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

tsallis statistics and fully developed turbulence an analysis of fully developed turbulence is developed based on the assumption that the underlying statistics of the system is that of the tsallis ensemble the multifractal spectrum ft corresponding to the tsallis type distribution function is determined self consistently in the sense that all parameters can be obtained through the observed value of the intermittency exponent it is shown that the scaling exponents m of the velocity structure function derived with the help of the multifractal spectrum fit very well with experimental data it is revealed that the asymptotic expression of m for m 1 has a log term the present self consistent approach narrowed down the value of intermittency exponent for the fully developed turbulence to 0 235 0 015

application of generalized thermostatistics to fully developed turbulence abstract we apply the formalism of non extensive statistical mechanics to fully developed turbulent flows we obtain analytical formulas for probability density functions of velocity differences depending on distance r and reynolds number r which are in very good agreement with turbulence experiments the skewness is taken into account by analysing universal contributions due to higher order correlations of the chaotic dynamics we also calculate the moment scaling exponents m which also agree well with experimental data

abstraction based failure diagnosis for discrete event systems in this paper we introduce the idea of abstraction based diagnosability for large scale composed discrete event systems that consist of multiple subsystems to this end we determine sufficient conditions such that diagnosability of the original system follows from diagnosability of an abstracted system model on a smaller state space in addition we prove that also the reverse implication is true if an additional requirement for the abstraction is fulfilled then we show how our method can be applied to compute abstracted models for the diagnosability verification of composed systems without enumerating the whole system state space in this way considerable computational savings can be achieved as illustrated by a small manufacturing system example

possible canonical distributions for finite systems with nonadditive energy region des pays de la loire of france 2007 6088 science research fund 07bs105 huaqiao university people s republic of china

new entropy formula with fluctuating reservoir abstract finite heat reservoir capacity c and temperature fluctuation t t lead to modifications of the well known canonical exponential weight factor requiring that the corrections least depend on the one particle energy we derive a deformed entropy k s the resultingformula contains the boltzmann gibbs renyi and tsallis formulas as particular cases for extreme large fluctuations in the limit c t 2 t 2 a new parameter free entropy probability relation is gained the corresponding canonical energy distribution is nearly boltzmannian for high probability but for low probability approaches the cumulative gompertz distribution the latter is met in several phenomena like earthquakes demography tumor growth models extreme value probability etc

analysis of the spatial and temporal distributions between successive earthquakes nonextensive statistical mechanics viewpoint abstract the spatial and temporal distributions between successive earthquakes are treated in the framework of nonextensive statistical mechanics we find temporal distributions exhibit the power law behavior q exponential with q 1 it means the earthquakes are strongly correlated in time the spatial distributions obey the q exponential form with q 1 we also examine the dependence of the q exponent on magnitude range covering period time interval and size of the region where data are gathered the conjecture of abe et al s abe n suzuki physica a 350 2005 588 has been examined for different categories of data the results show a strange relation between q values of the spatial and temporal distributions

brief paper abstraction based verification of codiagnosability for discrete event systems in this paper we investigate the verification of codiagnosability for discrete event systems des that is it is desired to ascertain if the occurrence of system faults can be detected based on the information of multiple local sites that partially observe the overall des as an improvement of existing codiagnosability tests that resort to the original des with a potentially computationally infeasible state space we propose a method that employs an abstracted system model on a smaller state space for the codiagnosability verification furthermore we show that this abstraction can be computed without explicitly evaluating the state space of the original model in the practical case where the des is composed of multiple subsystems

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

derivation of power law distributions within standard statistical mechanics abstract we show that within classical statistical mechanics it is possible to naturally derive power law distributions which are of tsallis type the only assumption is that microcanonical distributions have to be separable from of the total system energy which is reasonable for any sensible measurement we demonstrate that all separable distributions are parametrized by a separation constant q which is one to one related to the q parameter in tsallis distributions the power laws obtained are formally equivalent to those obtained by maximizing the tsallis entropy under q constraints we further ask why nature fixes the separation constant q to 1 in so many cases leading to standard thermodynamics we answer this with an explicit example where it is possible to relate q to system size and interaction parameters characterizing the physical system we argue that these results might be helpful to explain the ubiquity of tsallis distributions in nature

microcanonical foundation for systems with power law distributions starting from a microcanonical basis with the principle of equal a priori probability it is shown using the method of steepest descents that besides ordinary boltzmann gibbs theory with the exponential distribution a theory describing systems with power law distributions can also be derived

thermodynamics with generalized ensembles the class of dual orthodes abstract we address the problem of the foundation of generalized ensembles in statistical physics the approach is based on boltzmann s concept of orthodes these are the statistical ensembles that satisfy the heat theorem according to which the heat exchanged divided by the temperature is an exact differential this approach can be seen as a mechanical approach alternative to the well established information theoretic one based on the maximization of generalized information entropy our starting point are the tsallis escort ensembles which have been previously proved to be orthodes and have been proved to interpolate between canonical and microcanonical ensembles here we shall see that the tsallis escort ensembles belong to a wider class of orthodes that include the most diverse types of ensembles all such ensembles admit both a microcanonical like parametrization via the energy and a canonical like one via the parameter for this reason we name them dual one central result used to build the theory is a generalized equipartition theorem the theory is illustrated with a few examples and the equivalence of all the dual orthodes is discussed

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

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

nonextensive normalized treatment of clausius equation abstract we revisit the first law of thermodynamics for nonextensive statistics by recourse to the optimal lagrange multipliers olm formalism we show firstly that information theory allows one to obtain thermodynamics first law in a general ensemble by dealing just with variations in the density operator without disturbing the system s hamiltonian after re deriving clausius equation we discuss it in some detail and show that for the tsallis mendes plastino tmp normalization i nonextensive reversible processes connecting off equilibrium states exist ii for any extensive reversible process between equilibrium states one can find some other equivalent nonextensive irreversible one and iii in some circumstances an extensive irreversible process can be assimilated to a nonextensive reversible one

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

a review on algorithms for maximum clique problems the maximum clique problem mcp is to determine in a graph a clique i e a complete subgraph of maximum cardinality the mcp is notable for its capability of modeling other combinatorial problems and real world applications as one of the most studied np hard problems many algorithms are available in the literature and new methods are continually being proposed given that the two existing surveys on the mcp date back to 1994 and 1999 respectively one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic mcp algorithms with a special focus on recent developments to be informative we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful by classifying the main search strategies and putting forward the critical elements of the most relevant clique methods this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches

on the extended kolmogorov nagumo information entropy theory the q 1 q duality and its possible implications for a non extensive two dimensional ising model abstract the aim of this paper is to investigate the q 1 q duality in an information entropy theory of all q generalized entropy functionals tsallis renyi and sharma mittal measures in the light of a representation based on generalized exponential and logarithm functions subjected to kolmogorov s and nagumo s averaging we show that it is precisely in this representation that the form invariance of all entropy functionals is maintained under the action of this duality the generalized partition function also results to be a scalar invariant under the q 1 q transformation which can be interpreted as a non extensive two dimensional ising model duality between systems governed by two different power law long range interactions and temperatures this does not hold only for tsallis statistics but is a characteristic feature of all stationary distributions described by q exponential boltzmann factors

ideal gas provides q entropy abstract a mathematical procedure is suggested to obtain deformed entropy formulas of type k s k p i k ln p i by requiring zero mutual k s k information between a finite subsystem and a finite reservoir the use of this method is first demonstrated on the ideal gas equation of state with finite constant heat capacity c where it delivers the renyi and tsallis formulas a novel interpretation of the q 2 q duality arises from the comparison of canonical subsystem and total microcanonical partition approaches in the sequel a new generalized deformed entropy formula is constructed for the linear c s c 0 c 1 s relation

thermodynamical relations for systems in contact with finite heat baths abstract we obtain the relations between macroscopic thermodynamical properties and microscopic ensemble averages of a system in contact with a heat bath which has a finite number of degrees of freedom our approach is based on the geometry of the accessible phase space of the system by using a suitable definition of temperature for such kind of system energy equipartition theorem it is shown that the relations obtained here have the same dependence on the system s partition function z 1 as in boltzmann gibbs statistics

a generalized framework for inference based diagnosis of discrete event systems capturing both disjunctive and conjunctive decision making we have previously introduced an inference based framework for decentralized decision making comprising of multiple observers each with its own partial observation where inferencing over the ambiguities of the self and the others is used to issue local decisions and a global decision is taken to be the one possessing the minimum ambiguity level in this setting we previously introduced the notion of n inference vee diagnosability to characterize the existence of a disjunctive decentralized diagnosis scheme so that any fault can be detected within a bounded delay using at most n levels of inferencing by one of the diagnosers while the disjunctive scheme relies on one of the diagnosers making the failure decision the dual conjunctive scheme relies on none of the diagnosers making the nonfailure decision it is known that the two schemes are incomparable and in this paper we extend our earlier work to provide a more general framework introducing the notion of n inference diagnosability capturing both disjunctive and conjunctive schemes we also develop a method for verifying n inference diagnosability as well as discuss several of its useful properties

tsallis power laws and finite baths with negative heat capacity it is often stated that heat baths with finite degrees of freedom i e finite baths are sources of tsallis distributions for classical hamiltonian systems by using well known fundamental statistical mechanics expressions we rigorously show that tsallis distributions with fat tails are possible only for finite baths with constant negative heat capacity while constant positive heat capacity finite baths yield decays with sharp cutoff with no fat tails however the correspondence between tsallis distributions and finite baths holds at the expense of violating the equipartition theorem for finite classical systems at equilibrium we comment on the implications of the finite bath for the recent attempts towards a q generalized central limit theorem

thermodynamical entropy and its additivity within generalized thermodynamics abstract this is an analysis of the thermodynamical entropy of systems with finite heat baths and of its additivity it is presented an expression for the physical entropy of weakly interacting ergodic systems and it is shown how it relates to the traditional entropies of the micro canonical constant energy the canonical boltzmann gibbs infinite heat bath and the tsallis finite heat bath ensembles this physical entropy contains one term that is a variant of the tsallis entropy and it becomes an additive function after a suitable choice of additive constants in a procedure reminiscent to the solution presented by gibbs to the paradox bearing his name

diagnosis of behaviors of interest in partially observed discrete event systems abstract in this paper we address the problem of diagnosing the behaviors of interest in discrete event systems to this end we introduce the notion of language diagnosability based on language specifications that generalizes diagnosability based on event specifications a polynomial time algorithm for verifying language diagnosability is developed building upon the verification algorithm we develop a polynomial time algorithm for computing the worst case detection delay of a given system the computation of the worst case detection delay involves the shortest path computation of a weighted directed graph we exploit a special weighting structure of the graph resulting from the verification algorithm which enables an algorithm with a lower complexity than the commonly used bellman ford shortest path algorithm

global and local consistencies in distributed fault diagnosis for discrete event systems in this paper we present a unified framework for distributed diagnosis we first introduce the concepts of global and local consistency in terms of supremal global and local supports then present two distributed diagnosis problems based on them after that we provide algorithms to achieve supremal global and local supports respectively and discuss in detail the advantages and disadvantages of each finally we present an industrial example to demonstrate our distributed diagnosis approach

fault diagnosis in discrete event systems framework and model reduction a state based approach for online passive fault diagnosis in systems modeled as finite state automata is presented in this framework the system and the diagnoser the fault detection system do not have to be initialized at the same time furthermore no information about the state or even the condition failure status of the system before the initiation of diagnosis is required the design of the fault detection system in the worst case has exponential complexity a model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design diagnosability of failures is studied and necessary and sufficient conditions for failure diagnosability are derived