混合模型的生物医学领域双语句子对齐
陈相，林鸿飞，杨志豪
（连理工大学信息检索研究室，宁大连ｌ６２）大辽１０４摘
一
要：双语术语词典在生物医学跨语言检索系统中有着非常重要的地位，而双语句子对齐是构建双语词典的第
征进行训练，得模型在测试语料上句子对齐的正确率得到较大ห้องสมุดไป่ตู้ 高。使
关键词：计算机应用；中文信息处理；句子对齐；高斯混合模型；迁移学习；信息锚

Advances in

Advances in Geosciences,4,17–22,2005 SRef-ID:1680-7359/adgeo/2005-4-17 European Geosciences Union©2005Author(s).This work is licensed under a Creative CommonsLicense.Advances in GeosciencesIncorporating level set methods in Geographical Information Systems(GIS)for land-surface process modelingD.PullarGeography Planning and Architecture,The University of Queensland,Brisbane QLD4072,Australia Received:1August2004–Revised:1November2004–Accepted:15November2004–Published:9August2005nd-surface processes include a broad class of models that operate at a landscape scale.Current modelling approaches tend to be specialised towards one type of pro-cess,yet it is the interaction of processes that is increasing seen as important to obtain a more integrated approach to land management.This paper presents a technique and a tool that may be applied generically to landscape processes. The technique tracks moving interfaces across landscapes for processes such as waterﬂow,biochemical diffusion,and plant dispersal.Its theoretical development applies a La-grangian approach to motion over a Eulerian grid space by tracking quantities across a landscape as an evolving front. An algorithm for this technique,called level set method,is implemented in a geographical information system(GIS).It ﬁts with aﬁeld data model in GIS and is implemented as operators in map algebra.The paper describes an implemen-tation of the level set methods in a map algebra program-ming language,called MapScript,and gives example pro-gram scripts for applications in ecology and hydrology.1IntroductionOver the past decade there has been an explosion in the ap-plication of models to solve environmental issues.Many of these models are speciﬁc to one physical process and of-ten require expert knowledge to use.Increasingly generic modeling frameworks are being sought to provide analyti-cal tools to examine and resolve complex environmental and natural resource problems.These systems consider a vari-ety of land condition characteristics,interactions and driv-ing physical processes.Variables accounted for include cli-mate,topography,soils,geology,land cover,vegetation and hydro-geography(Moore et al.,1993).Physical interactions include processes for climatology,hydrology,topographic landsurface/sub-surfaceﬂuxes and biological/ecological sys-Correspondence to:D.Pullar(d.pullar@.au)tems(Sklar and Costanza,1991).Progress has been made in linking model-speciﬁc systems with tools used by environ-mental managers,for instance geographical information sys-tems(GIS).While this approach,commonly referred to as loose coupling,provides a practical solution it still does not improve the scientiﬁc foundation of these models nor their integration with other models and related systems,such as decision support systems(Argent,2003).The alternative ap-proach is for tightly coupled systems which build functional-ity into a system or interface to domain libraries from which a user may build custom solutions using a macro language or program scripts.The approach supports integrated models through interface speciﬁcations which articulate the funda-mental assumptions and simpliﬁcations within these models. The problem is that there are no environmental modelling systems which are widely used by engineers and scientists that offer this level of interoperability,and the more com-monly used GIS systems do not currently support space and time representations and operations suitable for modelling environmental processes(Burrough,1998)(Sui and Magio, 1999).Providing a generic environmental modeling framework for practical environmental issues is challenging.It does not exist now despite an overwhelming demand because there are deep technical challenges to build integrated modeling frameworks in a scientiﬁcally rigorous manner.It is this chal-lenge this research addresses.1.1Background for ApproachThe paper describes a generic environmental modeling lan-guage integrated with a Geographical Information System (GIS)which supports spatial-temporal operators to model physical interactions occurring in two ways.The trivial case where interactions are isolated to a location,and the more common and complex case where interactions propa-gate spatially across landscape surfaces.The programming language has a strong theoretical and algorithmic basis.The-oretically,it assumes a Eulerian representation of state space,Fig.1.Shows a)a propagating interface parameterised by differ-ential equations,b)interface fronts have variable intensity and may expand or contract based onﬁeld gradients and driving process. but propagates quantities across landscapes using Lagrangian equations of motion.In physics,a Lagrangian view focuses on how a quantity(water volume or particle)moves through space,whereas an Eulerian view focuses on a localﬁxed area of space and accounts for quantities moving through it.The beneﬁt of this approach is that an Eulerian perspective is em-inently suited to representing the variation of environmen-tal phenomena across space,but it is difﬁcult to conceptu-alise solutions for the equations of motion and has compu-tational drawbacks(Press et al.,1992).On the other hand, the Lagrangian view is often not favoured because it requires a global solution that makes it difﬁcult to account for local variations,but has the advantage of solving equations of mo-tion in an intuitive and numerically direct way.The research will address this dilemma by adopting a novel approach from the image processing discipline that uses a Lagrangian ap-proach over an Eulerian grid.The approach,called level set methods,provides an efﬁcient algorithm for modeling a natural advancing front in a host of settings(Sethian,1999). The reason the method works well over other approaches is that the advancing front is described by equations of motion (Lagrangian view),but computationally the front propagates over a vectorﬁeld(Eulerian view).Hence,we have a very generic way to describe the motion of quantities,but can ex-plicitly solve their advancing properties locally as propagat-ing zones.The research work will adapt this technique for modeling the motion of environmental variables across time and space.Speciﬁcally,it will add new data models and op-erators to a geographical information system(GIS)for envi-ronmental modeling.This is considered to be a signiﬁcant research imperative in spatial information science and tech-nology(Goodchild,2001).The main focus of this paper is to evaluate if the level set method(Sethian,1999)can:–provide a theoretically and empirically supportable methodology for modeling a range of integral landscape processes,–provide an algorithmic solution that is not sensitive to process timing,is computationally stable and efﬁcient as compared to conventional explicit solutions to diffu-sive processes models,–be developed as part of a generic modelling language in GIS to express integrated models for natural resource and environmental problems?The outline for the paper is as follow.The next section will describe the theory for spatial-temporal processing us-ing level sets.Section3describes how this is implemented in a map algebra programming language.Two application examples are given–an ecological and a hydrological ex-ample–to demonstrate the use of operators for computing reactive-diffusive interactions in landscapes.Section4sum-marises the contribution of this research.2Theory2.1IntroductionLevel set methods(Sethian,1999)have been applied in a large collection of applications including,physics,chemistry,ﬂuid dynamics,combustion,material science,fabrication of microelectronics,and computer vision.Level set methods compute an advancing interface using an Eulerian grid and the Lagrangian equations of motion.They are similar to cost distance modeling used in GIS(Burroughs and McDonnell, 1998)in that they compute the spread of a variable across space,but the motion is based upon partial differential equa-tions related to the physical process.The advancement of the interface is computed through time along a spatial gradient, and it may expand or contract in its extent.See Fig.1.2.2TheoryThe advantage of the level set method is that it models mo-tion along a state-space gradient.Level set methods start with the equation of motion,i.e.an advancing front with velocity F is characterised by an arrival surface T(x,y).Note that F is a velocityﬁeld in a spatial sense.If F was constant this would result in an expanding series of circular fronts,but for different values in a velocityﬁeld the front will have a more contorted appearance as shown in Fig.1b.The motion of thisinterface is always normal to the interface boundary,and its progress is regulated by several factors:F=f(L,G,I)(1)where L=local properties that determine the shape of advanc-ing front,G=global properties related to governing forces for its motion,I=independent properties that regulate and inﬂu-ence the motion.If the advancing front is modeled strictly in terms of the movement of entity particles,then a straightfor-ward velocity equation describes its motion:|∇T|F=1given T0=0(2) where the arrival function T(x,y)is a travel cost surface,and T0is the initial position of the interface.Instead we use level sets to describe the interface as a complex function.The level set functionφis an evolving front consistent with the under-lying viscosity solution deﬁned by partial differential equa-tions.This is expressed by the equation:φt+F|∇φ|=0givenφ(x,y,t=0)(3)whereφt is a complex interface function over time period 0..n,i.e.φ(x,y,t)=t0..tn,∇φis the spatial and temporal derivatives for viscosity equations.The Eulerian view over a spatial domain imposes a discretisation of space,i.e.the raster grid,which records changes in value z.Hence,the level set function becomesφ(x,y,z,t)to describe an evolv-ing surface over time.Further details are given in Sethian (1999)along with efﬁcient algorithms.The next section de-scribes the integration of the level set methods with GIS.3Map algebra modelling3.1Map algebraSpatial models are written in a map algebra programming language.Map algebra is a function-oriented language that operates on four implicit spatial data types:point,neighbour-hood,zonal and whole landscape surfaces.Surfaces are typ-ically represented as a discrete raster where a point is a cell, a neighbourhood is a kernel centred on a cell,and zones are groups of mon examples of raster data include ter-rain models,categorical land cover maps,and scalar temper-ature surfaces.Map algebra is used to program many types of landscape models ranging from land suitability models to mineral exploration in the geosciences(Burrough and Mc-Donnell,1998;Bonham-Carter,1994).The syntax for map algebra follows a mathematical style with statements expressed as equations.These equations use operators to manipulate spatial data types for point and neighbourhoods.Expressions that manipulate a raster sur-face may use a global operation or alternatively iterate over the cells in a raster.For instance the GRID map algebra (Gao et al.,1993)deﬁnes an iteration construct,called do-cell,to apply equations on a cell-by-cell basis.This is triv-ially performed on columns and rows in a clockwork manner. However,for environmental phenomena there aresituations Fig.2.Spatial processing orders for raster.where the order of computations has a special signiﬁcance. For instance,processes that involve spreading or transport acting along environmental gradients within the landscape. Therefore special control needs to be exercised on the order of execution.Burrough(1998)describes two extra control mechanisms for diffusion and directed topology.Figure2 shows the three principle types of processing orders,and they are:–row scan order governed by the clockwork lattice struc-ture,–spread order governed by the spreading or scattering ofa material from a more concentrated region,–ﬂow order governed by advection which is the transport of a material due to velocity.Our implementation of map algebra,called MapScript (Pullar,2001),includes a special iteration construct that sup-ports these processing orders.MapScript is a lightweight lan-guage for processing raster-based GIS data using map alge-bra.The language parser and engine are built as a software component to interoperate with the IDRISI GIS(Eastman, 1997).MapScript is built in C++with a class hierarchy based upon a value type.Variants for value types include numeri-cal,boolean,template,cells,or a grid.MapScript supports combinations of these data types within equations with basic arithmetic and relational comparison operators.Algebra op-erations on templates typically result in an aggregate value assigned to a cell(Pullar,2001);this is similar to the con-volution integral in image algebras(Ritter et al.,1990).The language supports iteration to execute a block of statements in three ways:a)docell construct to process raster in a row scan order,b)dospread construct to process raster in a spreadwhile(time<100)dospreadpop=pop+(diffuse(kernel*pop))pop=pop+(r*pop*dt*(1-(pop/K)) enddoendwhere the diffusive constant is stored in thekernel:Fig.3.Map algebra script and convolution kernel for population dispersion.The variable pop is a raster,r,K and D are constants, dt is the model time step,and the kernel is a3×3template.It is assumed a time step is deﬁned and the script is run in a simulation. Theﬁrst line contained in the nested cell processing construct(i.e. dospread)is the diffusive term and the second line is the population growth term.order,c)doﬂow to process raster byﬂow order.Examples are given in subsequent sections.Process models will also involve a timing loop which may be handled as a general while(<condition>)..end construct in MapScript where the condition expression includes a system time variable.This time variable is used in a speciﬁc fashion along with a system time step by certain operators,namely diffuse()andﬂuxﬂow() described in the next section,to model diffusion and advec-tion as a time evolving front.The evolving front represents quantities such as vegetation growth or surface runoff.3.2Ecological exampleThis section presents an ecological example based upon plant dispersal in a landscape.The population of a species follows a controlled growth rate and at the same time spreads across landscapes.The theory of the rate of spread of an organism is given in Tilman and Kareiva(1997).The area occupied by a species grows log-linear with time.This may be modelled by coupling a spatial diffusion term with an exponential pop-ulation growth term;the combination produces the familiar reaction-diffusion model.A simple growth population model is used where the reac-tion term considers one population controlled by births and mortalities is:dN dt =r·N1−NK(4)where N is the size of the population,r is the rate of change of population given in terms of the difference between birth and mortality rates,and K is the carrying capacity.Further dis-cussion of population models can be found in Jrgensen and Bendoricchio(2001).The diffusive term spreads a quantity through space at a speciﬁed rate:dudt=Dd2udx2(5) where u is the quantity which in our case is population size, and D is the diffusive coefﬁcient.The model is operated as a coupled computation.Over a discretized space,or raster,the diffusive term is estimated using a numerical scheme(Press et al.,1992).The distance over which diffusion takes place in time step dt is minimally constrained by the raster resolution.For a stable computa-tional process the following condition must be satisﬁed:2Ddtdx2≤1(6) This basically states that to account for the diffusive pro-cess,the term2D·dx is less than the velocity of the advancing front.This would not be difﬁcult to compute if D is constant, but is problematic if D is variable with respect to landscape conditions.This problem may be overcome by progressing along a diffusive front over the discrete raster based upon distance rather than being constrained by the cell resolution.The pro-cessing and diffusive operator is implemented in a map al-gebra programming language.The code fragment in Fig.3 shows a map algebra script for a single time step for the cou-pled reactive-diffusion model for population growth.The operator of interest in the script shown in Fig.3is the diffuse operator.It is assumed that the script is run with a given time step.The operator uses a system time step which is computed to balance the effect of process errors with efﬁ-cient computation.With knowledge of the time step the it-erative construct applies an appropriate distance propagation such that the condition in Eq.(3)is not violated.The level set algorithm(Sethian,1999)is used to do this in a stable and accurate way.As a diffusive front propagates through the raster,a cost distance kernel assigns the proper time to each raster cell.The time assigned to the cell corresponds to the minimal cost it takes to reach that cell.Hence cell pro-cessing is controlled by propagating the kernel outward at a speed adaptive to the local context rather than meeting an arbitrary global constraint.3.3Hydrological exampleThis section presents a hydrological example based upon sur-face dispersal of excess rainfall across the terrain.The move-ment of water is described by the continuity equation:∂h∂t=e t−∇·q t(7) where h is the water depth(m),e t is the rainfall excess(m/s), q is the discharge(m/hr)at time t.Discharge is assumed to have steady uniformﬂow conditions,and is determined by Manning’s equation:q t=v t h t=1nh5/3ts1/2(8)putation of current cell(x+ x,t,t+ ).where q t is theﬂow velocity(m/s),h t is water depth,and s is the surface slope(m/m).An explicit method of calcula-tion is used to compute velocity and depth over raster cells, and equations are solved at each time step.A conservative form of aﬁnite difference method solves for q t in Eq.(5). To simplify discussions we describe quasi-one-dimensional equations for theﬂow problem.The actual numerical com-putations are normally performed on an Eulerian grid(Julien et al.,1995).Finite-element approximations are made to solve the above partial differential equations for the one-dimensional case ofﬂow along a strip of unit width.This leads to a cou-pled model with one term to maintain the continuity ofﬂow and another term to compute theﬂow.In addition,all calcu-lations must progress from an uphill cell to the down slope cell.This is implemented in map algebra by a iteration con-struct,called doﬂow,which processes a raster byﬂow order. Flow distance is measured in cell size x per unit length. One strip is processed during a time interval t(Fig.4).The conservative solution for the continuity term using aﬁrst or-der approximation for Eq.(5)is derived as:h x+ x,t+ t=h x+ x,t−q x+ x,t−q x,txt(9)where the inﬂow q x,t and outﬂow q x+x,t are calculated in the second term using Equation6as:q x,t=v x,t·h t(10) The calculations approximate discharge from previous time interval.Discharge is dynamically determined within the continuity equation by water depth.The rate of change in state variables for Equation6needs to satisfy a stability condition where v· t/ x≤1to maintain numerical stabil-ity.The physical interpretation of this is that aﬁnite volume of water wouldﬂow across and out of a cell within the time step t.Typically the cell resolution isﬁxed for the raster, and adjusting the time step requires restarting the simulation while(time<120)doflow(dem)fvel=1/n*pow(depth,m)*sqrt(grade)depth=depth+(depth*fluxflow(fvel)) enddoendFig.5.Map algebra script for excess rainfallﬂow computed over a 120minute event.The variables depth and grade are rasters,fvel is theﬂow velocity,n and m are constants in Manning’s equation.It is assumed a time step is deﬁned and the script is run in a simulation. Theﬁrst line in the nested cell processing(i.e.doﬂow)computes theﬂow velocity and the second line computes the change in depth from the previous value plus any net change(inﬂow–outﬂow)due to velocityﬂux across the cell.cycle.Flow velocities change dramatically over the course of a storm event,and it is problematic to set an appropriate time step which is efﬁcient and yields a stable result.The hydrological model has been implemented in a map algebra programming language Pullar(2003).To overcome the problem mentioned above we have added high level oper-ators to compute theﬂow as an advancing front over a land-scape.The time step advances this front adaptively across the landscape based upon theﬂow velocity.The level set algorithm(Sethian,1999)is used to do this in a stable and accurate way.The map algebra script is given in Fig.5.The important operator is theﬂuxﬂow operator.It computes the advancing front for waterﬂow across a DEM by hydrologi-cal principles,and computes the local drainageﬂux rate for each cell.Theﬂux rate is used to compute the net change in a cell in terms ofﬂow depth over an adaptive time step.4ConclusionsThe paper has described an approach to extend the function-ality of tightly coupled environmental models in GIS(Ar-gent,2004).A long standing criticism of GIS has been its in-ability to handle dynamic spatial models.Other researchers have also addressed this issue(Burrough,1998).The con-tribution of this paper is to describe how level set methods are:i)an appropriate scientiﬁc basis,and ii)able to perform stable time-space computations for modelling landscape pro-cesses.The level set method provides the following beneﬁts:–it more directly models motion of spatial phenomena and may handle both expanding and contracting inter-faces,–is based upon differential equations related to the spatial dynamics of physical processes.Despite the potential for using level set methods in GIS and land-surface process modeling,there are no commercial or research systems that use this mercial sys-tems such as GRID(Gao et al.,1993),and research systems such as PCRaster(Wesseling et al.,1996)offerﬂexible andpowerful map algebra programming languages.But opera-tions that involve reaction-diffusive processing are speciﬁc to one context,such as groundwaterﬂow.We believe the level set method offers a more generic approach that allows a user to programﬂow and diffusive landscape processes for a variety of application contexts.We have shown that it pro-vides an appropriate theoretical underpinning and may be ef-ﬁciently implemented in a GIS.We have demonstrated its application for two landscape processes–albeit relatively simple examples–but these may be extended to deal with more complex and dynamic circumstances.The validation for improved environmental modeling tools ultimately rests in their uptake and usage by scientists and engineers.The tool may be accessed from the web site .au/projects/mapscript/(version with enhancements available April2005)for use with IDRSIS GIS(Eastman,1997)and in the future with ArcGIS. 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