the principle of maximum causal entropy for estimating interacting processes the principle of maximum entropy provides a powerful framework for estimating joint conditional and marginal probability distributions however there are many important distributions with elements of interaction and feedback where its applicability has not been established this paper presents the principle of maximum causal entropy an approach based on directed information theory for estimating an unknown process based on its interactions with a known process we demonstrate the breadth of the approach using two applications a predictive solution for inverse optimal control in decision processes and computing equilibrium strategies in sequential games

maximum entropy density estimation with generalized regularization and an application to species distribution modeling we present a unified and complete account of maximum entropy density estimation subject to constraints represented by convex potential functions or alternatively by convex regularization we provide fully general performance guarantees and an algorithm with a complete convergence proof as special cases we easily derive performance guarantees for many known regularization types including l1 l2 l22 and l2 l22 style regularization we propose an algorithm solving a large and general subclass of generalized maximum entropy problems including all discussed in the paper and prove its convergence our approach generalizes and unifies techniques based on information geometry and bregman divergences as well as those based more directly on compactness our work is motivated by a novel application of maximum entropy to species distribution modeling an important problem in conservation biology and ecology in a set of experiments on real world data we demonstrate the utility of maximum entropy in this setting we explore effects of different feature types sample sizes and regularization levels on the performance of maxent and discuss interpretability of the resulting models

the existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays in this paper we establish sufficient conditions for the existence and global exponential stability of periodic solution to a type of neutral coupled system on networks with delays the key to prove the existence of periodic solutions is using the combined method of graph theory coincidence degree theory and lyapunov functional method and the sufficient conditions are easy to be checked finally a numerical simulation is carried out to show the correctness of our main results

blowup subalgebras of the sklyanin algebra we describe some interesting graded rings which are generated by degree 3 elements inside the sklyanin algebra s and prove that they have many good properties geometrically these rings r correspond to blowups of the sklyanin p2 at 7 or fewer points we show that the rings r are exactly those degree 3 generated subrings of s which are maximal orders in the quotient ring of the 3 veronese of s

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

a graph theoretic approach to boundedness of stochastic cohen grossberg neural networks with markovian switching in this paper a novel class of stochastic cohen grossberg neural networks with markovian switching scgnnmss is investigated where the white noise and the color noise are taken into account by utilizing lyapunov method some graph theory and m matrix technique several sufficient conditions are obtained to ensure the asymptotic boundedness of the scgnnmss these criteria have a close relation to the topology property of the network and are easy to be verified in practice two numerical examples are also presented to substantiate the theoretical results

a class of noncommutative projective surfaces let a k a 1 a 2 be a connected graded noetherian k algebra that is generated in degree one over an algebraically closed field k suppose that the graded quotient ring q a has the form q a k y t t 1 sigma where sigma is an automorphism of the integral projective surface y then we prove that a can be written as a naive blowup algebra of a projective surface x birational to y this enables one to obtain a deep understanding of the structure of these algebras for example generically they are not strongly noetherian and their point modules are not parametrized by a projective scheme this is despite the fact that the simple objects in the quotient category qgr a will always be in 1 1 correspondence with the closed points of the scheme x

gk dimension of birationally commutative surfaces let k be an algebraically closed field let k k be a finitely generated field extension of transcendence degree 2 let aut k k and let a q k t be an n graded subalgebra with dim k a n 0 then if a is big enough in q in an appropriate sense we prove that gk a 3 4 5 or oo with the exact value depending only on the geometric properties of the proof uses techniques in the birational geometry of surfaces which are of independent interest

stability analysis for coupled systems with time delay on networks abstract in this paper the stability problem for some coupled systems with time delay on networks csdns is investigated we provide a systematic method for constructing a global lyapunov functional for csdns by using graph theory the stability uniform stability and global uniform stability of the systems are investigated and by using the lyapunov functional constructed some sufficient conditions of stability are obtained

generalized synchronization in complex dynamical networks via adaptive couplings abstract this paper investigates generalized synchronization of three typical classes of complex dynamical networks scale free networks small world networks and interpolating networks the proposed synchronization strategy is to adjust adaptively a node s coupling strength based on the node s local generalized synchronization information by taking the auxiliary system approach and using the lyapunov function method we prove that for any given initial coupling strengths the generalized synchronization can take place in complex networks consisting of nonidentical dynamical systems it is demonstrated that the coupling strengths are affected by topologies of the networks furthermore it is found that there are hierarchical features in the processes of generalized synchronization in scale free networks because of their highly heterogeneous distributions of connection degree finally we discuss in detail how a network s degree of heterogeneity affects its generalization synchronization behavior

a simple adaptive procedure leading to correlated equilibrium we propose a new and simple adaptive procedure for playing a game regret matching in this procedure players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past it is shown that our adaptive procedure guarantees that with probability one the empirical distributions of play converge to the set of correlated equilibria of the game

algebras associated to elliptic curves this paper completes the classification of artin schelter regular algebras of global dimension three for algebras generated by elements of degree one this has been achieved by artin schelter tate and van den bergh we are therefore concerned with algebras which are not generated in degree one we show that there exist some exceptional algebras each of which has geometric data consisting of an elliptic curve together with an automorphism just as in the case where the algebras are assumed to be generated in degree one in particular we study the elliptic algebras a a and a a where a p2 which were first defined in an earlier paper we omit a set s p2 consisting of 11 specified points where the algebras a a become too degenerate to be regular theorem let a represent a a or a a where a p2 s then a is an artin schelter regular algebra of global dimension three moreover a is a noetherian domain with the same hilbert series as the appropriately graded commutative polynomial ring in three variables this combined with our earlier results completes the classification

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

the universal enveloping algebra of the witt algebra is not noetherian abstract this work is prompted by the long standing question of whether it is possible for the universal enveloping algebra of an infinite dimensional lie algebra to be noetherian to address this problem we answer a 23 year old question of carolyn dean and lance small namely we prove that the universal enveloping algebra of the witt or centerless virasoro algebra is not noetherian to show this we prove our main result the universal enveloping algebra of the positive part of the witt algebra is not noetherian we employ algebro geometric techniques from the first author s classification of noncommutative birationally commutative projective surfaces as a consequence of our main result we also show that the enveloping algebras of many other infinite dimensional lie algebras are not noetherian these lie algebras include the virasoro algebra and all infinite dimensional z graded simple lie algebras of polynomial growth

bounded h_ infty synchronization and state estimation for discrete time varying stochastic complex networks over a finite horizon in this paper new synchronization and state estimation problems are considered for an array of coupled discrete time varying stochastic complex networks over a finite horizon a novel concept of bounded h synchronization is proposed to handle the time varying nature of the complex networks such a concept captures the transient behavior of the time varying complex network over a finite horizon where the degree of bounded synchronization is quantified in terms of the h norm a general sector like nonlinear function is employed to describe the nonlinearities existing in the network by utilizing a timevarying real valued function and the kronecker product criteria are established that ensure the bounded h synchronization in terms of a set of recursive linear matrix inequalities rlmis where the rlmis can be computed recursively by employing available matlab toolboxes the bounded h state estimation problem is then studied for the same complex network where the purpose is to design a state estimator to estimate the network states through available output measurements such that over a finite horizon the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level again an rlmi approach is developed for the state estimation problem finally two simulation examples are exploited to show the effectiveness of the results derived in this paper

classical flag varieties for quantum groups the standard quantum sl n c abstract we suggest a possible programme to associate geometric flag like data to an arbitrary simple quantum group in the spirit of the noncommutative al gebraic geometry developed by artin tate and van den bergh we then carry out this programme for the standard quantum sl n of drinfel d and jimbo where the varieties involved are certain t stable subvarieties of the ordinary flag variety

two periodic solutions of second order neutral functional differential equations in this paper we consider a type of second order neutral functional differential equations we obtain some existence results of multiplicity and nonexistence of positive periodic solutions our approach is based on a fixed point theorem in cones

discriminative random fields in this research we address the problem of classification and labeling of regions given a single static natural image natural images exhibit strong spatial dependencies and modeling these dependencies in a principled manner is crucial to achieve good classification accuracy in this work we present discriminative random fields drfs to model spatial interactions in images in a discriminative framework based on the concept of conditional random fields proposed by lafferty et al 2001 the drfs classify image regions by incorporating neighborhood spatial interactions in the labels as well as the observed data the drf framework offers several advantages over the conventional markov random field mrf framework first the drfs allow to relax the strong assumption of conditional independence of the observed data generally used in the mrf framework for tractability this assumption is too restrictive for a large number of applications in computer vision second the drfs derive their classification power by exploiting the probabilistic discriminative models instead of the generative models used for modeling observations in the mrf framework third the interaction in labels in drfs is based on the idea of pairwise discrimination of the observed data making it data adaptive instead of being fixed a priori as in mrfs finally all the parameters in the drf model are estimated simultaneously from the training data unlike the mrf framework where the likelihood parameters are usually learned separately from the field parameters we present preliminary experiments with man made structure detection and binary image restoration tasks and compare the drf results with the mrf results

geometric algebras on projective surfaces abstract let x be a projective surface let aut x and let l be a ample invertible sheaf on x we study the properties of a family of subrings parameterized by geometric data of the twisted homogeneous coordinate ring b x l in particular we find necessary and sufficient conditions for these subrings to be noetherian we also study their homological properties their associated noncommutative projective schemes and when they are maximal orders in the process we produce new examples of maximal orders these are graded and have the property that no veronese subring is generated in degree 1 our results are used in the companion paper s j sierra 2009 sie09 to give defining data for a large class of noncommutative projective surfaces

the existence uniqueness and global attractivity of periodic solution for a type of neutral functional differential system with delays in this article by applying the coincidence degree theory and constructing a suitable lyapunov functional the authors study a kind of neutral functional differential system with delays some sufficient conditions which guarantee the existence uniqueness and global attractivity of periodic solution for this system are obtained

game theory maximum entropy minimum discrepancy and robust bayesian decision theory we describe and develop a close relationship between two problems that have customarily been regarded as distinct that of maximizing entropy and that of minimizing worst case expected loss using a formulation grounded in the equilibrium theory of zero sum games between decision maker and nature these two problems are shown to be dual to each other the solution to each providing that to the other although topsoe described this connection for the shannon entropy over 20 years ago it does not appear to be widely known even in that important special case we here generalize this theory to apply to arbitrary decision problems and loss functions we indicate how an appropriate generalized definition of entropy can be associated with such a problem and we show that subject to certain regularity conditions the above mentioned duality continues to apply in this extended context this simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust bayes acts we also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions this leads to an extension to arbitrary discrepancies of a well known minimax theorem for the case of kullback leibler divergence the redundancy capacity theorem of information theory for the important case of families of distributions having certain mean values specified we develop simple sufficient conditions and methods for identifying the desired solutions we use this theory to introduce a new concept of generalized exponential family linked to the specific decision problem under consideration and we demonstrate that this shares many of the properties of standard exponential families finally we show that the existence of an equilibrium in our game can be rephrased in terms of a pythagorean property of the related divergence thus generalizing previously announced results for kullback leibler and bregman divergences

periodic solutions of neutral differential equation with multiple deviating arguments in this paper by means of an abstract continuous theorem of k set contractive operator and some analysis techniques the authors study the existence of periodic solution of the nonlinear neutral differential equation with multiple deviating argumentsddt x t cx email protected email protected i 1 email protected i t f x email protected i t email protected j 1 email protected j t g x email protected j t p t a new result is obtained

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing results

naive noncommutative blowups at zero dimensional schemes abstract in an earlier paper d s keeler d rogalski j t stafford naive noncommutative blowing up duke math j 126 2005 491 546 mr 2120116 we defined and investigated the properties of the naive blowup of an integral projective scheme x at a single closed point in this paper we extend those results to the case when one naively blows up x at any suitably generic zero dimensional subscheme z the resulting algebra a has a number of curious properties for example it is noetherian but never strongly noetherian and the point modules are never parametrized by a projective scheme this is despite the fact that the category of torsion modules in qgr a is equivalent to the category of torsion coherent sheaves over x these results are used in the companion paper d rogalski j t stafford a class of noncommutative projective surfaces in press to prove that a large class of noncommutative surfaces can be written as naive blowups

global stability of multigroup epidemic model with group mixing and nonlinear incidence rates in this paper we introduce a basic reproduction number for a multigroup seir model with nonlinear incidence of infection and nonlinear removal functions between compartments then we establish that global dynamics are completely determined by the basic reproduction number r0 it shows that the basic reproduction number r0 is a global threshold parameter in the sense that if it is less than or equal to one the disease free equilibrium is globally stable and the disease dies out whereas if it is larger than one there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population finally two numerical examples are also included to illustrate the effectiveness of the proposed result

periodic solutions to a kind of neutral functional differential equation in the critical case in this paper we consider a kind of neutral functional differential equation as follows x t cx t gt xt t e t in the critical case c 1 by employing the topological degree theory and some analysis techniques we obtain some new results on the existence of periodic solutions

maximum likelihood estimation of discrete control processes consider the following inverse stochastic control problem a statistician observes a realization of a controlled stochastic process d t x t consisting of the sequence of states x t and decisions d t of an agent at times t 1 cdots t the null hypothesis is that the agent s behavior is generated from the solution to a markovian decision problem the inverse problem is to use the data d t x t to go backward and uncover the agent s objective function u and his beliefs about the law of motion of the state variables p the problem is complicated by the fact that the statistician generally only observes a subset x t of the state variables x t eta t observed by the agent this paper formulates the inverse problem as a problem of statistical inference explicitly accounting for unobserved state variables eta t in order to produce a nondegenerate and internally consistent statistical model specifically the functions u and p are assumed to depend on a vector of u

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

noncommutative graded domains with quadratic growth letk be an algebraically closed field and letr be a finitely generated connected gradedk algebra which is a domain of gelfand kirillov dimension two write the graded quotient ringq r ofr asd z z 1 for some automorphism of the division ringd we prove thatd is a finitely generated field extension ofk of transcendence degree one moreover we describer in terms of geometric data ifr is generated in degree one then up to a finite dimensional vector space r is isomorphic to the twisted homogeneous coordinate ring of an invertible sheaf over a projective curvey this implies in particular thatr is noetherian thatr is primitive when and thatr is a finite module over its centre when ifr is not generated in degree one thenr will still be noetherian and primitive if has infinite order butr need not be noetherian when has finite order

ample filters and frobenius amplitude abstract let x be a projective scheme over a field we show that the vanishing cohomology of any sequence of coherent sheaves is closely related to vanishing under pullbacks by the frobenius morphism we also compare various definitions of ample locally free sheaf and show that the vanishing given by the frobenius morphism is in a certain sense the strongest possible our work can be viewed as various generalizations of the serre vanishing theorem

naive noncommutative blowing up let b x mathscr l be the twisted homogeneous coordinate ring of an irreducible variety x over an algebraically closed field k with dim x 2 assume that c in x and in aut x are in sufficiently general position we show that if one follows the commutative prescription for blowing up x at c but in this noncommutative setting one obtains a noncommutative ring r r x c mathscr l with surprising properties 1 r is always noetherian but never strongly noetherian 2 if r is generated in degree one then the images of the r point modules in qgr r are naturally in one to one correspondence with the closed points of x however in both qgr r and gr r the r point modules are not parametrized by a projective scheme 3 while qgr r has finite cohomological dimension dim k h 1 mathscr o

global dynamics of a general class of multistage models for infectious diseases we propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages the models can describe disease progression through multiple latent or infectious stages as in the case of hiv and tuberculosis amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment the models also incorporate general nonlinear incidences and general nonlinear forms of population transfer among stages under biologically motivated assumptions we derive the basic reproduction number r 0 and show that the global dynamics are completely determined by r 0 if r 0 leq 1 the disease free equilibrium is globally asymptotically stable and the disease dies out if r 0 1 then the disease persists in all stages and a unique endemic equilibrium is globally asymptotically stable

global stability analysis for stochastic coupled systems on networks this paper considers the global stability problem for some stochastic coupled systems on networks scsns we provide a systematic method for constructing a global lyapunov function for these scsns by using graph theory and the lyapunov second method consequently a new global stability principle which has a close relation to the topology property of the network is given as an application to the results we employ the principle to two well known coupled systems in physical and ecology and then some easy verified sufficient conditions which guarantee the global stability are obtained

canonical maps to twisted rings if a is a strongly noetherian graded algebra generated in degree one then there is a canonically constructed graded ring homomorphism from a to a twisted homogeneous coordinate ring open image in new window which is surjective in large degree this result is a key step in the study of projectively simple rings the proof relies on some results concerning the growth of graded rings which are of independent interest

the stability of stochastic coupled systems with time delays and time varying coupling structure this paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time varying coupling structure sctvcs the coupling structure is time varying first second the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time varying coupling structure successfully combining graph theory with lyapunov method a systematic method is given to construct a lyapunov function for sctvcs several pth moment exponential stability criteria are presented including a lyapunov type theorem and some sufficient criteria in the form of coefficients furthermore the theoretical conclusions are applied to the stochastic coupled oscillators with time varying coupling structure and two stability criteria are obtained finally we give two numerical examples to illustrate the effectiveness of our results