coexistence in a predator prey system we propose a lattice model of two populations predators and prey the model is solved via monte carlo simulations each species moves randomly on the lattice and can live only a certain time without eating the lattice cells are either grass eaten by prey or tree giving cover for prey each animal has a reserve of food that is increased by eating prey or grass and decreased after each monte carlo step to breed a pair of animals must be adjacent and have a certain minimum of food supply the number of offspring produced depends on the number of available empty sites we show that such a predator prey system may finally reach one of the following three steady states coexisting with predators and prey pure prey or an empty one in which both populations become extinct we demonstrate that the probability of arriving at one of the above states depends on the initial densities of the prey and predator populations the amount of cover and the way it is spatially distributed

damping mechanisms in the path integral approach to special effects in superconductivity abstract previous work on semiclassical approximations in squids which involved feynman s path integral technique is here extended to damped josephson systems quantum decay rates of unstable energy levels near the bottom of the quartic potential well are examined rates diagram is compared with that obtained for the undamped case agreement with caldeira leggett results is discussed a description of continuous flux measurements is developed the spreading of the wave function leads to the treatment of flux and charge as canonically conjugate variables

a general formula for the calculation of gaussian path integrals in two and three euclidean dimensions abstract the method which was used in a preceding article for the analytical evaluation of gaussian path integrals in one euclidean dimension is generalized as before the final results are formulae directly applicable to all gaussian path integrals this time in two and in three euclidean dimensions respectively the classical action is almost entirely integrated and the proportionality factor f tb ta in front of the exponential part is expressed in terms of a number of time dependent functions which one encounters in the description of the motion along the classical path the quadratic lagrange function is kept as general as possible e g involving twenty eight terms in the three dimensional case the well known time discretization procedure for path integrals has been avoided instead one of the main steps in the theoretical development consists in applying the convolution property of quantum mechanical green s functions i e in three euclidean dimensions k r b t b r a t a k r b t b r t k r t r a t a d r this equality leads to a non linear algebraic relation between f tb ta f tb t and f t ta the solution of this equation yields the f factor which appears in the propagator represented by the gaussian path integral at two locations the use of some remarkable determinantal identity previously unknown to the author has been indispensable in order to attain the desired final result in the appendix the n dimensional generalization of these identities is formulated

association models and the bivariate normal for contingency tables with ordered categories summary association models considered by goodman 1979 for contingency tables with ordered categories are presented here in a somewhat different form to facilitate comparison with the bivariate normal association models can be applied when an underlying bivariate normal is assumed and also under more general conditions and they provide alternatives to tetrachoric and polychoric correlation these models agree more closely with the bivariate normal than does plackett s model 1965 when the row and column classifications arise from underlying univariate normal distributions the general utility of the association models is illustrated here

a survey of strategies for modeling cross classifications having ordinal variables abstract a survey is given of the main strategies for modeling cross classifications that contain ordinal variables models are described for two way tables in which one or both classifications are ordered and for multidimensional tables in which at least one classification is ordered primary emphasis is given to construction interpretation and implications of loglinear and logit models

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

dynamics of competing predator prey species abstract we study the predator prey model described by the lotka volterra equations n s goel et al rev mod phys 43 1971 231 these coupled non linear differential equations are solved numerically and compared with monte carlo simulations spectral analysis of the data indicate the presence of a fixed set of frequencies and the absence of power law behaviour features introduced to make the model more realistic such as age structures and ageing are found to have no qualitative effect

study of interacting particle systems the transition to the oscillatory behavior of a prey predator model abstract a prey predator system with intelligent pursuit and evasion is studied by means of computer simulations it is found that the model exhibits a coexistence state between prey and predators in this state and depending on the parameters the system may evolve toward two different regimes characterized by the behavior of the prey predator population whitin the oscillatory fixed point regime the specie s density changes periodically remains constant respectively the transition between such regimes is rationalized in terms of a dynamic percolation process

self organized packs selection in predator prey ecosystems received 19 july 2005 revised manuscript received 3 october 2005 published 23 february 2006we present a lattice model of a system of predators of ve kinds competing for prey the predators aregrouped in packs and characterized by two parameters the energy spent on hunting and energy gained by thekill the success of hunting depends on the actual competition among predators found near a prey wedetermine via monte carlo simulations the numbers of predators of each kind as a function of time and thedistribution of the size of their packs we show that the ratio of the energy spent by the competing predatorsdetermines their fate the energy gain plays only a secondary role we show also that the system self organizesitself into groups of predators living in well de ned packs which size depends on the energy spent the mostpreferred size dependence on the energy spent follows a very simple power law we present also a mean eld type approach to the problem and we discuss the differences in the results obtained by the two methods showing in particular that the simulation approach produces more reliable results doi 10 1103 physreve 73 021913 pacs number s 87 23 cc 87 23 kg 05 10 ln 87 23 n

phase transitions and oscillations in a lattice prey predator model a coarse grained description of a two dimensional prey predator system is given in terms of a simple three state lattice model containing two control parameters the spreading rates of prey and predator the properties of the model are investigated by dynamical mean field approximations and extensive numerical simulations it is shown that the stationary state phase diagram is divided into two phases a pure prey phase and a coexistence phase of prey and predator in which temporal and spatial oscillations can be present besides the usual directed percolationlike transition the system exhibits an unexpected different type of transition to the prey absorbing phase the passage from the oscillatory domain to the nonoscillatory domain of the coexistence phase is described as a crossover phenomena which persists even in the infinite size limit the importance of finite size effects are discussed and scaling relations between different quantities are established finally physical arguments based on the spatial structure of the model are given to explain the underlying mechanism leading to local and global oscillations

some models for the analysis of association in multiway cross classifications having ordered categories abstract goodman recently presented a class of models for the analysis of association between two discrete ordinal variables the association was measured in terms of the odds ratios in 2 2 subtables formed from adjacent rows and adjacent columns of the cross classification and models were devised that allowed the odds ratios to depend on an overall effect on row effects on column effects and on other effects this article presents some generalizations of this approach appropriate for multiway cross classifications including a models for the analysis of conditional association b models for the analysis of partial association and c models for the analysis of symmetric association three cross classifications are analyzed with these models and methods and rather simple interpretations of the association in each are provided

models for the analysis of association in multivariate contingency tables abstract the present work describes a family of models that can be used for the analysis of association in multiway cross classifications the models are complementary to the usual i e the so called hierarchical log linear models an advantage of this family of models is that it is frequently possible to give a more parsimonious description of the association than is possible with the usual log linear models approach the models will be especially useful when some or all of the variables are ordinal the models are derived from a reparameterization of the saturated model based on singular value decompositions of interaction terms in the log linear parameterization multivariate association models given in goodman 1979 1986 clogg 1982a b agresti and kezouh 1983 gilula and haberman 1988 and becker and clogg 1989 are obtained as special cases the utility of the models developed in this article is demonstrated with the analysis of two examples the first example a cross classification of

multivariate normal integrals and contingency tables with ordered categories ak dimensional multivariate normal distribution is made discrete by partitioning thek dimensional euclidean space with rectangular grids the collection of probability integrals over the partitioned cubes is ak dimensional contingency table with ordered categories it is shown that loglinear model with main effects plus two way interactions provides an accurate approximation for thek dimensional table the complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables this approach imposes no restriction on the correlation matrix comparisons with other numerical integration algorithms are reported the approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories

semiclassical treatment of the path integral approach to special effects in superconductivity abstract distinctive features of the flux mode regime in the anderson josephson potential are analyzed using both semiclassical path integral and instanton techniques this potential governs the behavior of a superconducting ring interrupted by a weak josephson junction after establishing the relation between wkb and functional integral approximations semiclassical expansions are derived from a discretized version of the feynman propagator the physical meaning of instantons is extended to the condensed matter problem of energy spectrum for weak link ring states localized near the minimum energy regions under certain circumstances an improved wkb approximation enables us to find expression for the decay rates of metastable states performing the reduction of the original anderson josephson shape to a double hump structure although we have not discussed here the temperature dependence of the josephson plasma frequency our calculations are consistent with recent theories for systems at finite temperatures with two metastable states separated by a potential energy barrier

scaling in animal group size distributions an elementary model of animal aggregation is presented the group size distributions resulting from this model are truncated power laws the predictions of the model are found to be consistent with data that describe the group size distributions of tuna fish sardinellas and african buffaloes

the analytical evaluation of one dimensional gaussian path integrals abstract in the introductory section 1 it is outlined how path integrals have made their appearance in quantum mechanics through feynman s formalism in section 2 it is recalled that gaussian path integrals defined as those in which the action is an integral whose integrand is a polynomial of at most the second degree in every dynamical variable involved can be cast into the form f t b t a exp i s cl b a where f t b t a is a coefficient solely depending on the initial time instant t a and the final time instant t b and s cl b a denotes the classical action section 3 is devoted to the calculation of a simple formula for the factor f t b t a in the case of a single particle in one euclidean dimension whereby the most general quadratic form of the lagrange function is considered the method is based upon successive transformations of various related auxiliary gaussian path integrals which are introduced applying feynman s theorem and making use of the well known property k x b t b x a t a k x b t b x t k x t x a t a dx satisfied by quantummechanical green s functions constitute important steps in the theoretical development at the end f t b t a is expressed solely in terms of two functions which one encounters in the description of the classical particle trajectory in section 4 four examples of practical application are given the last one concerns the linear harmonic oscillator with time dependent period and damping subject to a time dependent perturbative force

phase space path integral approach to harmonic oscillator with a time dependent force constant the quantum statistical mechanical propagator for a harmonic oscillator with a time dependent force constant m omega 2 t has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest in a previous work we had obtained the exact propagator for motion in an arbitrary time dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of levy flights a result that can be easily extended to brownian motion in this paper we make a connection between the overdamped brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly we find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time dependent force constant has the form omega 2 t lambda 2 t d lambda t dt where lambda t is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously we also employ this method to arrive at a formal solution of the propagator for both levy flights and brownian subjected to a time dependent harmonic potential in the underdamped limit of friction c 2015 elsevier b v all rights reserved