integrability of the 2d lotka volterra system via polynomial first integrals and polynomial inverse integrating factors we present new first integrals of the two dimensional lotka volterra systems which have a polynomial inverse integrating factor moreover we characterize all the polynomial first integrals of the two dimensional lotka volterra systems

an essay on statistical decision theory 2000 an essay on statistical decision theory journal of the american statistical association vol 95 no 452 pp 1277 1281

integrable hamiltonians with higher transcendental invariants a new family of integrable two dimensional hamiltonians is found the corresponding potentials v x y are determined by the relation phi v y x a1v a2 0 where phi is an arbitrary function and a1 a2 are arbitrary parameters the second constants of motion are higher transcendental functions in momenta these results are found by deriving non separable solutions of the hamilton jacobi equation

on the non integrability of a family of duffing van der pol oscillators we investigate the non integrability of a family of duffing van der pol oscillators x alpha x x2 1 x beta x3 gamma cos omega t by studying the analytic properties of the dynamics in complex time we find that the solutions of have no worse than algebraic singularities at t with only t t 1 2 terms present in their series expansions unlike for example the alpha 0 duffing case where typically log t t terms arise still when integrating around long enough contours a remarkably intricate pattern of square root singularities emerges on different sheets which appears to prevent solutions from ever returning to the original sheet such evidence of infinitely sheeted solutions termed the iss property has also been observed in a number of hamiltonian systems and is illustrated here on a simple example of a single first order differential equation we suggest that the iss property is a necessary condition for non integrability i e non existence of a complete set of analytic single valued constants of the motion which would permit the complete integration of a dynamical system in terms of quadratures

a criterion for non integrability based on poincare s theorem abstract the non integrability of a two degrees of freedom hamiltonian is investigated by a method based on a well known theorem of poincare it is proved that the perturbed system is non integrable for values of the perturbative parameter in an open interval around zero if on a dense set of resonant tori of the unperturbed system the average value of the perturbative function evaluated along the periodic orbits on each torus depends on the particular orbit an application to the separable quartic oscillator with a quadratic perturbation is made and it is shown that if the perturbation is non separable in the same coordinates the system is non integrable

on the number of isolating integrals in perturbed hamiltonian systems with n or 3 degrees of freedom we consider a perturbed hamiltonian system with n or 3 degrees of freedom of the form h h0 epsilon h1 and show that the properties of the average value of the perturbing function h1 along the periodic orbits of the unperturbed integrable part h0 supply criteria for non integrability which restrict the allowed total number of independent integrals of motion

non integrable systems with algebraic singularities in complex time dynamical arguments are presented which suggest that there are non integrable systems without clustering of singularities without infinite singularities or singularities with an infinite number of branches in the complex t plane several examples with only algebraic singularities are studied for which strong numerical evidence is presented for non integrability and infinitely sheeted solutions weak painleve potentials are also analysed from this point of view and all integrable cases are found to possess only finitely sheeted solutions

kowalevski s analysis of the swinging atwood s machine we study the kowalevski expansions near singularities of the swinging atwood s machine we show that there is an infinite number of mass ratios m m where such expansions exist with the maximal number of arbitrary constants these expansions are of the so called weak painleve type however in view of these expansions it is not possible to distinguish between integrable and nonintegrable cases

galoisian obstruction to the integrability of general dynamical systems abstract the galoisian approach to study the integrability of classical hamiltonian systems the so called morales ramis theory has been proved to be useful and powerful by many applications here two analogous forms of the morales ramis theory for general dynamical systems both in vector field and mapping forms are given galois groups of the corresponding variational equations are studied and some necessary conditions of the system to possess a certain number of integrals are presented several applications are given at last to illustrate our results

non integrability of homogeneous two dimensional hamiltonians with velocity dependent potential the non integrability of classes of homogeneous two dimensional hamiltonian systems with a polynomial velocity dependent potential is shown on the basis of ziglin s theorem an analytic expression for the trace of the relevant monodromy matrices is presented which fits the numerical data perfectly an application is made to fokker planck hamiltonians with quadratic and with cubic drift terms

non integrability of gross neveu systems abstract we investigate a class of hamiltonian systems with n degrees of freedom the so called gross neveu systems they appear in the classical and quantum field theories and statistical physics till now it has been proved that these systems are non integrable only for small n in this paper we prove that these systems are not meromorphically integrable in the liouville sense for an arbitrary large n in our proof we apply the morales ramis theory we also propose a certain n parametric generalisation of the classical gross neveu systems and analyse their integrability some comments concerning the proved non integrability and the presence of chaos are also given

on the nonintegrability of yang mils potentials the nonintegrability of three hamiltonian systems obtained by simplifications of the yang mills classical field theory is proved by application of two theorems of yoshida 1987 1988 it is also shown that for the two four degree of freedom systems there exists a set of three independent integrals of motion in involution

admissible predictive density estimation let xj np v xi and y j np v yi be independent p dimensional multivariate normal vectors with common unknown mean based on observing x x we consider the problem of estimating the true predictive density p yj of y under expected kullback leibler loss our focus here is the characterization of admissible procedures for this problem we show that the class of all generalized bayes rules is a complete class and that the easily interpretable conditions of brown and hwang 1982 are sucient for a formal bayes rule to be admissible 1 introduction let xj np v xi and yj np v yi be independent p dimensional multivariate normal vectors with a common unknown mean 2 r p we assume that vx 0 and vy 0 are known we let p xj and p yj denote the conditional densities of x and y suppressing the dependence onvx and vy throughout based on observing only x x we consider the problem of estimating the density p yj of y the natural action spacea0 consists of all proper densities on r p i e

non integrability of the anisotropic stormer problem and the isosceles three body problem abstract we study the anisotropic stormer problem asp and the isosceles three body problem ip from the viewpoint of integrability using morales ramis theory and its generalization the study of their integrability presents particular interest since they model important physical phenomena both problems can be reduced with respect to the s 1 symmetry almeida and stuchi m a almeida t j stuchi non integrability of the anisotropic stormer problem with angular momentum physica d 189 2004 219 233 proved that the reduced asp is non integrable for almost all values of the parameters in this paper we establish the non integrability in the extended liouville sense of the remaining cases the ip is a special case of the three body problem and it can be considered as a generalization of the sitnikov problem here we prove that the complexified reduced ip does not admit an additional independent meromorphic first integral

non integrability of the truncated toda lattice hamiltonian at any order two sufficient conditions for the non existence of an additional analytic integral are given for hamiltonian systems with non homogeneous polynomial potential of an arbitrary degree an application is made to the truncated three particle toda lattice which is proved to be non integrable at any order

a necessary condition for the integrability of homogeneous hamiltonian systems with two degrees of freedom a necessary condition for the integrability of hamiltonian systems with a two dimensional homogeneous potential due to morales ruiz and ramis is extended for more general hamiltonian systems of the form h t p v q with homogeneous functions t p and v q

eaton s markov chain its conjugate partner and mathscr p admissibility suppose that x is a random variable with density f x and that x is a proper posterior corresponding to an improper prior the prior is called p admissible if the generalized bayes estimator of every bounded function of is almost admissible under squared error loss eaton showed that recurrence of the markov chain with transition density r x f x dx is a sufficient condition for p admissibility of we show that eaton s markov chain is recurrent if and only if its conjugate partner with transition density r y x f y x d is recurrent this provides a new method of establishing p admissibility often one of these two markov chains corresponds to a standard stochastic process for which there are known results on recurrence and transience for example when x is poisson and an improper gamma prior is placed on the markov chain defined by r y x is equivalent to a branching process with immigration we use this type of argument to establish p admissibility of some priors when f is a negative binomial mass function and when f is a gamma density with known shape

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

darboux points and integrability of hamiltonian systems with homogeneous polynomial potential in this paper we study the integrability of natural hamiltonian systems with a homogeneous polynomial potential the strongest necessary conditions for their integrability in the liouville sense have been obtained by a study of the differential galois group of variational equations along straight line solutions these particular solutions can be viewed as points of a projective space of dimension smaller by one than the number of degrees of freedom we call them darboux points we analyze in detail the case of two degrees of freedom we show that except for a radial potential the number of darboux points is finite and it is not greater than the degree of the potential moreover we analyze cases when the number of darboux points is smaller than maximal for two degrees of freedom the above mentioned necessary condition for integrability can be expressed in terms of one nontrivial eigenvalue of the hessian of potential calculated at a darboux point we prove that for a given potential these nontrivial eigenvalues calculated for all darboux points cannot be arbitrary because they satisfy a certain relation which we give in an explicit form we use this fact to strengthen maximally the necessary conditions for integrability and we show that in a generic case for a given degree of the potential there is only a finite number of potentials which satisfy these conditions we also describe the nongeneric cases as an example we give a full list of potentials of degree four satisfying these conditions then investigating the differential galois group of higher order variational equations we prove that except for one discrete family among these potentials only those which are already known to be integrable are integrable we check that a finite number of potentials from the exceptional discrete family are not integrable and we conjecture that all of them are not integrable

on the non integrability of some generalized toda lattices abstract we consider a one parameter family of two degrees of freedom generalized toda hamiltonians using ziglin s theorem with some extensions we prove the non existence of an additional single valued analytic integral except for special values of the parameter

stochasticity in yang mills theory some stochastic properties of a subsystem of yang mills classical mechanics are studied which do not fulfill automatically gauss law a possibility not considered before however significant differences with other subsystems already studied are not found for this system

existence of exponentially unstable periodic solutions and the non integrability of homogeneous hamiltonian systems abstract in hamiltonian systems with polynomial potential of homogeneous degree characteristic multipliers floquet multipliers permit an explicit expression for straight line periodic solutions by use of ziglin s theorem it is shown that the existence of an exponentially unstable straight line periodic solution implies the non integrability of the system

non perturbative non integrability of non homogeneous nonlinear lattices induced by non resonance hypothesis abstract we succeeded in applying ziglin s test on non integribility to non homogeneous nonlinear lattices fermi pasta ulam fpu lattices by explicit calculations of the eigenvalues of the monodromy matrices concerning the normal variational equations of lame type and with the use of the non resonance hypothesis about the eigenvalues we obtained a theorem proving the non existence of additional analytic conserved quantities other than the hamiltonian itself for the fpu lattices in the low energy limit furthermore after introducing a concept of degree of non integrability we investigated the classification of non homogeneous nonlinear lattices using a transformation r from a non homogeneous nonlinear lattice to another non homogeneous nonlinear lattice which preserves their degree of non integrability

justification of painleve analysis for hamiltonian systems by differential galois theory abstract the discovery of the kowalevski top 1889 as a new integrable system posed the question whether there exists a rigorous relation between integrability of a hamiltonian system and the analytic property of the solution in the complex time plane many examples suggest a hidden relation between the nature of singularities of solution and the integrability of the system without enough justification of the method itself this so called painleve analysis to determine the values of parameters such that the singularities are only poles made it possible to discover some new integrable systems in this paper a recent justification of this analysis will be reviewed which is based on the differential galois theory a rigorous statement is that possessing the weak painleve property is a necessary condition for integrability of hamiltonian systems with a homogeneous potential

regular and chaotic motion in some quartic potentials the hamiltonian halpha x y px py 1 2 px2 py2 valpha x y with o or alpha or 1 and valpha x y 1 24 x y 4 x y 4 1 24 alpha x4 y4 is integrable for alpha 0 and for alpha 1 the potential is v1 x y 1 2 x2y2 a detailed numerical study using surfaces of section and properties of periodic orbits for the entire range of alpha strongly indicates that there are no invariants for h1 so the motion is completely chaotic this result presents problems for the semiclassical quantisation of gauge fields

lie symmetries and invariants of the lotka volterra system in this paper we use the lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3d lotka volterra system

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

lie symmetries for the reduced three wave interaction problem the authors show how the method of lie symmetries can be used to obtain first integrals and for the identification of completely or partially integrable cases of the reduced three wave interaction problem

nonintegrability of nonhomogeneous nonlinear lattices we study the integrability of nonlinear lattices with nonhomogeneous polynomial potentials we prove a nonintegrability theorem for these dynamical systems

on the integrability of bianchi cosmological models in this paper we investigate the problem of the integrability of bianchi class a cosmological models this class of systems is reduced to the form of hamiltonian systems with exponential potential forms the dynamics of bianchi class a models is investigated through the euler lagrange equations and geodesic equations in the jacobi metric on this basis we have come to some general conclusions concerning the evolution of the volume of 3 space of constant time the general form of this function has been found it can serve as a controller during numerical calculations of the dynamics of cosmological models the integrability of cosmological models is also discussed from the points of view of different integrability criteria we show that the dimension of the phase space of bianchi class a hamiltonian systems can be reduced by two we prove that the vector field of the reduced system is polynomial and that it does not admit any analytic or even formal first integral

differential galois obstructions for integrability of homogeneous newton equations in this paper we formulate necessary conditions for the integrability in the jacobi sense of newton equations q f q where q cn and all components of f are polynomial and homogeneous of the same degree l these conditions are derived from an analysis of the differential galois group of variational equations along special particular solutions of the newton equations we show that taking all admissible particular solutions we restrict considerably the set of newton s equations satisfying the necessary conditions for the integrability moreover we apply the obtained conditions for a detailed analysis of the newton equations with two degrees of freedom i e n 2 we demonstrate the strength of the obtained results analyzing general cases with degfi l 4 for l 3 we have found an integrable case when the newton equations have two polynomial first integrals and both of them are of degree 4 in the momenta p1 q1 and p2 q2 moreover for an arbitrary l we found a particular family of newton equations d

integrability of hamiltonians with polynomial potentials in this work we study dynamical systems with polynomial potentials such as those of henon heiles yang mills and various generalizations by means of the nonintegrability theory developed by the authors all these problems have also been investigated by using other theories like those proposed by ziglin yoshida morales or the painleve analysis in the examples considered our method allows us to reproduce with quite less work or even to improve the results obtained by other authors

non integrability of the spacial n center problem abstract we prove the non integrability of the spacial n center problem in order to prove it we focus on the singularity of the differential equations extended to the complex space and then apply the morales ramis theory to it we also show the non integrability of the spacial restricted n 1 body problem

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

some applications of quasisymmetry summary we give three applications of quasisymmetry the first two applications involve derived conditional distributions in a study involving matched individuals where the parameters associated with the matching are eliminated by appropriate conditioning extensions to matched triplets or to larger blocks lead to generalizations of quasisymmetry the third application involves reversibility of markov chains where the connexion between reversibility and quasisymmetry is exploited to construct tests for reversibility and tests for homogeneity of several reversible chains

integrability and orbits in quartic polynomial potentials the effect of enlarging the class of admissible movable singularities in painleve analysis to include all rational algebraic branch points is examined for a class of quartic polynomial potentials eight homogeneous quartic potentials are found in addition to the seven integrable cases given by weak painleve analysis they are examined using various numerical techniques and ziglin s theorem only one of them remains a candidate for integrability which indicates that in general most rational algebraic branch points are incompatible with integrability movable logarithmic singularities also appear to be inconsistent with integrability however the remaining potentials are either regular or nearly regular for the energies examined and are therefore still of interest for numerical purposes the corresponding surfaces of section are found to be particularly simple in structure and belong to a small number of topologically distinct classes their stable and unstable periodic orbit structures are examined to provide information about their regularity and for use in ziglin s theorem there appears to be a correlation between the resonances of the stable periodic orbits and the order of the corresponding movable singularities

a list of all integrable two dimensional homogeneous polynomial potentials with a polynomial integral of order at most four in the momenta we searched for integrable two dimensional homogeneous polynomial potentials with a polynomial first integral by using the so called direct method of searching for first integrals we proved that there exist no polynomial first integrals which are genuinely cubic or quartic in the momenta if the degree of homogeneous polynomial potentials is greater than four

critical phenomena for spitzer s reversible nearest particle systems motivated by several results and open problems concerning harris basic contact process we consider the relationship between the critical behavior of the finite and infinite versions of spitzer s reversible nearest particle systems we show that the critical values for the finite and infinite systems agree but that the behavior of the two systems at the common critical value can differ the nash williams recurrence criterion for reversible markov chains is an important tool used in the proofs of the main results and we give a new treatment of that theory finally we compute several critical exponents for the nearest particle systems

a criterion for the non existence of an additional integral in hamiltonian systems with a homogeneous potential abstract a non integrability criterion on the basis of ziglin s theorem is given for two degrees of freedom hamiltonians with a homogeneous potential of integer degree as simple examples the anisotropic kepler problem and the one dimensional newtonian three body problem are proved to be non integrable a self contained proof of ziglin s theorem n dimensional homogeneous potential version is also given

non integrability criteria for hamiltonians in the case of lame normal variational equations abstract we consider complex analytic classical hamiltonian systems with two degrees of freedom and an invariant plane furthermore we assume that the normal variational equations nve are of lame type we describe the possible potentials giving rise to this kind of problems and non integrability criteria based on the differential galois approach to the ziglin theorem some examples are included

non integrable character of hamiltonian systems with global and symmetric coupling abstract a new sufficient condition to prove non integrability of hamiltonian systems with symmetric variational equations is proposed though the present condition is taken as an extension of ziglin and yoshida s non resonant condition the algorithmic bottle neck proving non integrability in high dimensional cases can be removed here as a result the non existence of additional integrals of various symmetric hamiltonian systems with an arbitrary number of degrees of freedom is proven

integrability partial integrability and nonintegrability for systems of ordinary differential equations the integrability of systems of ordinary differential equations with polynomial vector fields is investigated by using the singularity analysis methods three types of results are obtained first a general relationship between the degrees of first integrals and the so called kowalevskaya exponents is derived second it is shown that all solutions of algebraically integrable systems can be expanded in puiseux series third a new method to study partially integrable systems is studied these different aspects allow us to study algorithmically the integrability partial integrability and nonintegrability of differential systems

a new necessary condition for the integrability of hamiltonian systems with a two dimensional homogeneous potential abstract recently morales ruiz and ramis obtained a strong necessary condition for the integrability of hamiltonian systems with a homogeneous potential based on their own theorem on the differential galois theory picard vessiot theory for hamiltonian systems the theorem claims that if the original hamiltonian system is integrable then the variational equation around a particular solution is solvable in the sense of the differential galois theory i e the solution is obtained only by a combination of quadratures exponential of quadratures and algebraic functions in this paper a direct and independent proof of this statement is given for hamiltonian systems with a two dimensional homogeneous potential which leads to the new necessary condition for integrability this new necessary condition well justifies the so called weak painleve conjecture of ramani et al for the first time

evaluation of formal posterior distributions via markov chain arguments we consider evaluation of proper posterior distributions obtained from improper prior distributions our context is estimating a bounded function of a parameter when the loss is quadratic if the posterior mean of 0 is admissible for all bounded the posterior is strongly admissible we give sufficient conditions for strong admissibility these conditions involve the recurrence of a markov chain associated with the estimation problem we develop general sufficient conditions for recurrence of general state space markov chains that are also of independent interest our main example concerns the p dimensional multivariate normal distribution with mean vector 0 when the prior distribution has the form g 6 2 d on the parameter space r p conditions on g for strong admissibility of the posterior are provided

invariant hyperplanes and darboux integrability of polynomial vector fields this paper is composed of two parts in the first part we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables this result generalizes those given in artes et al 1998 pac j math 184 207 30 and llibre and rodriguez 2000 bull sci math 124 599 619 the second part gives an extension of the darboux theory of integrability to polynomial vector fields on algebraic varieties

darboux integrability for 3d lotka volterra systems we describe the improved darboux theory of integrability for polynomial ordinary differential equations in three dimensions using this theory and computer algebra we study the existence of first integrals for the three dimensional lotka volterra systems only working up to degree two with the invariant algebraic surfaces and the exponential factors we find the major part of the known first integrals for such systems and in addition we find three new classes of integrability the method used is of general interest and can be applied to any polynomial ordinary differential equations in arbitrary dimension

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

global integrability of cosmological scalar fields we investigate the liouvillian integrability of hamiltonian systems describing a universe filled with a scalar field possibly complex the tool used is the differential galois group approach as introduced by morales ruiz and ramis the main result is that the generic systems with minimal coupling are non integrable although there still exist some values of parameters for which integrability remains undecided the conformally coupled systems are only integrable in four known cases we also draw a connection with the chaos present in such cosmological models and the issues of the integrability restricted to the real domain

asymmetry models for contingency tables abstract for the quasi symmetry qs model applicable to square contingency tables with commensurable classification variables it is proved that under certain conditions it is the closest model to symmetry in terms of the kullback leibler distance replacing the kullback leibler distance by f divergence we introduce a generalized quasi symmetry model the qs f and develop interpretational aspects for its parameters qs is a special case of qs f whereas the most characteristic of the newly introduced qs type models is the pearsonian qs model we compute maximum likelihood estimates of the parameters of the pearsonian qs model and compare it through examples and simulation studies to the classical qs model in terms of goodness of fit and of the powers of the tests for marginal homogeneity conditional on the qs and pearsonian qs models

admissible estimation dirichlet principles and recurrence of birth death chains on ℤ p we establish a connection between admissible simultaneous estimation and recurrence of reversible markov chains on specifically to each generalized bayes estimator of the mean of a vector of p independent poisson variables for a weighted quadratic loss we associate a variational problem and a reversible birth and death chain on the variational problem is closely related to the dirichlet principle for reversible chains studied recently by griffeath liggett and lyons under side conditions admissibility of the estimator is equivalent to zero infimal energy in the variational problem and to recurrence of the markov chain this yields analytic and probabilistic criteria for inadmissibility which are applied to establish a broad class of results and previous conjectures