a note on the markov property of stochastic processes described by nonlinear fokker planck equations abstract we study the markov property of processes described by generalized fokker planck equations that are nonlinear with respect to probability densities such as mean field fokker planck equations and fokker planck equations related to generalized thermostatistics we show that their transient solutions describe non markov processes in contrast stationary solutions can describe markov processes as a result nonlinear fokker planck equations can be used to model transient non markov processes that converge to stationary markov processes

regularity for solutions of nonlinear evolution equations with nonlinear perturbations abstract the approximate controllability for the nonlinear control system with nonlinear monotone hemicontinuous and the nonlinear perturbations is studied the existence uniqueness and a variation of solutions of the system are also given

a procedure for obtaining general nonlinear fokker planck equations abstract a procedure for deriving general nonlinear fokker planck equations fpes directly from the master equation is presented the nonlinear effects are introduced in the transition probabilities which present a dependence on the probabilities for finding the system in a given state it is shown that the fpes obtained from master equations describing transitions among discrete and continuous sets of states are identical within such a procedure we construct nonlinear fpes that appear to be very general our general fpes recover as particular cases nonlinear fpes investigated previously by many authors introduced on a purely phenomenological basis and they lead to the possibility of more complete and complex diffusive equations

dynamic mean field models h theorem for stochastic processes and basins of attraction of stationary processes abstract stochastic processes of dynamic mean field models are studied in terms of nonlinear fokker planck equations we show that h theorems for single time point distributions can be used to derive h theorems for hierarchies of joint distributions in doing so we prove the convergence of transient stochastic processes to stationary ones for multistable systems we furthermore determine the basins of attraction of these stationary processes our results are illustrated by means of a mean field model exhibiting bistability

nonlinear evolution equations with nonmonotonic perturbations soit v un espace de banach reflexif densement et continument plonge dans un espace de hilbert reel h on considere l existence des solutions du probleme aux valeurs initiales du dt au g u f 0 t t u 0 u 0 ou a est un operateur monotone de v dans v g v h est une application continue et f 0 t v est une fonction mesurable

generation of compound non gaussian random processes with a given correlation function a compound representation of random processes is considered each independent component of such a process is considered as the solution of the proper stochastic differential equation sde this guarantees that the process obtained is stationary and ergodic the analytical expressions are developed for nonlinear coefficients of the generating sde theoretical results are compared with numerical simulation

reduced order solution to the finite time optimal control problems of linear weakly coupled systems the optimal solution to the finite time optimal control problem of weakly coupled linear systems is found in terms of completely decoupled reduced order differential equations for both closed loop and open loop control this is achieved through the use of the decoupling transformation that block diagonalizes the hamiltonian matrix of the weakly coupled linear quadratic control problem the convergence to the optimal solution is pretty rapid the proposed technique is very well suited for parallel computations

first passage time for subdiffusion the nonadditive entropy approach versus the fractional model we study the similarities and differences between different models concerning subdiffusion more particularly we calculate first passage time fpt distributions for subdiffusion derived from greens functions of nonlinear equations obtained from sharma mittal s tsallis s and gauss s nonadditive entropies then we compare these with fpt distributions calculated from a fractional model using a subdiffusion equation with a fractional time derivative all of greens functions give us exactly the same standard relation x 2 2d t which characterizes subdiffusion 0 1 but generally fpt distributions are not equivalent to one another we will show here that the fpt distribution for the fractional model is asymptotically equal to the sharma mittal model over the long time limit only if in the latter case one of the three parameters describing sharma mittal entropy r depends on and satisfies the specific equation derived in this paper whereas the other two models mentioned above give different fpt distributions with the fractional model greens functions obtained from the sharma mittal and fractional models for r obtained from this particular equation are very similar to each other we will also discuss the interpretation of subdiffusion models based on nonadditive entropies and the possibilities of the experimental measurement of subdiffusion models parameters

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

multivariate ornstein uhlenbeck processes with mean field dependent coefficients application to postural sway we study the transient and stationary behavior of many particle systems in terms of multivariate ornstein uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields mean field approximations of this kind of system are derived in terms of fokker planck equations in such systems multiple stationary solutions as well as bifurcations of stationary solutions may occur in addition strictly monotonically decreasing steady state autocorrelation functions that decay faster than exponential functions are found which are used to describe the erratic motion of the center of pressure during quiet standing

numerical method for the nonlinear fokker planck equation a practical method based on distributed approximating functionals dafs is proposed for numerically solving a general class of nonlinear time dependent fokker planck equations the method relies on a numerical scheme that couples the usual path integral concept to the daf idea the high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear fokker planck equation and the method is compared with the accurate k point stirling interpolation formula finite difference method the approach is also used successfully to solve a nonlinear self consistent dynamic mean field problem for which both the cumulant expansion and scaling theory have been found by drozdov and morillo phys rev e 54 931 1996 to be inadequate to describe the occurrence of a long lived transient bimodality the standard interpretation of the transient bimodality in terms of the flat region in the kinetic potential fails for the

rotationally invariant order parameter equations for natural patterns in nonequilibrium systems we discuss a theoretical description of the formation of cellular patterns exhibiting defects grain boundaries and spiral patterns in nonequilibrium large aspect ratio systems by means of rotationally invariant order parameter equations starting from evolution equations of general form we show that the order parameter equations which can be derived close to a bifurcation point in general involve nonlinear terms which are nonlocal we present a suitable approximation scheme of these terms by local ones which is based on a gradient expansion a truncation of this expansion leads to model equations which are widely used in the theoretical treatment of natural patterns in complex systems

stochastic feedback nonlinear families of markov processes and nonlinear fokker planck equations abstract we discuss two fundamental aspects of fokker planck equations that are nonlinear with respect to probability densities first we show that evolution equations of this kind describe processes involving stochastic feedback and interpret stochastic feedback processes in terms of hitchhiker processes and path integral solutions second we demonstrate that nonlinear fokker planck equations can be interpreted as linear fokker planck equations describing nonlinear families of markov diffusion processes we exploit this finding in order to derive complete hierarchies of probability densities from nonlinear fokker planck equations

nonequilibrium phase transitions induced by multiplicative noise we review a mean field analysis and give the details of a correlation function approach for spatially distributed systems subject to multiplicative noise white in space and time we confirm the existence of a pure noise induced reentrant nonequilibrium phase transition in the model introduced in c van den broeck et al phys rev lett 73 3395 1994 give an intuitive explanation of its origin and present extensive simulations in dimension d52 the observed critical properties are compatible with those of the ising universality class s1063 651x 97 08704 7

decoupling transformation for weakly coupled linear systems the non singular transformation that completely decouples a weakly coupled linear system under non restrictive conditions is defined the transformation matrices are obtained from two algebraic matrix equations algorithms that efficiently generate solutions to these equations are derived the proposed transformation also completely decouples the corresponding lyapunov matrix differential equation

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

stochastic resonance in a mean field model of cooperative behavior we study the long time response of a stochastic system formed by very many interacting subsystems coupled by a mean field interaction and subject to a time periodic external field in the absence of a driving field the system shows an order disorder phase transition and its time evolution is well described by a fokker planck equation which is nonlinear in the probability density we carry out an analysis of the dynamics in the case of a weak driving field by means of a perturbation analysis linear response theory the response of the system is then given in terms of a generalized susceptibility its evaluation shows that the phenomenon of stochastic resonance typical of driven bistable systems is greatly enhanced by the dynamical feedback induced by mean field coupling

kkm fan s lemma for solving nonlinear vector evolution equations with nonmonotonic perturbations abstract in this paper we are interested in the existence of solutions of the following initial value problem du dt a u g u f on 0 t with u 0 u 0 where a v v is a monotone operator g v v is a nonlinear nonmonotone operator and f 0 t v is a measurable function by means of a recent generalization of the famous kkm fan s lemma

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

nonlinear fokker planck equations whose stationary solutions make entropy like functionals stationary abstract the present study extends the correspondence principle of martinez et al that establishes a link between nonlinear fokker planck equations nlfpes and the variational principle approach of the theory of canonical ensembles by virtue of the extended correspondence principle we reobtain results of kaniadakis and quarati for bose and fermi systems and find relations similar to those derived by plastino and plastino and recently by borland concerning the entropy of nonextensive thermostatistics introduced in physics by tsallis moreover we propose nlfpes related to the renyi entropy and to the entropy proposed by sharma and mittal the latter comprises tsallis entropy and the renyi entropy

stability analysis of stationary states of mean field models described by fokker planck equations abstract so far the stability of stationary solutions of mean field models described by fokker planck equations has only been determined analytically in some special cases following two earlier studies j korean phys soc 40 2002 1037 prog theoret phys suppl 150 2003 48 we discuss a stability analysis for a large class of mean field models based on fokker planck equations to this end we use linear stability analysis in addition to the well known approaches by means of transcendent equations and lyapunov s direct method we demonstrate that all three methods yield consistent results for systems that exhibit free energy functionals e g equilibrium systems we show that the simple transcendent equation analysis fails for systems that do not exhibit free energy functionals e g nonequilibrium systems and show how to solve this problem by means of a more sophisticated transcendent equation analysis furthermore we propose a norm for the perturbations of stationary states and illustrate some of our results by a model that exhibits a reentrant noise induced phase transition

existence of multiple solutions for quasilinear and semilinear elliptic equations has been studied by many authors cf l 3 4 161 under the assumption that g r r is a continuous function such that g t t closes finite many eigenvalues when t varies from 0 to a the existence of one nontrivial solution for 1 2 was proved by amann and zehnder 3 and thews 21 the existence of two nontrivial solutions was studied by castro and lazer lo and ambrosetti and mancini 4 most of the multiplicity results for problem 1 2 are based on the fact that 1 2 can be rewritten as

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

new method for optimal control and filtering of weakly coupled linear discrete stochastic systems abstract the algebraic regulator and filter riccati equations of weakly coupled discrete time stochastic linear control systems are completely and exactly decomposed into reduced order continuous time algebraic riccati equations corresponding to the subsystems that is the exact solution of the global discrete algebraic riccati equation is found in terms of the reduced order subsystem nonsymmetric continuous time algebraic riccati equations in addition the optimal global kaiman filter is decomposed into local optimal filters both driven by the system measurements and the system optimal control inputs as a result the optimal linear quadratic gaussian control problem for weakly coupled linear discrete systems takes decomposition and parallelism between subsystem filters and controllers

entropy and complexity analysis of dirac delta like quantum potentials abstract the dirac delta like quantum mechanical potentials are frequently used to describe and interpret numerous phenomena in many scientific fields including atomic and molecular physics condensed matter and quantum computation the entropy and complexity properties of potentials with one and two dirac delta functions are here analytically calculated and numerically discussed in both position and momentum spaces we have studied the information theoretic lengths of fisher renyi and shannon types as well as the cramer rao fisher shannon and lmc shape complexities of the lowest lying stationary states of one delta and twin delta they allow us to grasp and quantify different facets of the spreading of the charge and momentum of the system far beyond the celebrated standard deviation

families of fokker planck equations and the associated entropic form for a distinct steady state probability distribution with a known external force field a method of finding entropic form for a given stationary probability distribution and specified potential field is discussed using the steady state fokker planck equation as examples starting with the boltzmann and tsallis distribution and knowing the force field we obtain the boltzmann gibbs and tsallis entropies also the associated entropy for the gamma probability distribution is found which seems to be in the form of the gamma function moreover the related fokker planck equations are given for the boltzmann tsallis and gamma probability distributions

optimal reduced order solution of the weakly coupled discrete riccati equation the optimal solution of the weakly coupled algebraic discrete riccati equation is obtained in terms of a reduced order continuous type algebraic riccati equation via the use of a bilinear transformation the proposed method has a rate of convergence of o epsilon sup 2 where epsilon represents a small coupling parameter a real world physical example a chemical plant model demonstrates the efficiency of the proposed method simulation results obtained using a package for a computer aided control system are presented for this specific real world example the algorithm perfectly matches the presented theory since convergence with an accuracy of 10 sup 4 is achieved after nine iterations i e 0 68 sup 18 10 sup 4

fractal surfaces from simple arithmetic operations fractal surfaces patchwork quilts are shown to arise under most general circumstances involving simple bitwise operations between real numbers a theory is presented for all deterministic bitwise operations on a finite alphabet it is shown that these models give rise to a roughness exponent h that shapes the resulting spatial patterns larger values of the exponent leading to coarser surfaces

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

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

stochastic evolution of systems of particles obeying an exclusion principle abstract we present numerical solutions of a nonlinear fokker planck equation to describe a fermi gas the model equation g kaniadakis p quarati phys rev e 49 1994 5103 includes a nonlinear term due to the pauli exclusion principle which has been disregarded up to now a new numerical method to study the time evolution of the distribution function is presented the method can be applied to any potential and allows us to describe accurately and efficiently a fermi gas in this work we focus on the differences between the results of the linear case in which the effects of the exclusion principle are not considered and the nonlinear case in which these effects are taken into account

a langevin approach for the microscopic dynamics of nonlinear fokker planck equations abstract for stochastic processes defined by nonlinear fokker planck equations a microscopic dynamics is proposed in terms of generalized langevin equations these langevin equations can for example be used to model stochastic processes with mean field interactions and random walks related to the generalized thermostatistics suggested by tsallis

solutions of nonlinear evolution inclusions abstract in this paper the solution of the nonlinear evolution inclusion problem of the form u t b t u t f t is studied in this problem the operators are of type m or type s which are different from those of pseudo monotone operators that had been studied by many authors at the same time we study the perturbation problem in fact many kinds of evolution equations can be generalized by this problem the former results are improved and generalized by our conclusions and we will give more applications

disequilibrium complexity the schottky effect and q entropies in paramagnetism abstract we investigate connections between statistical quantifiers and paramagnetism more concretely we apply the notions of i disequilibrium and ii statistical complexity to a paramagnetic system of non coupled dipoles interesting insights are thereby obtained in particular we encounter a kind of criticality not associated to the temperature but to the disequilibrium

on the stability of generalized entropies by the use of a probabilistic coupling technique and generalizing a recent result of zhang 2007 lett math phys 80 171 we derive several sharp inequalities concerning the uniform continuity of some generalized entropies these inequalities capture certain aspects of the interplay between the entropies and the uniform distance variational distance and establish the stability of the involved entropies

indices for testing neural codes one of the most critical challenges in systems neuroscience is determining the neural code a principled framework for addressing this can be found in information theory with this approach one can determine whether a proposed code can account for the stimulus response relationship specifically one can compare the transmitted information between the stimulus and the hypothesized neural code with the transmitted information between the stimulus and the behavioral response if the former is smaller than the latter i e if the code cannot account for the behavior the code can be ruled out the information theoretic index most widely used in this context is shannon s mutual information the shannon test however is not ideal for this purpose while the codes it will rule out are truly nonviable there will be some nonviable codes that it will fail to rule out here we describe a wide range of alternative indices that can be used for ruling codes out the range includes a continuum from shannon information to measures of the performance of a bayesian decoder we analyze the relationship of these indices to each other and their complementary strengths and weaknesses for addressing this problem

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

on the bilinear transformation of riccati equations an interpretation of the bilinear transformation of the riccati equation is presented the bilinear transformation of a continuous type algebraic riccati equation are to a discrete type are and its inverse transformation have been used for solving are numerically however its physical meaning has not been clear and the problem formulation was complicated this note gives a physical interpretation and derivation of the bilinear transformation of the are finally cheap control for continuous time linear systems is considered from the view of the bilinearly transformed system

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

a nonextensive maximum entropy approach to a family of nonlinear reaction diffusion equations we consider a monoparametric family of reaction diffusion equations endowed with both a nonlinear diffusion term and a nonlinear reaction one that possess exact time dependent particular solutions of the tsallis maximum entropy maxent form the evolution of these solutions is governed by a system of three coupled nonlinear ordinary differential equations that are integrated numerically a simple population dynamics interpretation provides a qualitative understanding of the behaviour of the q maxent solutions when the reaction term vanishes the time dependent distributions studied here reduce to the previously known tsallis maxent solutions for the nonlinear diffusion equation

student s t and r distributions unified derivation from an entropic variational principle abstract the optimization of the recently generalized entropy of the form s q 1 dx p x q q 1 with the constraints dx p x 1 and x 2 q dx x 2 p x q 1 yields the student s t distribution for q 1 and the r distribution for q

towards a comprehensive theory of brain activity coupled oscillator systems under external forces abstract recently jirsa et al and haken discussed a theory comprising the brain wave equation proposed by nunez the wilson cowan ermentrout cowan model and hopfield networks this theory was applied to model findings obtained in an experiment that relates brain activity and behavior the so called julliard experiment in previous works of jirsa et al and frank et al the focus was on the brain wave aspect recently we conducted similar experiments the results obtained are modeled in this paper in terms of coupled oscillator systems coupled oscillator systems are considered to represent the wilson cowan ermentrout cowan model aspect of the unifying theory building on a model proposed by haken kelso and bunz and the theory of weakly coupled oscillators established by winfree and by kuramoto we derive a nonlinear fokker planck equation whose stationary solutions mimic the neocortical brain activity observed in our experiments

complete description of a generalized ornstein uhlenbeck process related to the nonextensive gaussian entropy abstract we consider a generalized ornstein uhlenbeck process described by a nonlinear fokker planck equation related to the one parametric nonextensive gaussian entropy which is a special case of the two parametric sharma mittal entropy we derive the entire hierarchy of distribution functions for that process and in doing so derive a complete description of a stochastic process related to a nonextensive entropy measure

a family of evolution equations with nonlinear diffusion verhulst growth and global regulation exact time dependent solutions abstract a family of evolution equations describing a power law nonlinear diffusion process coupled with a local verhulst like growth dynamics and incorporating a global regulation mechanism is considered these equations admit an interpretation in terms of population dynamics and are related to the so called conserved fisher equation exact time dependent solutions exhibiting a maximum nonextensive q entropy shape are obtained

zeroth law compatibility of nonadditive thermodynamics nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules corrected in this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics we find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these our result offers a possible solution to the long standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

multiwavelet packet entropy and its application in transmission line fault recognition and classification multiwavelets possess better properties than traditional wavelets multiwavelet packet transformation has more high frequency information spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal this paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults and uses a radial basis function rbf neural network to recognize and classify 10 fault types of power transmission lines first the preprocessing and postprocessing problems of multiwavelets are presented shannon entropy and tsallis entropy are introduced and their difference is discussed second multiwavelet packet energy entropy time entropy shannon singular entropy and tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals third the plan of transmission line fault recognition using multiwavelet packet entropies and an rbf neural network is proposed finally the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition the performance with sa4 symmetric antisymmetric multiwavelet packet tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies

recursive algorithm for the optimal static output feedback control problem of linear weakly coupled systems a recursive algorithm is developed for solving the algebraic equations comprising the solution of the optimal static output feedback control problem of linear weakly coupled systems the proposed algorithm is very efficient from the numerical point of view since only low order systems are involved in algebraic calculations and the required solution can easily be obtained up to an arbitrary order of accuracy that is 0 e2k where e is a small weak coupling parameter the real world example demonstrates the effectiveness of the proposed reduced order algorithm and its advantages over the global full order algorithm

non linear kinetics underlying generalized statistics abstract the purpose of the present effort is threefold firstly it is shown that there exists a principle that we call kinetical interaction principle kip underlying the non linear kinetics in particle systems independently on the picture kramers boltzmann used to describe their time evolution secondly the kip imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution both as stationary solution of the non linear evolution equation and as the state which maximizes the generalized entropy thirdly the kip allows on one hand to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and on the other hand suggests how we can introduce naturally new distributions finally as a working example of the approach to the non linear kinetics here presented a new non extensive statistics is constructed and studied starting from a one parameter deformation of the exponential function holding the relation f x f x 1

derivation of nonlinear fokker planck equations by means of approximations to the master equation nonlinear fokker planck equations fpes are derived as approximations to the master equation in cases of transitions among both discrete and continuous sets of states the nonlinear effects introduced through the transition probabilities are argued to be relevant for many real phenomena within the class of anomalous diffusion problems the nonlinear fpes obtained appear to be more general than some previously proposed on a purely phenomenological basis ones in spite of this the same kind of solution applies i e it is shown that the time dependent tsallis s probability distribution is a solution of both equations obtained either from discrete or continuous sets of states and that the corresponding stationary solution is in the infinite time limit a stable solution

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

nested e decompositions and clustering of complex systems abstract a graph theoretic method of extreme simplicity is proposed for decomposition and clustering of complex systems into interconnected subsystems with prescribed interaction strength the method is suitable for stability analysis via vector lyapunov functions and decentralized control and estimation of large scale systems the new decomposition scheme can be used in clustering aggregation of models in economics queuing networks and computer systems as well as decompositions in block iterative methods for solutions of linear algebraic equations

subsystem interconnection and near optimum control of discrete balanced systems the relationship between subsystem interconnection of discrete balanced systems and the hankel singular values is explored upper bounds on the spectral norm of the submatrices of the discrete balanced representation are derived by approximating the matrix riccati equation by its power series expansion with respect to two scalar parameters related to the hankel singular values for diagonalizable symmetric discrete time systems the relation between the eigenvalues of the subsystems and the eigenvalues of the overall system is explored it is shown that an upper bound on the distance between corresponding eigenvalues in these two sets is related to the ratio of the hankel singular values

exact time dependent solutions of the renyi fokker planck equation and the fokker planck equations related to the entropies proposed by sharma and mittal abstract exact time dependent solutions representing generalized one dimensional ornstein uhlenbeck processes are derived from nonlinear fokker planck equations and the corresponding diffusion processes are studied the corresponding systems are related to the renyi entropy and entropies proposed by sharma and mittal in the former case normal diffusion is found with a diffusion rate depending on the order of the renyi entropy in the latter case we find anomalous diffusion processes

on the derivation of power law distributions within classical statistical mechanics far from the thermodynamic limit we show that within classical statistical mechanics without taking the thermodynamic limit the most general boltzmann factor for the canonical ensemble is a q exponential function the only assumption here is that microcanonical distributions have to be separated from the total system energy which is the prerequisite for any sensible measurement we derive that all separable distributions are parametrized by a mathematical separation constant q which can be related to the non extensivity q parameter in tsallis distributions we further demonstrate that nature fixes the separation constant q to 1 for large dimensionality of gibbs phase space our results will be relevant for systems with a low dimensional space for example nanosystems comprised of a small number of particles or for systems with a dimensionally collapsed phase space which might be the case for a large class of complex systems

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

relaxation and phase space singularities in time series of human magnetoencephalograms as indicator of photosensitive epilepsy to analyze the crucial role of fluctuation and relaxation effects for the function of the human brain we studied some statistical quantifiers that support the information characteristics of neuromagnetic brain responses magnetoencephalogram meg the signals to a flickering stimulus of different color combinations have been obtained from a group of control subjects which is then contrasted with those of a patient suffering photosensitive epilepsy pse we found that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium dynamics of the chaotic behavior of the signals in separate areas in a patient provide likely indicators for the zones which are responsible for the appearance of pse