monte carlo approximation of bayes factors via mixing with surrogate distributions by mixing the target posterior distribution with a surrogate distribution of which the normalizing constant is tractable we propose a method for estimating the marginal likelihood using the wang

constructing n 1 lie algebras from n lie algebras n lie algebras have close relationships with many important fields in mathematics and mathematical physics in this paper we construct n 1 lie algebras by two dimensional extensions of metric n lie algebras and construct n 1 lie algebras in terms of n lie algebras and certain linear functions along this approach we obtain n 1 lie algebras by n lie algebras with the generating index n and 4 lie algebras by non nilpotent 3 lie algebras with the generating index 4

convergence of the wang landau algorithm we analyze the convergence properties of the wang landau algorithm this sampling method belongs to the general class of adaptive importance sampling strategies which use the free energy along a chosen reaction coordinate as a bias such algorithms are very helpful to enhance the sampling properties of markov chain monte carlo algorithms when the dynamics is metastable we prove the convergence of the wang landau algorithm and an associated central limit theorem

on foundation of the generalized nambu mechanics we outline basic principles of a canonical formalism for the nambu mechanics a generalization of hamiltonian mechanics proposed by yoichiro nambu in 1973 it is based on the notion of a nambu bracket which generalizes the poisson bracket a binary operation on classical observables on the phase space to the multiple operation of higher ordern 3 nambu dynamics is described by the phase flow given by nambu hamilton equations of motion a system of ode s which involvesn 1 hamiltonians we introduce the fundamental identity for the nambu bracket a generalization of the jacobi identity as a consistency condition for the dynamics we show that nambu bracket structure defines a hierarchy of infinite families of subordinated structures of lower order including poisson bracket structure which satisfy certain matching conditions the notion of nambu bracket enables us to define nambu poisson manifolds phase spaces for the nambu mechanics which turn out to be more rigid than poisson manifolds phase spaces for the hamiltonian mechanics we introduce the analog of the action form and the action principle for the nambu mechanics in its formulation dynamics of loops n 2 dimensional chains for the generaln ary case naturally appears we discuss several approaches to the quantization of nambu mechanics based on the deformation theory path integral formulation and on nambu heisenberg commutation relations in the latter formalism we present an explicit representation of the nambu heisenberg relation in then 3 case we emphasize the role ternary and higher order algebraic operations and mathematical structures related to them play in passing from hamilton s to nambu s dynamical picture

stochastic approximation in monte carlo computation the wang landau wl algorithm is an adaptive markov chain monte carlo algorithm used to calculate the spectral density for a physical system a remarkable feature of the wl algorithm is that it is not trapped by local energy minima which is very important for systems with rugged energy landscapes this feature has led to many successful applications of the algorithm in statistical physics and biophysics however there does not exist rigorous theory to support its convergence and the estimates produced by the algorithm can reach only a limited statistical accuracy in this article we propose the stochastic approximation monte carlo samc algorithm which overcomes the shortcomings of the wl algorithm we establish a theorem concerning its convergence the estimates produced by samc can be improved continuously as the simulation proceeds samc also extends applications of the wl algorithm to continuum systems the potential uses of samc in statistics are discussed through two classes of applications i

convergence and efficiency of adaptive importance sampling techniques with partial biasing we consider a generalization of the discrete time self healing umbrella sampling method which is an adaptive importance technique useful to sample multimodal target distributions the importance function is based on the weights of disjoint sets which form a partition of the space in the context of computational statistical physics the logarithm of these weights is up to a multiplicative constant the free energy and the discrete valued function defining the partition is called the reaction coordinate the algorithm is a generalization of the original self healing umbrella sampling method in two ways i the updating strategy leads to a larger penalization strength of already visited sets and ii the target distribution is biased using only a fraction of the free energy in order to increase the effective sample size and reduce the variance of importance sampling estimators the algorithm can also be seen as a generalization of well tempered metadynamics we prove the convergence of the algorithm and analyze numerically its efficiency on a toy example

the generating index of an n lie algebra we introduce a notion of generating index of an n lie algebra the classification of the complex n lie algebras with the generating index n is given we also introduce a notion of an eigenvalue number of an n lie algebra which is used to interpret the complex n lie algebras with the generating index n 1 in particular we give some classification results of the complex 3 lie algebras with the generating index 4 moreover we show that the generating index of a metric 3 lie algebra which is neither simple nor nilpotent is greater than 4 this work provides a new structural tool to study n lie algebras

lorentzian lie n algebras we classify lie n algebras possessing an invariant lorentzian inner product we classify lie n algebras possessing an invariant lorentzian inner product

bifurcation and distribution of limit cycles for quadratic differential systems of type ii abstract in this paper we first solve an open problem of quadratic differential systems of type ii l 0 in the chinese classification then by making use of the theory of rotated vector fields we investigate the bifurcation phenomena and all the possible distributions of the limit cycles for quadratic systems of type ii moreover under a conjecture of ye yanqian we prove that the 2 2 limit cycle distribution is impossible

realizations of 3 lie algebras 3 lie algebras have close relationships with many important fields in mathematics and mathematical physics in this paper we provide a construction of 3 lie algebras in terms of lie algebras and certain linear functions moreover with the construction from matrices and two dimensional extensions of metric lie algebras all the complex 3 lie algebras in dimension 5 are obtained along this approach as a special case we study the structure of the 3 lie algebras constructed from the general linear lie algebras with trace forms and prove that they are semisimple and local

split 3 lie algebras in order to begin an approach to the structure of 3 lie algebras with restrictions neither on the dimension nor on the base field we introduce the class of split 3 lie algebras as the natural extension of the class of split lie algebras by developing techniques of connections of roots for this kind of ternary algebras we show that any of such split 3 lie algebras t is of the form t u jij with u a subspace of the 0 root space t0 and any ij a well described ideal of t satisfying ij t ik 0 if j k under certain conditions the simplicity of t is characterized and it is shown that t is the direct sum of the family of its minimal ideals each one being a simple split 3 lie algebra

stability of stochastic approximation under verifiable conditions in this paper we address the problem of the stability and convergence of the stochastic approximation procedure theta n 1 theta n gamma n 1 h theta n xi n 1 the stability of such sequences theta n is known to heavily rely on the behavior of the mean field h at the boundary of the parameter set and the magnitude of the stepsizes used the conditions typically required to ensure convergence and in particular the boundedness or stability of theta n are either too difficult to check in practice or not satisfied at all this is the case even for very simple models the most popular technique for circumventing the stability problem consists of constraining theta n to a compact subset mathcal k in the parameter space this is obviously not a satisfactory solution as the choice of mathcal k is a delicate one in this paper we first prove a deterministic stability result which relies on simple conditions on the sequences xi n and gamma n we then propose and analyze an algorithm based on projections on adaptive truncation sets which ensures that the aforementioned conditions required for stability are satisfied we focus in particular on the case where xi n is a so called markov state dependent noise we establish both the stability and convergence with probability 1 w p 1 of the algorithm under a set of simple and verifiable assumptions we illustrate our results with an example related to adaptive markov chain monte carlo algorithms

the classification of six dimensional 4 lie algebras this paper concerns properties of n 2 dimensional n lie algebras and shows the classification of six dimensional 4 lie algebras over an algebraically closed field of characteristic zero

separatrix cycles and multiple limit cycles in a class of quadratic systems abstract in this paper a class of quadratic systems is studied by quadratic systems we mean autonomous quadratic vector fields in the plane the class under consideration is class ii n 0 in the chinese classification of quadratic systems bifurcation sets l m m 2 l 0 and sep l m l 2 4 if m 1 m 1 are proved to exist corresponding to a semistable limit cycle and a separatrix cycle appearing in ii n 0 respectively the asymptotic behaviour of and sep is investigated if l m tend to the boundary of its domain of existence especially the case of large parameters which is related to singularly perturbed differential equations relaxation oscillations is considered after a blowing up of the variables the problem is studied with the use of pontryagin integral techniques for bifurcation of limit cycles from hamilton systems

3 lie algebras with an ideal n we define the hypo nilpotent ideal in n lie algebras and obtain all solvable 3 lie algebras with an m dimensional simplest filiform 3 lie algebra as a maximal hypo nilpotent ideal we prove that the dimension of such solvable 3 lie algebras is at most m 2 and there is no solvable 3 lie algebra with the simplest filiform 3 lie algebra as the nilradical

convergence of adaptive and interacting markov chain monte carlo algorithms adaptive and interacting markov chain monte carlo algorithms mcmc have been recently introduced in the literature these novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions motivated by some recently introduced algorithms such as the adaptive metropolis algorithm and the interacting tempering algorithm we develop a general methodological and theoretical framework to establish both the convergence of the marginal distribution and a strong law of large numbers this framework weakens the conditions introduced in the pioneering paper by roberts and rosenthal j appl probab 44 2007 458 475 it also covers the case when the target distribution is sampled by using markov transition kernels with a stationary distribution that differs from

on perturbed proximal gradient algorithms we study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by monte carlo methods and in particular markov chain monte carlo we derive conditions on the step size and the monte carlo batch size under which convergence is guaranteed both increasing batch size and constant batch size are considered we also derive non asymptotic bounds for an averaged version our results cover both the cases of biased and unbiased monte carlo approximation to support our findings we discuss the inference of a sparse generalized linear model with random effect and the problem of learning the edge structure and parameters of sparse undirected graphical models

rota baxter 3 lie algebras in this paper we introduce the concepts of a rota baxter operator and differential operator with weights on an n algebra we then focus on rota baxter 3 lie algebras and show that they can be derived from rota baxter lie algebras and pre lie algebras and from rota baxter commutative associative algebras with derivations we also establish the inheritance property of rota baxter 3 lie algebras