non uniform specification and large deviations for weak gibbs measures we establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak gibbs measures under some mild assumptions we obtain upper and lower bounds for the measure of deviation sets of some non uniformly expanding maps including quadratic maps and robust multidimensional non uniformly expanding local diffeomorphisms for that purpose a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non uniformly expanding local diffeomorphisms and viana maps

machine learning and nonparametric bandit theory in its most basic form bandit theory is concerned with the design problem of sequentially choosing members from a given collection of random variables so that the regret i e r sub n spl sigma sub j spl mu spl mu sub j et sub n j grows as slowly as possible with increasing n here spl mu sub j is the expected value of the bandit arm i e random variable indexed by j t sub n j is the number of times arm j has been selected in the first n decision stages and spl mu sup sup sub j spl mu sub j the present paper contributes to the theory by considering the situation in which observations are dependent to begin with the dependency is presumed to depend only on past observations of the same arm but later we allow that it may be with respect to the entire past and that the set of arms is infinite this brings queues and more generally controlled markov processes into our purview thus our black box methodology is suitable for the case when the only observables are cost values and in particular the probability structure and loss function are unknown to the designer the conclusion of the analysis is that under lenient conditions using algorithms prescribed herein risk growth is commensurate with that in the simplest i i d cases our methods represent an alternative to stochastic approximation perturbation analysis ideas for tuning queues

lmi conditions for the stability of linear uncertain polynomially time varying systems this technical note investigates the robust stability of uncertain linear time varying systems with a mode switch dynamics each mode is characterized by a dynamical matrix containing elements whose time behavior over bounded time intervals is described by interval polynomials of arbitrary degree using a quadratic lyapunov function polynomially depending on time stability conditions for each mode are stated in terms of linear matrix inequalities lmis the stability conditions of the switching system are stated both in terms of minimum and average dwell time a salient feature of the technical note is that the single mode stability conditions given here allow the parameters and their derivatives to take values over arbitrarily large uncertainty sets

a resolution principle for constrained logics abstract we introduce a constrained logic scheme with a resolution principle for clauses whose variables are constrained by a constraint theory constraints can be seen as quantifier restrictions filtering out the values that any interpretation of the underlying constraint theory can assign to the variables of a formula with such restricted quantifiers we present a resolution principle for constrained clauses where unification is replaced by testing constraints for satisfiability over the constraint theory we show that constrained resolution is sound and complete in that a set of constrained clauses is unsatisfiable over the constraint theory if and only if for each model of the constraint theory we can deduce a constrained empty clause whose constraint is satisfiable in that model we demonstrate that we cannot require a better result in general but we give conditions under which at most finitely many such empty clauses are needed or even better only one empty clause as in classical resolution sorted resolution or resolution with theory unification

efficient lmi based quadratic stabilization of interval lpv systems with noisy parameter measures the purpose of this note is to consider the quadratic stabilization of lpv systems in the realistic case where only gaussian noisy parameter measures are available though neglected in the actual literature on lpv systems this question is particular important because in all situations of a practical interest the parameter measurements or estimates are never exact the assumed noisy nature of physical parameter readings requires a specifically developed approach consisting of mixed robust and lpv control methods in the present case an approach based on a vertex result on interval time varying itv matrices is proposed this allows the solvability conditions to be stated in terms of a set of lmi s whose number is independent of the number of time varying parameters

gibbs markov young structures with stretched exponential tail for partially hyperbolic attractors abstract in this work we extend the results obtained by gouezel in 12 to partially hyperbolic attractors we study a forward invariant set k on a riemannian manifold m whose tangent space splits as dominated decomposition t k m e c u e s for which the center unstable direction e c u is non uniformly expanding on some local unstable disk we prove that the stretched exponential decay of recurrence times for an induced scheme can be deduced under the assumption of stretched exponential decay of the time that typical points need to achieve some uniform expanding in the center unstable direction as an application of our results we obtain exponential decay of correlations and exponential large deviations for a class of partially hyperbolic diffeomorphisms considered in 1

on inexact lpv control design of continuous time polytopic systems robust dynamic output design most often relies on nonconvex problems this is precisely the case with linear parameter varying lpv control when the measured varying parameters do not exactly fit the real ones this paper provides a solution in the convex programming framework with the use of linear matrix inequality lmi solvers in the case of polytopic parameter dependence a bounded uncertainty set is defined from the difference between the measured and the true parameters from which lmi stabilization and performance conditions are obtained after bounding as a desired property the proposed conditions reduce to the classical lpv ones whenever the true parameters are available for control synthesis

statistical properties for flows with unbounded roof function including the lorenz attractor for geometric lorenz attractors including the classical lorenz attractor we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors we also obtain the functional central limit theorem and moment estimates as well as iterated versions of these results a consequence is deterministic homogenisation convergence to a stochastic differential equation for fast slow dynamical systems whenever the fast dynamics is singularly hyperbolic of codimension two

correspondence robust stabilization of uncertain time varying discrete systems and comments on an improved approach for constrained robust model predictive control this paper addresses the robust stabilizability problem of linear discrete time systems with time varying polytopic uncertainties a state feedback control law is proposed based on the construction of a parameter dependent lyapunov function also it points out that the main results of cuzzola geromel and morari automatica 38 2002 1183 1189 are incorrect and presents the corrected version of these results

an efficient lmi approach for the quadratic stabilisation of a class of linear uncertain time varying systems the purpose of this article is to provide a numerically efficient method for the quadratic stabilisation of a class of linear discrete time uncertain time varying systems the considered class of systems is characterised by an interval time varying itv matrix and constant sensor and actuator matrices it is required to find a linear time invariant lti static output feedback controller yielding a quadratically stable closed loop system independently of the parameter variation rate the solvability conditions are stated in terms of linear matrix inequalities lmis the set of lmis includes the stability conditions for the feedback connection of a unique suitably defined extreme plant with an lti output controller and the positivity of a closed loop extremal matrix a consequent noticeable feature of the article is that the total number of lmis is independent of the number of uncertain parameters this greatly enhances the numerical efficiency of the design procedure

central limit theorems and invariance principles for time one maps of hyperbolic flows we give a general method for deducing statistical limit laws in situations where rapid decay of correlations has been established as an application of this method we obtain new results for time one maps of hyperbolic flows

a mechanical solution of schubert s steamroller by many sorted resolution abstract we demonstrate the advantage of using a many sorted resolution calculus by a mechanical solution of a challenge problem this problem known as schubert s steamroller had been unsolved by automated theorem provers before our solution clearly demonstrates the power of a many sorted resolution calculus the proposed method is applicable to all resolution based inference systems

spatio temporal large deviations principle for coupled circle maps we consider the d 1 dimensional an dynamical system constituted by weakly coupled expanding circle maps on zd together with the spatial shifts this viewpoint allows us to use thermodynamic formalism and to describe the asymptotic behavior of the system in this setup we obtain a volume lemma which describes the exponential behavior of the size under lebesgue measure of dynamical balls around any orbit and then a large deviations principle for the empirical measure associated to this dynamical system the proofs are direct we do not use the coding constructed by jiang for such systems

many sorted unification many sorted unification is considered that is unification in the many sorted free algebras of terms where variables as well as the domains and ranges of functions are restricted to certain subsets of the universe given as a potentially infinite hierarchy of sorts it is shown that complete and minimal sets of unifiers may not always exist for many sorted unification conditions for sort hierarchies that are equivalent for the existence of these sets with one finitely many or infinitely many elements are presented it is also proved that being a forest structured sort hierarchy is a necessary and sufficient criterion for the robinson unification theorem to hold for many sorted unification an algorithm for many sorted unification is given

an order sorted logic for knowledge representation systems abstract hybrid knowledge representation systems such as those of the kl one family distinguish between taxonomical information that is represented in the t box and assertional information which is contained in the a box the basic concepts that establish a particular view of the world are considered static and given once the knowledge base is set up and these concepts are represented in the taxonomical hierarchy of the t box for some applications in natural language processing this approach is insufficient as the taxonomical hierarchy may be changed while parsing new sentences it may thus become necessary to express the changing taxonomical information in both the taxonomical hierarchy the t box and in the assertional knowledge base the a box in this case the notorious problems of coupling the two kinds of information i e the a box and the t box within one deductive calculus become even more complex and we distinguish two approaches a close coupling and a loose coupling within the framework of an order sorted predicate logic we present a close coupling between the taxonomic information that is expressed in the sort hierarchy and the axiomatic part we give a rigorous model theoretic semantics and present a deduction calculus that is based on three specially tailored rules of inference extended order sorted resolution subsort resolution and elimination these rules are shown to be sound and complete for a clausal knowledge base which represents taxonomic information partly through sorts and partly by explicit sortal predication this approach has been implemented in the knowledge representation language llilog which is used in a natural language understanding project for german

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

large deviations for nonuniformly hyperbolic systems we obtain large deviation estimates for a large class of nonuniformly hyperbolic systems namely those modelled by young towers with summable decay of correlations in the case of exponential decay of correlations we obtain exponential large deviation estimates given by a rate function in the case of polynomial decay of correlations we obtain polynomial large deviation estimates and exhibit examples where these estimates are essentially optimal in contrast with many treatments of large deviations our methods do not rely on thermodynamic formalism hence for holder observables we are able to obtain exponential estimates in situations where the space of equilibrium measures is not known to be a singleton as well as polynomial estimates in situations where there is not a unique equilibrium measure

spectral theory zeta functions and the distribution of periodic points for collet eckmann maps we study unimodal interval mapst with negative schwarzian derivative satisfying the collet eckmann condition dtn tc k cn for some constantsk 0 and c 1 c is the critical point oft we prove exponential mixing properties of the unique invariant probability density oft describe the long term behaviour of typical in the sense of lebesgue measure trajectories by central limit and large deviations theorems for partial sum processes of the form s n sigma i 0 n 1 f t i x and study the distribution of typical periodic orbits also in the sense of a central limit theorem and a large deviations theorem

order sorted logic programming with predicate hierarchy order sorted logic has been formalized as first order logic with sorted terms where sorts are ordered to build a hierarchy called a sort hierarchy these sorted logics lead to useful expressions and inference methods for structural knowledge that ordinary first order logic lacks nitta et al pointed out that for legal reasoning a sort hierarchy or a sorted term is not sufficient to describe structural knowledge for event assertions which express facts caused at some particular time and place the event assertions are represented by predicates with n arguments i e n ary predicates and then a particular kind of hierarchy called a predicate hierarchy is built by a relationship among the predicates to deal with such a predicate hierarchy which is more intricate than a sort hierarchy nitta et al implemented a typed sorted logic programming language extended to include a hierarchy of verbal concepts corresponding to predicates however the inference system lacks a theoretical foundation because its hierarchical expressions exceed the formalization of order sorted logic in this paper we formalize a logic programming language with not only a sort hierarchy but also a predicate hierarchy this language can derive general and concrete expressions in the two kinds of hierarchies for the hierarchical reasoning of predicates we propose a manipulation of arguments in which surplus and missing arguments in derived predicates are eliminated and supplemented as discussed by allen mcdermott and shoham in research on temporal logic and as applied by nitta et al to legal reasoning if each predicate is interpreted as an event or action not as a static property then missing arguments should be supplemented by existential terms in the argument manipulation based on this we develop a horn clause resolution system extended to add inference rules of predicate hierarchies with a semantic model restricted by interpreting a predicate hierarchy the soundness and completeness of the horn clause resolution is proven

large deviation probabilities for correlated gaussian processes and intermittent dynamical systems in its classical version the theory of large deviations makes quantitative statements about the probability of outliers when estimating time averages if time series data are identically independently distributed we study large deviation probabilities ldps for time averages in short and long range correlated gaussian processes and show that long range correlations lead to subexponential decay of ldps a particular deterministic intermittent map can depending on a control parameter also generate long range correlated time series we illustrate numerically in agreement with the mathematical literature that this type of intermittency leads to a power law decay of ldps the power law decay holds irrespective of whether the correlation time is finite or infinite and hence irrespective of whether the central limit theorem applies or not

biquadratic stability of uncertain linear systems deals with the problem of stability analysis for linear systems with uncertain real possibly time varying parameters a robust stability approach based on a lyapunov function which depends quadratically on the uncertain parameters as well as in the system state is proposed this robust stability approach referred to as biquadratic stability is suited to deal with uncertain real parameters with magnitude and rate of change which are confined to a given convex region a linear matrix inequality based sufficient condition for biquadratic stability is developed the proposed robust stability analysis method includes quadratic stability and affine quadratic stability as particular cases

observer based control of discrete time lpv systems with uncertain parameters in this note linear matrix inequality based design conditions are presented for observer based controllers that stabilize discrete time linear parameter varying systems in the situation where the parameters are not exactly known but are only available with a finite accuracy the presented framework allows to make tradeoffs between the admissible level of parameter uncertainty on the one hand and the transient performance on the other in addition the level of parameter uncertainty can be maximized while still guaranteeing closed loop stability

limit theorems in the stadium billiard we prove that the birkhoff sums for almost every relevant observable in the stadium billiard obey a non standard limit law more precisely the usual central limit theorem holds for an observable if and only if its integral along a one codimensional invariant set vanishes otherwise a open image in new window normalization is needed as one of the two key steps in the argument we obtain a limit theorem that holds in young towers with exponential return time statistics in general an abstract result that seems to be applicable to many other situations

almost sure invariance principle for nonuniformly hyperbolic systems we prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems discrete time systems and flows are covered by this result in particular the result applies to the planar periodic lorentz flow with finite horizon statistical limit laws such as the central limit theorem the law of the iterated logarithm and their functional versions are immediate consequences

robust observer based control of systems with state perturbations via lmi approach in this note the observer based control for a class of uncertain linear systems is considered exponential stabilizability for the systems is studied and the convergence rate of the system is estimated a linear matrix inequality lmi approach is used to design the observer based control the control and observer gains are given from lmi feasible solution a numerical example is given to illustrate our results

robust static output feedback control for linear discrete time systems with time varying uncertainties this paper is concerned with the problem of designing robust static output feedback controllers for linear discrete time systems with timevarying polytopic uncertainties sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities and the results are extended to h2 and h static output feedback controller designs numerical examples are given to illustrate the effectiveness of the proposed design methods 2007 elsevier b v all rights reserved

sporadicity between periodic and chaotic dynamical behaviors abstract we define the class of sporadic dynamical systems as the systems where the algorithmic complexity of kolmogorov kolmogorov a n 1983 russ math surv 38 29 40 and chaitin chaitin g j 1987 algorithmic information theory cambridge univ press cambridge u k as well as the logarithm of separation of initially nearby trajectories grow as nv0 log n v1 with 0 v0 1 or v0 1 and v1 0 as time n these systems present a behavior intermediate between the multiperiodic v0 0 v1 1 and the chaotic ones v0 1 v1 0 we show that intermittent systems of manneville manneville p 1980 j phys paris 41 1235 1243 as well as some countable markov chains may be sporadic and furthermore that the dynamical fluctuations of these systems may be of levy s type rather than gaussian

large deviation principle in one dimensional dynamics we study the dynamics of smooth interval maps with non flat critical points for every such a map that is topologically exact we establish the full level 2 large deviation principle for empirical means in particular the large deviation principle holds for every non renormalizable quadratic map this includes the maps without physical measure found by hofbauer and keller and challenges the widely shared view of the large deviation principle as a refinement of laws of large numbers

fluctuation of the entropy production for the lorentz gas under small external forces in this paper we study the physical and statistical properties of the periodic lorentz gas with finite horizon driven to a non equilibrium steady state by the combination of non conservative external forces and deterministic thermostats a version of this model was introduced by chernov eyink lebowitz and sinai and subsequently generalized by chernov and the third author non equilibrium steady states for these models are srb measures and they are characterized by the positivity of the steady state entropy production rate our main result is to establish that the entropy production in this context equal to the phase space contraction satisfies the gallavotti cohen fluctuation relation the main tool needed in the proof is the family of anisotropic banach spaces introduced by the first and third authors to study the ergodic and statistical properties of billiards using transfer operator techniques

large deviations for non uniformly expanding maps we obtain large deviation bounds for non uniformly expanding maps with non flat singularities or criticalities and for partially hyperbolic non uniformly expanding attracting sets that is given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map showing that the lebesgue measure of the set of points whose time averages stay away from the space average tends to zero exponentially fast with the number of iterates involved as easy by products we deduce escape rates from subsets of the basins of physical measures for these types of maps the rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states

homogenization for deterministic maps and multiplicative noise a recent paper of melbourne stuart a note on diffusion limits of chaotic skew product flows nonlinearity 24 2011 1361 1367 gives a rigorous proof of convergence of a fast slow deterministic system to a stochastic differential equation with additive noise in contrast to other approaches the assumptions on the fast flow are very mild in this paper we extend this result from continuous time to discrete time moreover we show how to deal with one dimensional multiplicative noise this raises the issue of how to interpret certain stochastic integrals it is proved that the integrals are of stratonovich type for continuous time and neither

a typed resolution principle for deduction with conditional typing theory the formal reasoning involved in solving a real world problem usually consists of two parts type reasoning associated with the type structure of the problem domain and general reasoning associated with the kernel formulation this paper introduces a typed resolution principle for a typed predicate calculus this principle permits a separation of type reasoning from general reasoning even when the background typing theory shares the same language constructs with the kernel formulation such a typing theory is required for an accurate formulation of the type structure of a computer program which contains partial functions and predicate subtypes and also is useful for efficiently proving certain theorems from mathematics and logic by typed sorted formulation and deduction the paper presents a typed deduction procedure which employs type reasoning as a form of constraints to general reasoning for speeding up the proof discovery the paper also discusses further refinements of the procedure by incorporating existing refinements of untyped resolution

a supervised switching control policy for lpv systems with inaccurate parameter knowledge this technical note deals with the switched supervised control of linear parameter varying systems whose parameters values are online acquirable only with an arbitrarily large degree of uncertainty the purpose is to define a switching policy inside a family of predesigned controllers so that the switched closed loop system result to be exponentially stable the proposed switching logic is based on a performance evaluation criterion which uses a measurable lyapunov like functional of the output the exponential stability condition is derived imposing a sufficient long time interval over which the functional is decreasing an interesting feature of the technical note is that no particular structure on the kind of uncertainty affecting the parameter values is assumed

bmi based stabilization of linear uncertain plants with polynomially time varying parameters this technical note considers the robust stabilization of uncertain linear time varying continuous time systems with a mode switch dynamics each mode is characterized by a theoretically unbounded dynamical matrix containing elements whose time behavior over bounded time intervals is sufficiently smooth to be well described by interval polynomials of arbitrary degree using a parameter dependent lyapunov function polynomially depending on time the stabilizing controller for each single mode is directly obtained by the solution of some bmi s which become lmi s by fixing two positive scalars the stability conditions of the switching closed loop system are derived defining a switched lyapunov function and involving the permanence time interval of the switching plant over each single mode a salient feature of the technical note is that unlike all the other existing methods each plant mode can be stabilized over arbitrarily large uncertain domains of parameters and their derivatives

random continued fractions levy constant and chernoff type estimate abstract given a stochastic process a n n 1 taking values in natural numbers the random continued fractions are defined as a 1 a 2 a n analogously to the continued fraction expansion of real numbers assume that a n n 1 is ergodic and the expectation e log a 1 we give a levy type metric theorem which covers that of real case presented by levy in 1929 moreover a corresponding chernoff type estimate is obtained under the conditions that a n n 1 is mixing and for each 0 t 1 e a 1 t

entropy production and information gain in axiom a systems anosov systems are mathematical models for chaotic systems in statistical mechanics and fluid dynamics most of these systems enjoy the property of positive entropy production we introduce the concept of specific information gain or specific relative entropy h in anosov systems and prove that it is identical to the entropy production rate e p defined by ruelle and gallavotti in anosov systems from this point of view the entropy production rate e p characterizes the degree of macroscopic irreversibility of the system

some large deviation results for dynamical systems we prove some large deviation estimates for continuous maps of compact metric spaces and apply them to attractors in differentiable dynamics rate of escape problems and to shift spaces

robust stability of time varying polytopic systems abstract this paper provides global asymptotic stability conditions for time varying continuous time polytopic systems using a parameter dependent lyapunov function the time varying parameter uncertainty as well as its time derivative are modelled as belonging to polytopic convex sets and their dependence is made explicit to get less conservative results a particular case characterized by the parameter uncertainty satisfying a linear differential equation is analyzed and a simpler version of the aforementioned stability conditions is presented the results are expressed in terms of linear matrix inequalities being thus numerically solvable with no big difficulty the theory is illustrated by the determination of the asymptotic stability region of a mathieu s type equation with an uncertain time varying parameter

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem