fourier transform of self affine measures abstract suppose f is a self affine set on r d d 2 which is not a singleton associated to affine contractions f j a j b j a j gl d r b j r d j a for some finite a we prove that if the group generated by the matrices a j j a forms a proximal and totally irreducible subgroup of gl d r then any self affine measure p j f j p j 1 0 p j 1 j a on f is a rajchman measure the fourier transform 0 as as an application this shows that self affine sets with proximal and totally irreducible linear parts are sets of rectangular multiplicity for multiple trigonometric series moreover if the zariski closure of is connected real split lie group in the zariski topology then has a power decay at infinity hence is l p improving for all 1 p and f has positive fourier dimension in dimension d 2 3 the irreducibility of and non compactness of the image of in pgl d r is enough for power decay of the proof is based on quantitative renewal theorems for random walks on the sphere s d 1

ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

maps of intervals with indifferent fixed points thermodynamic formalism and phase transitions we develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points for such systems the formalism yields onedimensional systems with many body infinite range interactions for which the thermodynamics is well defined but gibbs states are not piecewise linear systems of this kind yield the soluble in a sense fisher models we prove that such systems exhibit phase transitions the order of which depends on the behavior at the indifferent fixed points we obtain the critical exponent describing the singularity of the pressure and analyze the decay of correlations of the equilibrium states at all temperatures our technique relies on establishing and exploiting a relation between the transfer operators of the original map and its suitable expanding induced version the technique allows one also to obtain a version of the bowen ruelle formula for the hausdorff dimension of repellers for maps with indifferent fixed points and to generalize fisher results to some nonsoluble models

evaluation of stability of k means cluster ensembles with respect to random initialization many clustering algorithms including cluster ensembles rely on a random component stability of the results across different runs is considered to be an asset of the algorithm the cluster ensembles considered here are based on k means clusterers each clusterer is assigned a random target number of clusters k and is started from a random initialization here we use 10 artificial and 10 real data sets to study ensemble stability with respect to random k and random initialization the data sets were chosen to have a small number of clusters two to seven and a moderate number of data points up to a few hundred pairwise stability is defined as the adjusted rand index between pairs of clusterers in the ensemble averaged across all pairs nonpairwise stability is defined as the entropy of the consensus matrix of the ensemble an experimental comparison with the stability of the standard k means algorithm was carried out for k from 2 to 20 the results revealed that ensembles are generally more stable markedly so for larger k to establish whether stability can serve as a cluster validity index we first looked at the relationship between stability and accuracy with respect to the number of clusters k we found that such a relationship strongly depends on the data set varying from almost perfect positive correlation 0 97 for the glass data to almost perfect negative correlation 0 93 for the crabs data we propose a new combined stability index to be the sum of the pairwise individual and ensemble stabilities this index was found to correlate better with the ensemble accuracy following the hypothesis that a point of stability of a clustering algorithm corresponds to a structure found in the data we used the stability measures to pick the number of clusters the combined stability index gave best results

from rates of mixing to recurrence times via large deviations abstract a classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties for example the existence of invariant measures with stochastic like behaviour such as large deviations or decay of correlations such geometric structures are generally highly non trivial and thus a natural question is the extent to which this approach can be applied in this paper we show that in many cases stochastic like behaviour itself implies that the system has certain non trivial geometric properties which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration as a by product of our techniques we also obtain some new results on large deviations for certain classes of systems which include viana maps and multidimensional piecewise expanding maps

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

statistical properties of a nonuniformly hyperbolic map of the interval we prove a power law upper bound for the decay of the correlations for holder observables in the case of a nonuniformly hyperbolic map of the interval introduced by gaspard and wang as a piecewise linear approximation of the intermittent map of manneville pomeau the result is then applied to compute the central limit theorem for the same class of observables

random forests with ensemble of feature spaces random forests receive much attention from researchers because of their excellent performance as breiman suggested the performance of random forests depends on the strength of the weak learners in the forests and the diversity among them however in the literature many researchers only considered pre processing of the data or post processing of the random forests models in this paper we propose a new method to increase the diversity of each tree in the forests and thereby improve the overall accuracy during the training process of each individual tree in the forest different rotation spaces are concatenated into a higher space at the root node then the best split is exhaustively searched within this higher space the location where the best split lies decides which rotation method to be used for all subsequent nodes the performance of the proposed method here is evaluated on 42 benchmark data sets from various research fields and compared with the standard random forests the results show that the proposed method improves the performance of the random forests in most cases

rates of mixing for non markov infinite measure semiflows we develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows previously such results were restricted to the situation where there is a first return poincare map that is uniformly expanding and markov as illustrations of the method we consider semiflows over non markov pomeau manneville intermittent maps with infinite measure and we also obtain mixing rates for semiflows over collet eckmann maps with nonintegrable roof function

phase transitions for countable markov shifts we study the analyticity of the topological pressure for some one parameter families of potentials on countable markov shifts we relate the non analyticity of the pressure to changes in the recurrence properties of the system we give sufficient conditions for such changes to exist and not to exist we apply these results to the manneville pomeau map and use them to construct examples with different critical behavior

equidistribution for nonuniformly expanding dynamical systems and application to the almost sure invariance principle let t m mt m m be a nonuniformly expanding dynamical system such as logistic or intermittent map let v m rdv m rd be an observable and vn n 1k 0v tkvn k 0n 1v tk denote the birkhoff sums given a probability measure on m we consider vn as a discrete time random process on the probability space m m in smooth ergodic theory there are various natural choices of such as the lebesgue measure or the absolutely continuous t invariant measure they give rise to different random processes we investigate relation between such processes we show that in a large class of measures it is possible to couple redefine on a new probability space every two processes so that they are almost surely close to each other with explicit estimates of closeness the purpose of this work is to close a gap in the proof of the almost sure invariance principle for nonuniformly hyperbolic transformations by melbourne and nicol

formulas for calculating supremal controllable and normal sublanguages abstract supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis in this paper we discuss the computation of supremal controllable and normal sublanguages we derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed as a result those languages can be computed without applying recursive algorithms we also discuss those aspects of these formulas

decay of correlations for slowly mixing flows we show that polynomial decay of correlations is prevalent for a class of nonuniformly hyperbolic flows these flows are the continuous time analogue of a class of nonuniformly hyperbolic dieomorphisms for which young proved polynomial decay of correlations roughly speaking in situations where the decay rate o 1 n has previously been proved for dieomorphisms we establish the decay rate o 1 t for flows applications include certain classes of semidispersing billiards as well as dispersing billiards with vanishing curvature in addition we obtain results for suspension flows with unbounded roof functions in particular the classical planar lorentz flow with a doubly periodic array of circular scatterers has decay rate 1 t as anticipated by physicists

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

greedy optimization classifiers ensemble based on diversity decreasing the individual error and increasing the diversity among classifiers are two crucial factors for improving ensemble performances nevertheless the kappa error diagram shows that enhancing the diversity is at the expense of reducing individual accuracy hence a new method named matching pursuit optimization ensemble classifiers mpoec is proposed in this paper in order to balance the diversity and the individual accuracy mpoec method adopts a greedy iterative algorithm of matching pursuit to search for an optimal combination of entire classifiers and eliminates some similar or poor classifiers by giving zero coefficients in mpoec approach the coefficient of every classifier is gained by minimizing the residual between the target function and the linear combination of the basis functions especially when the basis functions are similar their coefficients will be close to zeros in one iteration of the optimization process which indicates that obtained coefficients of classifiers are based on the diversity among ensemble individuals because some classifiers are given zero coefficients mpoec approach may be also considered as a selective classifiers ensemble method experimental results show that mpoec improves the performance compared with other methods furthermore the kappa error diagrams indicate that the diversity is increased by the proposed method compared with standard ensemble strategies and evolutionary ensemble

statistical properties of maps with indifferent periodic points in this note we present an axiomatic approach to the decay of correlations for maps of arbitrary dimension with indifferent periodic points as applications we apply our results to the well known manneville pomeau equation and the inhomogeneous diophantine approximation algorithm

non stationary almost sure invariance principle for hyperbolic systems with singularities we investigate a wide class of two dimensional hyperbolic systems with singularities and prove the almost sure invariance principle asip for the random process generated by sequences of dynamically holder observables the observables could be unbounded and the process may be non stationary and need not have linearly growing variances our results apply to anosov diffeomorphisms sinai dispersing billiards and their perturbations the random processes under consideration are related to the fluctuation of lyapunov exponents the shrinking target problem etc

statistical properties and decay of correlations for interval maps with critical points and singularities we consider a class of piecewise smooth one dimensional maps with critical points and singularities possibly with infinite derivative under mild summability conditions on the growth of the derivative on critical orbits we prove the central limit theorem and a vector valued almost sure invariance principle we also obtain results on decay of correlations and large deviations

central limit theorem and stable laws for intermittent maps in the setting of abstract markov maps we prove results concerning the convergence of renormalized birkhoff sums to normal laws or stable laws they apply to one dimensional maps with a neutral fixed point at 0 of the form x x1 for 0 1 in particular for 1 2 we show that the birkhoff sums of a holder observable f converge to a normal law or a stable law depending on whether f 0 0 or f 0 0 the proof uses spectral techniques introduced by sarig and wiener s lemma in non commutative banach algebras

on infinite volume mixing in the context of the long standing issue of mixing in infinite ergodic theory we introduce the idea of mixing for observables possessing an infinite volume average the idea is borrowed from statistical mechanics and appears to be relevant at least for extended systems with a direct physical interpretation we discuss the pros and cons of a few mathematical definitions that can be devised testing them on a prototypical class of infinite measure preserving dynamical systems namely the random walks

a note on deciding the controllability of a language k with respect to a language l it has been shown by p j ramadge and w m wonham 1987 if g is a plant automaton and k contained in l g is a prefix closed language there exists a supervisor theta that is complete with respect to g so that l theta g k intersection l g k if and only if k is controllable with respect to the plant language l d it is shown that if l g and k are represented as free labeled petri nets then the controllability of k with respect to l g is detectable this result is a direct consequence of the decidability of the petri net and reachability problem in effect a modeling framework capable of finitely representing a class of infinite state systems is identified and controllability is decidable within this framework

an invariance principle for maps with polynomial decay of correlations we give a general method of deriving statistical limit theorems such as the central limit theorem and its functional version in the setting of ergodic measure preserving transformations this method is applicable in situations where the iterates of discrete time maps display a polynomial decay of correlations

lyapunov statistics and mixing rates for intermittent systems we consider here a recent conjecture stating that correlation functions and tail probabilities of finite time lyapunov exponents would have the same power law decay in weakly chaotic systems we demonstrate that this conjecture fails for a generic class of maps of the pomeau manneville type we show further that typically the decay properties of such tail probabilities do not provide significant information on key aspects of weakly chaotic dynamics such as ergodicity and instability regimes our approaches are firmly based on rigorous results particularly the aaronson darling kac theorem and are also confirmed by exhaustive numerical simulations

local limit theorem for nonuniformly partially hyperbolic skew products and farey sequences we study skew products of the form x omega mapsto tx omega phi x where t is a nonuniformly expanding map on a space x preserving a possibly singular probability measure tilde mu and phi x to s 1 is a c 1 function under mild assumptions on tilde mu and phi we prove that such a map is exponentially mixing and satisfies the central and local limit theorems these results apply to a random walk related to the farey sequence thereby answering a question of guivarc h and raugi

subexponential decay of correlations we describe a method for proving subexponential lower bounds for correlations functions and apply it to study decay of correlations for maps with countable markov partitions one result is that ls young s upper estimates y2 are optimal in many situations our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on banach spaces which we apply to the iterates of the transfer operator

generalized lyapunov exponent as a unified characterization of dynamical instabilities the lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits a positive lyapunov exponent exponential dynamical instability is a manifestation of chaos here we propose the lyapunov pair which is based on the generalized lyapunov exponent as a unified characterization of nonexponential and exponential dynamical instabilities in one dimensional maps chaos is classified into three different types i e superexponential exponential and subexponential chaos using one dimensional maps we demonstrate superexponential and subexponential chaos and quantify the dynamical instabilities by the lyapunov pair in subexponential chaos we show superweak chaos which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth the scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process which is related to infinite ergodic theory

a note on the properties of the supremal controllable sublanguage in pushdown systems consider an event alphabet sigma the supervisory control theory of ramadge and wonham asks the question given a plant model g with language lm g sube sigma and another language k sube lm g is there a supervisor phi such that lm phi g k ramadge and wonham showed that a necessary condition for this to be true is the so called controllability of k with respect to lm g they showed that when g is a finite state automaton and k is a regular language also generated by a finite state automaton then there is a regular supremal controllable sublanguage supc k sube k that is effectively constructable from generators of k and g in this paper we show 1 there is an algorithm to compute the supremal controllable sublanguage of a prefix closed k accepted by a deterministic pushdown automaton dpda when the plant language is also prefix closed and accepted by a finite state automaton and 2 in this case we show that this supremal controllable sublanguage is also accepted by a dpda

optimal concentration inequalities for dynamical systems for dynamical systems modeled by a young tower with exponential tails we prove an exponential concentration inequality for all separately lipschitz observables of n variables when tails are polynomial we prove polynomial concentration inequalities those inequalities are optimal we give some applications of such inequalities to specific systems and specific observables

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

continuous phase transitions for dynamical systems we study the asymptotic expansion of the topological pressure of one parameter families of potentials at a point of non analyticity the singularity is related qualitatively and quantitatively to non gaussian limit laws and to slow decay of correlations with respect to the equilibrium measure

markov approximations and decay of correlations for anosov flows we develop markov approximations for very general suspension flows based on this we obtain a stretched exponential bound on time correlation functions for 3 d anosov flows that verify uniform nonintegrability of foliations these include contact anosov flows and geodesic flows on compact surfaces of variable negative curvature our bound on correlations is stable under small smooth perturbations

renewal sequences and intermittency in this paper we examine the generating function z of a renewal sequence arising from the distribution of return times in the turbulent region for a class of piecewise affine interval maps introduced by gaspard and wang and studied by several authors we prove that it admits a meromorphic continuation to the entire complex z plane with a branch cut along the ray 1 moreover we compute the asymptotic behavior of the coefficients of its taylor expansion at z 0 from this we obtain the exact polynomial asympotics for the rate of mixing when the invariant measure is finite and of the scaling rate when it is infinite

produits aleatoires d operateurs matrices de transfert nous etudions le comportement asymptotique de produits aleatoires d operateurs de ruelle perron frobenius nous etendons le travail de ruelle obtenu dans le cas homogene au cas aleatoire

spectral gap and transience for ruelle operators on countable markov shifts we find a necessary and sufficient condition for the ruelle operator of a weakly holder continuous potential on a topologically mixing countable markov shift to act with spectral gap on some rich banach space we show that the set of potentials satisfying this condition is open and dense for a variety of topologies we then analyze the complement of this set in a finer topology and show that among the three known obstructions to spectral gap weak positive recurrence null recurrence transience transience is open and dense and null recurrence and weak positive recurrence have empty interior

almost sure invariance principle for sequential and non stationary dynamical systems we establish almost sure invariance principles a strong form of approximation by brownian motion for non stationary time series arising as observations on dynamical systems our examples include observations on sequential expanding maps perturbed dynamical systems non stationary sequences of functions on hyperbolic systems as well as applications to the shrinking target problem in expanding systems

linear response for intermittent maps we consider the one parameter family alpha mapsto t alpha alpha in 0 1 of pomeau manneville type interval maps t alpha x x 1 2 alpha x alpha for x in 0 1 2 and t alpha x 2x 1 for x in 1 2 1 with the associated absolutely continuous invariant probability measure mu alpha for alpha in 0 1 sarig and gouezel proved that the system mixes only polynomially with rate n 1 1 alpha in particular there is no spectral gap we show that for any psi in l q the map alpha to int 0 1 psi d mu alpha is differentiable on 0 1 1 q and we give a linear response formula for the value of the derivative this is the first time that a linear response formula for the srb measure is obtained in the setting of slowly mixing dynamics our argument shows how cone techniques can be used in this context for alpha ge 1 2 we need the n 1 alpha decorrelation obtained by gouezel under additional conditions

a dirichlet process gaussian state machine model for change detection in transient processes abstractthe ability to detect incipient and critical changes in real world process esessential for system integrity assurance is currently impeded by the mismatch between the key assumption of stationarity underlying most change detection methods and the nonlinear and nonstationary transient dynamics of most real world processes the current approaches are slow or outright unable to detect qualitative changes in the behaviors that lead to anomalies we present a dirichlet process gaussian state machine dpgsm model to represent dynamic intermittency which is one of the most ubiquitous real world transient behaviors the dpgsm model treats a signal as a random walk among a dirichlet process mixture of gaussian clusters hypothesis tests and a numerical scheme based on this nonparametric representation were developed to detect subtle changes in the transient intermittent dynamics experimental investigations suggest that the dpgsm approach can consistently detect incipient critical changes in intermi

convergence to equilibrium for intermittent symplectic maps we investigate a class of area preserving non uniformly hyperbolic maps of the two torus first we establish some results on the regularity of the invariant foliations then we use this knowledge to estimate the rate of mixing

a new maximal inequality and invariance principle for stationary sequences we derive a new maximal inequality for stationary sequences under a martingale type condition introduced by maxwell and woodroofe ann probab 28 2000 713 724 then we apply it to establish the donsker invariance principle for this class of stationary sequences a markov chain example is given in order to show the optimality of the conditions imposed

rapid decay of correlations for nonuniformly hyperbolic flows we show that superpolynomial decay of correlations rapid mixing is prevalent for a class of nonuniformly hyperbolic flows these flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which young proved exponential decay of correlations the proof combines techniques of dolgopyat and operator renewal theory it follows from our results that planar periodic lorentz flows with finite horizons and flows near homoclinic tangencies are typically rapid mixing

selective multiple kernel learning for classification with ensemble strategy abstract multiple kernel learning mkl aims to seek a better result than single kernel learning by combining a compact set of sub kernels however mkl with l1 norm easily discards the sub kernels with complementary information and mkl with lp norm p 2 often gets the redundant solution to address these problems a selective multiple kernel learning smkl method inspired by ensemble learning el is proposed comparing mkl with lp norm p 2 smkl obtains a sparse solution by a pre selection procedure comparing mkl with l1 norm smkl preserves the sub kernels with complementary information by guaranteeing the high discrimination and large diversity of pre selected sub kernels for quantifying the discrimination and diversity of sub kernels a new kernel evaluation is designed smkl reduces the scale of mkl optimization and saves the memory storing of the sub kernels which extends the scale of problem that mkl could solve specially a fast smkl method using l norm constraint is focused which needs no mkl optimization process it means that the memory is hardly a limitation for mkl with the large scale problem experiments state that our method is effective for classification

on the supermal controllable sublanguage of a given language the concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes in this paper the supremal controllable sublanguage s of a given language l is characterized as the largest fixpoint of a monotone operator omega in the case where the languages involved are regular it is shown that the fixpoint s can be computed as the limit of the finite sequence k j given by k j 1 omega k j k 0 l an effective computational algorithm is developed and three examples are provided for illustration

intermittency and regularized fredholm determinants we consider real analytic maps of the interval i 0 1 which are expanding everywhere except for a neutral fixed point at 0 we show that on a certain function space the associated perron frobenius operator has a continuous and residual spectrum contained in the line segment c 0 1 and a point spectrum p which has no points of accumulation outside 0 and 1 furthermore points in p 0 1 are eigenvalues of finite multiplicity we construct a regularized fredholm determinant d which has a holomorphic extension to c and can be analytically continued from each side of c to an open neighborhood of c 0 1 on different riemann sheets in c the zero set of d is in one to one correspondence with the point spectrum of through the conformal transformation the function d z extends to a holomorphic function in a domain which contains the unit disc

decay of correlations dedicated to micheline ishay i would like to thank p boyland l chierchia v donnay g de martino c gole j l lebowitz m lyubich m rychlik i g schwarz s vaienti and especially g gallavotti for helpful and enlightening discussions particularly warm thanks go to n chernov for carefully reading and finding a mistake in an early version the present paper benefits from several improvements due to his sharp criticism in addition i am indebted to p collet and most of all m wojtkowski for introducing me to the magical world of cones finally i thank j milnor director of the institute for mathematical sciences at stony brook university where i was visiting during part of this work and the italian c n r gnfm for providing travel funds

mixing rates for intermittent maps of high exponent we obtain higher order theory for the long term behavior of the transfer operator associated with the unit interval map f x x 1 2 alpha x alpha if 0 1 which corresponds to the infinite measure preserving case higher order theory for alpha ge 2 is more challenging and requires new techniques along the way we provide higher order theory for scalar and operator renewal sequences with infinite measure and regular variation although the present work considers the unit interval map mentioned above as a toy model our interest focuses on finding sufficient conditions under which the asymptotic behavior of the transfer operator associated to dynamical systems preserving an infinite measure is almost like the asymptotic behavior of scalar renewal sequences associated to null recurrent markov chains characterized by regular variation

weighted classifier ensemble based on quadratic form diversity and accuracy are the two key factors that decide the ensemble generalization error constructing a good ensemble method by balancing these two factors is difficult because increasing diversity is at the cost of reducing accuracy normally in order to improve the performance of an ensemble while avoiding the difficulty derived of balancing diversity and accuracy we propose a novel method that weights each classifier in the ensemble by maximizing three different quadratic forms in this paper the optimal weight of individual classifiers is obtained by minimizing the ensemble error rather than analyzing diversity and accuracy since it is difficult to minimize the general form of the ensemble error directly we approximate the error in an objective function subject to two constraints w i 1 and 1 w i 1 particularly we introduce an error term with a weight vector w0 and subtract this error with the quadratic form to obtain our approximated error this subtraction makes minimizing the approximation form equivalent to maximizing the original quadratic form theoretical analysis finds that when the value of the quadratic form is maximized the error of an ensemble system with the corresponding optimal weight w will be smallest especially compared with the ensemble with w0 finally we demonstrate improved classification performance from the experimental results of an artificial dataset uci datasets and polsar image data a new weighted classifier ensemble method is proposed an approximation form of the ensemble error is introduced an optimal weight vector is sought based on minimizing the approximation form it is converted into maximizing quadratic forms by invoking a known weight vector the larger the value of the quadratic form is the lower the ensemble error is

almost isomorphism for countable state markov shifts countable state markov shifts are a natural generalization of the well known subshifts of finite type they are the subject of current research both for their own sake and as models for smooth dynamical systems in this paper we investigate their almost isomorphism and entropy conjugacy and obtain a complete classification for the especially important class of strongly positive recurrent markov shifts this gives a complete classification up to entropyconjugacy of the natural extensions of smooth entropy expanding maps e g c smooth interval maps with non zero topological entropy

support vector machinery for infinite ensemble learning ensemble learning algorithms such as boosting can achieve better performance by averaging over the predictions of some base hypotheses nevertheless most existing algorithms are limited to combining only a finite number of hypotheses and the generated ensemble is usually sparse thus it is not clear whether we should construct an ensemble classifier with a larger or even an infinite number of hypotheses in addition constructing an infinite ensemble itself is a challenging task in this paper we formulate an infinite ensemble learning framework based on the support vector machine svm the framework can output an infinite and nonsparse ensemble through embedding infinitely many hypotheses into an svm kernel we use the framework to derive two novel kernels the stump kernel and the perceptron kernel the stump kernel embodies infinitely many decision stumps and the perceptron kernel embodies infinitely many perceptrons we also show that the laplacian radial basis function kernel embodies infinitely many decision trees and can thus be explained through infinite ensemble learning experimental results show that svm with these kernels is superior to boosting with the same base hypothesis set in addition svm with the stump kernel or the perceptron kernel performs similarly to svm with the gaussian radial basis function kernel but enjoys the benefit of faster parameter selection these properties make the novel kernels favorable choices in practice

a note on deciding controllability in pushdown systems consider an event alphabet spl sigma the supervisory control theory of ramadge and wonham asks the question given a plant model g with language k l sub m g spl sube spl sigma sup and another language k spl sube l sub m g is there a supervisor spl psi such that l sub m spl psi g k ramadge and wonham showed that a necessary condition for this to be true is the so called controllability of k with respect to l sub m g they showed that when g is a finite state automaton and k is a regular language also generated by a finite state automaton then the controllability property was decidable for k the class of languages generated by pushdown automata properly includes the regular languages they are accepted by finite state machines coupled with pushdown stack memory this makes them interesting candidates as supervisory languages since the supervisor will have nonfinite memory in this note we show the following i if s is a specification given by a deterministic pushdown automaton and l is generated by a finite state machine then there is an algorithm to decide whether k s spl cap l is controllable with respect to l ii it is undecidable for an arbitrary specification s generated by a nondeterministic pushdown automaton and plant language l generated by a finite state machine whether k s spl cap l is controllable with respect to l

on controllability and normality of discrete event dynamical systems abstract this paper studies the supervisor synthesis problem of discrete event dynamical systems deds s through the use of synchronous composition of the plant and the supervisor and discusses some of the simplifications achieved by using the synchronous composition to model supervisory control an alternate definition of controllability is presented this definition of controllability is then used to derive an algorithm that is computationally more efficient than previously existing ones for the construction of the supremal controllable sublanguage the algorithm is also shown to be optimal the observability and normality issues arising due to the partial observation of the system dynamics under an arbitrary mask are then investigated closed form representations of the supremal normal and supremal closd and normal sublanguages are derived in the more general setting of arbitrary mask and nonclosed languages thus extending earlier results of the authors and others

operator renewal theory and mixing rates for dynamical systems with infinite measure we develop a theory of operator renewal sequences in the context of innite ergodic theory for large classes of dynamical systems preserving an innite measure we determine the asymptotic behaviour of iterates l n of the transfer operator this was previously an intractable problem examples of systems covered by our results include i parabolic rational maps of the complex plane and ii not necessarily markovian nonuniformly expanding interval maps with indierent xed points in addition we give a particularly simple proof of pointwise dual ergodicity asymptotic behaviour of p n 1 l j for the class of systems under consideration in certain situations including pomeau manneville intermittency maps we obtain higher order expansions for l n and rates of mixing also we obtain error estimates in the associated dynkin lamperti arcsine laws

equilibriums of some non holder potentials we consider one sided subshifts with some potential functions which satisfy the holder condition everywhere except at a fixed point and its preimages we prove that the systems have conformal measures and invariant measures absolutely continuous with respect to where may be finite or infinite we show that the systems are exact and are weak gibbs measures and equilibriums for we also discuss uniqueness of equilibriums and phase transition these results can be applied to some expanding dynamical systems with an indifferent fixed point

invariance principles for interval maps with an indifferent fixed point in this note we establish an almost sure invariance principle for a large class of interval maps with indifferent fixed points including the manneville pomeau map this implies a number of well known corollaries including the weak invariance principle and the law of the iterated logarithm

the random subspace method for constructing decision forests much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes the dilemma between overfitting and achieving maximum accuracy is seldom resolved a method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity the classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector that is trees constructed in randomly chosen subspaces the subspace method is compared to single tree classifiers and other forest construction methods by experiments on publicly available datasets where the method s superiority is demonstrated we also discuss independence between trees in a forest and relate that to the combined classification accuracy

cluster approximation for the farey fraction spin chain we consider the farey fraction spin chain in an external field h utilising ideas from dynamical systems the free energy of the model is derived by means of an effective cluster energy approximation this approximation is valid for divergent cluster sizes and hence appropriate for the discussion of the magnetizing transition we calculate the phase boundaries and the scaling of the free energy at h 0 we reproduce the rigorously known asymptotic temperature dependence of the free energy for h 0 our results are largely consistent with those found previously using mean field theory and renormalization group arguments