Correlation functions between monopoles and instantons

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外源性磷输入改变农业河岸带湿地中土壤溶解有机碳的复杂性

Exogenous phosphorus inputs alter complexity of soil-dissolved organic carbon in agricultural riparianwetlandsMeng Liu a ,Zhijian Zhang a ,⇑,Qiang He b ,Hang Wang a ,Xia Li a ,Jonathan Schoer caCollege of Natural Resource and Environmental Sciences,China Academy of West Region Development,ZheJiang University,Yuhangtang Avenue 866,HangZhou,ZheJiang Province 310058,China bDepartment of Civil and Environmental Engineering,University of Tennessee,Knoxville,TN 37996-2010,USA cDepartment of Chemistry,Valparaiso University,Valparaiso,IN 46383,USAh i g h l i g h t sExternal P input stimulated the production of sediment active C fractions.External P input decreased DOC humicity and increased its microbial-derived sources. Sediments with gradient P loading rate had a blue shift of ﬂuorescence ﬁngerprint. Spectra measurements were helpful for describing sediment DOC composition.a r t i c l e i n f o Article history:Received 29June 2013Received in revised form 23September 2013Accepted 25September 2013Available online 30October 2013Keywords:Dissolved organic carbon (DOC)Phosphorous (P)Riparian wetlandsStructural compositiona b s t r a c tHigh-strengthened farmland fertilization leads to mass inputs of nutrients and elements to agricultural riparian wetlands.The dissolved organic carbon (DOC)of such wetland sediments is an important inter-mediate in global carbon (C)cycling due to its role in connecting soil C pools with atmospheric CO 2.But the impact of phosphorus (P)on sediment DOC is still largely unknown,despite increasing investigations to emphasize P interception by riparian wetlands.Here,we simulated the temporal inﬂuences of exoge-nous P on sediment DOC of riparian wetlands by integrating gradient P loading at rates of 0%,5%,10%,20%,30%,and 60%relative to the initial total phosphorus content of the sediment with the purpose of illustrating the role of external P on the complexity of soil DOC in terms of its amount and composition.After incubating for nine months,a dramatic linear correlation between Olsen-P and ﬂuorescent and ultraviolet spectral indices considered DOC skeleton was observed.Together with a more microbial-derived origin of DOC and a reduction of DOC aromaticity or humicity,the excitation-emission matrix had shown a blue shift reﬂecting a trend towards a simpler molecular structure of sediment DOC after P addition.Meanwhile,the content of soil DOC and its ratio with total organic carbon (TOC)were also increased by P loading,coupled with enhanced values of highly labile organic carbon and two C-related enzymes.While TOC and recalcitrant organic carbon decreased signiﬁcantly.Such implications of DOC amounts and composition stimulated by external P loading may enhance its bioavailability,thereby inducing an accelerated effect on soil C cycling and a potential C loss in response to global climate change.Ó2013Elsevier Ltd.All rights reserved.1.IntroductionSince the 1980s,as agricultural activity has intensiﬁed signiﬁ-cantly in Eastern China,the extensive application of fertilizers to farmlands and production of livestock manure have led to great phosphorus (P)loss from agricultural areas to adjacent ecosystems (Zhang and Shan,2008).Enhanced levels of P not only have led to great eutrophication with characteristic algal blooms (Roberts et al.,2012),but have also impacted the ecological remediationand resilience of such aquatic ecosystems (Jeppesen et al.,2005;Wang et al.,2013).For this particular purpose,many riparian wet-lands have been arranged in agricultural catchments in use world-wide to reduce the concentration of nutrients in through-ﬂowing water and improve water quality (Verhoeven et al.,2006;Hoff-mann et al.,2009).Currently,total phosphorus (TP)content in riparian wetland sediment located in the southern region of the Taihu Basin has reached 169–1200mg kg À1after interception (Wang et al.,2010).Some researchers have found the decomposi-tion of longer-term or mineral-associated soil carbon (C)fractions and soil organic C sink strengths could be enhanced by P availability (Mack et al.,2004;Cleveland and Townsend,2006;0045-6535/$-see front matter Ó2013Elsevier Ltd.All rights reserved./10.1016/j.chemosphere.2013.09.117Corresponding author.Tel.:+8657186971854;fax:+8657186971719.E-mail addresses:zhangzhijian@ (Z.Zhang),qhe2@ (Q.He).Bradford et al.,2008).Other authors pointed out that undesired ef-fects such as additional risks for global warming may be induced as a result of nutrients overloading wetland sediment(Verhoeven et al.,2006;Zhang et al.,2012;Wang et al.,2013).However,the is-sue of sediment P accumulation on the sediment C pool has at-tracted less attention during past years,while policymakers mostly focus on the interception of P in riparian wetlands.Global warming signiﬁcantly correlates to CO2loss from soils and creates a feedback to oceanic and land ecosystems(Cox et al.,2011).In soils,dissolved organic carbon(DOC),as the impor-tant fraction in the active soil organic C pool(Song et al.,2012), intimately correlates with CO2evolution from soil although DOC makes up only a small portion of total soil organic matter(Fang and Moncrieff,2005;Bengtson and Bengtsson,2007;Zhao et al., 2008).Meanwhile,soil DOC not only contains both substrates and end products of enzymatic reactions of varying molecular weight,but also constitutes the most bioavailable moiety for soil microorganisms(Song et al.,2012).Some researchers have also found that soil microbial respiration is signiﬁcantly limited by large differences in the complexity of DOC(Fang and Moncrieff, 2005).Moreover,the microbial degradability of DOC and,there-fore,the relationship with C mineralization from soils may also be affected by its composition(Zhao et al.,2008),although not al-ways linearly dependent in amounts(Liu et al.,2012).The features of the DOC skeleton,particularly percent aromaticity,degree of structural conjugation,and humicity(Johnson et al.,2011;Guo et al.,2013),are of fundamental signiﬁcance to indicating the retention or out-gassing processes for soil C pools(Wilson and Xenopoulos,2008).For instance,aromatic compounds probably derived from lignin are stable components,whereas carbohydrates are preferentially respired(Kalbitz et al.,2003).Thus,connecting DOC content variance with its structural complexity would better reﬂect the status and bioavailability of the soil C pool and its fur-ther retention.Among analytical characterization methods,the ra-pid,non-destructive,cost-effective,and informative density nature ofﬂuorescence spectroscopy(Guo et al.,2013)is well suited to provide informative data on the aromatic content and humicity of DOC,speciﬁc locations of differentﬂuorophores,andﬂuorescent characteristics of structure,functional group,conﬁguration,heter-ogeneity,and molecular dynamics,which gives information about DOC composition(Fellman et al.,2008;Johnson et al.,2011;Guo et al.,2013).In soils,environmental factors such as climate(tem-perature,precipitation)and vegetation,or anthropic disturbances such as land-use,acidiﬁcation,tillage,and application of fertilizer, may affect the DOC amount and composition indirectly via micro-bial consumption and lysis(Hishi et al.,2004;Jinbo et al.,2006). However,until recently,few studies have focused on the impacts of external P amendment on DOC of agricultural riparian wetland sediment,both in amount and composition,and thus the underly-ing mechanisms are largely unknown.Obviously,it is important to investigate the impact of P addition on wetland sediment DOC amounts,as well as its composition in agricultural areas.In this study,we designed a simulative experi-ment to illustrate the complex status of DOC by conducting labora-tory-scale incubation with P addition at rates of0%(P-0),5%(P-5), 10%(P-10),20%(P-20),30%(P-30),and60%(P-60)relative to the initial TP content of the sediment(0.29g kgÀ1;Supplementary Information,SI-1).Fluorescent and ultraviolet(UV)spectral mea-surements directly describe the effect on soil DOC composition. Moreover,the use of chemical or biochemical tests,with respect to their relationships withﬂuorescent and UV indices,gives in-sights into the complexity and biological degradability of soil DOC under disturbance of P inputs will be discussed.Further,we hypothesize that P loading could induce the variance of sediment DOC amount and composition to that of a simpler molecular struc-ture and enhance the bioavailability of soil DOC,thereby leading to a weakening effect on potential retention processes of soil C pool and accelerate soil C cycling in response to climate changes.2.Material and methods2.1.Site description and experimental designsRiparian wetland soil samples for this study were collected from the Southwest part of the Taihu Lake Basin(30°18051.8400N and119°54013.3700E).This area is one of the most productive and intensively farmed agricultural areas in the downstream delta re-gion of the Yangtze River in Southeast China.This region possesses a subtropical monsoon climate with an average summer tempera-ture of28°C and an average annual rainfall of1550mm.The most common agricultural land uses in this area include riceﬁelds,veg-etable gardens,aquaculture,and swine farms.During the pastﬁve years,the annual soil P application rate has been30–85kg haÀ1-yrÀ1.In order to best proﬁle the impact of exogenous P on soil DOC features,sediment was selected from a site(pH7.24;mois-ture57%)that contained a relatively low initial TP concentration of0.29g kgÀ1,compared to other similar wetland sediments in this region(0.17–1.20g kgÀ1of TP)(Wang et al.,2010).An average water depth around this particular sampling riparian wetland was1.4m with macrophyte plants on bank,and there was no arti-ﬁcial channel existing nearby this natural isolated pond.The or-ganic C of this riparian wetland stored in the sediment and no other C inputs in this region,and the basic properties of the wet-land sediment were provided in Table2.The sediment samples were collected using a lab-made stain-less steel sampler at a depth of0–10cm from20different points. Samples were wiped clear of macro-particles and transported on ice to the lab within3h after collection.Plastic barrels(35cm diameterÂ35cm height)wereﬁlled with8kg of mixed wet soil (5kg dry weight)to a depth of20cm.Water-soluble superphos-phate(CaP2H4O8)was chosen to be the external P in our study, which was recognized by Justus Liebig as P-related fertilizer and applied widely to agricultural production(Brunner,2010).Super-phosphate of different mass was dissolved with deionized water, then the mixed solution was added to those soil-ﬁlled barrels homogeneously with a spray without disturbing soil cores,of which TP concentration accounted for0%(P-0),5%(P-5),10% (P-10),20%(P-20),30%(P-30),and60%(P-60)relative to the initial sediment TP content.See supplementary information(SI-1)for the rationale for selecting the spiking levels of P in the sediment sam-ples.After several minutes,all the samples were covered with a 10cm layer of deionized water and were incubated in the labora-tory.To avoid the growth of aquatic plants and disturbance from other environmental factors,the barrels were placed in lab with dam-board to keep the samples in the dark at room temperature (20–25°C)for the nine months incubation.Deionized water was replenished every three months to maintain the liquid depth.Trip-licates of each sample were prepared.2.2.Soil samplingSoil samples for multifarious analyses were collected after incu-bating them for nine months.Each barrel was divided into four sub-barrels to minimize edge effects for grab-sampling.The soil samples for each barrel consisted of four composited2cm diame-terÂ10cm deep cores.50g fresh soil was collected from each bar-rel and then divided into two aliquots.One aliquot was stored at 4°C in the dark for microbial biomass and enzyme studies while the other was air-dried and ground to pass through a1mm mesh sieve for subsequent chemical analyses and spectral measurements.M.Liu et al./Chemosphere95(2014)572–5805732.3.Analytical methods2.3.1.Spectral measurementsBased on reported methods(Wilson and Xenopoulos,2008;Guo et al.,2013),the Solutions for UV andﬂuorescence measurements to determine DOC structure were prepared by water extraction of the air-dried and sieved(100mesh sieves)soil in a1:5w/w ratio to Milli-Q water,then shaking for4h at room temperature.Extracts were centrifuged at7000rpm(Hitachi Inc.,CR22G,Japan)for 10min at4°C andﬁltered through a0.45l m membraneﬁlter. The quantity of DOC in the extract was measured with a total or-ganic carbon(TOC)analyzer(Shimadzu Inc.,TOC-VCHP,Japan).Four UV andﬂuorescence–related indices were determined in this study:ﬂuorescence index(FI),humiﬁcation index(HI),fresh-ness index(b/a),and speciﬁc UV absorbance at280nm(E280).De-tails about the determination of these indices are provided in the supplementary information(SI-2).Brieﬂy,FI,b/a,and HI were determined using aﬂuorescence spectrophotometer(Hitachi Inc., F-4500,Japan).While E280was determined using a UV scanning spectrophotometer(Shimadzu Inc.,UV-2550,Japan).Milli-Q high-purity water was used as the reference for all measurements. Spectralﬂuorometric3D excitation-emission matrix(EEM)mea-surements were obtained for excitation wavelengths from200to 400nm and at emission wavelengths from300to600nm at 5nm increments as previously described(Wilson and Xenopoulos, 2008).Data analysis was then performed using an in-house pro-gram SigmaPlot12.0.2.3.2.Chemical and biochemical analysisMeasurements of sediment TOC,DOC,TP,and available P(pH 8.5,0.5mol LÀ1NaHCO3extractable P,i.e.,Olsen-P)were con-ducted according to standard methods of physicochemical analysis (ISSCAS,1978;Westerman,1990).Due to the susceptibility of or-ganic C to KMnO4oxidation,the contents of three fractions of labile organic components in soil samples,namely highly labile organic carbon(HLOC),mid-labile organic carbon(MLOC),and labile or-ganic carbon(LOC),were determined using33,167,and 333mmol LÀ1KMnO4,respectively(Loginow et al.,1987).Recalci-trant organic carbon(ROC)was calculated as the difference be-tween these three labile C forms and the TOC.Soil microbial biomass C(MBC)and P(MBP)were determined by the chloroform fumigation extraction method(Inubushi et al.,1991).Moist soil samples were split into two subsamples with one immediately ex-tracted with either0.5mol LÀ1K2SO4for MBC or0.5mol LÀ1 NaHCO3for MBP,while the other was fumigated with chloroform and then extracted.Following centrifugation,C and P concentra-tions of soil microbial biomass were calculated from the difference between the fumigated and non-fumigated soil samples.2.3.3.Enzyme analysisThree eco-enzymes,b-1,4-glucosidase(BG),cellobiohydrolase (CBH),and acid phosphatase(AP)(Sinsabaugh et al.,2009)were se-lected as indicators of microbial nutrient demand in the C and P cy-cles,respectively.Sample suspensions were prepared by using a vortex mixer for1min to homogenize1g(wet weight)of soil with 125mL of50mmol LÀ1sodium acetate buffer(pH6.0to match the mean soil pH of the environmental samples).Sample suspensions, buffer,references,and substrates(the substrate solutions for BG, CBH and AP are4-MUB-b-D-glucoside,4-MUB-b-D-cellobioside, and4-MUB-phosphate,respectively)were pipetted into96-well blankﬂuorescent plates(Corning Inc.,costar3603,USA)following the strict order and position on the well plate according to the work of Saiya-Cork(Saiya-Cork et al.,2002).The micro-plates were covered and incubated in the dark at20°C for4h.Then,10l L of 1.0mol LÀ1NaOH was added to each well to stop the reaction and increase theﬂuorescence of residual substrates.Finally,standard high-throughputﬂuorometric detection of the enzyme assays were carried out using a Bio-Tek Synergy HT microplate reader(Bio-Tek Inc.,Winooski,VT,USA)with365nm excitation and460nm emissionﬁlters(Saiya-Cork et al.,2002).Enzyme activities were calculated and expressed as nmol hÀ1gÀ1(Sinsab-augh et al.,2008).2.4.Statistical analysisData were tested for homogeneity of group variances using the Pearson test.Data were square root transformed if necessary.The data were analyzed by analysis of variance using SPSS16.0statis-tical software.For the enzymes analysis,each data point was char-acterized by a response ratio(RR)and the log of the response ratio (L RR).RR was calculated as the mean of the experimental samples divided by the mean of the control samples(sample P-0)to provide an index of response magnitudes,while L RR was calculated as the log10of RR.The use of L RR is preferred over the use of RR because it equally weighs the negative and positive responses and facili-tates statistical analysis(Marklein and Houlton,2012).Positive values of L RR represented an increase in enzyme activity relative to the control sample,whereas negative values indicated sup-pressed activity.Before analysis,each class was summarized by the weighted mean of L RR(LÃRR).3.Results3.1.Structural complexity of soil DOC under phosphorus loadingSpectral analysis showed that P input was an excellent factor for soil DOC composition of the riparian wetlands(Table1).FI in soil solutions was raised from P-0to P-60by a range of0.65%to a max-imum6.5%.Meanwhile,the ratio of b/a was observed to follow the same trend as FI,with an increment of21–64%.As to aromatic sub-strate,E280and HI were reduced in all P loading samples by a fac-tor of3–12%and12–47%,respectively.Moreover,we found that all spectral indices changed signiﬁcantly with P availability.Brieﬂy,FI and b/a correlated positively with Olsen-P content(Fig.1A and C; p<0.05),but the relationship with respect to HI was negative (Fig.1D;p<0.05),while there existed a less linear correlation with E280(Fig.1B).Two remarkableﬂuorophores in3D EEMs were revealed from the tested six treatments:one at Ex/Em280–320/ 400–450nm and another at Ex/Em210–240/395–450nm(Fig.2). Usually,the peak at longer wavelengths was recognized as the humic-likeﬂuorescence peak C in the UV region,while the other was determined to be the humic-like peak A in the visible region (Klotzbücher et al.,2012).Compared to humic-likeﬂuorophores reported in Fig.2,a clear blue shift about the positions of the ﬂuorophores both in the visible and UV region was observed with the increment of P loading,displaying a trend towards shorterTable1Spectral parameters of sediment dissolved organic carbon(DOC)in the tested samples,namelyﬂuorescence index(FI),humiﬁcation index(HI),UV absorption at 280nm(E280),and freshness index(b/a).Treatment FI E280b/a HIP-0 1.53±0.05b0.63±0.08ab0.91±0.07cd0.48±0.01a P-5 1.54±0.01b0.64±0.03a0.88±0.08d0.42±0.01b P-10 1.56±0.02ab0.61±0.03ab0.90±0.03cd0.40±0.03b P-20 1.59±0.03ab0.56±0.01ab 1.00±0.06c0.32±0.01c P-30 1.59±0.05ab0.55±0.03b 1.31±0.02b0.22±0.01d P-60 1.63±0.07a0.57±0.02ab 1.49±0.03a0.22±0.01d Values in parentheses are standard deviations.Different letters listed beside the data represent signiﬁcant differences at p<0.05 (Duncan test,One-way ANOVA).574M.Liu et al./Chemosphere95(2014)572–580wavelengths(black line)relative to the maximum emission of the humic-like peak which moved towards to the left side of the emis-sion axis(Fig.2).3.2.Overall C-P features and enzyme activities under P loadingThe data calculated from the mean value of three tested soils for each sampling pot(Table2)showed that soil TOC content de-creased about12–18%relative to each sample without P amend-ment.Meanwhile,DOC content increased by a factor of0.7–25.5%,as did the ratio of DOC/TOC with the incremental addition of P(Fig.3C).Soil TP and Olsen-P were signiﬁcantly increased with the rate of P application.Remarkable increases were also found for MBC and MBP by a rate of22–50%and5–54%,respectively.The ratio of HLOC/TOC followed the enhanced tendency of soil MBC compared to blank treatment(Fig.3A),while the ROC/TOC ratio was found to decrease with the rate of P addition(Fig.3B).As summarized in Table3,the activities of both soil BG and CBH were stimulated consistently with P amendment.The RR of BG ranged by a factor of31–62%;at the same time an increment of 14–19%was found for CBH.The positive weighted mean of L RR illustrated an enhancement effect on the activities of these two C-related enzymes induced by external P loading.P amendment depressed AP activity due to all weighted means of L RR about AP, which showed negative values reduced by16–43%,except for P-5.3.3.Pearson correlation for soil chemical or biochemical properties in relation to soil DOC characteristicsPearson correlation analysis showed that soil chemical or bio-chemical properties had a strongly signiﬁcant correlation with1.Relationships between spectral parameters and Olsen-P after incubation.Shown are selected univariate linear regressions with the highestthe structure of soil DOC(Table4).Both TP and Olsen-P greatly promoted the change of DOC composition,considering its signiﬁ-cantly positive relationship with b/a,FI,and HI values(p<0.05).Moreover,the DOC composition intimately correlated with soil C-related features.For example,FI and b/a correlated positively to soil DOC,MBC,HLOC/TOC,DOC/TOC,and C-relatedenzymes,but negatively to the ROC/TOC ratio (p <0.05),while HI positively correlated with the ROC/TOC ratio (p <0.01),but negatively to MBC,DOC,and C-related enzymes (p <0.05).4.Discussion4.1.Structural complexity of soil DOC under external P loading The characteristics of soil DOC composition are quite different from one another in gradient P input treatments.High FI and b /a values for P amendment samples represent a ‘‘ﬁrst ﬂush’’of predominant microbial-derived sources that builds up soil DOC (Table 1)with an intimate correlation with soil DOC content and DOC/TOC ratio (Table 4;p <0.05).This increase is consistent with standard interpretation of FI values,where higher values are representative of microbial decomposition of soil C and most labile C sources have already been microbially acquired (Wilson and Xenopoulos,2008;Johnson et al.,2011).Some authors have re-ported that P availability is one of the limiting factors for microbial growth (Ahn et al.,2007).Thus,the input of external P can be responsible for the enrichment of microbial-derived origins in soil DOC (Table 4;p <0.05),which is supported by the signiﬁcant linear correlation between Olsen-P and FI,as well as b /a (Fig.1A and C;p <0.05),illustrating an enhanced function of autochthonous pro-duction of soil DOC of a simpler molecular structure as well as microorganism activities after gradient P irrigation.At the same time,the humicity of soil DOC intimately correlated with soil TP content (Table 4;p <0.05)and showed a negative linear relation-ship with available P (Fig.1D;p <0.05).HI,related to the degree of condensation or conjugation (Klotzbücher et al.,2012;GuoTable 3Eco-enzymes as indicators of microbial nutrient demand in the cycles of sediment carbon (C)and phosphorus (P)respectively:b -1,4-glucosidase,acid phosphate and cellobiohydrolase in the tested sediment.TreatmentAcid phosphatase b -1,4-glucosidase Cellobiohydrolase RRL ÃRR ±ClRR L ÃRR ±Cl RR L ÃRR ±Cl P-5 1.000.002±0.013a 1.090.036±0.008c 1.360.128±0.078b P-100.83À0.082±0.005b 1.310.116±0.047b 1.340.122±0.094b P-200.84À0.076±0.015b 1.570.196±0.031a 1.590.201±0.012a P-300.63À0.201±0.020c 1.660.220±0.037a 1.560.191±0.049a P-600.57À0.247±0.014d1.770.247±0.039a1.620.209±0.047aR,the response ratio;L ÃRR ,the weighted mean;Cl,95%conﬁdence interval.Values in parentheses are standard deviations.Different letters listed beside the data represent signiﬁcant differences at p <0.05(Duncan test,One-way ANOVA).et al.,2013),was signiﬁcantly smaller in the sample with the high-est P loading rate(Table1),characterized by the lowest ROC/TOC ratio(Fig.3B),and showed a positive relationship with the refrac-tory moiety(Table4;p<0.01).The same tendency is deduced for E280from UV absorbance(Table1),but without much linear sig-niﬁcance to Olsen-P(Fig.1B).The decreased HI and E280values (Table1)indicate that soil DOC contains less aromatic compounds as gradient rates of P loading increases,which further veriﬁes selective removal of aromatic structures with a shift towards less aromatic precursors induced by external P.A clearer trend,considered qualitative information of soil DOC composition,induced by P loading is displayed by3D EEMs (Fig.2).Previous studies have demonstrated that the humic-like component or aromatic C content is negatively correlated with bio-degradation of DOC(Fellman et al.,2008;Hassouna et al.,2012), andﬂuorophores with long emission wavelengths are highly con-jugated and more aromatic in nature(Klotzbücher et al.,2012; Guo et al.,2013).Thus,as the black line shifted to the left side of the emission axis(Fig.2),the weakened humicﬂuorescence inten-sity indicated that addition of external P drives the transition of soil DOC composition to much more labile components with a sim-pler molecular structure and a lower degree of aromatic polycon-densation,which coincided with the data collected by spectral measurements(Table1).Since the molecular structure of organic material has long been thought to determine long-term decompo-sition rates in soil humic substances(Schmidt et al.,2011),the re-duced degree of DOC humicity and aromaticity(Table1and Fig.1B)combined with enhanced microbial-derived production of soil DOC(Table1and Fig.1A and C)may weaken the chemical stability and residence time of soil organic C components(Zhao et al.,2008),thereby accelerating cycling of the soil C pool.4.2.Is the transition of sediment DOC composition harmful for the retention of wetland sediment C pools under P loading?Previous studies have demonstrated the importance of soil DOC composition to soil microbial respiration(Fang and Moncrieff, 2005)and C mineralization(Zhao et al.,2008).As mentioned above,P input is a signiﬁcant factor for the transition of soil DOC composition.Does this trend towards simpler structural complex-ity of soil DOC increase the possibility of the loss of soil C fractions and have a bad impact on C sequestration at the same time?In order to test this hypothesis,soil C-P features and enzymology were examined synchronously after incubation for a better under-standing of the complexity of soil DOC subjected to P loading and its implications for the retention of wetland sediment C pools.As P does not have a signiﬁcant gaseous removal mechanism and therefore remains in the system to which it is added(Bostic et al.,2010),P loading to wetland systems results in a chemical gradient with P non-limiting conditions for microbial nutrient de-mand(Ahn et al.,2007)and mitigates the severity of P limitation to microbial biomass after enzymatic mineralization(Roberts et al., 2012).An obvious increase in content of MBC and MBP inﬁve treatments was observed under P addition(Table2)indicating that microbial utilization of C and P might simply be stimulated by add-ing P due to the greater availability of labile organic components (Fig.3A and C),which generally implies enhanced availability of substrates for microbial growth(Lipson and Schmidt,2004).The increased microbial biomass positively correlated to DOC origins of microbial-derivation and negatively to soil humicity(Table4; p<0.05),better indicating the enhanced bioavailability of soil DOC after P incubation.Meanwhile,the response of enzyme activ-ities has provided insight into organic matter decomposition and soil Cﬁxing(Sinsabaugh et al.,2008).The corresponding activities of C-related enzymes(BG and CBH)were signiﬁcantly stimulated after P amendment(Table3;L RR>0)due to increased DOC content (Table2and Fig.3C)since DOC contains both substrates and end products of enzymatic reactions of varying molecular weight(Bon-nett et al.,2006).In addition,enhanced DOC in soil results in en-riched substrate abundance for microbial metabolism and supports the synthesis of new enzymes(Song et al.,2012).BG and CBH are enzymes that contribute to the degradation of cellu-lose and other b-1,4glucans into glucose by deconstructing micro-bial cell walls and reducing macromolecules to soluble substrates for microbial assimilation(Sinsabaugh et al.,2008;Peoples and Koide,2012).Such mechanisms combined with the results of en-hanced microbial utilization of soil C(Table2)are highly respon-sive to changes in soil DOC composition.The Pearson analysis shown in Table4veriﬁes that the activities of BG were closely linked to FI and b/a(p<0.05),but negatively correlated to HI and E280(p<0.05),illustrating the decomposition of soil organic mat-ter(Sinsabaugh et al.,2008)induced by P addition.Moreover,we found an average decrease of12–18%in TOC(Ta-ble2)and a reduced ROC/TOC ratio(Fig.3B)after P addition. Although this data changes little supported by the statistic analysis among the six treatments,but we can certainly predict a loss of sediment organic carbon since a more stable stage of the carbon pool appears due to the activities of microorganism during the long-term incubation.The lowest TOC content and ROC/TOC ratio in P-60,along with the highest MBC content(Table2),DOC/TOC, HLOC/DOC(Fig.3A and C),and enzymatic values(Table3),may as-sert a loss of organic resources and metabolized organic material at faster rates due to microorganism growth and activities stimulated by external P loading.Similar changes in the soil C pool subjected to P amendment are supported by Bradford et al.,who demon-strated enzyme-catalyzed depolymerization induced by P inputs would increase decomposition of soil C fractions that constituted the longer-term C pool(Bradford et al.,2008).The refractory C components comprising the C pool in the sediment were decom-posed during incubation(Fig.3B),when other interfering C-im-ports such as aquatic plants and animals were excluded,which are revealed to be positively correlated with soil humicity (p<0.01)and negatively related to b/a(Table4;p<0.05).Since humiﬁcation has been deﬁned as the conversion of fresh organic matter inputs into more stabilized substances(Kirkby et al., 2013),the reduction of the refractory moiety(Fig.3B)and TOC fractions(Table2)in our study undoubtedly caused a loss in the soil C pool,which asserts an intimate relationship with soil DOCTable4Pearson correlation coefﬁcients between sediment chemical or biochemical proper-ties and sediment dissolved organic carbon(DOC)spectral characters responding toexogenous phosphorus(P)application of the riparian wetland.FI E280b/a HITOCÀ0.3950.318À0.802**0.804**DOC0.554*À0.4270.847**À0.830**MBC0.542*À0.485*0.551*À0.731**HLOC/TOC0.395À0.1790.717**À0.793**ROC/TOCÀ0.542*0.322À0.674**0.581*DOC/TOC0.514*À0.3900.902**À0.881**TP0.708**À0.3850.874**À0.824**Olsen-P0.580*À0.3910.864**À0.753**MBP0.736**À0.490*0.894**À0.805**APÀ0.628**0.529*À0.918**0.933**BG0.661**À0.632**0.819**À0.946**CBH0.478*À0.3720.545*À0.783**Sediment chemical or biochemical properties and DOC spectral characters aredimensionless.Pearson correlation coefﬁcients showed by correlation matrix.Thepositive data denotes positive correlation coefﬁcient,while the negative one rep-resents the opposite correlation coefﬁcient;the correlation increases with theabsolute numerical value.*p<0.05.**p<0.01.578M.Liu et al./Chemosphere95(2014)572–580。

Correlation

CorrelationXu JiajinNational Research Center for Foreign Language Education Beijing Foreign Studies University2Key points•Why correlation?•What is correlation analysis about?•How to make a correlation analysis?–Case studiesWhy Correlation?4Three things that stats can do •1.Summarizing univariate data •2.Testing the significance of differences •3.Exploring relationships b/t variables5Three things that stats can do •1.Summarizing univariate data •2.Testing the significance of differences •3.Exploring relationships b/t variables6探究事物之间的关联•植物的生长是否浇水的多少有关系，有多大关系•足球成绩好坏是否与身体（体质、人种）有关？•兴趣高、成绩好•元认知策略使用越多，学习进步越快•学好统计学有利于身体健康Key ides of correlationanalysis8•Correlation: co ‐relation . The co ‐relation is represented by a ‘correlation coefficient , r .•The range of the coefficient: ‐1to 1.•Three critical values: ‐1, 0and 1.Strength of correlationPositive correlation Strength of correlation Direction of correlationDirection of correlation Positive correlationDirection of correlation•Less Negative correlation12Two main types of correlation•Pearson : standard type, suitable for interval data (e.g. score, freq.)•Pearson r coefficient•Spearman : suitable for ordinal/rank data•Spearman rho coefficient13Significance•Similar to t ‐test and ANOVA statistics, the correlation coefficients need to be statistically significant.< .05Sig./P 值/alpha （α）值Coefficient of Determination r Ær2Æ% of variance explained15Coefficient of Determination •The squared correlation coefficient is called the coefficient of determination .•Multiplied by 100, this proportion of variance indicates the percentage of variance that is accounted for.•Correlation coefficients of .30 account for about 9% of the variance. Correlation of .70 explains about 49% of variance.Effect sizeCase Study 1Is connector use by Chinese EFL learners correlated with theirwriting quality?SPSS ProceduresAnalyze‐Correlate‐Bivariate1921Reporting correlations•In correlation tables/matrices •Embedded in textCorrelation tablesCorrelation tables(Dörnyei2007: 227)2324Embedded in text •As one would expect from the extensive literature documenting the benefits of intrinsic motivation, there was a significant positive correlation between overall GPA and intrinsic motivation (r = .34, p < .oo1).(Dörnyei 2007: 227)Practice: CET4 and CET6 Correlational analysisHomework英语成绩是否与语文成绩有相关性？28Wrap Up & Look Forward •Correlation coefficients provide a way to determine the strength & the direction of the relationship b/t two variables.•This index does not ... demonstrate a causal association b/t two variables.29Wrap Up & Look Forward •The coefficient of determination determines how much variance in one variable is explained by another variable.•Correlation coefficients are the precursors to the more sophisticated statistics involved in multiple regression (Urdan 2005: 87).30Thank you32。

详细介绍Spearman's correlation相关分析(英文)

The boxplot for Uranium is fairly consistent with one from a normal distribution; the median is fairly close to the centre of the box and the whiskers are of approximate equal length. The boxplot for TDS is slightly disturbing in that the median is close to the lower quartile and the lower whisker is shorter than the upper one, which would be suggesting positive skewness. Also there is an outlier and Pearson’s correlation is sensitive to these as well as skewness. Since we have some doubts over normality, we shall examine the skewness coefficients to see if there is further evidence to suggest whether either of the variables is skewed.
If your data does not meet the above assumptions then use Spearman’s rank correlation!
Monotonic function
To understand Spearman’s correlation it is necessary to know what a monotonic function is. A monotonic function is one that either never increases or never decreases as its independent variable increases. The following graphs illustrate monotonic functions:

decay of correlation 数学名词

decay of correlation 数学名词Decay of correlation（相关性的衰减）refers to the decrease in correlation between two variables as the distance between them increases. It is a mathematical concept used to quantify the relationship between two variables across different spatial or temporal distances.1. The decay of correlation between rainfall and crop yield was observed as the distance between the two fields increased.雨量与农作物产量之间的相关性随着两个田地之间的距离增加而减弱。

2. The study analyzed the decay of correlation between interest rates and stock market performance over a one-year timespan.该研究分析了利率和股市表现之间的相关性在一年的时间内是如何衰减的。

3. As the distance between two cities increased, thedecay of correlation between their population sizes became more noticeable.随着两个城市之间的距离增加，它们的人口规模之间的相关性衰减变得更加明显。

4. The researchers used statistical methods to determine the decay of correlation between air pollution andrespiratory diseases in different neighborhoods.研究人员使用统计方法来确定不同社区之间空气污染和呼吸道疾病之间的相关性衰减。

协方差

1
18.05 class 7, Covariance and Correlation, Spring 2014
2
2.2
Sums and integrals for computing covariance
Since covariance is deﬁned as an expected value we compute it in the usual way as a sum or integral. Discrete case: If X and Y have joint pmf p(xi , yj ) then
n m
n
m
p(xi , yj )xi yj − µX µY .CovFra bibliotekX, Y ) =
i=1 j =1
p(xi , yj )(xi − µX )(yj − µY ) =
i=1 j =1
Continuous case: If X and Y have joint pdf f (x, y ) over range [a, b] × [c, d] then
18.05 class 7, Covariance and Correlation, Spring 2014
3
So Cov(XY ) = E (XY ) − µX µY =
5 1 −1= . 4 4 Next we redo the computation of Cov(X, Y ) using the properties of covariance. As usual, let Xi be the result of the ith ﬂip, so Xi ∼ Bernoulli(0.5). We have X = X1 + X2 and Y = X2 + X3 . We know E (Xi ) = 1/2 and Var(Xi ) = 1/4. Therefore using Property 2 of covariance, we have Cov(X, Y ) = Cov(X1 +X2 , X2 +X3 ) = Cov(X1 , X2 )+Cov(X1 , X3 )+Cov(X2 , X2 )+Cov(X2 , X3 ). Since the diﬀerent tosses are independent we know Cov(X1 , X2 ) = Cov(X1 , X3 ) = Cov(X2 , X3 ) = 0. Looking at the expression for Cov(X, Y ) there is only one non-zero term Cov(X, Y ) = Cov(X2 , X2 ) = Var(X2 ) = 1 . 4

Correlations between zeros and supersymmetry

Date : November 19, 2000. Research partially supported by NSF grants #DMS-9970625 ( rst author), #DMS-9800479 (second author), #DMS-0071358(third author). 1
CORRELATIONS BETWEEN ZEROS AND SUPERSYMMETRY
PAVEL BLEHER, BERNARD SHIFFMAN, AND STEVE ZELDITCH
Abstract. In our previous work BSZ2], we proved that the correlation functions for simultaneous zeros of random generalized polynomials have universal scaling limits and we gave explicit formulas for pair correlations in codimensions 1 and 2. The purpose of this paper is to compute these universal limits in all dimensions and codimensions. First, we use a supersymmetry method to express the n-point correlations as Berezin integrals. Then we use the Wick method to give a closed formula for the limit pair correlation function for the point case in all dimensions.

《概率论与数理统计》基本名词中英文对照表

《概率论与数理统计》基本名词中英文比较表英文中文Probability theory 概率论mathematical statistics 数理统计deterministic phenomenon 确立性现象random phenomenon 随机现象sample space 样本空间random occurrence 随机事件fundamental event 基本领件certain event 必定事件impossible event 不行能事件random test 随机试验incompatible events 互不相容事件frequency 频次classical probabilistic model古典概型geometric probability 几何概率conditional probability 条件概率multiplication theorem 乘法定理Bayes's formula 贝叶斯公式Prior probability 先验概率Posterior probability 后验概率Independent events 互相独立事件Bernoulli trials 贝努利试验random variable 随机变量probability distribution 概率散布distribution function 散布函数discrete random variable 失散随机变量distribution law 散布律hypergeometric distribution 超几何散布random sampling model 随机抽样模型binomial distribution 二项散布Poisson distribution 泊松散布geometric distribution 几何散布probability density 概率密度continuous random variable 连续随机变量uniformly distribution 平均散布exponential distribution 指数散布numerical character 数字特点mathematical expectation 数学希望variance 方差moment 矩central moment 中心矩n-dimensional random variable n-维随机变量two-dimensional random variable 二维失散随机变量joint probability distribution 结合概率散布joint distribution law 结合散布律joint distribution function 结合散布函数boundary distribution law 边沿散布律boundary distribution function 边沿散布函数exponential distribution 二维指数散布continuous random variable 二维连续随机变量joint probability density 结合概率密度boundary probability density 边沿概率密度conditional distribution 条件散布conditional distribution law 条件散布律conditional probability density 条件概率密度covariance 协方差dependency coefficient 有关系数normal distribution 正态散布limit theorem 极限制理standard normal distribution 标准正态散布logarithmic normal distribution 对数正态散布covariance matrix 协方差矩阵central limit theorem 中心极限制理Chebyshev's inequality 切比雪夫不等式Bernoulli's law of large numbers 贝努利大数定律statistics 统计量simple random sample 简单随机样本sample distribution function 样本散布函数sample mean 样本均值sample variance 样本方差sample standard deviation 样本标准差sample covariance 样本协方差sample correlation coefficient 样真有关系数order statistics 次序统计量sample median 样本中位数sample fractiles 样本极差sampling distribution 抽样散布parameter estimation 参数预计estimator 预计量estimate value 预计值unbiased estimator 无偏预计unbiassedness 无偏性biased error 偏差mean square error 均方偏差relative efficient 相对有效性minimum variance 最小方差asymptotic unbiased estimator 渐近无偏预计量uniformly estimator 一致性预计量moment method of estimation 矩法预计maximum likelihood method of estimation极大似然预计法likelihood function 似然函数maximum likelihood estimator极大似然预计值interval estimation 区间预计hypothesis testing 假定查验statistical hypothesis 统计假定simple hypothesis简单假定composite hypothesis复合假定rejection region拒绝域acceptance domain接受域test statistics查验统计量linear regression analysis线性回归剖析。

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2. Theory. In order to investigate monopole currents one has to project SU(3) onto its abelian degrees of freedom, such that an abelian U(1) U(1) theory remains 5]. This aim can be achieved by various gauge xing procedures. We employ the so-called maximal abelian gauge which is most favorable for our purposes. After gauge xing pure QCD may be regarded as a theory of color charges and color magnetic monopoles. A gauge transformation of a gauge eld element U(x; ) is given by ~ U(x; ) = g(x)U(x; )gy (x + ^) ; (1) where g(x) 2 SU(3). The maximal abelian gauge is imposed by maximizing the functional X ~ (2) R = jUii (x; )j2:
We analyze the relation between instantons and abelian projected monopoles in both phases of pure QCD by calculating local correlation functions between topological charge densities and monopole densities. On an 83 4 lattice, it turns out that topological quantities are correlated approximately two lattice spacings. The monopole-instanton correlations are rather insensitive under cooling of gauge elds.
hep-lat/9510024 13 Oct 1995
1. Introduction. It is assumed that gauge eld con gurations with non-trivial topology can explain the low-energy properties of QCD and thus could provide a solution to the con nement problem. There are two di erent kinds of topological objects which seem to be important for the connement mechanism: color magnetic monopoles and instantons. Color magnetic monopoles play the essential role in the dual superconductor hypothesis 1]. In this picture con nement emerges by condensation of abelian monopoles via the dual Meissner e ect. There is strong evidence from lattice calculations that the idea of dual superconductivity is an adequate description of the con nement phenomenon. On the other hand the role of instantons with respect to con nement is not so clear. It is suggested that instantons can only cause con nement in QCD by forming a socalled instanton liquid 2]. A fascinating question is whether color magnetic monopoles and instantons are related or not. In a recent study we analyzed the distribution of the topological charge density and the monopole density around static color sources 3]. We observed that both topological quantities show qualitatively the same behavior, namely a suppression in the vicinity of the external sources. Motivated by this similarity we calculate local correlation functions between the monopole density and the topological charge density 4]. Results for the size of the correlations between topological objects are reported.
23@f (x+ ^;
)
x; ;i
i
mod 2
Supported in part by "Fonds zur Forderung der wissenschaftlichen Forschung" under Contract P9428-PHY.
2 where ui (2) denotes a product of abelian links ui (x; ) around a plaquette 2 and f(x + ^; ) is an elementary cube perpendicular to the direction with origin x + ^. The magnetic currents form closed loops on the dual lattice as a consequence of monopole current conservation. Finally the local monopole density is given by X (5) (x) = 3 1 4V4 ;i jmi (x; )j : For the implementation of the topological charge on the lattice there exists no unique discretization. In this work we restrict ourselves to the so-called eld theoretic de nitions which approximate the topological charge in the continuum 6] g2 q(x) = 32 2 Tr F (x)F (x) ; (6) in the following ways: 4 X 1 (P;H ) ~ Tr O(P;H ) ; (7) q (x) = 24 32 2 ;:::= 1 with O(P ) = U (x)U (x) ; (8) for the plaquette prescription and O(H ) = U(x; )U(x+^; )U(x+^+^; ) U(x+^ +^ +^; )U y(x+^ +^+^ ; ) U y(x+^+^ ; )U y(x+^ ; )U y(x; ); (9) for the hypercube prescription. The lattice and continuum versions of the theory represent di erent renormalized quantum eld theories, which di er from one another by nite, non-negligible renormalization factors 7]. A simple procedure that enables one to get rid of renormalization constants, while preserving physical information contained in lattice con gurations, is the cooling method. In our investigation we have employed the so-called \Cabbibo{Marinari method". To measure the correlations between topological quantities we calculate the functions hq(0)q(d)i ; hq2 (0)q2 (d)i ; h (0) (d)i ; h (0)q2 (d)i : (10) Since topological objects with opposite sign are equally distributed, we correlate the monopole density with the square of the topological charge density. 3. Results. Our simulations were performed on an 83 4 lattice with periodic boundary conditions using the Metropolis algorithm. The observables were studied in pure QCD with the plaquette action both in the con nement and decon nement phase at inverse gluon coupling = 6=g2 = 5:6 and 5:8, respectively. We made 50000 iterations and measurements were taken after every 50th iteration. Each of these 1000 congurations was rst cooled and then subjected to 300 gauge xing steps enforcing the maximal abelian gauge. The correlation functions between topological quantities according to Eq. (10) are shown in Fig. 1 for several cooling steps at = 5:6. They are normalized after the subtraction of their cluster values. The hypercube de nition is used for q. The range of the instanton auto-correlations qq and q2 q2 which are originally -peaked grows rapidly with cooling re ecting the occurance of extended instantons 8]. In contrast the correlation decreases since monopole loops become dilute with cooling. The q2 -correlation seems rather insensitive to cooling and clearly extends over more than two lattice spacings, indicating some non-trivial local correlation between monopoles and topological charges. Fig. 2 presents row q2 -correlations for the plaquette and the hypercube de nition of the topological charge density in the con nement (l.h.s.) and the decon nement phase (r.h.s.) for 6 and 11 cooling steps. The agreement between the two de nitions is almost perfect. The absolute value of the correlations is smaller in the decon nement phase since both instantons and monopoles become dilute. But there are practically no differences between the q2 -correlations in the two phases after normalization (not shown). This holds also for the other topological correlation functions. In Fig. 3 the sumP the squared topological of charge density K := x q2 (x) (hypercube de nition) is plotted against the number of monopoles P Nmon = x (x) for each con guratinctions between monopoles and instantons