learning equivalence classes of bayesian network structures two bayesian network structures are said to be equivalent if the set of distributions that can be represented with one of those structures is identical to the set of distributions that can be represented with the other many scoring criteria that are used to learn bayesian network structures from data are score equivalent that is these criteria do not distinguish among networks that are equivalent in this paper we consider using a score equivalent criterion in conjunction with a heuristic search algorithm to perform model selection or model averaging we argue that it is often appropriate to search among equivalence classes of network structures as opposed to the more common approach of searching among individual bayesian network structures we describe a convenient graphical representation for an equivalence class of structures and introduce a set of operators that can be applied to that representation by a search algorithm to move among equivalence classes we show that our equivalence class operators can be scored locally and thus share the computational efficiency of traditional operators defined for individual structures we show experimentally that a greedy model selection algorithm using our representation yields slightly higher scoring structures than the traditional approach without any additional time overhead and we argue that more sophisticated search algorithms are likely to benefit much more

a characterization of markov equivalence classes for acyclic digraphs undirected graphs and acyclic digraphs adgs as well as their mutual extension to chain graphs are widely used to describe dependencies among variables in multivariate distributions in particular the likelihood functions of adg models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building bayesian networks for expert systems whereas the undirected graph associated with a dependence model is uniquely determined there may however be many adgs that determine the same dependence markov model thus the family of all adgs with a given set of vertices is naturally partitioned into markov equivalence classes each class being associated with a unique statistical model statistical procedures such as model selection or model averaging that fail to take into account these equivalence classes may incur substantial computational or other inefficiencies here it is shown that each markov equivalence class is uniquely determined by a single chain graph the essential graph that is itself simultaneously markov equivalent to all adgs in the equivalence class essential graphs are characterized a polynomial time algorithm for their construction is given and their applications to model selection and other statistical questions are described

learning linear cyclic causal models with latent variables identifying cause effect relationships between variables of interest is a central problem in science given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables we provide a detailed description of the model family full proofs of the necessary and sufficient conditions for identifiability a search algorithm that is complete and a discussion of what can be done when the identifiability conditions are not satisfied the algorithm is comprehensively tested in simulations comparing it to competing algorithms in the literature furthermore we adapt the procedure to the problem of cellular network inference applying it to the biologically realistic data of the dreamchallenges the paper provides a full theoretical foundation for the causal discovery procedure first presented by eberhardt et al 2010 and hyttinen et al 2010

permanence of dispersal population model with time delays permanence of a dispersal single species population model is considered where environment is partitioned into several patches and the species requires some time to disperse between the patches the model is described by delay differential equations the existence of food rich patches and small dispersions among the patches are proved to be sufficient to ensure partial permanence of the model it is also shown that partial permanence ensures permanence if each food poor patch is connected to at least one food rich patch and if each pair in food rich patches is connected furthermore it is proved that partial persistence is ensured even under large dispersion among food rich patches if the dispersion time is relatively small

an explicit unconditionally stable variable time step method for one dimensional stefan problems modelling of heat conduction processes with phase changes benefits from the application of variable time step methods when the behaviour of the moving boundary is not known a priori due to convergence and stability constraints only implicit difference equations have been used with these methods implicit methods show a significant loss of accuracy and exhibit convergence difficulties when used for relatively slow or rapid moving boundary problems

finding optimal bayesian network given a super structure classical approaches used to learn bayesian network structure from data have disadvantages in terms of complexity and lower accuracy of their results however a recent empirical study has shown that a hybrid algorithm improves sensitively accuracy and speed it learns a skeleton with an independency test it approach and constrains on the directed acyclic graphs dag considered during the search and score phase subsequently we theorize the structural constraint by introducing the concept of super structure s which is an undirected graph that restricts the search to networks whose skeleton is a subgraph of s we develop a super structure constrained optimal search cos its time complexity is upper bounded by o m n where m 2 depends on the maximal degree m of s empirically complexity depends on the average degree m and sparse structures allow larger graphs to be calculated our algorithm is faster than an optimal search by several orders and even finds more accurate results when given a sound super structure practically s can be approximated by it approaches significance level of the tests controls its sparseness enabling to control the trade off between speed and accuracy for incomplete super structures a greedily post processed version cos still enables to significantly outperform other heuristic searches

a recursive method for structural learning of directed acyclic graphs in this paper we propose a recursive method for structural learning of directed acyclic graphs dags in which a problem of structural learning for a large dag is first decomposed into two problems of structural learning for two small vertex subsets each of which is then decomposed recursively into two problems of smaller subsets until none subset can be decomposed further in our approach search for separators of a pair of variables in a large dag is localized to small subsets and thus the approach can improve the efficiency of searches and the power of statistical tests for structural learning we show how the recent advances in the learning of undirected graphical models can be employed to facilitate the decomposition simulations are given to demonstrate the performance of the proposed method

estimating high dimensional directed acyclic graphs with the pc algorithm we consider the pc algorithm spirtes et al 2000 for estimating the skeleton and equivalence class of a very high dimensional directed acyclic graph dag with corresponding gaussian distribution the pc algorithm is computationally feasible and often very fast for sparse problems with many nodes variables and it has the attractive property to automatically achieve high computational efficiency as a function of sparseness of the true underlying dag we prove uniform consistency of the algorithm for very high dimensional sparse dags where the number of nodes is allowed to quickly grow with sample size n as fast as o na for any 0 a the sparseness assumption is rather minimal requiring only that the neighborhoods in the dag are of lower order than sample size n we also demonstrate the pc algorithm for simulated data

a numerical method for oxygen diffusion and absorption in a sike cell oxygen diffusion in a sike cell with simultaneous absorption is an important problem and has a wide range of medical applications the problem mathematically formulated through two different stages the present paper concerns mainly on the second stage in which the injected oxygen through the cell starts absorbing the basic idea of the proposed numerical method is to form a double linear system of equations each of dimension 4x4 the first system is formed through applying first second third and fourth moments and using assumed profile for the concentration containing four unknowns functions of time numerical solution through a proposed scheme leads to the unknown functions the second system is formed through applying the boundary conditions given in addition to another assumed condition that is the concentration at x 0 is unknown function of time the results of the first system becomes an entry data for the second one leading to the concentration at the fixed surface x 0 the results obtained by the present method were compared with two different methods and the results gave a good agreement

counting and exploring sizes of markov equivalence classes of directed acyclic graphs when learning a directed acyclic graph dag model via observational data one generally cannot identify the underlying dag but can potentially obtain a markov equivalence class the size the number of dags of a markov equivalence class is crucial to infer causal effects or to learn the exact causal dag via further interventions given a set of markov equivalence classes the distribution of their sizes is a key consideration in developing learning methods however counting the size of an equivalence class with many vertices is usually computationally infeasible and the existing literature reports the size distributions only for equivalence classes with ten or fewer vertices in this paper we develop a method to compute the size of a markov equivalence class we first show that there are five types of markov equivalence classes whose sizes can be formulated as five functions of the number of vertices respectively then we introduce a new concept of a rooted sub class the graph representations of rooted subclasses of a markov equivalence class are used to partition this class recursively until the sizes of all rooted subclasses can be computed via the five functions the proposed size counting is efficient for markov equivalence classes of sparse dags with hundreds of vertices finally we explore the size and edge distributions of markov equivalence classes and find experimentally that in general 1 most markov equivalence classes are half completed and their average sizes are small and 2 the sizes of sparse classes grow approximately exponentially with the numbers of vertices

permanence in nonautonomous lotka volterra system with predator prey the nonautonomous lotka volterra system with m predators and n preys is considered in this paper average conditions are obtained for permanence and global attractivity in the system it is shown that our results are generalization of those of the periodic system

existence and global attractivity of positive periodic solutions for the impulsive delay nicholson s blowflies model in this paper we shall consider the following nonlinear impulsive delay population model 0 1 x t d t x t p t x t m w e a t x t m w a e t 0 t t k x t k 1 b k x t k k 1 2 where m is a positive integer d t a t and p t are positive periodic continuous functions with period w 0 in the nondelay case m 0 we show that 0 1 has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate linear periodic impulsive perturbations the impulsive delay equation 0 1 preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

estimation of sparse directed acyclic graphs for multivariate counts data the next generation sequencing data called high throughput sequencing data are recorded as count data which are generally far from normal distribution under the assumption that the count data follow the poisson log normal distribution this article provides an l1 penalized likelihood framework and an efficient search algorithm to estimate the structure of sparse directed acyclic graphs dags for multivariate counts data in searching for the solution we use iterative optimization procedures to estimate the adjacency matrix and the variance matrix of the latent variables the simulation result shows that our proposed method outperforms the approach which assumes multivariate normal distributions and the log transformation approach it also shows that the proposed method outperforms the rank based pc method under sparse network or hub network structures as a real data example we demonstrate the efficiency of the proposed method in estimating the gene regulatory networks of the ovarian cancer study

dynamics of a class of nonautonomous semi ratio dependent predator prey systems with functional responses abstract in this paper we investigate the dynamics of a class of the so called semi ratio dependent predator prey interaction models with functional responses based on systems of nonautonomous differential equations with time dependent parameters the functional responses are classified into five types and typical examples of each type are provided then we establish sufficient criteria for the boundedness of solutions the permanence of system and the existence uniqueness and globally asymptotic stability of positive periodic solution and positive almost periodic solution some conclusive discussion is presented at the end of this paper

asymptotic behaviors of competitive lotka volterra system with stage structure in this paper a two species competitive model with stage structure is presented and studied results on the global extinction and permanence are given which generalize the well known three theorems for the two species competitive system and moreover they confirm the negative effect of stage structure on the permanence of populations as well as estimate the degree of such effect conclusions in this paper suggest that for a competitive community stage structure is also one of the important reasons that cause permanence and extinction

permanence of a delayed non autonomous gilpin ayala competition model abstract in this paper we consider a delayed non autonomous n species gilpin ayala competitive system which is more general and more realistic then classical lotka volterra competition model by means of ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the permanence of the system it is shown that our result is the generalization of those of zhao et al j d zhao j f jiang a c lazer the permanence and global attractivity in a nonautonomous lotka volterra system nonlinear analysis real world applications 5 4 2004 265 276 our results also supplement the results of fan and wang m fan k wang global periodic solutions of a generalized n species gilpin ayala competition model computer and mathematics with applications 40 2000 1141 1151

stochastic complexity and modeling on demontre un theoreme fondamental qui donne une borne inferieure pour la longueur de code et donc pour les erreurs de prediction on definit les notions d information a priori et d information utile dans les donnees

a new semi analytical method for phase transformations in binary alloys in the present paper a new semi analytical method is developed to cover a wide range of phase transformation problems and their practical applications the solution procedure consists of two parts first determination of the position of the moving boundary named the homogenous part and second determination of the concentration named the non homogenous part the homogenous part leads to a system of homogenous linear equations based on the mathematical fact that a homogenous system has a non trivial solution if the determinant of the coefficient matrix equals zero this determinant leads to an ordinary differential equation for the moving boundary and its solution leads to a closed form formula for the position of the moving boundary the non homogenous part transforms the governing equations to a non homogenous linear system of equations having three unknowns that appear in the concentration profile assumed in the beginning of the proposed method solution of the non homogenous system leads to a value of these unknowns once these unknowns are computed the concentration at any time and at any point can be found easily

the effect of dispersal on permanence in a predator prey population growth model abstract in this paper we consider a periodic predator prey system where the prey can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation we assume a volterra within patch dynamic under the assumption that the average of dispersal rate from patch 1 to patch 2 is less than that of the intrinsic growth rate of prey in patch 1 we provide a sufficient and necessary condition to guarantee the prey and predator species to be permanent by using the main techniques in 1

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

optimal structure identification with greedy search in this paper we prove the so called meek conjecture in particular we show that if a dag h is an independence map of another dag g then there exists a finite sequence of edge additions and covered edge reversals in g such that 1 after each edge modification h remains an independence map of g and 2 after all modifications g h as shown by meek 1997 this result has an important consequence for bayesian approaches to learning bayesian networks from data in the limit of large sample size there exists a two phase greedy search algorithm that when applied to a particular sparsely connected search space provably identifies a perfect map of the generative distribution if that perfect map is a dag we provide a new implementation of the search space using equivalence classes as states for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain finally using both synthetic and real world datasets we demonstrate that the two phase greedy approach leads to good solutions when learning with finite sample sizes

three dimensional periodic systems with trivial dynamics ii 3 where t g r u s u u u g v v r is open and f t u 1 2 3 f t u u f t u f t u u is continuous in v is t periodic in the i 1 2 2 3 2 3 time t and has continuous partial derivative fr u defined on r v we also assume that the following hypotheses hold h f r u f r u f r u and f r u 0 on r v 1 1 2 2 1 2 3 3 2 3 h f has a continuous extension f r v a r such that 2 0 0 f r u is defined and continuous in a neighborhood v of v 0 0

global dynamics of delay equations for populations with competition among immature individuals abstract we analyze a population model for two age structured species allowing for inter and intra specific competition at immature life stages the dynamics is governed by a system of delay differential equations ddes recently introduced by gourley and liu the analysis of this model presents serious difficulties because the right hand sides of the ddes depend on the solutions of a system of nonlinear odes and generally cannot be solved explicitly using the notion of strong attractor we reduce the study of the attracting properties of the equilibria of the ddes to the analysis of a related two dimensional discrete system then we combine some tools for monotone planar maps and planar competing lotka volterra systems to describe the dynamics of the model with three different birth rate functions we give easily verifiable conditions for global extinction of one or the two species and for global convergence of the positive solutions to a coexistence state

a scoring function for learning bayesian networks based on mutual information and conditional independence tests we propose a new scoring function for learning bayesian networks from data using score search algorithms this is based on the concept of mutual information and exploits some well known properties of this measure in a novel way essentially a statistical independence test based on the chi square distribution associated with the mutual information measure together with a property of additive decomposition of this measure are combined in order to measure the degree of interaction between each variable and its parent variables in the network the result is a non bayesian scoring function called mit mutual information tests which belongs to the family of scores based on information theory the mit score also represents a penalization of the kullback leibler divergence between the joint probability distributions associated with a candidate network and with the available data set detailed results of a complete experimental evaluation of the proposed scoring function and its comparison with the well known k2 bdeu and bic mdl scores are also presented

numerical treatment of moving and free boundary value problems with the tau method this paper reports numerical experiments on the implementation of the operational formulation of the tau method for moving and free boundary value problems we consider problems defined by linear and nonlinear ordinary differential equations and by linear partial differential equa tions we compare the accuracy attainable with the technique introduced in this paper with that of standard numerical techniques we find that the tau method provides accurate results even using approximations of a low degree this paper reports numerical experiments on the implementation of the operational formulation of the tan method for the numerical treatment of moving and free boundary value problems we consider first problems involving linear and nonlinear ordinary differential equations and develop on them basic strategies for their tau method approximate solution we then discuss a tau lines formulation of these techniques and apply it to the approximate solution of a moving boundary value problem for partial differential equations the problem considered is related to a model for the diffusion and absorption of oxygen in biological tissue we compare our results with those obtained in the related literature using seven different numerical techniques we find that the tan method provides accurate results even using low degree polynomial approximations

efficient structure learning of bayesian networks using constraints this paper addresses the problem of learning bayesian network structures from data based on score functions that are decomposable it describes properties that strongly reduce the time and memory costs of many known methods without losing global optimality guarantees these properties are derived for different score criteria such as minimum description length or bayesian information criterion akaike information criterion and bayesian dirichlet criterion then a branch and bound algorithm is presented that integrates structural constraints with data in a way to guarantee global optimality as an example structural constraints are used to map the problem of structure learning in dynamic bayesian networks into a corresponding augmented bayesian network finally we show empirically the benefits of using the properties with state of the art methods and with the new algorithm which is able to handle larger data sets than before

exact bayesian structure discovery in bayesian networks learning a bayesian network structure from data is a well motivated but computationally hard task we present an algorithm that computes the exact posterior probability of a subnetwork e g a directed edge a modified version of the algorithm finds one of the most probable network structures this algorithm runs in time o n 2n nk 1c m where n is the number of network variables k is a constant maximum in degree and c m is the cost of computing a single local marginal conditional likelihood for m data instances this is the first algorithm with less than super exponential complexity with respect to n exact computation allows us to tackle complex cases where existing monte carlo methods and local search procedures potentially fail we show that also in domains with a large number of variables exact computation is feasible given suitable a priori restrictions on the structures combining exact and inexact methods is also possible we demonstrate the applicability of the presented algorithm on four synthetic data sets with 17 22 37 and 100 variables

on inclusion driven learning of bayesian networks two or more bayesian network structures are markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies therefore the search space of bayesian network structures may be organized in equivalence classes where each of them represents a different set of conditional independencies the collection of sets of conditional independencies obeys a partial order the so called inclusion order this paper discusses in depth the role that the inclusion order plays in learning the structure of bayesian networks in particular this role involves the way a learning algorithm traverses the search space we introduce a condition for traversal operators the inclusion boundary condition which when it is satisfied guarantees that the search strategy can avoid local maxima this is proved under the assumptions that the data is sampled from a probability distribution which is faithful to an acyclic digraph and the length of the sample is unbounded the previous discussion leads to the design of a new traversal operator and two new learning algorithms in the context of heuristic search and the markov chain monte carlo method we carry out a set of experiments with synthetic and real world data that show empirically the benefit of striving for the inclusion order when learning bayesian networks from data

a generalized back door criterion we generalize pearl s back door criterion for directed acyclic graphs dags to more general types of graphs that describe markov equivalence classes of dags and or allow for arbitrarily many hidden variables we also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back door criterion when considering a single intervention and a single outcome variable moreover if such a set exists we provide an explicit set that fulfills the criterion we illustrate the results in several examples r code is available in the r package pcalg

bnc pso structure learning is a very important problem in the field of bayesian networks bns it is also an active research area for more than 2 decades therefore many approaches have been proposed in order to find an optimal structure based on training samples in this paper a particle swarm optimization pso based algorithm is proposed to solve the bn structure learning problem named bnc pso bayesian network construction algorithm using pso edge inserting deleting is employed in the algorithm to make the particles have the ability to achieve the optimal solution while a cycle removing procedure is used to prevent the generation of invalid solutions then the theorem of markov chain is used to prove the global convergence of our proposed algorithm finally some experiments are designed to evaluate the performance of the proposed pso based algorithm experimental results indicate that bnc pso is worthy of being studied in the field of bns construction meanwhile it can significantly increase nearly 15 in the scoring metric values comparing with other optimization based algorithms

learning gaussian tree models analysis of error exponents and extremal structures the problem of learning tree structured gaussian graphical models from independent and identically distributed i i d samples is considered the influence of the tree structure and the parameters of the gaussian distribution on the learning rate as the number of samples increases is discussed specifically the error exponent corresponding to the event that the estimated tree structure differs from the actual unknown tree structure of the distribution is analyzed finding the error exponent reduces to a least squares problem in the very noisy learning regime in this regime it is shown that the extremal tree structure that minimizes the error exponent is the star for any fixed set of correlation coefficients on the edges of the tree if the magnitudes of all the correlation coefficients are less than 0 63 it is also shown that the tree structure that maximizes the error exponent is the markov chain in other words the star and the chain graphs represent the hardest and the easiest structures to learn in the class of tree structured gaussian graphical models this result can also be intuitively explained by correlation decay pairs of nodes which are far apart in terms of graph distance are unlikely to be mistaken as edges by the maximum likelihood estimator in the asymptotic regime

numerical approximation for the oxygen diffusion problem oxygen diffusion problem examines the injection of oxygen into a sick cell and diffusion of the injected oxygen inside the cell mathematical model of the problem has two steps at the first step the stable case having no oxygen transition in the isolated cell is searched while at the second step the moving boundary problem of oxygen absorbed by the tissues in the cell is searched in this study trace of moving boundary of the oxygen diffusion problem is determined using constrained integral method the profile of moving boundary is determined by the third and the fourth order polynoms and the results are compared with the preceding studies

variable time step method with coordinate transformation abstract the variable time step methods for solving moving boundary problems are presented by transforming the variable space domain this results in dissociating the mode of advancement of the boundary from the size of the space mesh that is a small movement of the moving boundary may be chosen for computing the time interval while the space domain is subdivided into larger space meshes as a consequence an enormous amount of saving in computer time may be achieved by using the proposed method two sample problems are selected for the illustration of the method

extinction in periodic competitive stage structured lotka volterra model with the effects of toxic substances in this paper we consider a periodic competitive stage structured lotka volterra model with the effects of toxic substances it is shown that toxic substances play an important role in the extinction of species we obtain a set of sufficient conditions which guarantee that one of the components is driven to extinction while the other is globally attractive the numerical simulation of an example verifies our main results

optimal search on clustered structural constraint for learning bayesian network structure we study the problem of learning an optimal bayesian network in a constrained search space skeletons are compelled to be subgraphs of a given undirected graph called the super structure the previously derived constrained optimal search cos remains limited even for sparse super structures to extend its feasibility we propose to divide the super structure into several clusters and perform an optimal search on each of them further to ensure acyclicity we introduce the concept of ancestral constraints acs and derive an optimal algorithm satisfying a given set of acs finally we theoretically derive the necessary and sufficient sets of acs to be considered for finding an optimal constrained graph empirical evaluations demonstrate that our algorithm can learn optimal bayesian networks for some graphs containing several hundreds of vertices and even for super structures having a high average degree up to four which is a drastic improvement in feasibility over the previous optimal algorithm learnt networks are shown to largely outperform state of the art heuristic algorithms both in terms of score and structural hamming distance

search for additive nonlinear time series causal models pointwise consistent feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests but no such procedures are available for non linear systems we describe a feasible procedure for learning a class of non linear time series structures which we call additive non linear time series we show that for data generated from stationary models of this type two classes of conditional independence relations among time series variables and their lags can be tested efficiently and consistently using tests based on additive model regression combining results of statistical tests for these two classes of conditional independence relations and the temporal structure of time series data a new consistent model specification procedure is able to extract relatively detailed causal information we investigate the finite sample behavior of the procedure through simulation and illustrate the application of this method through analysis of the possible causal connections among four ocean indices several variants of the procedure are also discussed

permanence for a class of periodic time dependent competitive system with delays and dispersal in a patchy environment in this paper we study m species time delayed competitive lotka volterra type dispersal system with periodic coefficients in n patches by utilizing analytic method sufficient and realistic conditions on permanence and the existence of periodic solution are established the theoretical results are confirmed by a special example and numerical simulations

permanence and extinction in logistic and lotka volterra systems with diffusion abstract in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments differing from former studies our discussion includes the important situation in conservation biology in which species live in a weak patchy environment in the sense that species will become extinct in some of the isolated patches for the single population model we show that identical species can persist for some diffusion rates and can also vanish for another set of restrictions on the diffusion rates although the single endangered species will vanish in some isolated patches without contributions from other patches furthermore we consider the existence uniqueness and global stability of the positive periodic solution for prey predator systems we can make both the prey and the predator species permanent by choosing the diffusion rates appropriately even if the prey species has a negative intrinsic growth rate in some patches moreover we introduce an exotic competitive species y into the habitat occupied by the native species x competitive permanence and competitive exclusion both are considered the implications of these results are significant for the conservation of endangered species

permanence and asymptotic behavior of the n species nonautonomous lotka volterra competitive systems abstract in this paper we study the permanence and global asymptotic behavior for the n species nonautonomous lotka volterra competitive systems where all the parameters are time dependent and asymptotically approach periodic functions respectively some new criteria are established the corresponding results given by peng and chen in 1 are improved and extended

notes on the stability of non rectangular space time finite elements the method of space time finite elements enables the simple solution of quite new problems it is possible to assume the arbitrary partition of the structure area in each moment of integration of the motion equation instability is caused by a too large time step and too great changes of joint locations in successive time steps a changeable spatial partition is useful in contact dynamic problems in the case of a travelling support generally in problems with movable edges in this paper a stability problem is described and some investigations for chosen types of non rectangular space time finite elements are carried out linear and surface elements which in time space gain an additional time dimension are presented some numerical examples prove the efficiency of the described method under determined limitations

permanence extinction and periodic solution of predator prey system with beddington deangelis functional response in this paper we study permanence extinction and periodic solution of periodic predator prey system with beddington deangelis functional response we provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent in addition sufficient condition is derived for the existence of positive periodic solution this paper improves some main results obtained by fan and kuang m fan y kuang dynamics of nonautonomous predator prey system with the beddington deangelis functional response j math anal appl 295 2004 15 39

stability of the boundary solution of a nonautonomous predator prey system with the beddington deangelis functional response abstract the dynamics of a nonautonomous predator prey system with the beddington deangelis functional response is studied from the perspective of extinction of the predator with the help of a fluctuation lemma we obtain a set of new sufficient conditions on the global asymptotic stability of the boundary solution which means the extinction of the predator the result not only improves but also complements some existing ones moreover the result indicates that the effect of the parameters is accumulative rather than pointwise

on the periodic lotka volterra competition model abstract we analyze the existence stability and multiplicity of t periodic coexistence states for the classical nonautonomous periodic lotka volterra competing species model this is done by treating the average values of the birth rates of species as parameters and studying the global structure of the set of coexistence states as these parameters vary as a result of this analysis we can explain the interesting differences between the results for the periodic case and the associated autonomous model

complete numerical solution of the oxygen diffusion problem involving a moving boundary abstract a problem of oxygen diffusion in an absorbing tissue first discussed by crank and gupta 1 is solved by a variable time step method this problem has been attempted by many other authors using various techniques different authors have traced the moving boundary to different stages and the total absorption time has been calculated by some kind of interpolation extrapolation at the end in the present method the time for complete absorption emerges as part of the computing procedure itself in addition the method described here requires in general a smaller number of time steps than do the other methods yet the numerical results compare extremely well with those due to earlier authors

asymptotic classification of the positive solutions of the nonautonomous two competing species problem and assumed that the coefficients were continuous and periodic functions of the same period using a geometric analysis combined with the monotonicity properties of the solutions they obtained interesting consequences w x on the dynamics of this system one of the key results of 4 is theorem 4 8 this result partially describes the possible configurations of the attracting set of the semitrivial periodic solutions and is implicitly used several times throughout the paper in particular in theorems 5 4 and 5 9 w x while this result is correct the proof provided in 4 is somehow incomplete actually it assumes a priori that only certain configurations should be considered and does not look at a situation that at that moment of the proof cannot be disregarded see the remark to theorem 5 6 in our paper in the opinion of the present author the modifications required to complete the proof are nontrivial see proposition 5 4 and theorem 5 6 of our paper and this fact has motivated this paper in the process we obtain a full characterization of the attracting set of the semitrivial periodic solutions and a new formulation of the results that allows an extension to the nonperiodic case

time delayed parabolic system in a two species competitive model with stage structure a two species competitive model with stage structure is discussed the dynamics of coupled system of semilinear parabolic equations with time delays are investigated results on the local and global stabilities of the axial equilibria and positive equilibrium are given our results show that the introduction of diffusion does not affect the permanence and extinction of the species though the introduction of stage structure brings negative effect on it

periodicity and stability for a lotka volterra type competition system with feedback controls and deviating arguments abstract this paper deals with the general periodic lotka volterra type competition systems with feedback controls and deviating arguments by employing fixed point index theory on cone an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved by constructing a suitable lyapunov functional a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given

population systems with nonlinear discrete diffusion terms where fi gi r r r are continuous functions which are t periodic in t and locally lipschitz continuous in xi yi and d d1 dn e e1 en are t periodic nonlinear diffusion functions in the sense of 9 that is d t x e t x are positive homogeneous in x cooperative and irreducible 9 as usual xi yi represent the population density of the species at the patch i we will assume that

average growth and extinction in a competitive lotka volterra system abstract in this paper we answer an earlier conjecture consider a class of nonautonomous competitive lotka volterra systems we show that certain inequalities involving the interaction coefficients and averages of the growth rates imply that the system is persistent however reversing one of these inequalities implies that the n th species goes to extinction

reversible mcmc on markov equivalence classes of sparse directed acyclic graphs author s he y jia j yu b abstract graphical models are popular statistical tools which are used to represent dependent or causal complex systems statistically equivalent causal or directed graphical models are said to belong to a markov equivalent class it is of great interest to describe and understand the space of such classes however with currently known algorithms sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices in this paper we design reversible irreducible markov chains on the space of markov equivalent classes by proposing a perfect set of operators that determine the transitions of the markov chain the stationary distribution of a proposed markov chain has a closed form and can be computed easily specifically we construct a concrete perfect set of operators on sparse markov equivalence classes by introducing appropriate conditions on each possible operator algorithms and their accelerated versions are provided to efficiently generate markov chains and to explore properties of markov equivalence classes of sparse directed acyclic graphs dags with thousands of vertices we find experimentally that in most markov equivalence classes of sparse dags 1 most edges are directed 2 most undirected subgraphs are small and 3 the number of these undirected subgraphs grows approximately linearly with the number of vertices institute of mathematical statistics 2013

characterization and greedy learning of interventional markov equivalence classes of directed acyclic graphs the investigation of directed acyclic graphs dags encoding the same markov property that is the same conditional independence relations of multivariate observational distributions has a long tradition many algorithms exist for model selection and structure learning in markov equivalence classes in this paper we extend the notion of markov equivalence of dags to the case of interventional distributions arising from multiple intervention experiments we show that under reasonable assumptions on the intervention experiments interventionalmarkov equivalence defines a finer partitioning of dags than observational markov equivalence and hence improves the identifiability of causal models we give a graph theoretic criterion for two dags being markov equivalent under interventions and show that each interventional markov equivalence class can analogously to the observational case be uniquely represented by a chain graph called interventional essential graph also known as cpdag in the observational case these are key insights for deriving a generalization of the greedy equivalence search algorithm aimed at structure learning from interventional data this new algorithm is evaluated in a simulation study

a variable time step galerkin method for a one dimensional stefan problem a variable time step vts method is presented for the solution of a one dimensional stefan problem describing the evaporation of droplets the method uses a simple coordinate transformation and transforms the moving boundary problem into a problem on a fixed domain the weak or galerkin formulation of the resulting initial boundary value problem is then used to derive a system of initial value problems in ordinary differential equations the solution is advanced in time by an implicit marching technique coupled with an iterative computation of the time step for a given advancement of the moving boundary an integral relationship is used to correct the time step in each iteration the numerical results obtained by the present method exhibit very good agreement with those obtained by previous methods

extinction and permanence in nonautonomous competitive system with stage structure in this paper the n species nonautonomous stage structured competitive system is constructed and considered sufficient conditions for its extinction and permanence are obtained results here generalize and unify some previous ones moreover it is concluded that stage structure in this system is one of the important factors that effect the extinction and permanence of species

numerical solution of the thermistor problem in this paper we consider the numerical solution of a one dimensional thermistor thermo electric problem with a bulk electrical conductivity which is an inherently non linear function of the temperature the aims of this paper are to present approximate steady state solutions to the thermistor problem using second order central difference weighted approximation methods socdwams and constrained integral methods cims and make their comparison with the exact solution so first of all we apply the cim to each of the cold warm and hot phases to obtain approximate temperature distributions and then the cim is constructed by assuming a quadratic polynomial approximation for the temperature profile a variety of socdwams are applied to solve the problem using a bulk electrical conductivity to be satisfied the physical phenomena of the problem both methods are in very good agreement with the exact solutions