当前位置：文档库 › BIOINFORMATICS

BIOINFORMATICS

BIOINFORMATICS Vol.21Suppl.22005,pages ii151–ii158

doi:10.1093/bioinformatics/bti1125 Phylogenetics

A Gamma mixture model better accounts for among

site rate heterogeneity

Itay Mayrose1,Nir Friedman2and Tal Pupko1,?

1Department of Cell Research and Immunology,George S.Wise Faculty of Life Sciences,

Tel Aviv University,Ramat Aviv69978,Israel and2School of Computer Science and Engineering,

Hebrew University,Jerusalem91904,Israel

ABSTRACT

Motivation:Variation of substitution rates across nucleotide and amino acid sites has long been recognized as a characteristic of molecular sequence evolution.Evolutionary models that account for this rate heterogeneity usually use a gamma density function to model the rate distribution across sites.This density function,however,may not?t real datasets,especially when there is a multimodal distribu-tion of rates.Here,we present a novel evolutionary model based on a mixture of gamma density functions.This model better describes the among-site rate variation characteristic of molecular sequence evol-ution.The use of this model may improve the accuracy of various phylogenetic methods,such as reconstructing phylogenetic trees,dat-ing divergence events,inferring ancestral sequences and detecting conserved sites in proteins.

Results:Using diverse sets of protein sequences we show that the gamma mixture model better describes the stochastic process under-lying protein evolution.We show that the proposed gamma mixture model?ts protein datasets signi?cantly better than the single-gamma model in9out of10datasets tested.We further show that using the gamma mixture model improves the accuracy of model-based prediction of conserved residues in proteins.

Availability:C++source codes are available from the authors upon request.

Contact:talp@post.tau.ac.il

1INTRODUCTION

Probabilistic models of evolution are considered to be the-state-of-art methods for phylogeny inference.Likelihood methods calculate the probability of observing the data conditioned on the hypothesis, as speci?ed by the phylogenetic tree and the probabilistic evol-utionary model.The maximum-likelihood(ML)principle is then invoked to choose the hypothesis that yields the highest likelihood of the observed sequences.This paradigm allows for statistically robust parameter estimation and vigorous testing of evolutionary hypotheses(Whelan et al.,2001).

A basic dilemma when using probabilistic models within the ML paradigm is controlling the expressiveness of the model.Models with too many parameters might over?t the observations.However, models with too few parameters may be unrealistic,resulting in erroneous conclusions.A classical example of oversimpli?cation is the assumption of equal evolutionary rates at all sites of a protein (Felsenstein,2001).Nevertheless,in proteins the rates of evolution To whom correspondence should be addressed.vary due to different selective constraints that are acting on different sites.Indeed,a vital advance in the reconstruction of evolutionary trees has been the consideration of heterogeneity of evolutionary rates among sequence sites(reviewed in Swofford et al.,1996;Yang, 1996).Accordingly,the rate at each site is modeled as a random variable drawn from a speci?ed prior distribution.By far,the most commonly chosen distribution for modeling rate variation across sites is the gamma distribution.

Assuming a gamma prior over the rate distribution is mathem-atically convenient and requires the?tting of a single additional parameter.However,as noted by Felsenstein(2001),there is no reason to believe that the rate across sites is gamma distributed.Biolo-gical insight suggests that rate distributions are not always unimodal. For example,a protein may be composed of several domains, each having its own rate distribution.As shown in Figure1A and B,the unimodal gamma distribution poorly?ts the observed rate distribution of the adenylate kinase protein family.

In a step toward a more realistic evolutionary model we propose a gamma mixture model,which generalizes the traditional single-gamma distribution model.This model assumes the existence of K gamma distributions(components),each characterized by its own set of parameters.The model further de?nes the a priori probability for each gamma component.The adjustable parameters of the model are optimized using an expectation–maximization(EM)algorithm.The resulting model can accommodate a multimodal rate distribution, where the number of modes depends on the number of gamma com-ponents and how different each component is from another(Fig.1C). The outline of the paper is as follows.Section2presents and formulates the gamma mixture model of among-site rate variation. In Section3we develop an ef?cient EM algorithm for estimating the model parameters.In Section4we apply the gamma mixture model to a wide range of datasets.We show that the mixture model signi?cantly outperforms the traditional single-gamma model.In Section5we study the relationship between the data size and the number of gamma components that the data support.In Section6we demonstrate that by using the gamma mixture model more accurate predictions of the conserved residues within a protein are obtained. We conclude with a discussion(Section7).

2THEORY

2.1Among-site rate variation

A phylogenetic tree T=(τ,t),is de?ned by its tree topologyτand associated branch lengths t.The branch lengths of the phylogenetic

Published by Oxford University Press2005ii151

I.Mayrose et

al.

Fig.1.An example of the rate distribution inferred for the adenylate kinase

protein family(?rst row in Table1).(A)The rate distribution as inferred

using ML with the Rate4Site program(Pupko et al.,2002).(B)The?tted rate

distribution inferred using a model that assumes one-gamma component is

unimodal.(C)The?tted rate distribution inferred using a model that assumes

three gamma components is bimodal.The individual gamma components are

shown by dashed lines.The method used for estimating the model parameters

is described in Section3.

tree represent the average evolutionary rate across all sites.The sub-

stitution model describes how characters(amino acids,nucleotides

or codons)evolve on the tree.A phylogenetic tree and a substitu-

tion model induce probabilities over assignments of characters to the

leaves of the tree(see Felsenstein,2004for a detailed description).

Let D denote a dataset that consists of aligned sequences of current

day taxa corresponding to the leaves of the tree.In the standard ML

models,we view each column of the alignment as evolving independ-

ently.Thus,if we denote by D i the data at site i,then P(D i|T)is the probability of the i-th column of the alignment given the https://www.wendangku.net/doc/0a17355094.html,-

puting this probability requires summing over all possible character

assignments to internal nodes of the tree(ancestral states).This com-

putation can be done ef?ciently using Felsenstein’s(1981)post-order

tree traversal algorithm.

The standard ML model assumes that each site evolves at the same

rate.However,biology suggests that some sites are more conserved

and undergo fewer substitutions,whereas other sites are less con-

served and undergo more substitutions.Since longer branches imply

more substitutions,we can model such differences by shrinking or

expanding the branch lengths.The site-speci?c rate,r i,indicates how

fast site i evolves compared with the average rate across all sites.For

example,a rate of2indicates a site that evolves twice as fast as the

average.Thus,site-speci?c rates are not absolute evolutionary rates

that require knowledge of divergence times,but instead represent a comparative quantity.We de?ne T×r to be the tree T with all branch lengths multiplied by rate r.

Since we do not know the actual value of r i,we need to consider all possible values when computing the probability of D i.Thus,the likelihood of site i is de?ned as

L(i)=

∞

P(D i|T×r i)g(r i:θ)dr i,(1) and the likelihood of the complete alignment is the product

L(i),(2)

where g(r:θ)is a prior density function over the rates which is governed by parametersθ.Choosingθdetermines how rate variation is modeled.Here we focus on the key question of how to choose the prior g(r:θ)and its effect.

2.2The gamma distribution

The most commonly used prior distribution over evolutionary rates is the gamma distribution(Swofford et al.,1996;Yang,1996).This distribution has two parameters;a shape parameter,α,and a scale parameter,β.A variable R is gamma distributed,denoted R～ (α,β),if its density function is

g(r·α,β)=

βα

(α)

e?βr rα?1.(3)

The mean of the gamma distribution isα/β.Standard applications of the gamma distribution prior require that the mean of the prior is1(otherwise,we can rescale the original tree).This implies thatβ=α,leaving one free parameter.The shape of the gamma distribution is determined by theαparameter,which is indicat-ive of rate variation.Whenα>1the distribution is bell-shaped, suggesting little rate heterogeneity.In the case ofα<1,the dis-tribution is highly skewed and is L-shaped,which indicates high levels of rate variation.This?exibility makes the distribution suit-able for accommodating different levels of rate variation in different datasets.

2.3A mixture of gamma

We suggest modeling the prior density over evolutionary rates by a mixture of gamma distributions.This assumes that the rates are pulled from a few possible gamma components,each with its ownαandβparameters.Let K be the number of such gamma components,with αk andβk being the parameters of the k-th component.We denote byγk the prior probability that a speci?c rate was drawn from the k-th distribution.We now haveθ={ αk,βk,γk :k=1,...,K}, with

k=1

γk=1.A variable R is distributed with a mixture of gamma if

gm(r:θ)=

k=1

γk g(r:αk,βk),(4)

where g(r:αk,βk)is the gamma distribution of the k-th component. Such a mixture provides additional?exibility in specifying the prior distribution.Moreover,by choosing K we can consider a range of dis-tributions with growing expressiveness with corresponding increase in the number of parameters.Since we restrict the expectation of the mixture to equal1,the number of free parameters for K components is3K?2.

ii152

Gamma mixture model

2.4Likelihood computation

An important technical issue is how to compute the likelihood L(i)

with its integration.The standard solution is to approximate the

integral by a weighted sum over a set of discrete rates.Thus,we

approximate the integral in Equation(1)by a sum

L(i)～=

j=1

P(D i|T×?r j)w(?r j),(5)

where(?r1,...,?r S)are representative rates and(w(?r1),...,w(?r S)) are the corresponding weights.

For the case of a single gamma prior a common choice is based on Yang’s(1994)quantile approximation,where the weights of representative rates are identical.Here,we apply a more accurate approximation based on the generalized Laguerre quadrature method as suggested by Felsenstein(2001).A detailed description of the Laguerre quadrature method is given in the Appendix.

We can also use Laguerre quadrature for approximating L(i)with a mixture of gamma distribution by?nding the representative weights of each component,and then use the approximation

L(i)～=

k=1

γk

j=1

P(D i|T×?r k j)w(?r k j),(6)

where?r k

j is the rate of the j-th discrete rate category in the k-th

component.Since now each gamma component is approximated by S discrete categories the total number of categories is K×S.

3AN EM ALGORITHM FOR OPTIMIZING THE GAMMA MIXTURE PARAMETERS

When the parameters of the mixture model are known,computing the likelihood is simple.However,the parameters of the model are usu-ally unknown and have to be estimated for each dataset.In this section we address this multidimensional maximization problem.We adopt an ML approach and aim to maximize P(D|T,θ).Our approach for maximizing the likelihood is to use an EM procedure(Dempster et al.,1977)that is described below.For succinctness,we assume throughout this discussion that the phylogenetic tree T is?xed,and we do not explicitly refer to it in the equations.

To develop the EM procedure,it is useful to introduce a random variable H i,which explicitly denotes the mixture component at site i.Our model can thus be cast as a graphical probabilistic model (Buntine,1994)as shown in Figure2.We want to estimate the vector parametersα,βandγ.We start by reviewing how to estimate these parameters from complete data where we observe H i and R i for each site,and then consider the more challenging case where we do not observe them.

Consider the complete data case where M is the sequence length. The distribution P(H i:γ)is a multinomial distribution.The suf?cient statistics for this distribution are

M k=

i=1

1{H i=k},(7)

where1{}is the indicator function.Given the vector{M k:k= 1,...,K},the ML estimate forγis simply M k/M.

H i

R i

D i

Fig.2.A graphical plate model representation of the mixture of gamma distribution model.Site-speci?c variables are shown within the plate.The variables outside the plate are parameters shared among all positions.The variable H i denotes the mixture component,R i the rate and D i the observed characters for the i-th site.

The distribution P(R i|H i=k:αk,βk)is a gamma distribution. The suf?cient statistics for this distribution are the sum of R and the sum of ln R in those sites where H i=k.Thus,

A k=

i=1

1{H i=k}R i,(8)

B k=

i=1

1{H i=k}ln R i.(9)

Finding the ML estimates ofαk andβk requires solving a pair of equations

B k=

M k

A k

αk(10) and

0=ln M k+lnαk?ln A k+

B k

M k

?φ(αk)(11)

whereφ(α)= (α)/ (α)is the digamma function that can be approximated by a series expansion(Abramowitz and Stegun,1972). The second equation cannot be solved analytically,but can be solved numerically by a line search.

To conclude,given complete data,we can accumulate the suf?cient statistics{M k,A k,and B k,k=1,...,K}and then?nd the ML estimates ofα,β,andγ.

Unfortunately,we do not observe the variables H i and R i for dif-ferent sites.Thus,we need to learn from incomplete data.The EM algorithm for learning with incomplete data uses the‘plug in’estim-ators of the complete data case as a sub-procedure.The algorithm starts with an initial estimate of the unknown parameters and iter-atively improves them.Letθt denote the parameters after the t-th iteration.Starting with a guess,θ0,the EM algorithm iterates between the following two steps:

https://www.wendangku.net/doc/0a17355094.html,pute the expected suf?cient statistics given the data and the parametersθt.This requires computing E[M k|D,θt], E[A k|D,θt]and E[B k|D,θt]for each k(see Equations(15–18) below).

ii153

I.Mayrose et al.

M-step.Given these expected suf?cient statistics,setθt+1to be the ML estimate as though these statistics were obtained from complete data.In our case,this implies solving

0=ln E[M k|D,θt]+lnαt+1k?ln E[A k|D,θt]

+E[B k |D,θt]

E[M k|D,θt]

?φ(αt+1k);(12)

βt+1 k =E[M k

|D,θt]

E[A k|D,θt]

αt+1

;(13)

γt+1 k =E[M k

|D,θt]

.(14)

Each EM iteration is monotonically non-decreasing in terms of the data likelihood(Dempster et al.,1977).The algorithm converges (i.e.the likelihood does not increase)only at stationary points of the likelihood function.Thus,EM will converge to local maxima of the likelihood surface.The quality of the convergence point depends on the starting guess and the properties of the speci?c problem.

The key computational step in performing EM is computing the expected suf?cient statistics given the parametersθhttps://www.wendangku.net/doc/0a17355094.html,ing linearity of expectations,we can rewrite these as

E[M k|D,θt]=

i=1

P(H i=k|D i,θt)

E[A k|D,θt]=

i=1

P(H i=k|D i,θt)E[R i|H i=k,D i,θt](15)

E[B k|D,θt]=

i=1

P(H i=k|D i,θt)E[ln R i|H i=k,D i,θt].

These computations require the following terms:

P(H i=k|D i,θt)=P(H i=k,D i|θt)

P(D i|θt)

;(16)

P(H i=k,D i|θt)= ∞

P(r i,H i=k,D i|θt)dr i

=γt k ∞

P(D i|r i)g(r i:αt k,βt k)dr i;(17)

E[R|H i=k,D i,θt]= ∞

r i P(r i|H i=k,D i,θt)dr i

= ∞

r i P(D i|r i)g(r i:αt k,βt k)dr i

P(D i|H i=k,θt)

.(18)

E[ln R i|H i=k,D i,θt]can be similarly obtained.These terms require integration of terms of the form f(r i)g(r i:αk,βk). Again,we use Laguerre quadrature to approximate these integrals (Appendix).

4ANALYSIS OF EXAMPLED DATASETS

4.1Datasets

To test the utility of the proposed model we selected10datasets from the HSSP database(Sander and Schneider,1993).We refer to each dataset by its protein data bank(PDB;Sussman et al.,1998) identi?er.These datasets encompass a broad range of organisms (from bacteria to mammals)and biological processes,such as cell

growth(3adk),metabolism(3pgk,1rhd,1ppl,1rnd,4mt2and3dfr),

apoptosis(1bxl),ion transport(1bl8)and signal transduction(1a6q).

Sequences with many gapped positions were manually removed.

To avoid prohibitive computation time,we limited the number of

sequences such that the50most divergent sequences in each dataset

were selected.Gapped positions were treated as missing characters.

For each dataset the tree topology was constructed according to

the neighbor-joining(NJ)algorithm(Saitou and Nei,1987)with

pairwise distances estimated by ML with a homogenous rate model.

Branch lengths in the resulting tree and the gamma mixture para-

meters were then optimized iteratively until convergence of the

likelihood function.The choice of the number of discrete rate cat-

egories can slightly in?uence the resulting likelihood score.In order

to equally compare results of models with different number of com-

ponents,we chose the total number of categories in each model to

be36.For example,a model with2components had18discrete cat-

egories in each component.We note that our results were essentially

the same when the number of categories per component was identical

for all models,although this second discretization scheme slightly

favored models with more components(data not shown).

4.2The evolutionary model

All analyses conducted in this study used the JTT model of amino

acid replacements(Jones et al.,1992).However,incorporating the

gamma mixture model into any desired nucleotide or amino acid

substitution model is an easy extension.

4.3Model comparisons

In this study we considered models with1,2and3components,

denoted by M1,M2and M3,respectively.We used the likelihood

ratio test(LRT)to test whether models with larger number of com-

ponents?t a particular dataset signi?cantly better than a model with

fewer components.Table1contains maximum log-likelihood estim-

ates obtained when analyzing each of the10datasets with models

M1,M2and M3.Adding one-gamma component requires three more

free parameters(αandβ,the distribution parameters andγ,the com-

ponent probability)and is statistically justi?ed if the log-likelihood

improvement is>3.95(P<0.05;χ2with3degrees of freedom).In

9of10datasets examined(Table1)M2gives a signi?cantly better

?t to the data than the commonly used M1model.The only excep-

tion is the4mt2dataset.One explanation to this exception is that the

sequence length of the proteins in this dataset is only62amino acids

long(see Section5).In contrast to the signi?cant difference between

M1and M2,the addition of a third gamma component(M3)is statist-

ically unjusti?ed in all but the3pgk dataset,i.e.the dataset with the

longest sequence length.We note that although the models are nested,

the use of the LRT may not be justi?ed because of boundary problems

(Anisimova et al.,2001).In addition,the LRT does not account for

the size of the data.We thus also used a second order Akaike Inform-

ation Criterion(AIC c)(Burnham and Anderson,2002),de?ned as

AIC c=?2LL+2pM/(M?p?1),where LL is the log-likelihood, p the number of free parameters and M is sequence length.In all

datasets examined signi?cant LRT results were also supported by bet-

ter AIC c scores.The exact distribution of the LRT statistics can be

approximated using parametric bootstrapping(Susko et al.,2003).

However,this approach is computationally intensive and was not

applied here.

ii154

Gamma mixture model Table1.Maximum log-likelihood(LL)estimates for the analysis of10datasets under the M1,M2,M3and G+I models

Dataset NS a SL b M1M2c M3c G+I

3adk50194?16429.3?16406.5?16406.1?16423.1 3pgk50415?31380?31364.3?31359.7?31376 1rhd50293?17583.3?17572.5?17571.3?17579 1ppl50323?26402?26389.7?26387?26397 1rnd50124?8388.9?8378.5?8377.5?8382.5 4mt25061?1000.4?997.8?997.6?1000.3 3dfr50163?12831.9?12820.3?12818.5?12829.4 1bxl36181?3155.2?3141.3?3140.5?3155.2 1bl85097?8352.6?8343.7?8340.2?8347.7 1a6q50363?27470.7?27461.2?27459.1?27468.1

a Number of sequences.

b Sequence length.

c Observe

d LL values ar

e shown in bold type i

f the LRT between M2(M3)and M1(M2)is signi?cant(P<0.05).

We have also compared the gamma mixture model to the Gamma+ Invariant(G+I)site model(Gu et al.,1995).This model may rep-resent a variant of M2in which the second gamma component is constrained to invariable rates only.As expected,the G+I model gave intermediate log-likelihoods between M1and M2(Table1). Nevertheless,for all datasets examined,the AIC c scores of M2were better than that of G+I.For some datasets(3adk,3pgk and1bxl)the AIC c difference was>20,whereas in the4mt2dataset the superi-ority of M2was only marginal.For the datasets tested,it seems that M2superiority over G+I was most pronounced in those cases where the expectation of the component with the lower average rate (the‘slower’gamma component)highly deviated from zero.For example,in all cases where the AIC c difference was>20the expect-ation of the‘slower’gamma component was>0.4,resulting in a relatively large log-likelihood difference between M2and G+I.

5THE INFLUENCE OF DATA SIZE

We tested the hypothesis that adding more components to the model will become more justi?ed as the sequence length increases.Two datasets were analyzed(3adk and3pgk).In each dataset we ran-domly selected l sites to produce a new alignment that is a subset of the original multiple sequence alignment(MSA).We then optimized the gamma mixture parameters and branch lengths(only two rounds of optimization iterations were performed since each such iteration is computationally intensive).For each sequence length,10inde-pendent runs were conducted.As shown in Figure3A(for the3adk dataset)the average difference between models M2and M1increases as the sequence length increases.The same trend,though to a lesser extent,is also apparent when comparing M3and M2.Similar results were obtained for the3pgk dataset(data not shown).

We further analyzed whether the inclusion of more sequences in the MSA contributes to the?t of more complex models.We analyzed this hypothesis with the3adk and3pgk datasets.s random sequences were sampled from each dataset to produce a new MSA.For each value of s(ranged from10to80),10independent runs were con-ducted.Our results indicate that the average difference between M2 and M1increases as the number of sequences increases(Fig.3B). Again,this is also true for the M3versus M2comparison to a lesser extent.Similar results were obtained for the3pgk dataset(data

not Fig.3.Log-likelihood(LL)difference obtained for the3adk dataset as a function of(A)sequence length and(B)number of sequences.The LL differ-ence is the average score obtained over10independent runs.The differences between models M2and M1,and between M3and M2are shown in black and grey lines,respectively.

shown).To conclude,when more information is available(number of sequences and sequence length)models that account for a complex distribution of rates better explain the data.

6BAYESIAN ESTIMATION OF SITE-SPECIFIC EVOLUTIONARY RATES USING THE

GAMMA MIXTURE MODEL

Our results above indicated that the mixture model can statistically explain sequence variability better than the traditional single-gamma

ii155

I.Mayrose et al.

model.We now investigate whether the use of our suggested model can also improve methods that aim to estimate the rate at which a site evolves as a means for inferring conserved and variable sites of a protein.

Within the Bayesian framework,the posterior probability of any given rate,r,is obtained from the likelihood function and the prior distribution.Given an estimated phylogeny and a discrete gamma

mixture prior distribution(for which w(?r k

j )is the probability of rate

category j in component k),this probability is then

P(R i=?r k j|D i,T,θ)～=

P(D i|?r k j,T)γk w(?r k j)

k=1

j=1

P(D i|?r k j,T)γk w(?r k j)

.(19)

Our site-speci?c rate estimate is de?ned as the expectation of r over its posterior rate distribution

E(R i|D i,T,θ)～=

k=1

j=1

P(R i=?r k j|D i,T,θ)?r k j.(20)

6.1Simulations setup

We have previously shown that an empirical Bayesian site-speci?c rate inference method is superior to an ML-based approach(Mayrose et al.,2004).Here,simulations were used in order to test whether a prior that assumes a mixture of gamma components(models M2and M3)can improve the accuracy of site-speci?c rate estimates over a model with a single component(M1).We simulate a given site with a speci?c‘true’rate.An MSA is thus generated based on a vector of true rates.Subsequently,a rate for each column is inferred using either the M1,M2or M3model.The closer the inferred rates to the true rates are,the better the inference is.For the simulations, one must determine the true rate in each site.In order to obtain true rates that are biologically relevant,characteristic rates were com-puted based on two empirical datasets:3adk with172sequences and194sites,and3pgk with150sequences and415sites.For each dataset,ML was used to estimate the site speci?c rates.Thus,no prior was assumed when constructing the empirical rate distribution. (Inferring the rates using a gamma mixture with a speci?ed number of components would bias the results toward this speci?c distribu-tion.)True rates were scaled such that the average was set to1.For estimating the ML rates,the3adk and3pgk phylogenetic trees were reconstructed using NJ(Saitou and Nei,1987).

For each dataset and for each number of sequences tested,a total of 20identical and independent simulation runs were conducted.The accuracy of inference was analyzed by the mean relative absolute deviations(MRAD)distance between the simulated and estimated rates:

MRAD=1

i=1

|estimated r i?true r i|

true r i

,(21)

where M is the sequence length.The division of each absolute devi-ation by the true rate compensates for the larger variance in large rates and the smaller variance in low rates.

A two-sided Wilcoxon non-parametric test between two depend-ent samples(Sokal and Rohlf,1981)was then performed in order to determine whether the difference in accuracy obtained from models with a different number of gamma components is statistically signi-?cant.A non-parametric test was used to eliminate the assumption Table2.Simulation results:accuracy of site-speci?c rate inference based on models with a different number of gamma components

Dataset NS a Mean MRAD

M1M2b M3c

3adk100.8910.790(P<0.0005)0.770(P=0.093) 200.5700.490(P<0.0001)0.475(P<0.005)

300.4290.365(P<0.0001)0.356(P<0.01)

400.3740.316(P<0.0001)0.311(P=0.19)

500.3510.305(P<0.0001)0.304(P=0.25)

3pgk100.7750.740(P<0.0001)0.728(P<0.01) 200.5340.502(P<0.0001)0.493(P<0.0005)

300.4220.395(P<0.0001)0.388(P<0.0001)

400.3820.359(P<0.0001)0.352(P<0.0005)

500.3490.330(P<0.0001)0.324(P<0.0005)

a Number of sequences.

b P-value between M2and M1.

c P-value between M3an

d M2.

Values are shown in boldtype if the difference between M2(M3)and M1(M2)is signi?cant(P<0.05).

that the MRAD measures are normally distributed,although similar results were obtained with a parametric t-test(data not shown).For each empirical dataset,the in?uence of the number of sequences on the inference accuracy was tested.For this purpose model trees with10,20,30,40and50taxa were constructed using NJ.In order to construct a model tree with N sequences,the N most divergent sequences were selected.

6.2Simulation results

A comparison between the accuracy of site-speci?c rate inference as a function of the number of sequences under the M1,M2and M3 models is shown in Table2.For a given model,our simulations show that the accuracy increases as the number of sequences increases. This?nding is expected since more data are available at each site for rate inference.

It is not clear that more complex models will result in better rate inference.When comparing the effect of the number of components on the accuracy of rate estimates,two contradicting factors may operate.When the amount of data is large,rate inference is accurate for all models,and using a rich model may not be justi?ed.However, when the number of sequences increases,the use of models with additional free parameters is more justi?ed(Fig.3).

Comparing M2and M1,the?rst was always signi?cantly more accurate than the latter(for the two datasets,regardless of the data-set size).M3was signi?cantly better than M2for the3pgk dataset regardless of dataset size.The difference between M3and M2for the3adk dataset is more complex.Although M3is more accurate than M2with every number of sequences tested,the differences between the models is signi?cant only for the intermediate-sized data(20and30sequences).With40and50sequences,the differ-ence between M3and M2is not signi?cant,probably because of the substantial data size that renders inference with the M2model suf?ciently accurate.An additional increase in data size is expec-ted to reduce the difference between the two models even further. In the case of10sequences,there are probably not enough data to accurately estimate the parameters of the M3model,which can explain why the rates estimated by M3were not signi?cantly more

ii156

Gamma mixture model

accurate than those of M2.Indeed,the log-likelihood difference between M3and M2for the case of10sequences was not stat-istically signi?cant(LRT test)in all20simulation runs(data not shown).

7DISCUSSION

Evolutionary models may provide misleading results if their underly-ing assumptions are violated(Whelan et al.,2001).With the dramatic increase in sequence-data availability,we are now in a position to suggest models that better mimic known biological processes and patterns.By using realistic models,we may be able to remove pos-sible sources of error caused by oversimpli?ed assumptions.In this study we explored a model that better describes the among-site rate variation characteristic of molecular sequence evolution.We showed that by using a mixture of a few gamma distributions the model?t the data signi?cantly better than the commonly used single-gamma model.

The G+I model can be regarded as the?rst,albeit restricted, gamma mixture approach.Although the G+I model is intuitively very appealing,the estimates of the model parameters are highly sensitive to taxon sampling(Yang,1996;Sullivan et al.,1999).In addition,the high correlation between the proportion of the invariable sites and the gamma shape parameter indicates model inadequacy (Sullivan et al.,1999).Our results here indicated that,in term of AIC c scores,none of the datasets examined could be best explained by the G+I model,whereas the M1,M2and M3models best?tted 1,7and2datasets,respectively.

Recently,a few studies have suggested alternatives to the single-gamma model.Yang et al.(2000)have studied codon substitutions models with a range of different distributions for modeling the non-synonymous/synonymous rate ratio among sites,including a two-gamma distribution(model M6).Kosakovsky Pond and Frost (2005)have suggested a hierarchical model,in which the baseline gamma distribution is discretized into several categories using a beta https://www.wendangku.net/doc/0a17355094.html,ing AIC scores it was shown that this model better?ts several nucleotide coding datasets.Susko et al.(2003) investigated a non-parametric model that does not involve a prior on the rate distribution.Instead,the rate distribution is estim-ated using a large number of free parameters.Although these two models may capture deviations from the gamma distribution,the mixture model approach suggested in our study adds an additional ?exibility since the exact number of components needed to cap-ture the complexity of the rate distribution is adjustable and can be statistically inferred.As an alternative to using a mixture of gammas,a mixture of other positive distributions,such as the log-normal,can be applied using a similar mechanism described in this study.Clearly,more analyses are needed in order to study the merits of these different models under a range of evolutionary scenarios.

Phylogenetic reconstructions based on large datasets are becoming increasingly popular.For example,Murphy et al.(2001)investigated placental phylogeny using16.4kb molecular data for44taxa.Reyes et al.(2004)used the complete mitochondrial genomes of77species to reconstruct a mammalian https://www.wendangku.net/doc/0a17355094.html,rge molecular datasets have the potential to resolve longstanding controversies in system-atics.In such analyses,the data may support accurate parameter estimates of complex https://www.wendangku.net/doc/0a17355094.html,ing a mixture of gamma approach is a natural extension of the single-gamma model,allowing a better ?t to the distribution of evolutionary rates yet without introducing too many free parameters.Our results showed that the M2model was superior to M1for all data analyzed(Table1).We also showed that the better?t of M2increases as larger datasets are analyzed(Fig.3). This suggests that the gamma mixture model will be particularly valuable for such large datasets analyses.

The EM algorithm used in the optimization process only guaran-tees to?nd a local maximum,rather than a global one.Unfortunately, local optima are a practical dif?culty,especially when the number of parameters increases.Initiating the EM algorithm from several ran-dom points of the parameter space is needed to avoid local optima. Our practical experience suggests that with M1,the EM algorithm constantly reaches the global maxima(as a few dispersed starting points reach indistinguishable results).However,as the number of components increases,the EM algorithm often terminates at local optima.This implies that the observed superiority of models with more gamma components is underestimated.

Discretization of the continuous gamma distribution can be better achieved using the Laguerre quadrature method compared with Yang’s(1994)quantile approximation(Felsenstein,2001; Kosakovsky Pond and Frost,2005).The Laguerre quadrature method was used here not only to compute the likelihood of a tree,but also for the various numerical integrations that are a part of the EM algorithm. Using the Laguerre quadrature we obtained faster and more consist-ent results than the more commonly used quantile approach(data not shown).

Knowledge of relative evolutionary rates is crucial not only to de?ne more appropriate evolutionary models,but also because it serves as a means to evaluate the importance of a site in maintaining the structure or function of a protein.Furthermore,covarion models can be used to detect sites that exhibit different evolutionary rates in different branches of the phylogenetic tree.Such rate shifts may indicate change in the selection intensity at speci?c sites during evol-ution(Knudsen and Miyamoto,2001;Gaucher et al.,2002;Pupko and Galtier,2002;Susko et al.,2002).We have recently shown that an empirical Bayesian method produces signi?cantly more accurate rate estimations than an ML method,indicating that the gamma prior that is integrated into the Bayesian computation signi?cantly improves performance(Mayrose et al.,2004).Here we further showed that the incorporation of a gamma mixture prior leads to even better rate inferences.

ACKNOWLEDGEMENTS

We thank D.Burstein,A.Doron-Faigenboim,M.Ninio,E.Privamn, N.Rubinstein and A.Stern for their insightful comments.This work is supported in part by ISF grant number1208/04to N.F.and T.P. T.P.was also supported by a grant in Complexity Science from the Yeshaia Horvitz Association.

REFERENCES

Abramowitz,M.and Stegun,I.A.(1972)Handbook of Mathematical Functions with Formulas,Graphs,and Mathematical Tablesprinting.Dover,New York. Anisimova,M.et al.(2001)Accuracy and power of the likelihood ratio test in detecting adaptive molecular evolution.Mol.Biol.Evol.,18,1585–1592.

Buntine,W.(1994)Operations for learning with graphical models.J.Artif.Intel.Res.2, 159–225.

ii157

I.Mayrose et al.

Burnham,K.P.and Anderson,D.R.(2002)Model Selection and Multimodel Inference:A Practical Information-Theoretic Approach.Springer-Verlag, New York,NY.

Dempster,A.P.et al.(1977)Maximum likelihood estimation from incomplete data via the EM algorithm(with discussion).J.Roy.Statist.Soc.Ser.B.,39, 1–38.

Felsenstein,J.(1981)Evolutionary trees from DNA sequences:a maximum likelihood approach.J.Mol.Evol.,17,368–376.

Felsenstein,J.(2001)Taking variation of evolutionary rates between sites into account in inferring phylogenies.J.Mol.Evol.,53,447–455.

Felsenstein,J.(2004)Inferring Phylogenies.Sinauer Associates,Sunderland,MA. Gaucher,E.A.et al.(2002)Predicting functional divergence in protein evolution by site-speci?c rate shifts.Trends Biochem.Sci.,27,315–321.

Gu,X.et al.(1995)Maximum likelihood estimation of the heterogeneity of substitution rate among nucleotide sites.Mol.Biol.Evol.,12,546–557.

Jones,D.T.et al.(1992)The rapid generation of mutation data matrices from protein https://www.wendangku.net/doc/0a17355094.html,put.Appl.Biosci.,8,275–282.

Knudsen,B.and Miyamoto,M.M.(2001)A likelihood ratio test for evolutionary rate shifts and functional divergence among proteins.Proc.Natl https://www.wendangku.net/doc/0a17355094.html,A,98, 14512–14517.

Kosakovsky Pond,S.L.and Frost,S.D.(2005)A simple hierarchical approach to modeling distributions of substitution rates.Mol.Biol.Evol.,22, 223–234.

Mayrose,I.et al.(2004)Comparison of site-speci?c rate-inference methods for pro-tein sequences:empirical Bayesian methods are superior.Mol.Biol.Evol.,21, 1781–1791.

Murphy,W.J.et al.(2001)Resolution of the early placental mammal radiation using Bayesian phylogenetics.Science,294,2348–2351.

Press,W.H.,Teukolsky,S.A.,Vetterling,W.T.and Flannery,B.P.(2002)Numerical Recipes in C++:The Art of Scienti?c Computing.Cambridge University Press, Cambridge.

Pupko,T.and Galtier.N.(2002)A covarion-based method for detecting molecular adapt-ation:application to the evolution of primate mitochondrial genomes.Proc.R.Soc.

Lond.B.Biol.Sci.,269,1313–1316.

Pupko,T.et al.(2002)Rate4Site:An algorithmic tool for the identi?cation of functional regions in proteins by surface mapping of evolutionary determinants within their homologues.Bioinformatics,18,S71–S77.

Reyes,A.et al.(2004)Congruent mammalian trees from mitochondrial and nuclear genes using Bayesian methods.Mol.Biol.Evol.,21,397–403.

Saitou,N.and Nei,M.(1987)The neighbor-joining method:a new method for recon-structing phylogenetic trees.Mol.Biol.Evol.,4,406-425.

Sander,C.and Schneider,R.(1993)The HSSP data base of protein structure-sequence alignments.Nucleic Acids Res.,21,3105–3109.

Sokal,R.R.and Rohlf,F.J.(1981)Biometry:The Principles and Practice of Stat-istics in Biological Research.W.H.Freeman and Company,New York,NY, pp.447–450.

Sullivan,J.et al.(1999)The effect of taxon sampling on estimating rate het-erogeneity parameters of maximum-likelihood models.Mol.Biol.Evol.,16, 1347–1356.

Susko,E.et al.(2002)Testing for differences in rates-across-sites distributions in phylogenetic subtrees.Mol.Biol.Evol.,19,1514–1523.

Susko,E.et al.(2003)Estimation of rates-across-sites distributions in phylogenetic substitution models.Syst.Biol.,52,594–603.

Sussman,J.L.et al.(1998)Protein Data Bank(PDB):database of three-dimensional structural information of biological macromolecules.Acta.Crystallogr.D.Biol.

Crystallogr.,54,1078–1084.

Swofford,D.L.,Olsen,G.J.,Waddell,P.J.and Hillis,D.M.(1996)Phylogenetic inference.

In:Hillis,D.M.,Moritz,C.and Mable,B.K.(eds),Molecular Systematics.Sinauer Associates,Sunderland,MA.

Whelan,S.et al.(2001)Molecular phylogenetics:state-of-the-art methods for looking into the past.Trends Genet.,17,262–272.

Yang,Z.(1994)Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites:Approximate methods.J.Mol.Evol.,39, 306–314.

Yang,Z.(1996)Among-site rate variation and its impact on phylogenetic analyses.

Trends Ecol.Evol.,11,367–372.

Yang,Z.et al.(2000)Codon-substitution models for heterogeneous selection pressure at amino acid sites.Genetics,155,431–449.APPENDIX:A LAGUERRE QUADRATURE METHOD FOR APPROXIMATING THE

GAMMA DISTRIBUTION

Felsenstein(2001)suggested that the Laguerre quadrature method for the discretization of the gamma distribution can better approxim-ate the continuous distribution compared with Yang’s(1994)quantile approximation.We used the Laguerre method not only to compute the likelihood of a tree,but also for the various numerical integrations that are a part of the EM algorithm.For the EM we approximate a gamma distribution with bothαandβparameters.We,thus,give a detailed explanation of this approximation.

When approximating a continuous distribution by a discrete one [Equation(5)],discrete values(rates)?r i and probabilities w(?r i)must be chosen so as to approximate the integral most accurately.The idea of Gaussian quadrature is to give ourselves the freedom to choose not only the location of the abscissas at which the function is to be evaluated,as in Yang’s(1994)discrete approximation,but also the weighting coef?cients.Speci?cally,we want to approximate the integral

W(x)f(x)dx,where W(x)is called the weighting func-tion.Given an integer N we can?nd weights w j and abscissas x j such that the approximation

W(x)f(x)dx～=

j=1

w i f(x i)(A1)

is exact,if f(x)is a polynomial of degree2N?1or less.The x j are the roots of a set of orthogonal polynomials that depend on the weighting function W(x).Once the abscissas are determined,the weights w j can be found(w j are constructed such that their sum equals1).The problem is usually how to construct the associated set of orthogonal polynomials.Different numerical quadrature methods depend on which weighting function is used.

Fortunately,the gamma density function can be converted into a classical weighting function W(m)=e?m mα.The abscissas and weights of this weighting function can be easily calculated using the generalized Laguerre quadrature method(Press et al.,2002).In what follows we detail how to convert between these two functions.

We want to approximate the integrals,such as those presented in Equations(1),(17)and(18)

∞

g(r:α,β)f(r)dr=

βα

(α)

∞

e?βr rα?1f(r)dr.(A2) By setting m=βr we get

(α)

∞

e?m mα?1f

dm.(A3)

By settingα =α?1,we obtain the desired weighting function. To conclude,given N,the approximation is

∞

g(r:α,β)f(r)dr～=

j=1

f(?r j)w(?r j),(A4)

where w(?r j)=w j

(α)

,?r j=m jβ.The terms m j and w j are the roots and weights of the Gauss–Laguerre quadrature formula withα =α?1.

ii158

管理运筹学期末试卷B

一、二、三、填空题（每小题分，共 ?分）、设原??问题为?????? ?≥-=++-≥--≤++++-= ,0,5232 4 7 532min 3213213213213 21无约束x x x x x x x x x x x x x x x Z 则它的标准形和对偶规划问题分别为：________________________ 和 ________________________。、用分枝定界法求整数规划12 12121121min 5 2 56 30 4,0Z x x x x x x x x x x =---≥-??+≤?? ≤??≥?且为整数的解时，求得放松问题的解为? ＝ ? ? ? ? ? ?，则可将原问题分成如下两个子问题与求解。、右图的最小支撑图是。、右边的网络图是标号算法中的图，其中每条弧上的数表示其容量和流量。该图中得到的可行流的增广链 (-3,1) (2,1) ②5(4) ④ ① 6(6) 6(4) ⑥ (0, ∞) 8(8) 3(2 ) 9(9)(5,1)

为：，在其上可增的最大流量为。、已知某线性规划问题，最优单纯形表如下则其最优解为：，最优值 max Z 。二、单项选择题（每小题分，共分）、下列表格是对偶单纯形表的是（ ? ）

、关于线性规划模型的可行域，叙述正确的为（） ?、可行域必有界；、可行域必然包括原点；、可行域必是凸的；、可行域内必有无穷多个点。、在运输问题中如果总需求量大于总供应量，则求解时应（） ?、虚设一些供应量； ?、虚设一个供应点；、根据需求短缺量，虚设多个需求点； ?、虚设一个需求点。、下列规划问题不可用动态规划方法求解的是（） ?、背包问题； ?、最短路径问题、线性规化： ???≥≥=++++=0 ,010 34..max 321 3 32211y x x x x t s x c x c x c Z ?、22 min (,)(2)3(1).. 460,0f x y x y s t xy y x y ?=++-?+

第三方支付平台

D 实验三关于第三方支付平台（2学时） 1、现在第三方支付平台的格局如何以及各自所占有的市场情况是多少？ 2、请同学上网查询目前主要的第三方支付平台有哪些?大的网上商城采用的有哪些?(列表说明) 网上商快钱易宝支付宝Paypal 财付通首信易城淘宝√ 易趣√ 当当网√√√√ 卓越网银行卡支付拍拍网√你认为哪几家第三方支付平台最有生命力,会长期生存下去? 我觉得易宝的生命力比较强，会长期生存下去。（1）如果消费者可以享受到：安全的在线支付，方便的电话支付，免费的会员服务，为您的手机充植，精彩活动积分奖励。（2）可以为商户提供：网上、电话、汇款，多种收款方式，支持外卡，让你您的生意做到全球，7*24小时客服，技术支持快速反应，接入更简单，交易更安全，结算更及时！（3）功能有：会员登录安全设置：通过验证图片、提示问题、常用机校验等手段实现的双向安全验证机制，确保用户在任意场所登录易宝网站时的安全。快捷查单服务：消费者通过此项服务可以方便快捷的查到自己选择YeePay易宝支付的网上购物订单！商户通过接入“快捷查单”功能，为客户提供贴心增值服务，提升服务品质和形象！自主接入服务：商户可通过自助方式网上注册并使用易宝在线支付服务，不仅可以在线收款，而且还能登录商户系统进行定单管理和交易结算。依托易宝强大平台，确保安全交易，并享受7*24小时客户服务及快捷查单等增值服务。 3、第三方支付牌照的颁发会对现行的网络支付以及银联会产生什么样的影响？易观国际分析认为，牌照发放后，获得牌照的企业将可接入超级网银，第三方支付企业以提高企业资金周转效率的定制化解决方案，将会逐步向传统企业进行渗透，也将出现从单一产业链的支付服务向跨产业链的融合转移的趋势。支付企业通过整合各种支付产品，为企业进行深度定制化服务，加快资金周转效率，而保险、基金等行业将是一个新的蓝海市场。一旦涉及到钱，那么这个庞大的支付产业必定摆脱不了银行的介入。在《支付机构客户备付金存管暂行办法(06.02会议征求意见稿)》出台前，仅有支付宝等少数国内第三方支付公司委托银行每月对客户的交易保证金做托管审计，其他公司则会依托三四家银行提供备付金托管与清算服务。而随着今年5月26日首批支付牌照正式发放，一场第三方支付公司挑

管理运筹学期中复习题答案

《管理运筹学》期中测试题第一部分线性规划一、填空题 1．线性规划问题是求一个目标函数在一组约束条件下的最值问题。 2．图解法适用于含有两个 _ 变量的线性规划问题。 3．线性规划问题的可行解是指满足所有约束条件_ 的解。 4．在线性规划问题的基本解中，所有的非基变量等于零。 5．在线性规划问题中，基本可行解的非零分量所对应的列向量线性无关 6．若线性规划问题有最优解，则最优解一定可以在可行域的顶点_ 达到。 7．若线性规划问题有可行解，则一定 _ 有基本可行解。 8．如果线性规划问题存在目标函数为有限值的最优解，求解时只需在其可行解的集合中进行搜索即可得到最优解。 9．满足非负 _ 条件的基本解称为基本可行解。 10．在将线性规划问题的一般形式转化为标准形式时，引入的松驰变量在目标函数中的系数为正。 11．将线性规划模型化成标准形式时，“≤”的约束条件要在不等式左_端加入松弛 _ 变量。 12．线性规划模型包括决策变量、目标函数、约束条件三个要素。 13．线性规划问题可分为目标函数求最大 _ 值和最小 _值两类。 14．线性规划问题的标准形式中，约束条件取等 _ 式，目标函数求最大 _值，而所有决策变量必须非负。 15．线性规划问题的基本可行解与基本解的关系是基本可行解一定是基本解，反之不然 16．在用图解法求解线性规划问题时，如果取得最值的等值线与可行域的一段边界重合，则 _ 最优解不唯一。 17．求解线性规划问题可能的结果有唯一最优解，无穷多最优解，无界解，无可行解。 18.如果某个约束条件是“ ”情形，若化为标准形式，需要引入一个剩余 _ 变量。 19.如果某个变量X j 为自由变量，则应引进两个非负变量X j ′ , X j 〞, 同时令X j ＝ X j ′ - X j 〞 j 。 20.表达线性规划的简式中目标函数为线性函数 _ 。 21.线性规划一般表达式中，a ij 表示该元素位置在约束条件的第i 个不等式的第j 个决策变量的系数。 22．线性规划的代数解法主要利用了代数消去法的原理，实现_ 基变量的转换，寻找最优解。 23．对于目标函数最大值型的线性规划问题，用单纯型法代数形式求解时，当非基变量检验数_ 非正时，当前解为最优解。 24．在单纯形迭代中，选出基变量时应遵循_ 最小比值法则。二、单选题 1．如果一个线性规划问题有n 个变量，m 个约束方程(m

第三方支付平台教案

第三方支付平台教学设计授课人：宋文鑫授课时间：2016年12月30日?学习目标： ?1、认识第三方支付平台的概念组成； ?2、理解两种第三方支付平台的运行机制以及优缺点； ?3、使学生认识到第三方支付平台的发展可以改变我们的生活。教学过程一：案例导入 1.共同阅读案例，学生思考案例问题，得出问题答案。 2.进而引出对之前学习的知识的复习，回顾电子商务支付方式。 3.导入本课内容“第三方支付平台”，说明本课的学习目标，开始新课教学。二：新课教学 1.第三方支付平台概念（1）学生阅读课本，找出第三方平台概念，通过课本知识填写学案。（2）展示PPT，讲解第三方平台概念。但此概念过长不易记忆，教授学生记忆方法，将概念拆解进行记忆，引出课堂思考。（3）学生思考学案问题，通过PPT引导学生理解概念以组块的方式进行记忆。 2.第三方支付平台分类（1）学生阅读课本找出第三方支付平台的种类，可分为网关型第三方支付平台与信用担保型第三方支付平台。（2）通过PPT学习网关型平台的运行模式以及优缺点，利用画图的方式使学生理解此类平台的运行模式，并回顾之前学过的知识点“支付网关”。（3）理解信用担保型第三方支付平台运行模式，点出其典型代表支付宝，引出探究讨论。学生分小组讨论“支付宝的工作流程是什么？”并将讨论结果并落实纸面。提问小组代表，而后利用PPT分步展示其工作流程。（4）简单介绍支付宝的产生、发展以及作用，讲解信用担保型第三方支付平台的优点。结合日常生活中支付宝付款、收款等功能，使学生认识到第三方支付平台的便利，相信第三方支付平台可以改变我们的生活。三：总结总结本课所学内容，与本课开始时提出的学习目标相呼应。四：作业 1.以支付宝为例介绍第三方支付的交易流程并画出其流程图。 2.利用课后时间搜集其他的第三方支付平台，并比较其相同点和不同点。

浅谈生物信息学在生物医药方面的应用

浅谈生物信息学在生物医药方面的应用生物信息学（Bioinformatics）是在生命科学的研究中，以计算机为工具对生物信息进行储存、检索和分析的科学。它是当今生命科学和自然科学的重大前沿领域之一，同时也将是21世纪自然科学的核心领域之一。其研究重点主要体现在基因组学（Genomics）和蛋白质组学（Proteomics）两方面，具体说就是从核酸和蛋白质序列出发，分析序列中表达的结构功能的生物信息。具体而言，生物信息学作为一门新的学科领域，它是把基因组DNA序列信息分析作为源头，在获得蛋白质编码区的信息后进行蛋白质空间结构模拟和预测，然后依据特定蛋白质的功能进行必要的药物设计。基因组信息学，蛋白质空间结构模拟以及药物设计构成了生物信息学的3个重要组成部分。是结合了计算机科学、数学和生物学的一门多学科交叉的学科。它依赖计算机科学、工程和应用数学的基础，依赖实验和衍生数据的大量储存。他将各种各样的生物信息如基因的DNA序列、染色体定位、基因产物的结构和功能及各种生物种间的进化关系等进行搜集、分类和分析，并实现全生命科学界的信息资源共享。从生物信息学研究的具体内容上看，生物信息学可以用于序列分类、相似性搜索、DNA序列编码区识别、分子结构与功能预测、进化过程的构建等方面的计算工具已成为变态反应研究工作的重要组成部分。针对核酸序列的分析就是在核酸序列中寻找过敏原基因，找出基因的位置和功能位点的位置，以及标记已知的序列模式等过程。针对蛋白质序列的分析，可以预测出蛋白质的许多物理特性，包括等电点分子量、酶切特性、疏水性、电荷分布等以及蛋白质二级结构预测，三维结构预测等。基因芯片是基因表达谱数据的重要来源。目前生物信息学在基因芯片中的应用主要体现在三个方面。 1、确定芯片检测目标。利用生物信息学方法，查询生物分子信息数据库，取得相应的序列数据，通过序列比对，找出特征序列，作为芯片设计的参照序列。 2、芯片设计。主要包括两个方面，即探针的设计和探针在芯片上的布局，必须根据具体的芯片功能、芯片制备技术采用不同的设计方法。 3、实验数据管理与分析。对基因芯片杂交图像处理，给出实验结果，并运用生物信息学方法对实验进行可靠性分析，得到基因序列变异结果或基因表达分析结果。尽可能将实验结果及分析结果存放在数据库中，将基因芯片数据与公共数据库进行链接，利用数据挖掘方法，揭示各种数据之间的关系。大规模测序是基因组研究的最基本任务，它的每一个环节都与信息分析紧密相关。目前，从测序仪的光密度采样与分析、碱基读出、载体标识与去除、拼接与组装、填补序列间隙，到重复序列标识、读框预测和基因标注的每一步都是紧

管理运筹学模拟试题及答案

四川大学网络教育学院模拟试题( A ) 《管理运筹学》一、单选题（每题２分，共20分。） 1．目标函数取极小（minZ ）的线性规划问题可以转化为目标函数取极大的线性规划问题求解，原问题的目标函数值等于（ C ）。 A. maxZ B. max(-Z) C. –max(-Z) D.-maxZ 2. 下列说法中正确的是（ B ）。Ａ．基本解一定是可行解Ｂ．基本可行解的每个分量一定非负Ｃ．若B 是基，则B 一定是可逆Ｄ．非基变量的系数列向量一定是线性相关的 3．在线性规划模型中，没有非负约束的变量称为（ D ）多余变量 B ．松弛变量 C ．人工变量 D ．自由变量 4. 当满足最优解，且检验数为零的变量的个数大于基变量的个数时，可求得（ A ）。Ａ．多重解Ｂ．无解Ｃ．正则解Ｄ．退化解 5．对偶单纯型法与标准单纯型法的主要区别是每次迭代的基变量都满足最优检验但不完全满足（ D ）。 A ．等式约束 B ．“≤”型约束 C ．“≥”约束 D ．非负约束 6. 原问题的第ｉ个约束方程是“＝”型，则对偶问题的变量i y 是（ B ）。Ａ．多余变量Ｂ．自由变量Ｃ．松弛变量Ｄ．非负变量 7.在运输方案中出现退化现象，是指数字格的数目( C )。 A.等于m+n B.大于m+n-1 C.小于m+n-1 D.等于m+n-1 8. 树Ｔ的任意两个顶点间恰好有一条（ B ）。Ａ．边Ｂ．初等链Ｃ．欧拉圈Ｄ．回路 9．若G 中不存在流f 增流链，则f 为G 的（ B ）。 A ．最小流 B ．最大流 C ．最小费用流 D ．无法确定 10.对偶单纯型法与标准单纯型法的主要区别是每次迭代的基变量都满足最优检验但不完全满足（ D ）Ａ．等式约束Ｂ．“≤”型约束Ｃ．“≥”型约束Ｄ．非负约束二、多项选择题（每小题4分，共20分） 1．化一般规划模型为标准型时，可能引入的变量有（） A ．松弛变量 B ．剩余变量 C ．非负变量 D ．非正变量 E ．自由变量 2．图解法求解线性规划问题的主要过程有（） A ．画出可行域 B ．求出顶点坐标 C ．求最优目标值 D ．选基本解 E ．选最优解 3．表上作业法中确定换出变量的过程有（） A ．判断检验数是否都非负 B ．选最大检验数 C ．确定换出变量 D ．选最小检验数 E ．确定换入变量 4．求解约束条件为“≥”型的线性规划、构造基本矩阵时，可用的变量有（） A ．人工变量 B ．松弛变量 C. 负变量 D ．剩余变量 E ．稳态变量 5．线性规划问题的主要特征有（） A ．目标是线性的 B ．约束是线性的 C ．求目标最大值 D ．求目标最小值 E ．非线性三、计算题（共60分） 1. 下列线性规划问题化为标准型。(10分)

管理运筹学模拟试题附答案

四川大学网络教育学院模拟试题( A ) 《管理运筹学》一、单选题（每题２分，共20分。） 1．目标函数取极小（minZ）的线性规划问题可以转化为目标函数取极大的线性规划问题求解，原问题的目标函数值等于（C）。 A. maxZ B. max(-Z) C. –max(-Z) D.-maxZ 2.下列说法中正确的是（B）。Ａ．基本解一定是可行解Ｂ．基本可行解的每个分量一定非负Ｃ．若B是基，则B一定是可逆Ｄ．非基变量的系数列向量一定是线性相关的3．在线性规划模型中，没有非负约束的变量称为（ D ）多余变量B．松弛变量C．人工变量D．自由变量 4. 当满足最优解，且检验数为零的变量的个数大于基变量的个数时，可求得（ A ）。Ａ．多重解Ｂ．无解Ｃ．正则解Ｄ．退化解5．对偶单纯型法与标准单纯型法的主要区别是每次迭代的基变量都满足最优检验但不完全满足（ D ）。 A．等式约束 B．“≤”型约束 C．“≥”约束 D．非负约束 y是（ B ）。 6. 原问题的第ｉ个约束方程是“＝”型，则对偶问题的变量i Ａ．多余变量Ｂ．自由变量Ｃ．松弛变量Ｄ．非负变量 7.在运输方案中出现退化现象，是指数字格的数目( C )。 A.等于m+n B.大于m+n-1 C.小于m+n-1 D.等于m+n-1 8.树Ｔ的任意两个顶点间恰好有一条（B）。Ａ．边Ｂ．初等链Ｃ．欧拉圈Ｄ．回路9．若G中不存在流f增流链，则f为G的（ B ）。 A．最小流 B．最大流 C．最小费用流 D．无法确定 10.对偶单纯型法与标准单纯型法的主要区别是每次迭代的基变量都满足最优检验但不完全满足（ D ）Ａ．等式约束Ｂ．“≤”型约束Ｃ．“≥”型约束Ｄ．非负约束二、多项选择题（每小题4分，共20分） 1．化一般规划模型为标准型时，可能引入的变量有（） A．松弛变量 B．剩余变量 C．非负变量 D．非正变量 E．自由变量 2．图解法求解线性规划问题的主要过程有（） A．画出可行域 B．求出顶点坐标 C．求最优目标值 D．选基本解 E．选最优解 3．表上作业法中确定换出变量的过程有（） A．判断检验数是否都非负 B．选最大检验数 C．确定换出变量 D．选最小检验数 E．确定换入变量 4．求解约束条件为“≥”型的线性规划、构造基本矩阵时，可用的变量有（）A．人工变量 B．松弛变量 C. 负变量 D．剩余变量 E．稳态变量 5．线性规划问题的主要特征有（） A．目标是线性的 B．约束是线性的 C．求目标最大值 D．求目标最小值 E．非线性三、计算题（共60分） 1. 下列线性规划问题化为标准型。(10分) 1 / 17

《运筹学》期末考试试卷A答案

《运筹学》试题样卷（一）一、判断题（共计10分，每小题1分，对的打√，错的打X ） 1. 无孤立点的图一定是连通图。 2. 对于线性规划的原问题和其对偶问题，若其中一个有最优解，另一个也一定有最优解。 3. 如果一个线性规划问题有可行解，那么它必有最优解。 4．对偶问题的对偶问题一定是原问题。 5．用单纯形法求解标准形式（求最小值）的线性规划问题时，与0 >j σ对应的变量都可以被选作换入变量。 6．若线性规划的原问题有无穷多个最优解时，其对偶问题也有无穷多个最优解。 7. 度为0的点称为悬挂点。 8. 表上作业法实质上就是求解运输问题的单纯形法。 9. 一个图G 是树的充分必要条件是边数最少的无孤立点的图。二、建立下面问题的线性规划模型（8分）某农场有100公顷土地及15000元资金可用于发展生产。农场劳动力情况为秋冬季3500人日；春夏季4000人日。如劳动力本身用不了时可外出打工，春秋季收入为25元 / 人日，秋冬季收入为20元 / 人日。该农场种植三种作物：大豆、玉米、小麦，并饲养奶牛和鸡。种作物时不需要专门投资，而饲养每头奶牛需投资800元，每只鸡投资3元。养奶牛时每头需拨出1.5公顷土地种饲料，并占用人工秋冬季为100人日，春夏季为50人日，年净收入900 元 / 每头奶牛。养鸡时不占用土地，需人工为每只鸡秋冬季0.6人日，春夏季为0.3人日，年净收入2元 / 每只鸡。农场现有鸡舍允许最多养1500 三、已知下表为求解某目标函数为极大化线性规划问题的最终单纯形表，表中54 ,x x 为松弛变量，问

(1)写出原线性规划问题；（4分） (2)写出原问题的对偶问题；（3分） (3)直接由上表写出对偶问题的最优解。（1分）四、用单纯形法解下列线性规划问题（16分） s. t. 3 x1 + x2 + x3?60 x 1- x 2 +2 x 3?10 x 1+x 2-x 3?20 x 1,x 2 ,x 3?0 五、求解下面运输问题。（18分）某公司从三个产地A1、A2、A3将物品运往四个销地B1、B2、B3、B4，各产地的产量、各销地的销量和各产地运往各销地每件物品的运费如表所示：问：应如何调运，可使得总运输费最小? 六、灵敏度分析（共8分）线性规划max z = 10x1 + 6x2 + 4x3 s.t. x1 + x2 + x3 ?100 10x1 +4 x2 + 5 x3 ?600 2x1 +2 x2 + 6 x3 ?300 x1 , x2 , x3 ?0 的最优单纯形表如下： (1)C1在何范围内变化，最优计划不变？(4分) (2)b1在什么范围内变化，最优基不变？(4分) 七、试建立一个动态规划模型。（共8分）

管理运筹学期末试卷题目B卷

运筹学期末试卷（B卷）系别：工商管理学院专业：考试日期：年月日姓名：学号：成绩： 1．[10分] 匹克公司要安排4个工人去做4项不同的工作，每个工人完成各项工作所消耗的时间（单位：分钟）如下表所示：要求：（1）建立线性规划模型(只建模型,不求解) （2）写出基于Lindo软件的源程序。 2.[15分]某公司下属甲、乙两个厂，有A原料360斤，B原料640斤。甲厂用A、B两种原料生产x1,x2两种产品，乙厂也用A、B两种原料生产x3,x4两种产品。每种单位产品所消耗各种原料的数量及产值、分配等如下

（1）建立规划模型获取各厂最优生产计划。（2）试用图解法求解最优结果。 3．[10分] 考虑下面的线性规划问题: 目标函数：Min Z=16x 1+16x 2 +17x 3 约束条件：利用教材附带软件求解如下: **********************最优解如下************************* 目标函数最优值为 : 148.916 变量最优解相差值 ------- -------- -------- x1 7.297 0 x2 0 .703 x3 1.892 0 约束松弛/剩余变量对偶价格 ------- ------------- -------- 13123123123300.56153420,,0 x x x x x x x x x x x +≤-+≥+-≥≥

1 20.811 0 2 0 -3.622 3 0 -4.73 目标函数系数范围: 变量下限当前值上限 ------- -------- -------- -------- x1 1.417 16 16.565 x2 15.297 16 无上限 x3 14.4 17 192 常数项数范围: 约束下限当前值上限 ------- -------- -------- -------- 1 9.189 30 无上限 2 3.33 3 15 111.25 3 -2.5 20 90 试回答下列问题：（1）第二个约束方程的对偶价格是一个负数(为-3.622)，它的含义是什么? （2）x2有相差值为0.703,它的含义是什么? （3）请对右端常数项范围的上、下限给予具体解释，应如何应用这些数

第三方支付安全性及风险防范问题教案资料

第三方支付安全性及风险防范一、第三方支付概念第三方支付是阿里巴巴集团主席马云在2005年瑞士达沃斯世界经济论坛上首先提出来的，目前为止学术界还没有给出一个非常明确的概念。第三方支付是非金融机构从事金融业务的重要渠道，人民银行发布的《非金融机构支付服务管理办法》中将其定义为依托公共网络或专用网络，在收付款人之间作为中介机构，提供网络支付、预付卡的发行与受理、银行卡收单以及中国人民银行规定的其他支付服务的非金融机构。从其形式上看，所谓第三方支付，就是具备一定实力和信誉的第三方独立机构提供的网络支付平台，它是以非银行机构的第三方支付公司为信用中介，以互联网为基础，通过与各家银行签约，使得其与商业银行间可以进行某种形式的数据交换和相关信息确认，实现持卡人或消费者与各个银行以及最终的收款人或者商家之间建立一个支付的流程。第三方支付通过其支付平台在消费者、商家和银行之间建立连接，起到信用担保和技术保障的作用，实现从消费者到商家以及金融机构之间的货币支付、现金流转、资金结算等功能。在网络交易中，买方选购商品后，使用第三方支付平台把货款支付给第三方，再由第三方通知卖家货款到达并要求卖家发货，买方收到商品并检验后通知第三方，由第三方将货款转至卖家账户。相对于传统的资金划拨交易方式，第三方支付可以对交易双方进行约束和监督，有效地保障货物质量、交易诚信、退换要求等环节，满足电子商务交易的安全性，为交易成功提供必要的支持。如支付宝、财付通等都属于此类平台。与其他支付方式相比，第三方支付服务具有以下特征：（1）支付中介。第三方支付的具体形式是付款人和收款人不直接发生货款往来，借助第三方支付平台完成款项在付款人、银行、支付服务商、收款人之间的转移。第三方支付平台所完成的资金转账都与交易订单密切相关。（2）中立、公正。第三方支付平台不直接参与商品或服务的买卖。公平、公正地维护参与各方的合法权益。

《管理运筹学》期末考试试题

《管理运筹学》期末考试试题一、单项选择题（共5小题，每小题3分，共15分） 1.如果一个线性规划问题有n个变量，m个约束方程(m

3. 写出下面线性规划问题的对偶问题： 123123123123123min z 25, 258, 23 3,.. 4 26, ,,0. x x x x x x x x x s t x x x x x x =++-+≤??++=??-+≤??≥? 四、计算下列各题（每题20分，合计40分） 1. 用单纯形法求解下列线性规划的最优解： 012121212max 2..32250,0x x x s t x x x x x x =+??≤??≤??+≤??≥≥? 2.用割平面法求解整数规划问题。 12 121212 max 7936735,0,z x x x x x x x x =+-+≤??+≤??≥?且为整数

以支付宝为例的第三方支付平台分析电子教案

以支付宝为例的第三方支付平台分析

以支付宝为例的第三方支付平台分析作者：马红梅来源：《今日财富》2018年第24期纵观市场上已经出现的第三方支付平台，支付宝实名用户超过5.8亿，是其中的佼佼者，其通过与众多知名的购物平台进行合作，迅速获取了知名度，在市场上获取了一席之地，并且成功坐上了第三方支付平台的霸主地位。本文阐述了以支付宝为例的第三方支付平台，通过其背景现状、主要服务、商业模式、技术手段与风险管理、发展前景这六个方面来对以支付宝为例的第三方支付平台进行分析。一、背景现状支付宝虽然已经发展为中国最大的第三方支付平台，但是支付宝的使用者大多数为年轻人，像一些中老年群体很少注册使用支付宝，这种情况也不难理解，支付宝极大的迎合了大部分群体方便快捷的消费需求，但还是有一部分人不愿意去使用支付宝，其中最主要的原因是其考虑到第三方支付的安全隐患。虽然这样，但是支付宝的使用人数却还是达到了让人叹为观止的程度。二、主要服务方便快速地查询账单、账户余额、物流信息；免费跨行转账，信用卡还款、生活缴费；消费信息智能提醒；为子女父母建立亲情账户；提供本地生活服务，推荐当地特色美食；买单打折尽享优惠；余额宝理财；支持接入手机健康数据，与好友一起互动，行走捐，参与公益。三、商业模式（一）运营模式支付宝运作的实质是以支付宝为信用中介。首先买家在网上选中自己所需商品后与卖家协商，确定交易后买方需把货款汇到支付宝这个第三方账户上，支付宝作为中介方立即通知卖方钱已经收到，可以发货，待买方收到商品并确认无误后，支付宝随即把货款汇到卖方的账户以完成整个交易。支付宝在这个流程中充当第三方的角色，同时为买卖双方提供信誉，确保交易安全进行。（二）主要盈利模式首先支付宝作为第三方支付，最显著的收益是支付宝页面各种广告的广告费用，主要盈利渠道是收取手续费，即支付宝在快速提现、网购、航空客票等方面以加上毛利润的费率，向客户收取费用。其次在2005年，支付宝进入B2C业务，根据用户不同级别，给予不同的免费额度，并对超出的部分收取手续费从而获得稳定的收入。再次支付宝还有服务费的收益，主要分为理财相关业务和代缴费业务的服务费。四、技术手段

最全第三方支付平台对比

最全第三网上支付平台对比今天的网上购物非常方便快捷,实现了不少人“足不出户买尽天下商品”的梦想,当然啦,网上购物之所以越来越流行,除了与网上商品越来越丰富有关外,也与网上购物的付款方式越来越简单、方便也是密不可分的,付款更容易,买卖自然更加畅通. 第三方网上支付、电话支付,甚至货到付款等不同的网上购物支付形式满足了不同的消费者需求,其中第三方网上支付系统平台无疑是网上购物付款的主要途径,今天我们就来详细对比一下流行的第三方支付平台,看看哪一个才是你的首选. 什么是第三方支付平台？第三方支付平台相当于一个中介人的角色,连接着商家与客户.客户在网上选定要购买的商品后,将货款支付给第三方支付平台,平台收到货款后通知商家发货,等客户收到商品后给出确认信息,第三方支付平台就会将货款转入商家的账户中.由于在整个交易过程中货款是寄存在第三方支付平台这个“中介人”处的,因此客户不用担心自己付款以后商家不发货,商家也不必担心发货以后客户不付款,就如客户在淘宝网、拍拍网等购物网站上购物,收到商品并确认商品没有质量问题,发出付款请求后,商家才能收到货款一样. 不过,随着第三方支付平台应用范围的扩大,在不少B2C网上商城购物也可以通过第三方支付平台付款,甚至订机票、交水电费、信用卡还款、网上买基金等都可以通过第三方支付平台来进行. 在目前主流的第三方支付平台中,阿里巴巴旗下的支付宝与腾讯旗下的财付通是最多人所熟悉的,他们分别有自己的购物网站淘宝网与拍拍网,支付宝与财付通这种依托自有网上购物网站发展起来的综合性支付平台是目前第三方网上支付市场的主力军,此外,也有一些购物网站与支付宝和财付通签约,客户可以通过它们来完成支付,因此综合性第三方支付平台的应用范围更为广泛. 此外,也有独立的第三方支付平台,如快钱、易宝支付（YeePay）、环迅支付、网银在线、首信易支付等,这类支付平台尽管缺少自有网上购物网站的支持,其独立的特点也让不少购物网站青睐；而且与综合性支付平台相比,它们的支付业务也各具特色,如快钱的生活类支付业务丰富,环迅支付的网游支付业务支持种类较多,首信易支付开展了不少支付返现的优惠活动……不得不提的一个第三方支付平台是ChinaPay,这是中国银联旗下的电子支付平台,作为一个“国”字辈的支付平台,ChinaPay 拥有的银行资源是最为丰富的,通过中国银联的平台,用户可以选择不同的银行卡进行网上支付. 下面我们就来全方位对比一下上述主流的第三方支付平台. 第三方支付平台大比拼

管理运筹学期末复习资料【韩伯棠】

运筹学（Operational Research）复习资料第一章绪论一、名词解释 1.运筹学：运筹学是应用分析、试验、量化的方法，对经济管理系统中的人力、物力、财力等资源进行统筹安排，为决策者提供有依据的最优方案，以实现最有效的管理。二、选择题 1.运筹学的主要分支包括（ABDE ） A图论B线性规划C非线性规划D整数规划E目标规划 2. 最早运用运筹学理论的是（ A ） A . 二次世界大战期间，英国军事部门将运筹学运用到军事战略部署 B . 美国最早将运筹学运用到农业和人口规划问题上 C . 二次世界大战期间，英国政府将运筹学运用到政府制定计划 D . 50年代，运筹学运用到研究人口，能源，粮食，第三世界经济发展等问题上第二章线性规划的图解法一、选择题/填空题 1.线性规划标准式的特点：（1）目标函数最大化（2）约束条件为等式（3 决策变量为非负（4 ) 右端常数项为非负2. 在一定范围内，约束条件右边常数项增加一个单位：（1）如果对偶价格大于0，则其最优目标函数值得到改进，即求最大值时，最优目标函数值变得更大，求最小值时最优目标函数值变得更小。（2）如果对偶价格小于0，则其最优目标函数值变坏，即求最大值时，最优目标函数值变小了；求最小值时，最优目标函数值变大了。（3）如果对偶价格等于0，则其最优目标函数值不变。 3.LP模型（线性规划模型）三要素：（1）决策变量（2）约束条件（3）目标函数 4. 数学模型中，“s·t”表示约束条件。 5. 将线性规划模型化成标准形式时，“≤”的约束条件要在不等式左端加上松弛变量。 6. 将线性规划模型化成标准形式时，“≥”的约束条件要在不等式左端减去剩余变量。7．下列图形中阴影部分构成的集合是凸集的是A

生物信息学选择题(Bioinformatics multiple-choice question)

生物信息学选择题（Bioinformatics multiple-choice question）The meaning of UTR is (B). A. coding region B. noncoding region C. low complexity region D. open reading frame The meaning of motif is (D). A. motif B. cross clonal population C. base pair D. domain The meaning of algorithm is (B). A. logon number B. algorithm C. alignment D. analogy

RGP is (D). A. online human Mendel genetic data B. national nucleic acid database C. human genome project D. rice genome project The following Fasta format is correct (B). A. seq1: agcggatccagacgctgcgtttgctggctttgatgaaaactctaactaaacactccctt a B. >seq1 agcggatccagacgctgcgtttgctggctttgatgaaaactctaactaaacactccctt a C. seq1:agcggatccagacgctgcgtttgctggctttgatgaaaactctaactaaacact ccctta D. >seq1agcggatccagacgctgcgtttgctggctttgatgaaaactctaactaaac actccctta If we are trying to do subcellular localization of proteins, we should use (D). A. NDB database

《管理运筹学期末复习题》

运筹学期末复习题一、判断题： 1、任何线性规划一定有最优解。（） 2、若线性规划有最优解，则一定有基本最优解。（） 3、线性规划可行域无界，则具有无界解。（） 4、基本解对应的基是可行基。（） 5、在基本可行解中非基变量一定为零。（） 6、变量取0或1的规划是整数规划。（） 7、运输问题中应用位势法求得的检验数不唯一。（） 8、产地数为3，销地数为4的平衡运输中，变量组{X11，X13，X22，X33，X34}可作为一组基变量.（） 9、不平衡运输问题不一定有最优解。（） 10、m+n-1个变量构成基变量组的充要条件是它们不包含闭回路。（） 11、含有孤立点的变量组不包含有闭回路。（） 12、不包含任何闭回路的变量组必有孤立点。（） 13、产地个数为m销地个数为n的平衡运输问题的系数距阵为A，则有r(A)≤m+n-1（） 14、用一个常数k加到运价矩阵C的某列的所有元素上,则最优解不变。（） 15、匈牙利法是求解最小值分配问题的一种方法。（） 16、连通图G的部分树是取图G的点和G的所有边组成的树。（） 17、求最小树可用破圈法.（） 18、Dijkstra算法要求边的长度非负。（） 19、Floyd算法要求边的长度非负。（） 20、在最短路问题中，发点到收点的最短路长是唯一的。（） 21、连通图一定有支撑树。（） 22、网络计划中的总工期等于各工序时间之和。

（） 23、网络计划中，总时差为0的工序称为关键工序。（） 24、在网络图中，关键路线一定存在。（） 25、紧前工序是前道工序。（） 26、后续工序是紧后工序。（） 27、虚工序是虚设的,不需要时间,费用和资源,并不表示任何关系的工序。（） 28、动态规划是求解多阶段决策问题的一种思路，同时是一种算法。（） 29、求最短路径的结果是唯一的。（） 30、在不确定型决策中，最小机会损失准则比等可能性则保守性更强。（） 31、决策树比决策矩阵更适于描述序列决策过程。（） 32、在股票市场中，有的股东赚钱，有的股东赔钱，则赚钱的总金额与赔钱的总金额相等，因此称这一现象为零和现象。（） 33、若矩阵对策A的某一行元素均大于0，则对应值大于0。（） 34、矩阵对策中，如果最优解要求一个局中人采取纯策略，则另一局中人也必须采取纯策略。（） 35、多阶段决策问题的最优解是唯一的。（） 36、网络图中相邻的两个结点之间可以有两条弧。（）

管理运筹学期末复习题一

管理运筹学期末复习题（一）一、单项选择题 1、下列关于运筹学的优点中，不正确的是( )。 A．凡是可以建立数学模型的问题，都一定能用运筹学的方法求得最优解 B．运筹学可以量化分析许多问题 C．大量复杂的运筹学问题，可以借助计算机来处理 D．对复杂的问题可以较快地找到最优的解决方法 2、对于线性规划问题，下列说法正确的是（）。 A．线性规划问题可能没有可行解 B．在图解法上，线性规划问题的可行解区域都是“凸”区域 C．线性规划问题如果有最优解，则最优解可以在可行解区域的顶点上到达 D．上述说法都正确 3、一般在应用线性规划建立模型时要经过四个步骤：（1）明确问题，确定目标函数，列出约束条件（2）收集资料，确定模型（3）模型求解与检验（4）优化后分析以上四步的正确顺序是（）。 A．（1）（2）（3）（4）B．（2）（1）（3）（4） C．（1）（2）（4）（3）D．（2）（1）（4）（3） 4、任何求最大目标函数值的纯整数规划或混合整数规划的最大目标函数值应（）相应的线性规划的最大目标函数值。 A．小于或等于B．大于或等于C．小于D．大于 5、求解需求量小于供应量的运输问题不需要做的是（）。 A．令供应点到虚设的需求点的单位运费为0 B．虚设一个需求点 C．取虚设的需求点的需求量为恰当值D．删去一个供应点 6、动态规划的求解思路与方法是（）。 A．位势法 B．最小元素法 C．逆序法 D．单纯形法 7、在图论中，( )不正确。 A．若树T有n个点，则其边数为n-1 B．树中若多出一边，必出现圈 C．树中点与点都可以不连通D．树中若除去一边，必不连通8、四个棋手单循环比赛，采用三局两胜制决出胜负，如果以棋手为节点，用图来表示比赛结果，则是个( )。 A．有向图B．无向图C．赋权图D．树 9、要用最少费用建设一条公路网，要求在一定时间内通过的车辆尽可能多，已知建设费用与公路长度成正比，那么该问题可以看成是（）。 A．最小生成树问题B．最大流量问题 C．最短路径问题D．最小费用最大流问题 10、存贮论主要解决存贮策略问题，即两个主要问题（）。 A．存贮费c1和订购费c3 B．每次补充存贮物资的数量Q和间隔时间T C．每次补充存贮物资的数量Q和一年的总费用TC D．每次补充存贮物资的周期T和一年的总费用TC 11、网络图中求解最短路的算法是（）。 A．单纯形法B．图上作业法C．双标号算法D．分枝定界法 12、若线性规划的可行域为空集，则该线性规划（）。

第三方支付平台典型案例

第三方支付平台典型案例目前中国国内的典型第三方支付产品主要有： Paypal（易公司产品，流行于欧美国家）、支付宝（阿里巴巴旗下）、财付通（腾讯公司）、网易宝（网易旗下）、百付宝（百度 C2C）、银联电子支付（中国银联）、快钱（qqbill）等。 1、支付宝（一）简介支付宝是阿里巴巴集团于2004年底创办的独立第三方支付平台。截至2012年12月，支付宝注册账户突破8亿，日交易额峰值超过200亿元人民币，日交易笔数峰值达到1亿零580万笔。目前除淘宝和阿里巴巴外，有超过46万的商家和合作伙伴支持支付宝的在线支付和无线支付服务，范围涵盖了B2C购物、航旅机票、生活服务、理财、公益等众多方面。这些商家在享受支付宝服务的同时，也同时拥有了一个极具潜力的消费市场。支付宝已经跟国内外160多家银行以及VISA、MasterCard国际组织等机构建立了深入的战略合作关系，成为金融机构在电子支付领域最为信任的合作伙伴。（2）发展历程

（三）商业模式核心能力：一是强大的后盾为其提供的庞大客户群，淘宝网、阿里巴巴中国站都支持支付宝，这为支付宝获得了其他任何第三方支付平台无法比拟的客户数量；二是安全保障，支付宝对外推出“全额赔付”的政策，使用户有了安全保障。盈利模式：截止2006年底，支付宝对所有用户均是免费使用，没有盈利模式。但从2007年2月开始，支付宝将向非淘宝网卖家收取一定比例的技术服务费用，收费标准约为交易总额1.5%。淘宝网用户可以继续免费使用支付宝。经营模式：1.支付宝前期为淘宝网定制，后扩展到阿里巴巴中国站和非阿里巴巴旗下网站。后来随着产品的成熟，开始在阿里巴巴中国站和非阿里巴巴旗下网站推广。 2.与各大银行、金融机构合作，圈地电子支付市场。支付宝目前已和国内工商银行、农业银行、建设银行、招商银行、上海浦发银行等各大商业银行以及中国邮政、VISA国际组织等各大机构建立了战略合作，成为金融机构在网上支付领域极为信任的合作伙伴。另外，支付宝还与中国建设银行合作，发布了国内首张真正专注于电子商务的联名借记卡———支付宝龙卡及电子支付新产品——支付宝卡通业务。 3. 推出“全额赔付”等措施，打造安全信用体系。 4. 免费模式置对手于被动，扩大市场占有率：不收取费用,大型交易额收取少量手续费；积极收集会员的心声。在论坛里有专门会员意