The solution space of sorting by reversals
Biogeochemical processes in intensive zero-effluent
Biogeochemical processes in intensive zero-effluent marine fish culture with recirculating aerobic and anaerobic biofiltersAmir Neori a,⁎,Michael D.Krom b ,Jaap van Rijn caIsrael Oceanographic and Limnological Research,The National Centre for Mariculture,P .O.Box 1212,Eilat 88112,Israel bEarth and Biosphere Institute,School of Earth and Environment,Leeds University,Leeds LS29JT,United KingdomcDepartment of Animal Sciences,Faculty of Agricultural,Food and Environmental Quality Sciences,The Hebrew University of Jerusalem,Rehovot 76100,IsraelReceived 14December 2006;received in revised form 11April 2007;accepted 20May 2007AbstractThe biogeochemical processes that drive nutrient transformations and recycling in organic marine sediment –water environments were studied for 17months in a zero-effluent intensive recirculating culture system.The system consisted of a 10m 3gilthead seabream (Sparus aurata )tank coupled to aerobic and anaerobic water treatment elements.Nutrients and alkalinity were measured in the system to quantify the main biogeochemical processes.Fractions of the carbon fed in feed were found in fish (18.3%)and in sludge (11%);the missing carbon was respired by fish (45%)and by aerobic (8.4%)and anaerobic (7.7%)microorganisms.Fractions of the nitrogen fed in feed were found in fish (15.4%)and in sludge (14.3%);the missing nitrogen was eliminated by nitrification –denitrification.Most of the phosphorus and ash fed in feed and not found in fish accumulated within the sludge in the system.The rates of nitrification,denitrification and sulphate reduction increased with time,reaching 0.3g N m −2d −1,53g N m −2d −1and 145g S m −2d −1,respectively.Nitrification developed more rapidly than denitrification,leading at first to nitrate accumulation (to 20mmol NO 3l −1by day 200)and a decrease in alkalinity.Once denitrification surpassed nitrification,nitrate concentrations decreased,eventually being reduced to b 0.3mmol NO 3l −1by day 510,and alkalinity stabilized.Toxic hydrogen sulphide,generated within the anaerobic sludge,was oxidized by oxygen and nitrate as it diffused through the anaerobic –aerobic sediment –water interface.When nitrate levels in the water above the sludge dropped below 2mmol l −1,sulphide was also oxidized in the fluidized bed reactor.Denitrification reduced nitrate in the water,respired (jointly with sulphate reduction)carbon in the sludge,oxidized the hydrogen sulphide,and contributed to stabilization of alkalinity and accumulation of polyphosphate in bacteria as a major sink of labile P.©2007Elsevier B.V .All rights reserved.Keywords:Alkalinity;Fish waste treatment;Nitrification –denitrification;Nutrients;Polyphosphate accumulation;Sludge;Sparus aurata ;Sulphate reduction1.IntroductionThe same microbial processes that occur naturally in organic-rich aerobic and anaerobic environments also occur in intensive aquaculture systems (van Rijn,1996).The observations from controlled fish culture systems provide insights into microbial processes and interactions driving the environmental situation in heavily-loaded natural ecosystems.The present study in a novel seawater fish culture system that does not require water discharge,quantified biogeochemical processes by long-term nutri-ent and alkalinity profiles and budgets.This approach has been useful to understand water quality processes andJournal of Experimental Marine Biology and Ecology 349(2007)235–247/locate/jembe⁎Corresponding author.Tel.:+97286361445;fax:+97286375761.E-mail address:aneori@ (A.Neori).0022-0981/$-see front matter ©2007Elsevier B.V .All rights reserved.doi:10.1016/j.jembe.2007.05.023problems in intensive aquaculture systems(e.g.,Krom and Neori,1989;Thoman et al.,2001).Specifically,such studies enable pinpointing of the principle biogeochem-ical processes within such systems(e.g.,Krom,1991). Several of the main processes occurring in sediments involve stoichiometric changes in alkalinity,a feature that provides additional information in the quantitative elucidation of the biogeochemical processes taking place(Lazar et al.,1989).Modern fish mariculture is increasingly criticized for its non-sustainability(Aldhous,2004).It is practiced almost exclusively in flow-through systems such as cages and ponds often in a narrow and heavily populated belt along the coast.Mariculture is subject to public controversy,since it generally discharges effluents without pollutant removal(Naylor et al.,1998).Recircu-lating aquaculture technology can overcome many of aquaculture's economic and environmental limitations, because it combines good regulation of the water quality characteristics with high fish yields,low water use and minimal nutrient export(Saylor et al.,1991;van Rijn, 1996;Gutierrez-Wing and Malone,2006).The advanced biofilter system of recirculating aqua-culture used in the present study is attractive for both freshwater fish(Shnel et al.,2002)and marine fish (Gelfand et al.,2003).The design consists of a fish basin stocked at high fish density.Water from this basin circulates through an aerobic nitrifying filter and through an anaerobic loop,with a sedimentation/digestion basin and a fluidized bed reactor.A particular novelty of the design is the use of the organic fish waste as the carbon and energy source for nitrate reduction(van Rijn,1996). This feature results in minimal environmental pollution and near zero water discharge,without addition of foreign chemicals(e.g.,methanol)to enhance microbial respira-tion.It is possible to operate this system for prolonged periods with water quality parameters remaining within the range of values acceptable for intensive fish culture (Shnel et al.,2002;Gelfand et al.,2003).An important limitation in the large-scale application of the recirculating fishculture approach is the scarcity of information on the microbial populations and processes that drive them(Blancheton,2000).Previous studies on this particular system have looked in detail at several individual microbial processes that occur in various modules of the system(e.g.,Barak et al.,2003;Gelfand et al.,2003;Cytryn et al.,2003,2005,2006).In the present study,biogeochemical processes were quantified through long-term nutrient and alkalinity profiles and budgets.It was found that the closed environment of the fish culture system allowed a fairly accurate estimation of the contribution of the main biochemical processes involved in carbon,nitrogen,sulphur and phosphorus transformations.Processes and rates were compared to those occurring in natural hypertrophic marine environments.2.Materials and methods2.1.Fish culture system2.1.1.ConfigurationThe physical setup has been described in detail (Gelfand et al.,2003;Cytryn et al.,2005).It comprised the following components(Fig.1):(1)a round10,000l polypropylene fish production basin(FT),3m diameter×1.5m depth;(2)a sedimentation basin(SB), 9.5m length×0.5m width×0.3–0.4m depth;working volume:1.5–2m3;(3)a cube-shaped trickling filter(TF), containing3.8m3of a PVC cross-flow medium with a specific surface area of240m2m−3(Jerushalmi Ltd., Israel);(4)a fluidized bed reactor(FBR),made of a Perspex column,200l volume,2m height,36cm diameter.The reactor was filled as bacterial carrier material with several kg sand(N97%SiO2)of1.1mm grain diameter(15%of grains N1.4mm and10%of grains b0.85mm).The system was designed to handle up to6kg d−1of fish feed input.Gilthead seabream(Sparus aurata)were cultured from May2000to August2001. The fish were stocked several times to replace mortalities and to increase fish density as the system matured and water qualitystabilized.Fig.1.A basic schematic of the main components(not to scale), dimensions and water flow rates of the studied facility.Solid arrows mark water flows.236 A.Neori et al./Journal of Experimental Marine Biology and Ecology349(2007)235–2472.1.2.OperationSeawater pumped from the nearby ultra-oligotrophic Gulf of Aqaba(Eilat)filled the system and compensated for water spills and dilutions of the culture water.Tap water diluted the seawater to36parts per thousands(ppt) from its N40ppt natural salinity.Tap water compensated for evaporation loss,which was intense in the summer. Two water loops constituted the water recirculation (Fig.1).In the aerobic loop,water from the top of the FT was pumped and sprinkled over the TF at a rate of15–20m3h−1and drained back to the top of the FT.In the anaerobic loop,the sediment-laden water from the bottom-center of the FT was continuously withdrawn through a standpipe into the SB.From there it was pumped at a rate of1.8–2.4m3h−1upward through the FBR and into the TF intake.A flow of about2.4m3h−1of the FTwater was diverted from the main pump's flow into a foam fractionator(model:TF8AZ,Top Fathom Ltd, USA)for clarification.The force of the water returning from the trickling filter drove a circular water velocity of between30and40cm s−1at the circumference of the FT. Ozone(Pacific Ozone Model G11ozone generator) injected into the foam fractionator disinfected all makeup water.The TF outflow water was enriched,when necessary,with pure oxygen from a liquid oxygen tank. A1hp blower drove air upward through the trickling filter for cooling.An automatic monitoring/alarm system(Point Four,Port Moody,BC,Canada)monitored water level, DO,pH and temperature.Additional measurements of DO were made with a portable Handy Gamma Meter (OxyGuard International A/S,Blokken,Denmark).The fish were fed a commercial feed(Matmor Ltd.,Evtach Israel)with8%water(105°C),44%carbon,45%protein (7.2%N),19.5%lipid,1.4%phosphorus(P),and5kcal energy g−1.Feed was offered according to a standard feeding table(Lupatsch and Kissil,1998,2001),based on the average fish density,size and average water temperature.Seabream of the size range used in this study and fed this diet contain on average317g OM, 212g C,27.2g N,7.2g P,43g ash and2100mega-cal energy per kilogram live weight(Lupatsch and Kissil, 1998,2001).These values were used in mass budgets.A fraction of feed(a total of100kg)was initially put daily into the SB to prime the anaerobic processes until a sufficient quantity of fish waste accumulated.2.2.Analytical procedures2.2.1.Solids analysisAt the end of the study,the sludge accumulated in the SB and the sand-sludge flocks in the FBR were collected and air-dried.The TF plastic medium was disassembled,air-dried and then each piece was strongly beaten over a container to release the dried sludge.For protein analysis, 50g sub samples of the residual solids from each of the biofilters was rinsed with tap water and oven-dried at 60°C for24h followed by drying at105°C to constant weights(%dw content)before TKN(total Kjeldahl N) analysis(Scheiner,1976).For total P content,the oven-dried sludge was pulverized;then500mg of the dry powder was mixed with9ml65%nitric acid and2ml HCl in120ml Teflon PFA digestion vessels.Samples and blanks were prepared for analysis by microwave-assisted digestion(10min in500W and another10min in580W of microwave radiation).Liquid residues were supple-mented with deionized water to a final volume of25ml. Analyses were conducted on portions of the solutions versus certified standards by inductively coupled plasma atomic emission spectrometry(ICP-AES,Spectro Ana-lytical Instruments GmbH&Co.,KG Boschstr.10,47533 Kleve,Germany),equipped with cross-flow nebulizers (precision:b2%;accuracy:b5%).2.2.2.Dissolved nutrients and other compoundsSeveral times a week,at08:00and14:00h,water samples for nutrient analyses were collected from the different components of the system.Nutrients were analyzed by an Auto Analyzer II(Technicon Instruments Co.,Tarrytown,New York).Total ammonia N(TAN)was analyzed by a modification of the Berthelot phenol reaction(Krom et al.,1985).Nitrate and nitrite were analyzed after Solorzano and Sharp(1980).Orthophos-phate was analyzed after Glibert and Loder(1977).Water samples for total hydrogen sulphide were sampled with minimum air exposure.They were preserved immediately with a stabilizing solution of sodium carboxymethyl cellulose and cadmium sulphate,sealed and then analyzed colorimetrically by a sulphide Auto Analyzer II cartridge (Bran+Luebbe GmbH,Werkstraβe4,22844Norder-stedt,Schleswig-Holstein,Germany),using a reaction with dimethyl-p-phenylenediamine dihydrochloride and ferric chloride to yield methylene blue(Method No.G-193-97of Bran+Luebbe,based on Grasshoff et al., 1983).The pH was measured with a HI8424pH meter (Hanna Instruments Ltd.,Bedfordshire,England)and total alkalinity(precision b2%)was determined by titration with hydrochloric acid(Parsons et al.,1984). 3.Results and discussion3.1.Feed,water use,fish growthThe fish were fed in total1158kg feed(8%moisture). An additional100kg feed was added directly to the SB in237A.Neori et al./Journal of Experimental Marine Biology and Ecology349(2007)235–247order to speed up the development of anaerobic conditions(i.e.,b1mg l−1DO),so that the total dw feed input was1157kg(Table1).Filling the tanks and making up for various water losses,mostly by evaporation(up to 0.5m3d−1in summer),consumed a total of only25m3of seawater and105m3of tap water.Specific total use of water was only0.265m3kg−1of gross fish production. Overall,699kg fish biomass was stocked and490kg biomass was produced.Over the entire512day study,the daily production rate averaged1.2kg(0.41%fish weight d−1)for an average seabream standing stock of271kg (partially reported in Gelfand et al.,2003).3.2.Carbon,nitrogen and phosphorus recovery in fish and sludgeThe fractions of the nutrients introduced into the system as feed that were recovered in fish growth were 18.3%C and15.4%N(Table1),at the low end of the range of15–30%reported from nutrient budgets of this fish(Krom and Neori,1989;Lupatsch and Kissil,1998). Higher values of C and N recovery in seabream growth have more recently been obtained in technically im-proved systems of this design(van Rijn,unpublished; Neori,unpublished).Only11%of the carbon budget and 14%of the nitrogen budget were recovered in sludge, mainly in the oxic sludge.The rest of the nutrients–over 70%of carbon and nitrogen inputs–were missing from this total budget.In contrast,nearly all added P was recovered,with21%in fish,5%in dissolved phosphate and the rest in sludge(Table1).The budgets for dry weight and for energy content paralleled those for C and N,while the ash budget paralleled the P budget.A comparison of the overall quantities of sludge production,composition and processes found in this study(Table1)with budgets reviewed by Chen et al. (1997)for several different recirculating culture systems with different fish,highlights similarities and differ-ences.The fraction of feed dw recovered in sludge in the present data(22.5%)was in the low range of the recoveries defined as“typical”in Chen et al.(1997)of 20%–50%;it is an expression of the high rate of sludge decomposition in the SB.The fraction of feed TKN recovered as sludge TKN in the present data was12.1%, compared with a recovery of9.8%that can be calculated from the data in Chen et al.(1997)for a channel catfish (Ictalurus punctatus)recirculating N content of4.2%in the accumulated sludge in the present study is similar to the mean of4.0%in Chen et al.(1997). However,while in the present system the remaining 70%N not assimilated by fish or in sludge was denitrified to N2(see below),in the single-loop culture systems reviewed in Chen et al.(1997)this N was discharged with effluents as nitrate and created a pollution hazard.An additional striking difference between the present data and other recirculating fish culture systems is in the fraction of feed P that was recovered in the sludge.In the present study nearly all P not found in fish was recovered as sludge,whose P content in dw totaled 5.9%(Table1).In other aquaculture systems,on the contrary,most of waste P was discharged as dissolved P while sludge P content averaged only0.7%(Chen et al.,1997).3.3.Dissolved nutrients dynamics and transformationsThe nutrients entered in the seawater and tap water constituted b1%of feed input for each of the nutrients, both because of the low water use and the low concentration of nutrients in both sources of water.Table1Budgets of the main ingredients of the fish feed introduced to the fish culture system in17monthsIngredient:DW C N P Ash Energy('000kcal) Budget component1.Feed inputa.(kg)11575579117.61456374b.%100100100100100100 Outputs2.In produced fish(%of line1)15.818.315.42115.216.83.In waste(%of line1)a.Anoxic sludge(SB+FBR)10 3.95 4.450.648.3 3.2b.Oxic sludge(TF)12.5 6.87.736.944.17.3c.Water0b0.1 2.2 5.1004.Total waste(%of line1)22.510.7514.392.692.410.55.Missing nutrient fractions(lines2and4subtracted from line1)a%of line161.770.9570.3−13.6−7.672.7a A negative value indicates that the system contained a quantity of the substance larger than the input.238 A.Neori et al./Journal of Experimental Marine Biology and Ecology349(2007)235–247Ammonia (analyzed as TAN),a major excretion product of the fish,accumulated in the water immedi-ately after initiation of feeding.TAN concentration peaked at nearly 200μmol l −1at day 10,and gradually decreased below 50μmol l −1(Fig.2).It remained low until day 370,except for a peak of ∼2700μmol l −1,which developed on day 78following a partial drying of the TF due to a burnout of the main water pump.After day 370,the ammonia concentration circulating through the system increased to between 50and 250μmol l −1.Nitrate concentration reached 20mmol l −1by day 200(Fig.2).After day 270,it gradually dropped,to b 5mmol l −1by day 370and b 0.3mmol l −1at the end of the study.Based on our data,nitrification and denitrification were the dominant microbial N transformations within the system.Nitrification developed shortly after start up of the system.A dynamic balance between ammonia production and nitrification kept ammonia levels at this time by and large below 50μmol l − nitrification,calculated by the difference between expected quantities of ammonia (5%of total feed input —Lupatsch and Kissil,1998,2001)and measured ammonia in the watermultiplied by water volume,matched the increase in feeding.It increased from 5.9mol N d −1(1–270days)to 10.0mol N d −1(270–370days)and to 16.5mol N d −1for the last 130days (Table 2).The overall average nitrification rate for the entire period was 9mol N d −1.It is likely that nitrification occurred mostly in the TF and on other wet surfaces,including the top of the SB sludge and in the FBR,where ammonia produced by anaerobic respiration processes could become exposedtoFig. 2.Total ammonia N (TAN),nitrate and orthophosphate concentrations in the fish basin during the study.Table 2Total changes in titration alkalinity and associated parameters in the system over the following three periods:Period 1)from day 1to day 270(270days)when the system operated in net nitrification mode;Period 2)from day 270to day 370(100days)when the system operated in net denitrification mode;Period 3)from day 370to day 500(130days)when the system operated in net denitrification mode with leakage of ammonia and hydrogen sulphide in the anaerobic loop Measured parameters Period 1Period 2Period 31.Alkalinity in seawater inflow (equivalents)6715.5572.Alkalinity in tap water inflow (equivalents)6210.6553.Alkalinity in water outflow (equivalents)−59−8.7504.Alkalinity added as bicarbonate (equivalents)321005.Measured net change in alkalinity (equivalents)5.28.5−9.86.Dissolved N excreted by fish asammonia and reactive DON (moles)142883219787.Dissolved N released from labile organic matter in SB (moles)175172165.58.Nitrate accumulation in FT water,Fig.2(moles)263.5−99−61.53Calculated parameters (see text)9.Total nitrification (TN)(moles)(Eq.(6))16031004214310.Total denitrification (TDN)(moles)(Eq.(8))13401103220511.Presumed net alkalinity production,sum of lines 1–5(equivalents)3871012212Calculated surplus of alkalinityproduced,line 11,but not matched by the accumulation of nitrate,line 8(equivalents)(Eq.(11))123109183Calculated daily rates of microbial processes 13.Total nitrification rate (mol d −1) 5.910.016.514.Total denitrification rate (mol d −1) 5.011.017.015.Alkalinity surplus (sulphate reduction)rate (equivalents d −1)0.461.1 1.4All units are equivalents (for alkalinity)or moles (for dissolved nitrogen).239A.Neori et al./Journal of Experimental Marine Biology and Ecology 349(2007)235–247dissolved oxygen in the overlying water(Blackburn, 1986).The average and maximum nitrification rates divided by the total area of the TF and other wet surfaces were0.126and0.3g N m−2d−1,respectively.Values of up to0.28g N m−2d−1have been reported for other marine nitrifying trickling filters(Nijhof and Boven-deur,1990;Eding et al.,2006).Denitrification devel-oped more slowly than nitrification(Tables2,3),so that a shift from net accumulation to net consumption of nitrate occurred only after day270.This was twice the time it took in freshwater systems of similar design (Shnell et al.,2002;Gelfand et al.,2003).Dissolved orthophosphate is produced by fish and microbial respiration.Orthophosphate concentrations in the water(Fig.2)gradually increased to a value of2.5mmol l−1by day300.Then,during the period of intense denitrification,dissolved phosphate levels decreased to1.2mmol l−1by day370.After nitrate dropped below5mmol l−1and begun to rise again, phosphate concentration also rose,to about3mmol l−1 by day410(Fig.2).There was no detectable hydrogen sulphide circulat-ing in the water until about day370(data not shown). Then as nitrate levels dropped below2mmol l−1, hydrogen sulphide gradually appeared in the water overlying the sludge in the SB.Concentrations of up to 500μmol l−1were measured there at the end of the study(Fig.3).Microbial processes in the FBR con-sumed most of the hydrogen sulphide that escaped the SB before the water returned to the main water loop. Hydrogen sulphide that escaped the FBR disappeared in the trickling filter,by either evaporation or oxidation, leading to levels considered safe for fish in Bagarinao and Lantin-Olaguer(1998)of b5μmol l−1in the fish basin water(Fig.3).The rate of hydrogen sulphide release to the SB water was inversely related to nitrate concentration(Fig.4). Sulphide release started at∼350mmol S d−1at nitrate concentrations below2mmol l−1increasing to18mol S d−1when nitrate concentration dropped below0.2mmol l−1(Fig.4).Nitrate concentrations above2mmol l−1have been shown to totally inhibit sulphate reduction in organically-rich aquatic sediments(Lucassen et al., 2004).The removal of sulphide and nitrate together in the FBR suggests that a principle process for sulphide oxidation was autotrophic denitrification(Cytryn et al., 2005,2006).Oxidation of hydrogen sulphide in the FBR was proportional to its concentration in the water leaving the SB(Fig.5),reaching a rate of over100mmol S l−1 d−1.Considering the extreme toxicity to fish of hydrogen sulphide(96h LC50=60μmol S l−1in Bagarinao and Lantin-Olaguer,1998),it can be calculated that without itsTable3Net rates of denitrification in the system,assuming it took place in the SB,based on maximal rates of nitrate disappearance from the water during the indicated periods(negative linear slopes in Fig.2nitrate curve)Denitrification rates Period:June–July2000July–August2000January–March2001Totalg N d−180187249mol N d−1 5.713.417.8Areal in SB ag N m−2d−1173953mol N m−2d−1 1.2 2.8 3.8 Volumetric in SB amg N l−1d−146106143m mol N l−1d−1 3.37.610.2a Per surface area and volume(4.75m2and1750l,respectively)of theSB.Fig.3.Hydrogen sulphide concentration in the water exiting the fish basin,sedimentation basin(SB)and FBR during the final months of thestudy.Fig.4.Concentration of hydrogen sulphide(open triangles,right Y axis)and rate of production(closed circles,left Y axis)in the SB as a function of nitrate concentration in the system water.240 A.Neori et al./Journal of Experimental Marine Biology and Ecology349(2007)235–247oxidation hydrogen sulphide concentration in the FT could have reached toxic levels in 1–2h.Significant sulphate reduction to sulphide apparently occurred in the lower layers of the SB all the time.Sulphate reduction estimates based on alkalinity surplus (explained below)increased with time in parallel with the increase in denitrification (Table 2).Hydrogen sulphide levels of up to 6mmol l −1were determined in the pore waters of the bottom layers of the SB anoxic sludge in a very similar system (Cytryn et al.,2003).However,during the first 370days of the present study,no sulphide was detected in the overlying water of the SB.This was probably due to oxidation in the boundary layer between sludge and water,where white patches of elemental S were often visible.Reduced solutes –sulphides and ammonia –escaped into the overlying water only when limits were reached with regard to the oxidative capacity of the boundary layer.Microbial redox recycling processes are characteristic of the aerobic/anaerobic boundary in organic marine sedi-ments and are particularly important in the oxidation of sulphide (Blackburn,1986).Typically,more than 90%of the sulphide produced in marine sediments is reoxidized in this boundary layer (Jorgensen,1980;Canfield et al.,1993).Oxidation by dissolved oxygen is generally considered the most important oxidative process occurring in marine sediments.However,here the artificial conditions created very high-nitrate con-centrations in the SB sludge's overlying water,a situation that is rare in nature.In natural marine sediments,autotrophic denitrification has been reported at nitrate concentration of only 0.025mmol l −1.Even at those low concentrations,the process was considered of quantitative importance for the C,N and S cycles in thatsediment (Fossing et al.,1995).With nitrate concentra-tions orders of magnitude higher,it is likely that oxidation by nitrate was the most significant process for the oxidation of sulphide in the present system.3.4.Alkalinity and the biogeochemical processes 3.4.1.Alkalinity dynamicsAlkalinity of the initial seawater was 2.3mEq l −1while the alkalinity of the tap water was 1.2mEq l −1.Alkalinity values for most of the first 3months of the study are missing.However,during this time only 72kg feed was introduced to the system out of a total of 1258kg during the entire 17months,and,therefore,the error introduced to the quantitative analyses of the processes should be minor.Initially,when nitrate accumulated in the system,pH dropped below 6.0while also alkalinity steeply declined,reaching a low point after 3months (Fig.6).Brief but sharp rises in alkalinity and pH (with a simultaneous sharp dropinFig.5.Relationship between concentration of hydrogen sulphide in the water leaving the SB into the FBR and the rate of change in hydrogen sulphide (negative units)in the FBR;data,solid circles;regression,line (Y =−29X −376;r 2=0.912;p b0.0001).Fig.6.Alkalinity in water exiting the trickling filter and the SB,and pH in the fish basin during the study.241A.Neori et al./Journal of Experimental Marine Biology and Ecology 349(2007)235–247nitrate concentration)followed the temporary removalof the fish between days 99and 128.Sodium bicarbonate buffer (totaling 27kg,321equivalents)was added occasionally between days 74to 99and days 194to 293to restore alkalinity.During the initial 3months period,once measured,alkalinity levels in the various modules of the system were low and did not differ significantly between the modules (Figs.6,7).Between day 200and 270,when denitrification matched and then surpassed nitrification (Table 2),alkalinity rose to 3mEq l −1and pH stabilized (Fig.6).After day 270,as a result of the intense denitrification,alkalinity gradually increased to 4–5mEq l −1.Typically,during this latter period there was an increase in alkalinity of 0.2–0.3mEq l −1in the water as it passed through the anaerobic loop (Fig.7),indicating large net alkalinity generation by anaerobic processes.After day 370,alkalinity generation in the SB was balanced by consumption elsewhere in the system and the overall alkalinity stabilized at close to 3mEq l −1without any further addition of bicarbonate buffer.From day 200until the end of the experiment,the pH of the entire fish culture system stabilized at just above 7with minor fluctuations (Fig.6).3.4.2.Alkalinity budgets and contingent biogeochem-ical processesAlkalinity budgets (Table 2)were calculated over the following three biogeochemically distinct periods:(1)period 1(first 270days)net nitrification (accumu-lation of nitrate);(2)period 2(from day 270to 370)net denitrification (nitrate levels dropped sharply);and (3)period 3(day 370–500)net denitrification accom-panied by leakage of ammonia and hydrogen sulphidefrom the SB sludge into the overlying SB water.The budgets were calculated using the following assumptions and equations (derived from Lazar et al.,1989;van Rijn et al.,2006).During microbial nitrification of ammonia 1equivalent (Eq)of alkalinity is consumed per mol of ammonia oxidized (Eq.(1)below).During denitrifica-tion 1Eq of alkalinity is produced per mol of nitrate reduced to nitrogen gas,whether the process involved is heterotrophic denitrification (Eq.(2))or autotrophic denitrification with H 2S (Eq.(3))coupled to sulphate reduction to produce H 2S (Eq.(4)).The rearrangement of Eqs.(3)and (4)in Eq.(5)assumes that dissimilatory reduction of nitrate to ammonia is not significant.Nitrification:NH 3þ2O 2¼NO −3þH þþH 2Oð1ÞHeterotrophic denitrification2NO −3þ½5H 2 þ2H þ¼N 2þ6H 2Oð2ÞAutotrophic denitrification with H 2S5H 2S þ8NO −3→5SO 2−4þ4N 2þ4H 2O þ2Hþð3ÞSulphate reduction to produce H 2S5SO 2−4þ½20H 2 þ10H þ→5H 2S þ20H 2Oð4ÞA rearrangement of Eqs.(3)and (4)8NO −3þ½20H 2 þ8H þ→4N 2þ24H 2Oð5ÞFor each of the three defined time periods,with insignificant amounts of ammonia accumulating in the system,total nitrification (TN)is the sum of the ammonia produced from fish excretion (N fish )and from decompo-sition of organic matter in the SB (N SB ;Eq.(6))TN ¼N fish þN SBð6ÞTotal net nitrification (TNN)is total nitrification (TN)minus total denitrification (TDN)and equals the amount of nitrate accumulated during the period considered.TNN ¼TN −TDN ¼▵NO 3ð7ÞRearranging Eq.(7)TDN ¼TN −▵NO 3ð8ÞAssuming that the only microbial processes that result in a change of alkalinity are nitrification and denitrification,then the change in alkalinity (▵Alk)Fig.7.The differences in water alkalinity between the trickling filter and fish basin and between the sedimentation basin and the fish basin during the study.242 A.Neori et al./Journal of Experimental Marine Biology and Ecology 349(2007)235–247。
WasEinsteinaSpaceAlien原文及翻译
Was Einstein a Space Alien?1 Albert Einstein was exhausted. For the third night in a row, his baby son Hans, crying, kept the household awake until dawn. When Albert finally dozed off ... it was time to get up and go to work. He couldn't skip a day. He needed the job to support his young family.1. 阿尔伯特.爱因斯坦精疲力竭。
他幼小的儿子汉斯连续三个晚上哭闹不停，弄得全家人直到天亮都无法入睡。
阿尔伯特总算可以打个瞌睡时，已是他起床上班的时候了。
他不能一天不上班，他需要这份工作来养活组建不久的家庭。
2 Walking briskly to the Patent Office, where he was a "Technical Expert, Third Class," Albert worried about his mother. She was getting older and frail, and she didn't approve of his marriage to Mileva. Relations were strained. Albert glanced at a passing shop window. His hair was a mess; he had forgotten to comb it again.2. 阿尔伯特是专利局三等技术专家。
在快步去专利局上班的路上，他为母亲忧心忡忡。
母亲年纪越来越大，身体虚弱。
她不同意儿子与迈尔娃的婚事，婆媳关系紧张。
Was Einstein a Space Alien原文及翻译
Was Einstein a Space Alien?1 Albert Einstein was exhausted. For the third night in a row, his baby son Hans, crying, kept the household awake until dawn. When Albert finally dozed off ... it was time to get up and go to work. He couldn't skip a day. He needed the job to support his young family.1. 阿尔伯特.爱因斯坦精疲力竭。
他幼小的儿子汉斯连续三个晚上哭闹不停，弄得全家人直到天亮都无法入睡。
阿尔伯特总算可以打个瞌睡时，已是他起床上班的时候了。
他不能一天不上班，他需要这份工作来养活组建不久的家庭。
2 Walking briskly to the Patent Office, where he was a "Technical Expert, Third Class," Albert worried about his mother. She was getting older and frail, and she didn't approve of his marriage to Mileva. Relations were strained. Albert glanced at a passing shop window. His hair was a mess; he had forgotten to comb it again.2. 阿尔伯特是专利局三等技术专家。
在快步去专利局上班的路上，他为母亲忧心忡忡。
母亲年纪越来越大，身体虚弱。
她不同意儿子与迈尔娃的婚事，婆媳关系紧张。
老师的办公室英语作文
老师的办公室英语作文The teachers office is a place of tranquility and learning a sanctuary where educators prepare their lessons grade assignments and engage in professional development. Here is a detailed description of a typical teachers office in an English composition setting. Location and AccessibilityThe teachers office is usually located in a quiet area of the school often near the English department to facilitate easy access for students and colleagues. It is designed to be accessible but private allowing the teacher to work without constant interruptions. Layout and FurnitureThe office is typically furnished with a large desk which serves as the central workspace. The desk is organized with various teaching materials including textbooks lesson plans and student assignments. A comfortable chair is placed behind the desk for the teacher while a couple of smaller chairs are available for students or visitors.Storage SolutionsTo keep the space organized the office is equipped with bookshelves that house an extensive collection of literary works reference materials and educational resources. There might also be filing cabinets to store graded papers tests and other important documents.TechnologyIn the modern educational landscape technology plays a significant role in a teachers office. A computer is an essential tool for lesson planning research and communication with students and parents. Additionally a printer scanner and sometimes an interactive whiteboard or projector might be present for presentations or demonstrations.Personal TouchesDespite the professional atmosphere a teachers office often reflects their personality and interests. This can be seen through the choice of artwork photographs or decorative items that add a touch of warmth and individuality to the space. A plant or two might also be present to bring a bit of nature indoors.Academic EnvironmentThe office is a hub for academic discussions and consultations. Students often visit to seek help with their coursework discuss their progress or simply to have a conversationabout literature and language. The teachers office is a place where critical thinking is encouraged and the love for the English language is evident.Professional DevelopmentThe office is not only a place for teaching but also for continuous learning. Teachers spend time in their offices reading up on the latest educational research attending online seminars or working on their own professional development plans.ConclusionIn essence a teachers office is more than just a place to work it is a reflection of their dedication to education their passion for the English language and their commitment to student success. It is a space that fosters learning creativity and growth both for the teacher and the students who visit.。
关于科学的创新小作文英语
Innovation is the lifeblood of science,driving progress and development across various fields.The following essay explores the essence of scientific innovation,its importance,and the role it plays in shaping our future.Title:The Spark of Scientific InnovationIntroductionScience is a vast ocean of knowledge,and innovation is the wind that propels the ship of discovery forward.It is the creative process through which new ideas,methods,and technologies emerge,transforming the way we understand and interact with the world.The Essence of Scientific InnovationScientific innovation is not merely about creating something new it is about improving upon existing knowledge and pushing the boundaries of what is known.It involves a deep understanding of the subject matter,a keen sense of observation,and the courage to challenge established norms.Importance of Scientific Innovation1.Problem Solving:Innovation addresses complex problems by offering novel solutions that may not have been previously considered.2.Economic Growth:It stimulates economic development by creating new industries, products,and services,leading to job creation and increased productivity.3.Social Advancement:Innovations in fields like medicine,agriculture,and education have a profound impact on the quality of life,improving health,food security,and access to knowledge.4.Environmental Sustainability:New technologies and methods can help address environmental challenges,promoting a more sustainable use of resources and reducing the impact of human activities on the planet.The Role of Scientific Innovation in Shaping the Future1.Healthcare:Innovations in medical research and technology are revolutionizing healthcare,enabling more effective treatments and preventive measures.2.Technology:The rapid pace of technological innovation is reshaping industries,from communication and transportation to energy production and artificial intelligence.3.Space Exploration:Innovative approaches in space technology are opening up new frontiers for exploration and the potential for human settlement beyond Earth.cation:Innovations in educational technology are making learning more accessible and personalized,breaking down barriers to education worldwide.Challenges and OpportunitiesWhile scientific innovation brings numerous benefits,it also presents challenges such as ethical considerations,the digital divide,and the potential for misuse of technology. However,these challenges are opportunities for further innovation,requiring responsible and thoughtful development of new technologies.ConclusionScientific innovation is a continuous journey of exploration and discovery.It is the key to unlocking a brighter future for humanity.By fostering a culture of innovation,we can ensure that the benefits of science are accessible to all,driving us towards a more equitable,healthy,and sustainable world.Call to ActionAs we stand on the precipice of new discoveries,it is incumbent upon scientists, policymakers,and society as a whole to embrace innovation responsibly.Let us work together to create an environment that nurtures creativity,encourages risktaking,and rewards those who dare to think differently.The future belongs to those who innovate.。
考试虫王若平的考研英语长难句过关第一部门
阅读基本功难句过关（王若平）第一部分难句分类辨析第一章定语从句定语从句的修饰对象一直是阅读中经常遇到而难以把握的问题，定语从句的关系词究竟修饰上文中的哪个单词、短语或整个句子，一要靠语言知识，二要根据上下文进行逻辑判断。
定语从句有限定性和非限定性之分。
此外，定语从句和主句之间还存在着状语关系，说明原因、目的、让步、假设等关系。
But he did not talk at length about the matter, which was not considered by the White House to be a particularly important question. (说明原因)他没有详细地谈这件事，因为白宫没有把它看作是个特别重要的问题。
Anyone who thinks that rational knowledge need not be derived from perceptual knowledge is an idealist. (假设)如果认为理性知识可以不从感性知识得来，他就是一个唯心主义者。
So my chances of getting to revolutionary China are pretty slim, although I have not given up y efforts to get a passport, that will enable me to visit the countries of Socialism. (目的) 因此，我到革命的中国的希望相当小了，然而我并没有放弃努力来争取一张护照，使我得以访问社会主义国家。
He insisted on buying a car, which he could not afford and had no use for. (表让步)他坚持要买辆轿车，尽管他买不起，而且也不需要。
1. Libraries made education possible, and education in its turn added to libraries; the growth of knowledge followed a kind of compound-interest law, which was greatly enhanced by the invention of printing.要点：从内容上分析，which修饰 “the growth of knowledge”图书馆的出现使教育的发展成为可能，而教育的发展又反过来使图书馆不断扩大充实。
Sorting out Your Sortation Options-一份关于选择自动排序系统的指南
SORTING OUT YOUR SORTATION OPTIONSGuiding You Through the Process of Evaluating and Selecting the Right “Mission-critical” Sortation SolutionTABLE OF CONTENTS1 Sorting out Your Sortation Options1 Sorting out your application2Sorting out Your Handling Requirements 3Sorting out Your Rate4 Sorting out Other Considerations4Summary5Case Study Example7GlossaryGuiding You Through the Process of Evaluating and Selecting the Right “Mission-critical” Sortation SolutionWhether from growth, consolidation of facilities, mainstreaming of processes, business acquisitions or simply a need to become more efficient, there are several reasons toconsider automated sortation solutions. Even if you have a specific solution envisioned, you may want to evaluate several significant factors to be considered when choosing the “mission-critical” solution for your sortation system.The purpose of this white paper is to guide you through the process of evaluating and selecting the right sortation solution for your facility. Several widely accepted sortation technologies will be examined on a number of aspects that you should consider before deciding on the right fit for your needs. This paper will walk through all of the important factors to consider as you “sort out your options” and ensure that you are making the right decisions for your facility’s needs today and years into the future.SORTING OUT YOUR APPLICATIONMost sorters can be grouped into one of two high-level classifications – line or loopsorters. Line sorters are configured in a straight line, with items entering the sorter at only one location. They typically need separate conveyors for any items that cannotbe successfully sorted on the first pass. By contrast, loop sorters are configured in acontinuous loop, often with more than one induction point in which items are introduced to the sorter. They also have built-in recirculation, which can help provide more confident, reliable divert confirmation signals from the control system.One of the first things to consider in a new sortation application is the nature of theoperation. Some applications, such as sorting to the proper shipping truck, are bestsuited to a solution that can efficiently accommodate the destination locations, like a sliding shoe sorter. Other applications, like order consolidation, are conducive to a system that can efficiently sort to a large number of destinations that do not occupy muchspace, such as a cross-belt sorter.SORTING OUT YOUR SORTATION OPTIONS1Figure A - The chart above represents typical “best fit” practices when it comes to matching the best technology with varying item types.Overall, there are several factors to consider, including:1. Types of items to be sorted (corrugated carton, tote, polybags, bubble mailers, loose items, etc.)2. Item packaging type (corrugate, shrink wrap case, bagged apparel, apparel on hangers, etc.)3. Item diversity (50 percent corrugated carton, 25 percent bagged apparel, etc.)4. Item structural integrity (how rigid and predictable the structure of the items is)One set of factors that have a significant influence on MHE technology selection are the physical features of the items to be sorted, including the types of items and their packaging. Items, for the purpose of this paper, are the individual products, units, cartons or totes that will be sorted. Not all sortation technology is ideal for all types of items.SORTING OUT YOUR HANDLING REQUIREMENTS2Keeping in mind that most applications do not handle a single item type, it is important to recognize that a system must accommodate a wide range of item types. The more item types the system can handle, the fewer non-conveyables there will be, increasing facility efficiency and shortening the payback of the investment. Therefore, when making your selection, take into account your entire product mix for present and future needs. Aspects such as size, weight, balance or shape of product to be sorted may rule out certain sortation technologies. Packaging integrity of the items, such as “perfect presentation” needs and durability concerns due to reproduced packaging, must alsobe considered.Note: for complete definitions of the technologies mentioned in this paper, please see the Glossary at the end of this paper.BombayPush tray High-density sliding shoeAnother critical factor to consider is the rate requirement of the system.For the purpose of this paper, “rate” relates to the item throughput per hour, or the rate at which the system must operate. In the material handling industry, this is also expressed in terms of cartons per hour (cph) or pieces per hour (pph).A common misunderstanding about rates is that “speed” (or how fast the equipment runs) is the same as throughput. However, concentration on speed alone can steer your selection in the wrong direction. Speed, without consideration of other factors suchas gapping, gentle handling and accuracy, can actually be an inefficient use of thetechnology.Instead, as systems have been pushed to continually increase rates, MHE vendors have worked to increase throughput without increasing machine speed.SORTING OUTYOUR RATE 3This reduces wear, energy usage and noise while extending equipment life. It also makesthe machine control system much more critical on sliding shoe and pop-up wheel sortingtechnologies. An increased rate at reduced speeds requires reducing gaps betweenitems while maintaining divert accuracy.In sortation equipment, as rate and handling capability increase, so does the cost of thetechnology. System implementation payback must be carefully balanced with rate tomeet an acceptable budget for any project.Some rate requirements may immediately rule out certain sortation technologies. Actualrates are highly dependent on a number of factors, but Figure B will help in learning themost common rates by technology.Figure B - The chart above represents typical “rules of thumb” rates by sortation technology. These rates assume average item sizes.4 SORTING OUT OTHERCONSIDERATIONSIn addition to handling, rate and applicationrequirements, several other factors can make abig impact on the technology decision.Floor space requirements – Many facilities are looking to add e-commerce-focusedsolutions in existing buildings, sometimes even in the back rooms of retail stores. Sometechnologies are designed to maximize the number of destinations in a very smallfootprint.Operating noise levels – Some sortation equipment operates at very low noise levelswhile maintaining very high rates, increasing ergonomic comfort while still maintainingthroughput.Investment level – While some sortation systems require more substantial technologiesand supporting subsystems, they can better prepare the operation for future growth.Energy usage – Energy usage is becoming an increasingly important aspect of thematerial handling system. If energy usage is an important factor in your enterprise, besure to share this concern with your MHE vendor at the project outset, as energy usagecan vary widely by technology and vendor.Maintenance and operator skill levels – Both the daily operation and maintenancetasks can vary widely by technology and by MHE vendor. Consider how your personnelwill interact with the equipment and how your current staff will be able to maintain thesystem.Future expansion – If there is a possibility for future expansion, this should be takenunder consideration at the project outset. The ability of future expansion, in terms of rateor divert locations, can be limited by the technology or by the initial system design.Divert accuracy – Divert accuracy and propensity for jams, hang-ups and mechanicalproblems can often be dependent on the specific design details by the MHE vendor andthe gapping requirements designed for the system.Divert confirmation – Confirming a divert can be a necessary step in some sortationprocesses. The method for confirming a divert varies by the sortation technology and themachine control software used by the MHE vendor.Depreciation schedule – Some sortation technologies may have a longer expected lifespan, which will affect the depreciation schedule. This must be clearly understood beforemaking the purchase so project costs are properly distributed.SUMMARYThis paper has discussed critical factors to evaluate during a typical automatedsortation investigation – but there are also several details which can only be learnedthrough experience. Before construction plans begin, be sure to talk to an MHE vendorwith significant, unbiased experience in a wide variety of sortation technologies. Thiswill ensure the best possible, cost-effective solution is developed prior to submitting abudget for capital approval.Now that we have discussed several factors that go into choosing the right sortation technology, we can look at a real-world example to see how all the factors must be considered to make the right decisions.CASE STUDY EXAMPLE5Sorting out Your OptionsThe summaries below will help further explain the basic sortation technologies available and typical specifications.Pop-up Wheel in Belt: Pop-up wheels or rollers embedded in a belt conveyor lift andtransfer items at an angle to a downstream conveyor. This technology requires a relatively low capital investment and provides medium sortation rates, but does not provide a positive divert, which limits its use to certain item types.Pop-up Wheel in Strip Belt: Pop-up wheels or rollers embedded in a strip belt conveyor lift and transfer items at an angle to an aftersort conveyor. Unlike the pop-up wheel in belt sorter, this technology keeps items in constant contact of the carrying surface until they are diverted, maintaining gaps across a machine with a high quantity of divert points.Tilt-tray: Trays mounted to carts running on a continuous-loop conveyor “tilt” and transfer items down into a chute when an item reaches its sorting destination. Items are inducted either manually or automatically onto the trays via induction stations at multiple locations throughout the loop. The technology is ideal for applications thatrequire a high number of sort locations, and it allows for easy future expansion. Low noise levels also make the tilt-tray sorter a good solution for operators who work within close proximity to the machine.MDR Divert/Transfer: Pop-up wheels or transfer bands embedded in a motor-driven roller (MDR) conveyor re-direct items to a downstream conveyor. A relatively simple and safe sortation option, MDR diverts or transfers are good for products requiring zero- contact accumulation. MDR systems usually achieve the best payback when there is a high concentration of divert and merge operations in a small footprint. Since MDR systems typically handle one item per zone, sortation rates can be limited.Sliding Shoe: Diverting “shoes” attached to the conveyor surface positively divert items onto an aftersort conveyor. Fed by a single stream of products merged from multiple areas of a building upstream, sliding shoe sorters are a popular choice for shipping sorters, as they can provide high rates with predictable divert accuracy for a wide range of items.Cross-belt: Motorized belt conveyors are mounted to carts running on a continuous loop conveyor and transfer items down into a chute when an item reaches its sorting destination. Cross-belt technology has similar functionality and features to the tilt-tray sorter. The belt can provide more predictable divert reliability with certain types of items.GLOSSARY69 Sweeper: Paddles “sweep” items off a modular belt into bins located on either side. Goodfor applications with high-density destinations and small e-commerce orders.Bombay: Items are dropped into bays which run around a continuous loop. Doors openfrom the bottom to allow items to fall into bins located below. Good solution for appareland circular items that can roll.Push Tray: Items are inducted onto carts running around a continuous loop, before beingpushed off by a sliding bar. This technology combines the benefits of sliding shoe andtilt-tray sorters.Sorting out Your Sortation Options | GlossaryHoneywell Intelligrated +1 866.936.7300********************** Follow us on Twitter:https:///intelligrated Learn more on YouTube:Honeywell Intelligrated SOYWP | 06/20© 2020 Honeywell International Inc.。
合并排序算法 Merge Sort 英语
合并排序Merge SortWhat it is and AlgorithmMerge sort is an effective sorting algorithm based on the comparison. The algorithm is based on “Divide and conquer,” meaning the initial collection will be split into smaller pieces in this situation. This concept can be introduced recursively so that the collection is split into single components and then rebuilt into a sorted set. The re-construction of the algorithm merging portion is the phase where the components are ordered. In each phase of merge sort, the components are placed in the positions theyhave sorted, in the sub-collection. Distributing the authentic collection into its elements may lead to the formation of additional elements which are essentially not required. The handling of the sub-collections may be in place so that distinct collections are not required. In this article, our experts from Assignment Help will explain to you about merge sort with the help of examples and infographics.There are different variants that exist regarding merge sort. These variants are mainly worried about decreasing the complexity of storage and the price of copying.A simple solution to minimize the space of overhead to n/2 is to keep left and right of the array as a structure which seems to be combined but are actually not. Then into thetemporary or cached space, a copy of the left partm is made and then the routine of the merge is directed to place the output of the merged sort in m. In order to make use of only one allocation in the memory, it is good to give temporary room outside the merge routine with this variant. As the last couple of lines before the return result declaration becomes superfluous, the unnecessary copying listed above is also mitigated.When applied on arrays, one drawback of merge type is its O(n) requirement of memory for its operation. Several variants were suggested in-place:There is an algorithm that needs a steady quantity of working memory: sufficient storage space to hold an input array element, and extra space to hold O(1) pointers in the input array. These algorithms are said to be not stable but yet they are able to achieve an O(n log n) time in spite of being unstable.There have been several attempts to create an in-place merge algorithm that can be combined with a conventional merge type (bottom-up or top-down) to establish an in-place merge type. In this case, in-place would mean the taking off the logarithmic space of the stacks, since the standard type of merge requires that amount of space for its own use. Stable merging is possible with a constant amount of scratch space in O(n log n) time, but yet again this algorithm is also complicated and has highfactors of consistency: merging lengths n and m can take 5n + 12 m + o(m) movements. This factor of high constant and complex nature of the algorithm has been produced easier to comprehend and simpler. A simple linear time algorithm known as in-place practical merging is implemented to merge a sorted list using a set quantity of extra space. It will be helping in merging the linear time and at the same time providing a continues space allocation.An option to reducing copying to various lists is to combine a fresh data field with each key (keys are called the elements in m). This field will be used to connect the keys and any related data in a sorted list (the record is called a key and its related data). Then the merging of the sorted lists takes place by altering the values of the link; there is no need to move documents at all. Afield containing only a connection will usually be larger than a whole record, so less room will be used as well. This is a normal method of sorting, not limited to sorting done through the use of merge sort.Natural merge sortA natural type of merge is comparable to a kind of bottom-up merge except that any naturally occurring runs (sort sequences) are utilized in the input. Both bitonic, as well as monotonic runs, can be utilized, with lists being convenient data structures (use as LIFO or FIFO). The starting point assumes that each run is one item long in the bottom-up merge type. In practice, there will be many brief runs of random input information that just occur to be sorted. In the typical situation, because there are fewer runs tomerge, the natural merge type may not need as many passes. In the best case, the input is already sorted (i.e. single run), so it only needs to make one pass through the data by the natural merge sort. Long natural runs are present in many practical instances, which is why natural merge type is utilized. Our experts from assignment help will now explain to you about theProcessThe process of merge sort involves three partsDividing the issue into a number of smaller subproblems of the same issue.Conquering the subproblems by continuously solving them. Solve the subproblems as basic cases if they are small enough.Combine the subproblem alternatives into the initial issue solution.Process of Merge ShortPerformance analysisThe merge sort algorithm output is very remarkable O(n log(n)). It is suggested to use a default library. Most languages nowadays use a better performing algorithm as the default sorting alternative in a true world implementation. In Java, there is a sort technique in the Util package, in the Arrays class. dual-pivot Quicksort, which conducts O(n log(n)) time complexity, is implemented based on the documentation.According to the below Java code, in the function mergeSort, only two statements can create extra space. One is the centre, which requires the complexity of O(1) space. The other is the merge feature, which due to the presence of a temporary array(tem) requires O(n) space complexity. The algorithm is also a deep-first algorithm. At some stage, there is only one merge feature that can be performed. Hence, the complexity of the room here is O(n).The median and worst-case performance of Merge Sorting n objects is O(n log n). Considering time of the merge sort for a length n list while it is in a running state is T(n), then the recurrence T(n)= 2T(n/2)+n follows from the algorithm definition which asks to put the algorithm to half the size of the two lists of the initial list and then the n steps made to mergethe two output lists are added. The closed-form follows from the dividing-and conquering recurrences master theorem.As multilevel memory hierarchies are used, the location of reference can be of paramount significance in software optimization on contemporary pcs. Some of the existing algorithms of merge sort which are mostly aware of the cache memory of the machine are introduced, whose tasks are notably selected to reduce the movements of the page that take place from the cache machine as well as outside the machine. For example, when subarrays of size S are reached, the merge sort having the tiled algorithm will immediately stop to divide the subarrays, where S is said to be the amount of cache memory that the machine or the CPU can hold. In order to prevent the memory fromgetting wrapped or no longer accessible, a sorting algorithm such as the insertion sort is used in this place first in order to have no cache memory issues and then with the mode of standard recursion, merge sort is then finally performed over it in order to get it sorted in the given manner be ascending or descending. On computers that profit from cache optimization, this algorithm has proved better efficiency.Merge Sort Performance Analysis Merge Sort Performance AnalysisImplementing merge sortThe function of merge sort should sort the subarray array p. r recursively. It means after calling merge sort on (array, p, r), the components should be sorted in ascending order from index p to index r of the array.The algorithm of merge sort explains that: –It is essential to realize that sorting need be performed of the size of the sub array is 0 and 1. Therefore, nothing is needed to be done.Otherwise, to sort the subarray, merge type utilizes divide-and-conquer.To combine the sorted sub-arrays array p. q and array q+1.. r, use merge (array, p, q, r).Uncomment the Program.assertEqual function at the bottom once implemented to verify the passing of the test assertion.Merge Sort ImplementationImportant characteristicsIn order to sort linked lists, Merge Sort is helpful.Merge Sort is a stable sort, meaning that the same component in an array maintains its initial positions in relation to each other.Merge sort overall time complexity is O(nLogn). It is more efficient because the runtime is also O(nlogn).In the worst case, the space complexity of the Merge sort is O(n). This implies that for the last information sets this algorithm requires a lot of room and can slow down activities.As multilevel memory hierarchies are used, the location of reference can be of paramount significance in software optimization on contemporary pcs. Cache-aware versions of the merge sort algorithm were proposed, whose operationswere specifically selected to minimize the movement of pages to and from the memory cache of a machine. For example, when subarrays of size S are reached, the tiled merge sort algorithm stops dividing the subarrays, where S is the number of data items that fit into the cache of a CPU. Each of these subarrays is sorted with an in-place sorting algorithm, such as the type of insertion, to discourage memory swaps, and then the normal sort of merge is completed in the standard recursive mode. This algorithm has shown better performance on computers benefiting from cache optimization. It is proposed an alternative type of merge using the continuous extra room. This algorithm was subsequently refined. Many internal sorting apps also use a type of parallel sorting where the input is divided up to a greater amount of sub-lists, ideally, a number for which merging stillmakes the presently processed collection of websites fit in the primary memory.Merge sort and other sorting techniquesWhile heapsort has the same time boundaries as merge sort, it requires only 1 auxiliary space instead of the n merge type. Effective quicksort implementations usually outperform merge sort on typical contemporary architectures to sort RAM-based arrays. On the other side, merge sort is a stable type and is more effective in managing slow sequential media access. Merge sort is often used in linked list and is said to be the best option for it: in this scenario, a merge sort is comparatively simple to execute in such a manner that it needs only some (1) additional room, and the slow random-access performance of a linked list makes some other algorithms(such as quicksort) perform badly and others (such as heapsort) impossible. The array is divided into only 2 halves (i.e. n/2) in the merge type. Whereas the array is divided into any proportion in the event of a quick sort. There is no compulsion to quickly split the range of components into equal components. Merge sort is able to work with any type of data set which is available without having any constraint on the size of the data set, whereas on the other hand, quick sort cannot work with large amount data setsExamples of the mergeSort program in JavaMerge sort is the sorting technique that follows the approach of dividing and then conquering. For instance, think of an Array called A having n number of elements in it. The algorithm of thissorting theme would be processing the elements in the following 3 steps.If it is found out that the array A contains 0 or only 1 element, then it is already said to be sorted in the given order. If it is not sorted then it would divide the array into two sub-arrays of equal parts.The conquering part involves sorting the two arrays so made in the previous step by the help of merge sort.Finally, all the sub-arrays are merged into a single and final file which is sorted in the given manner and thereby maintaining the order of the given array elements.Algorithm:Program：。
学术英语理工详解答案 Unit 4
Unit 4 Writing a Literature Review
1 Writing a literature Review
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1 Writing a literature Review
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Very high radiation doses can destroy body functions and lead to death within 60 days.
Unit 4 Writing a Literature Review
1 Writing a literature Review
Unit 4 Writing a Literature Review
1 Writing a literature Review
5 It seems that the Text 11, 12, 14 provide more scientific facts about nuclear radiation than Text 13 which is more emotionally charged by using many rhetorical questions and the phrases like “I am simply floored”, “let officials be oblivious”, “not to be outdone”, “Do not tell us about that”. Hence it appears less reliable and trustworthy.
我的奇思妙想作文之多功能垃圾桶
我的奇思妙想作文之多功能垃圾桶英文回答：The Multifunctional Waste Bin: A Comprehensive Solution for Waste Management.In the pursuit of sustainable living, waste management plays a crucial role. However, traditional waste bins often fall short in effectively addressing the challenges posed by the growing volume and complexity of waste. To overcome these limitations, the concept of a multifunctional waste bin has emerged as a promising solution.The multifunctional waste bin is an innovative device that combines multiple functionalities to provide a comprehensive approach to waste management. It goes beyond the basic function of storing waste by incorporating advanced features such as waste sorting, odor control, and even energy generation.1. Waste Sorting:The most significant feature of the multifunctional waste bin is its ability to effortlessly sort waste into different categories. This is achieved through integrated sensors and a specialized sorting mechanism. The waste is automatically sorted based on its material composition, such as paper, plastic, metal, and organic matter. By facilitating efficient waste sorting at the source, the multifunctional waste bin significantly enhances recycling rates and reduces the amount of waste sent to landfills.2. Odor Control:Unpleasant odors emanating from waste bins can pose a significant nuisance. The multifunctional waste bin addresses this issue by employing advanced odor control technology. Activated carbon filters or ozone generators are integrated into the bin, effectively absorbing or neutralizing odors and ensuring a clean and fresh environment.3. Energy Generation:In addition to waste sorting and odor control, the multifunctional waste bin can also harness the power of organic waste to generate renewable energy. Through a process known as anaerobic digestion, the bin converts organic matter into biogas. This biogas can then beutilized for various applications, such as cooking, heating, or electricity generation. By utilizing waste to produce energy, the multifunctional waste bin promotessustainability and reduces reliance on fossil fuels.4. Waste Compaction:To optimize space utilization and minimize thefrequency of waste collection, the multifunctional wastebin incorporates a waste compaction mechanism. This feature compresses the waste, reducing its volume and increasingthe bin's storage capacity. The increased efficiency in waste storage translates into fewer collection trips, resulting in reduced carbon emissions and operational costs.5. Smart Monitoring:The multifunctional waste bin is equipped with smart sensors and a wireless connection, enabling real-time monitoring of waste levels and bin status. This information is transmitted to a dedicated mobile application or dashboard, providing users with valuable insights into waste generation patterns and the need for collection. The data collected can also be used to optimize wastecollection routes and improve overall waste management efficiency.中文回答：多功能垃圾桶，废物管理的综合解决方案。
空间顺序法英语作文
空间顺序法英语作文As an English writing method, spatial order is a powerful tool that helps writers organize their ideas and details in a clear and logical manner. 空间顺序法是一种有力的英语写作方法，可以帮助作家清晰而逻辑地组织他们的思想和细节。
By structuring the content based on physical space or location, writers can effectively guide readers through a journey of information and ideas. 通过根据物理空间或位置构建内容，作家可以有效地引导读者进行信息和思想之旅。
This approach is particularly useful in descriptive writing, where vivid details and sensory imagery can transport readers to different places and create a strong sense of presence. 这种方法在描写性写作中特别有用，生动的细节和感官形象可以将读者带到不同的地方，并创造出强烈的存在感。
For example, describing a bustling marketplace using spatial order can take readers from the entrance of the market to the various stalls selling goods, providing a vivid picture of the sights, sounds, andsmells. 例如，用空间顺序来描述熙熙攘攘的市场可以将读者从市场入口引导到各种出售商品的摊位，提供一个生动的画面，包括视觉、听觉和嗅觉。
变废为宝的逻辑思维
变废为宝的逻辑思维英文回答：Waste-to-value thinking is a mindset that seeks opportunities to transform waste materials into valuable resources. It involves identifying the potential uses of waste products and developing innovative solutions to convert them into usable forms. This approach promotes sustainability, environmental stewardship, and economic benefits.Waste-to-value thinking aligns with the principles of circular economy, where materials are continuously reused and recycled, minimizing waste generation and maximizing resource utilization. By embracing this mindset,individuals and organizations can explore various waste streams to extract value and create new products, materials, or energy sources.The process of waste-to-value thinking begins withwaste characterization, which involves understanding the composition and properties of the waste material. This information helps identify potential uses and determine the most appropriate transformation technologies. Innovative approaches, such as advanced sorting techniques, chemical or biological treatment, can be employed to separate and convert waste components into valuable resources.Waste-to-value thinking also requires a multi-disciplinary approach that combines expertise in engineering, chemistry, biology, and economics. Collaboration between researchers, industry professionals, and policymakers is crucial to develop and implement sustainable waste-to-value solutions.Examples of waste-to-value transformations include converting organic waste into biofuels or compost,recycling plastics into new plastic products, and recovering metals from electronic waste. These initiatives not only reduce waste disposal costs and environmental impacts but also create new economic opportunities and foster resource sustainability.中文回答：变废为宝的逻辑思维是一种寻求机会将废弃物料转化为宝贵资源的思维方式。
怎样平衡杂乱与有序英文作文
怎样平衡杂乱与有序英文作文Balancing Chaos and Order in Our Lives.Life is a dynamic canvas where chaos and order coexist, often dancing a delicate duet. The art of living lies in finding the harmonious balance between the two, allowing us to navigate the unpredictability of daily life with ease and purpose.Chaos, often associated with disorder and randomness,is an inevitable aspect of existence. It manifests in the unexpected twists and turns of our daily lives, the spontaneity of human emotions, and the constant flux of the natural world. Chaos brings excitement, creativity, and the potential for growth. It is the engine of innovation, driving us to explore new territories and push the boundaries of possibility.On the other hand, order brings stability, predictability, and security. It is the foundation ofsociety, the glue that binds us together in communities and institutions. Order ensures that our basic needs are met, our daily routines are followed, and our goals are achieved with efficiency and precision.However, when order dominates, it can stifle creativity and innovation. Rigidity and inflexibility can lead to stagnation and even regression. Conversely, too much chaos can lead to confusion, anxiety, and a lack of direction. The challenge lies in finding the right balance between the two.One way to achieve this balance is through the practice of mindfulness. Mindfulness involves being aware of our thoughts, feelings, and actions in the present moment. It allows us to observe and understand the chaos and order in our lives without being overwhelmed by them. By being mindful, we can identify patterns and trends, making informed decisions about when to embrace chaos and when to seek order.Another key to balancing chaos and order is developinga strong sense of self-discipline. Self-discipline allows us to set clear goals and boundaries, ensuring that wedon't get lost in the maelstrom of chaos. It helps us to prioritize our actions and allocate our resources effectively, enabling us to achieve our goals with maximum efficiency.Moreover, embracing a growth mindset is crucial. A growth mindset encourages us to view challenges and setbacks as opportunities for growth and learning. It allows us to see chaos as a catalyst for innovation and creativity, rather than a hindrance to progress. By continuously seeking to improve ourselves, we can navigate the complexities of life with greater ease and resilience.In conclusion, balancing chaos and order is an ongoing process that requires constant attention and adjustment. It is about finding the right balance between spontaneity and predictability, creativity and stability, excitement and security. By cultivating mindfulness, self-discipline, and a growth mindset, we can navigate the challenges of lifewith greater ease and purpose, creating a rich and fulfilling existence.。
有关太空课堂的作文英语
Space classes,or space lessons,are an innovative educational concept that combines the excitement of space exploration with the traditional learning environment.These classes aim to inspire students to learn about science,technology,engineering,and mathematics STEM through interactive and immersive experiences.1.Introduction to Space Classes:Space classes are designed to take students beyond the confines of a regular classroom and into the vast expanse of the cosmos.They are often conducted in collaboration with space agencies,museums,or educational institutions that have access to spacerelated resources and experts.2.Curriculum and Learning Objectives:The curriculum in space classes typically revolves around the study of astronomy, physics,and the history of space exploration.The learning objectives may include understanding the basic principles of space travel,the technology used in spacecraft,and the scientific discoveries made by astronauts.3.Interactive Learning Experiences:Students in space classes often have the opportunity to participate in handson activities such as building model rockets,conducting experiments to understand the effects of zero gravity,and simulating space missions.These activities are designed to be both educational and engaging.4.Virtual Reality and Simulations:With the advancement of technology,virtual reality VR has become an integral part of space classes.Students can experience what its like to walk on the moon,explore the International Space Station,or pilot a spacecraft,all from the comfort of their classroom.5.Guest Lectures and Workshops:Experts in the field of space exploration,such as astronauts,engineers,and scientists, are often invited to give talks or conduct workshops.These sessions provide students with a firsthand account of what its like to work in the space industry and can be incredibly inspiring.6.Field Trips to SpaceRelated Facilities:Visits to space centers,observatories,or planetariums are common in space classes. These field trips allow students to see real spacecraft,learn about ongoing research,and observe celestial bodies through powerful telescopes.7.Importance of Space Education:The importance of space education cannot be overstated.It not only fosters a love for learning but also encourages students to consider careers in STEM fields.Moreover,it helps to develop critical thinking,problemsolving skills,and an appreciation for the universe we inhabit.8.Challenges and Solutions:While space classes offer numerous benefits,they also present challenges such as the need for specialized equipment,trained educators,and funding.Solutions may include partnerships with space agencies,grants for educational programs,and the use of affordable technology like VR headsets.9.Future of Space Classes:As technology continues to advance and space exploration becomes more accessible, the future of space classes looks promising.There is potential for even more immersive experiences,such as live feeds from space missions and the possibility of studentdesigned experiments being conducted in space.10.Conclusion:Space classes represent a forwardthinking approach to education that can captivate students imaginations and inspire them to learn about the universe.By combining traditional teaching methods with modern technology and realworld experiences,these classes have the potential to shape the next generation of scientists,engineers,and astronauts.In conclusion,space classes are a unique and effective way to educate students about the cosmos.They not only provide an engaging learning environment but also contribute to the development of a scientifically literate society that is prepared to explore and understand the universe.。
garbage sorting英语作文
garbage sorting英语作文The ubiquitous issue of garbage disposal has transcended mere inconvenience, evolving into a pressing environmental concern that demands immediate attention. As our insatiable consumption habits generate mountains of waste, the traditional "out of sight, out of mind" approach to trash has become woefully inadequate. The ramifications of our collective negligence are far-reaching, impacting the health of our planet and its inhabitants. Therefore, embracing the practice of garbage sorting emerges as an indispensable step towards mitigating the detrimentaleffects of our waste generation. One of the most compelling arguments for garbage sorting lies in its ability to facilitate recycling. By segregating recyclable materials such as paper, plastic, and glass, we create a streamlined process for these resources to be repurposed into new products. This not only conserves precious natural resources but also diminishes the strain on landfills, which are rapidly reaching their capacity in many parts of the world. Furthermore,recycling curtails the demand for virgin materials, thereby reducing the environmental footprint associated with extraction and processing. In essence, garbage sorting empowers us to close the loop on resource consumption, fostering a more sustainable and circular economy. Beyond its environmental merits, garbage sorting also yields substantial economic benefits. The recycling industry generates employment opportunities and stimulates economic growth. Moreover, by diverting waste from landfills, municipalities can save on disposal costs, freeing up funds for other essential public services. Additionally, the production of recycled materials often requires less energy than manufacturing from scratch, leading to lower production costs and ultimately, more affordable goods for consumers. In this way, garbage sorting presents a win-win scenario, promoting both environmental sustainability and economic prosperity. However, the successful implementation of garbage sorting hinges on effective public education and engagement. Many individuals remain unaware of the nuances of proper waste segregation or lack the motivation to participate actively. Therefore, comprehensive awareness campaigns are crucial to inform the public about the benefits of garbage sorting and to provide clear guidelines on how to sort waste correctly. Moreover, governments and local authorities must invest in convenientand accessible infrastructure, such as designated bins for different waste categories, to facilitate the sorting process. By fostering a culture of environmental responsibility and providing the necessary tools, we can empower individuals to become active participants in the solution. Of course, the issueof garbage sorting is not without its challenges. Contamination of recyclable materials with non-recyclables can render entire batches unusable, undermining the efficiency of the recycling process. To address this, clear labeling and consistent messaging are essential to prevent confusion and ensure proper sorting. Additionally, the economic viability of recycling certain materials can fluctuate depending on market conditions, posing challenges for the long-term sustainability of recycling programs. Therefore, ongoing research and development efforts are crucial to explore innovative recycling technologies and expand the range of materials that can be economically recycled. In conclusion, garbage sorting isnot merely a matter of environmental consciousness; it is an indispensablepractice that holds the key to a more sustainable future. By embracing garbage sorting, we can conserve natural resources, reduce pollution, mitigate climate change, and foster economic growth. While challenges remain, the potential rewards far outweigh the obstacles. Through collective action, public education, and continuous innovation, we can transform our throw-away culture into one of resourcefulness and responsibility, ensuring a healthier planet for generations to come.。
用空间法英语作文例子
用空间法英语作文例子Title: Exploring the Mysteries of Space。
Space, the final frontier, has always intrigued humanity with its vastness and mysteries. From thetwinkling stars to the enigmatic black holes, the cosmos beckons us to explore its depths. In this essay, we will delve into the wonders of space using the English language.Firstly, let us ponder the sheer magnitude of space. The universe spans billions of light-years, with countless galaxies, each containing billions of stars. The enormity of space is both humbling and awe-inspiring. Imagine gazing up at the night sky, contemplating the countless worlds beyond our own.One of the most fascinating aspects of space exploration is the search for extraterrestrial life. Are we alone in the universe, or are there other intelligent beings out there? Scientists have been scanning the cosmosfor signs of life, listening for signals from distant civilizations. While we have yet to make contact with aliens, the quest continues, fueled by curiosity and the desire to unravel the mysteries of the universe.Space exploration also offers practical benefits for humanity. Satellites orbiting the Earth provide vital data for weather forecasting, communication, and navigation. Space technology has led to advancements in medicine, materials science, and environmental monitoring. Moreover, the exploration of space fosters international collaboration, bringing together nations in pursuit of shared goals.However, space exploration is not without its challenges. The vast distances involved pose logistical hurdles, requiring advanced propulsion systems and long-duration space travel. Astronauts face numerous health risks, from radiation exposure to muscle atrophy, during extended missions in space. Furthermore, the cost of space exploration is substantial, requiring significant investment of resources and expertise.Despite these challenges, the benefits of space exploration are undeniable. The quest to understand the cosmos expands our knowledge of the universe and inspires future generations of scientists and explorers. Space exploration fuels technological innovation, driving progress in fields ranging from robotics to renewable energy.In conclusion, space exploration is a journey of discovery, pushing the boundaries of human knowledge and imagination. From the distant stars to the far reaches of the galaxy, the wonders of space await our exploration. Through international collaboration and scientific inquiry, we continue to unravel the mysteries of the cosmos, one discovery at a time.As we gaze up at the night sky, let us marvel at the beauty and complexity of the universe, knowing that the journey of exploration has only just begun.。
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The k-prefixes of an i-trace t are the traces that are formed by sequences which correspond to the first k reversals of the elements of t. The previous 4-trace has two 3-prefixes (3-traces): {1, 2, 4} {1, 3, 4} {2, 3, 4} {1, 2, 4} {1, 3, 4} {3} {1, 2, 4} {3} {1, 3, 4} {3} {1, 2, 4} {1, 3, 4}
- Given a permutation π, calculating d(π) and finding one optimal solution for π can be computed in polynomial time (Hannenhalli and Pevzner, 1995) - Several other approaches find one optimal solution...
(identity permutation)
ρ1 ρ2 ρ3 ρ4
Sorting by reversals (2)
- d(π) is the reversal distance for a permutation π (the minimum number of reversals required to sort π)
Traces (2)
Introduction
ISBRA 2007 Marília D. V. Braga
Two reversals ρ and θ commute if they are disjoint sets or if one is a subset of the other. Examples: {1,3,4} and {2,5} commute {1,3,4} and {3} commute {1,2,4} and {1,3,4} do not commute
Sorting by reversals (1)
Introduction
ISBRA 2007 Marília D. V. Braga
- A signed permutation π represents a genome (each value represents a marker and its orientation; duplications are not allowed) - Only reversal operations are considered (a reversal ρ reverts the order and orientation of the values in an interval of the permutation) - Example: Sorting the permutation π = (-3, +2, +1, -4): ( -3, +2, +1, -4) ( -3, +4, -1, -2) (+1, -4, +3, -2) (+1, +2, -3, +4) (+1, +2, +3, +4) ρ1 = {1, 2, 4} ρ2 = {1, 3, 4} ρ3 = {2, 3, 4} ρ4 = {3}
Introduction
ISBRA 2007 Marília D.V. Braga
- A sequence S of reversals which sorts π is an optimal solution for π if |S| = d(π). In the previous example, the sorting sequence of reversals S = {1, 2, 4} {1, 3, 4} {2, 3, 4} {3} is an optimal solution for π = (-3, +2, +1, -4)
If two reversals ρ and θ commute, then any optimal sequence of reversals containing ρθ as a substring is equivalent to the same sequence, replacing ρθ by θρ {1, 2, 4} {1, 3, 4} {3} {2, 3, 4} is equivalent to {1, 2, 4} {3} {1, 3, 4} {2, 3, 4} A trace is a set of optimal sequences which are all equivalent under the transitive closure of this commuting relation.
ISBRA 2007 Marília D. V. Braga
Identify all parsimonious scenarios of rearrangement restricted to reversal events (sorting by reversals) (a reversal reverts the order and orientation of the genes in an interval of the genome)
University of Lyon (France)
INRIA / CNRS / Program Alßan
Motivation
Genome rearrangement studies: when comparing the contents of two different genomes, try to identify the mutation events (reversals, insertions, deletions, transpositions...) that have transformed one genome into the other.
i-traces
and
prefixes
The algorithm
ISBRA 2007 Marília D. V. Braga
All elements of a trace have the same number of reversals. We call i-trace a trace which elements have i reversals. Example of a 4-trace (each element has 4 reversals): {1, 2, 4} {1, 3, 4} {2, 3, 4} {3} {1, 2, 4} {1, 3, 4} {3} {2, 3, 4} {1, 2, 4} {3} {1, 3, 4} {2, 3, 4} {3} {1, 2, 4} {1, 3, 4} {2, 3, 4}
Traces (1)
Bergeron et al (2002): - Many optimal solutions are equivalent {1, 2, 4} {1, 3, 4} {2, 3, 4} {3} {1, 2, 4} {1, 3, 4} {3} {2, 3, 4} {1, 2, 4} {3} {1, 3, 4} {2, 3, 4} {3} {1, 2, 4} {1, 3, 4} {2, 3, 4}
π = (-3, +2, +1, -4) d = 4 ; s = 28 π = (-6, +5, +7, -1, -4, +3, +2) d = 6 ; s = 496 π = (-4, +1, -3, +6, -7, -5, +2) d = 6 ; s = 204 π = (-4, -3, +12, -11, -8, +10, +9, +7, -6, -5, +2, -1) d = 8 ; s = 31 752
(a 3-trace with only one element) (a 3-trace with three elements) [ The size (number of elements) of the 4-trace is the sum of the sizes of its 3-prefixes ]
The solution space (1)
Introduction
ISBRA 2007 Marília D. V. Braga
- The number of optimal solutions for the sorting by reversals problem is usually huge - Some examples:
The solution space (2)
Introduction
ISBRA 2007 Marília D. V. Braga
Siepel (2003) proposed an algorithm that gives all optimal next reversals for a given permutation π. Example: For (-3, +2, +1, -4), the possible next reversals are {1}, {1,2,3}, {2}, {3}, {1,2,4}, {4} After aplying {1,2,4} to (-3, +2, +1, -4), we obtain (-3, +4, -1, -2), for which the possible next reversals are {3}, {1,3,4} This algorithm allows the enumeration of all existing optimal solutions for π. (but the number of optimal solutions for the sorting by reversals problem is usually huge)