bandt pompe approach to the classical quantum transition abstract by regarding the celebrated classical quantum transition problem as one pertaining to the domain of dynamic systems theory we present a discussion that exhibits the superiority of the bandt pompe approach to the extraction of a probability distribution from time series values

generalized relative entropies in the classical limit abstract our protagonists are i the cressie read family of divergences characterized by the parameter ii tsallis generalized relative entropies characterized by the q one and as a particular instance of both iii the kullback leibler kl relative entropy in their normalized versions we ascertain the equivalence between i and ii additionally we employ these three entropic quantifiers in order to provide a statistical investigation of the classical limit of a semiclassical model whose properties are well known from a purely dynamic viewpoint this places us in a good position to assess the appropriateness of our statistical quantifiers for describing involved systems we compare the behaviour of i ii and iii as one proceeds towards the classical limit we determine optimal ranges for and or q it is shown the tsallis quantifier is better than kl s for 1 5 q 2 5

chaos in time dependent variational approximations to quantum dynamics dynamical chaos has recently been shown to exist in the gaussian approximation in quan tum mechanics and in the self consistent mean eld approach to studying the dynamics ofquantum elds in this study we rst show that any variationalapproximationto the dynam ics of a quantum system based on the dirac action principle leads to a classical hamiltoniandynamics for the variational parameters since this hamiltonian is generically nonlinearand nonintegrable the dynamics thus generated can be chaotic in distinction to the exactquantum evolution we then restrict attention to a system of two biquadratically coupledquantum oscillators and study two variational schemes the leading order large n fourcanonical variables and hartree six canonical variables approximations the chaos seenin the approximate dynamics is an artifact of the approximations this is demonstrated bythe fact that its onset occurs on the same characteristic time scale as the breakdown of theapproximations when compared to numerical solutions of the time dependent schr odingerequation pacs numbers 05 45 b 03 65 sq 2 30 wd 03 65 w

fatou s lemma and lower epi limits of integral functionals abstract in this work with the introduction in the finite case of a modulus of equi integrability we prove some new extensions of fatou s lemma and some of its consequences in the convergence theory of integral functionals we present the case of a sequence of integral functionals using an analog of ioffe s criterion for a sequence of integrands

simple measure for complexity a measure of complexity is proposed based on appropriately defined notions of order and disorder which has a considerable degree of flexibility in its dependence on these concepts the possible functional dependencies which result encompass those of many earlier definitions of complexity the proposed measure is in principle easy to calculate and has the property of an intensive thermodynamic quantity with appropriate choices of parameters it behaves similarly to effective measure complexity for the logistic map it is also a generalization of the normalized complexity of lopez ruiz et al but does not suffer from over universality

on fatou s lemma and parametric integrals for set valued functions abstract in this paper we present new versions of the set valued fatou s lemma for sequences of measurable multifunctions and their conditional expectations then we use them to study the continuity and measurability properties of parameterized set valued integrals

intensive entropic non triviality measure abstract we discuss a way of characterizing probability distributions complementing that provided by the celebrated notion of information measure with reference to a measure of complexity that we call a nontriviality measure our starting point is the lmc measure of complexity advanced by lopez ruiz et al phys lett a 209 1995 321 and its analysis by anteneodo and plastino phys lett a 223 1997 348 an improvement of some of their troublesome characteristics is thereby achieved basically we replace the euclidean distance to equilibrium by the jensen shannon divergence the resulting measure turns out to be i an intensive quantity and ii allows one to distinguish between different degrees of periodicity we apply the cured measure to the logistic map so as to clearly exhibit its advantages

measurability and integrability of the weak upper limit of a sequence of multifunctions we provide several properties of the weak upper limit of a sequence of subsets of a separable banach space such as a criterion of non vacuity of closedness etc we also examine the measurability of the multifunction defined as the weak upper limit of a sequence of multifunctions at last applications to the existence of a measurable and bochner integrable selector for this multifunction are presented

convergence of conditional expectations for unbounded random sets integrands and integral functionals given a sequence of unbounded convex random sets we study under which conditions fatou s lemma for the weak upper limit of their conditional expectations holds we also give multivalued versions of dominated and monotone convergence theorems and we discuss the special case of the integral finally applications to epigraphic convergence of integrands and to mosco convergence of certain integral functionals are provided

characterization of time dynamical evolution of electroencephalographic epileptic records abstract since traditional electrical brain signal analysis is mostly qualitative the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals these methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of the brain dynamics the processing of information by the brain is reflected in dynamical changes of the electrical activity in time frequency and space therefore the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency the entropy defined from the wavelet functions is a measure of the order disorder degree present in a time series in consequence this entropy evaluates over eeg time series gives information about the underlying dynamical process in the brain more specifically of the synchrony of the group cells involved in the different neural responses the total wavelet entropy results independent of the signal energy and becomes a good tool for detecting dynamical changes in the system behavior in addition the total wavelet entropy has advantages over the lyapunov exponents because it is parameter free and independent of the stationarity of the time series in this work we compared the results of the time evolution of the chaoticity lyapunov exponent as a function of time with the corresponding time evolution of the total wavelet entropy in two different eeg records one provide by depth electrodes and other by scalp ones

deformed exponentials and logarithms in generalized thermostatistics abstract criteria are given that deformed logarithmic and exponential functions should satisfy with a pair of such functions one can associate another function called the deduced logarithmic function it is shown that generalized thermostatistics can be formulated in terms of deformed exponential functions together with the associated deduced logarithmic functions

a representation theorem for aumann integrals in recent years the study of set valued functions has been developed extensively by many authors with applications to mathematical economics and control theory see refs 5 11 15 161 in those papers three approaches can be distinguished according to whether the range space values of setvalued functions is z a banach space or a locally convex topological space the purpose of this paper is to establish properties of aumann s integrals of set valued functions f t 2 whose values are nonempty subsets of a real separable reflexive banach space x and to continue the work due to aumann 2 and datko 7 81 while previous analysis has always treated the case of special finite nonatomic measure spaces we focus here on the case of general a finite nonatomic measure spaces in this last situation moreover the analogous results we establish hold under less stringent hypotheses more precisely all through the paper we consider a measure space t c p where p is supposed to be positive nonatomic and u finite and we give the following statements

fatou s lemmas for the set of integrable selections abstract in this paper we prove fatou type results for the set of bochner integrable selections from a set valued function also we obtain some new dominated convergence theorems for the aumann integral our results have applications in economic theory

weak sequential convergence in l1 μ x and an exact version of fatouʼs lemma abstract the class of nonatomic finite measure spaces with the saturation property as developed in maharam 1942 and hoover keisler 1984 is characterized by the fatou and lebesgue property of a well dominated sequence of multifunctions taking values in a banach space with multifunctions reduced to functions this fatou characterization also extends to a variant of the closure property found in optimal control theory the results are developed through a considered overview of the relevant literature on the exact and approximate fatou lemma phrased in terms of bochner integration

tsallis deformation parameter q quantifies the classical quantum transition abstract we investigate the classical limit of a type of semiclassical evolution the pertinent system representing the interaction between matter and a given field on using tsallis q entropy as a quantifier of the ensuing dynamics we find that it not only appropriately describes the quantum classical transition but that the associated deformation parameter q itself characterizes the different regimes involved in the process detecting the most salient fine details of the changeover

bandt pompe tsallis quantifier and quantum classical transition abstract we concern ourselves with statistical quantifiers of semiclassical time evolutions and their classical limit the system of interest represents the interaction between matter and a given field our tool here is the so called permutation entropy evaluated by recourse to the so called bandt pompe technique within a tsallis scenario we encounter that the most salient details of the quantum classical transition are well described indeed in a better fashion than that of previous approaches

fatou s lemma in reflexive banach spaces a version of an approximate fatou lemma for a uniformly integrable sequence of functions with values in a reflexive banach space is proved the usual assumption that this sequence is pointwisely dominated in norm by a real valued integrable function is omitted

brain electrical activity analysis using wavelet based informational tools ii tsallis non extensivity and complexity measures the processing of information by the brain is reflected in dynamical changes of the electrical activity in i time ii frequency and iii space therefore the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency the present work complements the efforts described in rosso et al physica a 313 2002 587 devoted to non extensive information measures a la tsallis here we show that the notion of complexity using 1 appropriate information theory tools adapted to a non extensive scenario and 2 scalp eeg data provides one with valuable insights into the dynamics of neural activity in particular using different complexity measures we detect the presence of states characterized by both order and maximal complexity

on seminormality of integral functionals and their integrands we present a definition of seminormality which extends classical notions due to tonelli fondamenti di calcolo delle variazioni 1921 mcshane ann scuola norm sup pisa 2 3 1934 pp 181 211 287 315 and cesari traps amer math soc 124 1966 pp 369 412 j optim theory appl 6 1970 pp 114 137 siam j control optim 9 1971 pp 287 315 and applies to both integrands seminormality in the small and their integral functionals seminormality in the large our main result states that under very general hypotheses seminormality in the small and large are equivalent by introducing a notion called nagumo tightness we show that the usual sufficient conditions for the lower semicontinuity of an integral functional also imply a form of seminormality of the integral functional necessary conditions for the lower semicontinuity of an integral functional can also be obtained from our results

the tsallis complexity of a semiclassical time evolution abstract an investigation is undertaken of semiclassical time evolutions and their classical limit with the intent of getting insights into the classical quantum frontier we deal with a system that represents the interaction between matter and a given field and our main research tool is the so called q complexity quantifier for which two different versions are considered the probability distribution associated with the time evolution process is determined by recourse to the bandt pompe symbolic technique c bandt b pompe permutation entropy a natural complexity measure for time series phys rev lett 88 2002 174102 1 174102 4 the most salient details of the quantum classical transition turn out to be described not only well but also in a better fashion than that of previous literature

dynamical complexity detection in pre seismic emissions using nonadditive tsallis entropy abstract we investigate within the framework of nonextensive tsallis entropy particular aspects of the relation between signal analysis and signals originating in a very special nonlinear system the focal area of an impending earthquake the tsallis like time dependent entropy is shown to be a rather powerful tool for providing a novel quantitative strategy for monitoring the focal area states just before the earthquake occurrence

generalized boltzmann factors and the maximum entropy principle entropies for complex systems abstract we generalize the usual exponential boltzmann factor to any reasonable and potentially observable distribution function b e by defining generalized logarithms as inverses of these distribution functions we are led to a generalization of the classical boltzmann gibbs entropy s bg d e e b e ln b e to the expression s d e e 0 b e d x x which contains the classical entropy as a special case we show that this is the unique modification of entropy which is compatible with the maximum entropy principle for arbitrary non exponential distribution functions we demonstrate that this entropy has two important features first it describes the correct thermodynamic relations of the system and second the observed distributions are straightforward solutions to the jaynes maximum entropy principle with the ordinary not escort constraints tsallis entropy is recovered as a further special case

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

tsallis entropy and cortical dynamics the analysis of eeg signals abstract we undertake the study of eeg signals by recourse to a wavelet based multiresolution analysis as adapted to an information measure scenario different information measures are employed it is shown that non extensive ones seem to be of particular usefulness

generalized entropies from first principles a derivation of power law canonical distributions from first principle statistical mechanics including the exponential distribution as a particular case is presented it is shown that these distributions arise naturally and that the heat capacity of the heat bath is the condition that determines its type as a consequence a physical interpretation for the parameter q of the generalized entropy is given

on testing trained vector quantizer codebooks this paper discusses a criterion for testing a vector quantizer vq codebook that is obtained by training when a vq codebook is designed by a clustering algorithm using a training set time average distortion which is called the training set distortion tsd is usually calculated in each iteration of the algorithm since the input probability function is unknown in general and cumbersome to deal with the algorithm stops when the tsd ceases to significantly decrease in order to test the resultant codebook validating set distortion vsd is calculated on a separate validating set vs codebooks that yield small difference between the tsd and the vsd are regarded as good ones however the difference vsd tsd is not necessarily a desirable criterion for testing a trained codebook unless certain conditions are satisfied a condition that is previously assumed to be important is that the vs has to be quite large to well approximate the source distribution this condition implies greater computational burden of testing a codebook in this paper we first discuss the condition under which the difference vsd tsd is a meaningful codebook testing criterion then convergence properties of the vsd a time average quantity are investigated finally we show that for large codebooks a vs size as small as the size of the codebook is sufficient to evaluate the vsd this paper consequently presents a simple method to test trained codebooks for vq s experimental results on synthetic data and real images supporting the analysis are also provided and discussed

integration of correspondences on loeb spaces we study the bochner and gel fand integration of banach space valued correspondences on a general loeb space though it is well known that the lyapunov type result on the compactness and convexity of the integral of a correspondence and the fatou type result on the preservation of upper semicontinuity by integration are in general not valid in the setting of an infinite dimensional space we show that exact versions of these two results hold in the case we study we also note that our results on a hyperfinite loeb space capture the nature of the corresponding asymptotic results for the large finite case but the unit lebesgue interval fails to provide such a framework

infinite dimensional extension of a theorem of komlos a well known theorem of komlos is extended to integrable functions taking values in a reflexive banach space

a unifying note on fatou s lemma in several dimensions a general version of fatou s lemma in several dimensions is presented it subsumes the fatou lemmas given by schmeidler schmeidler d 1970 fatou s lemma in several dimensions proc amer math soc 24 300 306 hildenbrand hildenbrand w 1974 core and equilibria of a large economy princeton university press princeton cesari suryanarayana cesari l m b suryanarayana 1978 an existence theorem for pareto problems nonlinear anal 2 225 233 and artstein artstein z 1979 a note on fatou s lemma in several dimensions j math econom 6 277 282 also it is equivalent to an abstract variational existence result that extends and generalizes results by aumann perles aumann r j m perles 1965 a variational problem arising in economics j math anal appl 11 488 503 berliocchi lasry berliocchi h j m lasry 1973 integrands normales et mesures parametrees en calcul des variations bull soc math france101 129 184 artstein artstein z 1974 on a variational problem j math anal appl 45 404 415 and balder balder e j 1979 on a useful compactification for optimal control problems j math anal appl 72 391 398 in several respects

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

generalized equilibrium results for games with incomplete information milgrom and weber milgrom p r weber r j 1985 distributional strategies for games with incomplete information math oper res 10 619 632 gave an existence result for a nash equilibrium in a game with incomplete information using their notion of a distributional strategy here we obtain a substantial improvement of their existence result in terms of the more traditional concept of a behavioral strategy this improvement is reached very naturally as an application of a theory of weak convergence for transition probabilities which is recapitulated extensively in this paper also a new result on the weak convergence of product transition probabilities is included

fatou s lemma for multifunctions with unbounded values for multifunctions having unbounded sets as values we give fatou type inclusions for the kuratowski limes superior in finite as well as infinite dimensions these are derived from similar known fatou type inequalities for single valued multifunctions i e ordinary functions that is from balder s unifying fatou lemma in case the image set is finite dimensional and from an update of related results by balder in the infinite dimensional case for this extension from the single valued to the multivalued situation a lemma due to hess used to prove earlier fatou type inclusions is of critical importance also an asymptotic correction term introduced here plays an important role the two man results thus obtained subsume and extend an entire class of comparable fatou lemmas

weak sequential convergence in lp μ x we provide some new results on the weak convergence of sequences or nets lying in lp t x lp x 1 p i e the space of equivalence classes of x valued x is a banach space bochner integrable functions on the finite measure space t our theorems generalize in several directions recent resuls on weak sequential convergence in l1 x obtained by m a khan and m majumdar j math anal appl 114 1986 569 573 and z artstein j math econ 6 1979 277 282 and they can be used to obtain dominated convergence results for the aumann integral our results have useful applications in economics and game theory

fractional brownian motion fractional gaussian noise and tsallis permutation entropy abstract in this work we analyze two important stochastic processes the fractional brownian motion and fractional gaussian noise within the framework of the tsallis permutation entropy this entropic measure evaluated after using the bandt pompe method to extract the associated probability distribution is shown to be a powerful tool to characterize fractal stochastic processes it allows for a better discrimination of the processes than the shannon counterpart for appropriate ranges of values of the entropic index moreover we find the optimum value of this entropic index for the stochastic processes under study

multivalued mappings in generalized chaos synchronization the onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system a recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single valued function in this paper we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function specifically we study the properties of the multivalued mapping that occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one to one and address the issues of the existence and continuity of such mappings the basic theoretical framework underlying the considered synchronization regimes is then developed

a general approach to lower semicontinuity and lower closure in optimal control theory a self contained approach to lower semicontinuity and lower closure evolves from an extension of relaxed control theory which is based on a central relative weak compactness criterion called tightness and relaxation in all but one variable two lower closure results for outer integral functionals with variable abstract time domain are developed the first of these has a convexity condition for the integrand and generalizes all similar results in the literature the second lower closure result is of a new kind among other things it implies a quite general version of fatou s lemma in several dimensions