fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

hamiltonian perspective on compartmental reaction diffusion networks inspired by the recent developments in modeling and analysis of reaction networks we provide a geometric formulation of the reversible reaction networks under the influence of diffusion using the graph knowledge of the underlying reaction network the obtained reaction diffusion system is a distributed parameter port hamiltonian system on a compact spatial domain motivated by the need for computer based design we offer a spatially consistent discretization of the pde system and in a systematic manner recover a compartmental ode model on a simplicial triangulation of the spatial domain exploring the properties of a balanced weighted laplacian matrix of the reaction network and the laplacian of the simplicial complex we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points the paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction diffusion networks

self organized criticality in a nutshell in order to gain insight into the nature of self organized criticality soc we present a minimal model exhibiting this phenomenon in this analytically solvable model the state of the system is fully described by a single integer variable the system organizes in its critical state without external tuning we derive analytically the probability distribution of durations of disturbances propagating through the system as required by soc this distribution is scale invariant and follows a power law over several orders of magnitude our solution also reproduces the exponential tail of the distribution due to finite size effects moreover we show that large avalanches are suppressed when stabilizing the system in its critical state interestingly avalanches are affected in a similar way when driving the system away from the critical state with this model we have reduced soc dynamics to a leveling process as described by ehrenfest s famous flea model

a possibility measure is not a fuzzy measure abstract in this note we show that a possibility measure is not a particular type of fuzzy measure except in trivial cases

semiconormed possibility integrals and multi feature pattern classification abstract the semiconormed possibility integrals are proposed as a multi feature pattern classification model a semiconormed possibility integral is a nonlinear integration of a function and its corresponding non normalized possibility measures over feature space the function of an object s feature vector represents the possibilities with uncertainty that the object belongs to a class the uncertainty is due to the similar characteristics of objects from different classes and the distortion of the original characteristic information caused by feature data acquisition systems the uncertainty is assessed by the non normalized possibility measures a possibility measure of a feature is considered as the credibility of the feature to provide reliable information for pattern classification integration of a function and the possibility measures effectively reduces the uncertainty and improves the pattern classification results a pattern classification algorithm based on the semiconormed possibility integrals was used to classify a set of ellipse data and the well known iris data the classification results were compared with those obtained by using bayes classifier

analysis of self organized criticality in ehrenfest s dog flea model the self organized criticality in ehrenfest s historical dog flea model is analyzed by simulating the underlying stochastic process the fluctuations around the thermal equilibrium in the model are treated as avalanches we show that the distributions for the fluctuation length differences at subsequent time steps are in the shape of a q gaussian the distribution which is obtained naturally in the context of nonextensive statistical mechanics if one avoids the finite size effects by increasing the system size we provide clear numerical evidence that the relation between the exponent ensuremath tau of avalanche size distribution obtained by maximum likelihood estimation and the q value of appropriate q gaussian obeys the analytical result recently introduced by caruso et al phys rev e 75 055101 r 2007 this allows us to determine the value of q parameter a priori from one of the well known exponents of such dynamical systems

computing zero deficiency realizations of kinetic systems in the literature there exist strong results on the qualitative dynamical properties of chemical reaction networks also called kinetic systems governed by the mass action law and having zero deficiency however it is known that different network structures with different deficiencies may correspond to the same kinetic differential equations in this paper an optimization based approach is presented for the computation of deficiency zero reaction network structures that are linearly conjugate to a given kinetic dynamics through establishing an equivalent condition for zero deficiency the problem is traced back to the solution of an appropriately constructed mixed integer linear programming problem furthermore it is shown that weakly reversible deficiency zero realizations can be determined in polynomial time using standard linear programming two examples are given for the illustration of the proposed methods 2015 elsevier b v all rights reserved

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

turbulent self organized criticality abstract in the prototype sandpile model of self organized criticality time series obtained by decomposing avalanches into waves distinguished by the number of times the avalanche seed site has toppled show intermittent fluctuations the q th moments of wave size differences possess local multiscaling and global simple scaling regimes analogous to those holding for velocity structure functions in fluid turbulence the correspondence involves identity of a basic scaling relation and of the form of relevant probability distributions the sandpile provides a qualitative analog of many features of turbulent phenomena

aftershocks in coherent noise models the decay pattern of aftershocks in the so called coherent noise models m e j newman and k sneppen phys rev e54 6226 1996 is studied in detail analytical and numerical results show that the probability to nd a large event at timet after an initial major event decreases as t for smallt with the exponent ranging from 0 to values well above 1 this is in contrast to sneppen und newman who stated that the exponent is about 1 independent of the microscopic details of the simulation numerical simulations of an extended model c wilke t martinetz phys rev e56 7128 1997 show that the power law is only a generic feature of the original dynamics and does not necessarily appear in a more general context finally the implications of the results to the modeling of earthquakes are discussed

brief stabilization of positive systems with first integrals positive systems possessing first integrals are considered these systems frequently occur in applications this paper is devoted to two stabilization problems the first is concerned with the design of feedbacks to stabilize a given level set secondly it is shown that the same feedback allows to globally stabilize an equilibrium point if it is asymptotically stable with respect to initial conditions in its level set two examples are provided and the results are compared with those in the literature

escort mean values and the characterization of power law decaying probability densities escort mean values or q moments constitute useful theoretical tools for describing basic features of some probability densities such as those which asymptotically decay like power laws they naturally appear in the study of many complex dynamical systems particularly those obeying nonextensive statistical mechanics a current generalization of the boltzmann gibbs theory they recover standard mean values or moments for q 1 here we discuss the characterization of a non negative probability density by a suitable set of all its escort mean values together with the set of all associated normalizing quantities provided that all of them converge this opens the door to a natural extension of the well known characterization for the q 1 instance of a distribution in terms of the standard moments provided that all of them have finite values this question would be specially relevant in connection with probability densities having divergent values for all nonvanishing standard moments higher than a give

brief paper optimal distributed linear averaging a new optimal distributed linear averaging odla problem is presented in this paper this problem is motivated by the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering the aim of the odla problem is to compute the average of the initial values at nodes of a graph through an optimal distributed algorithm in which the nodes in the graph can only communicate with their neighbors optimality is given by a minimization problem of a quadratic cost functional under infinite horizon we show that this problem has a very close relationship with the notion of semistability by developing new necessary and sufficient conditions for semistability of linear discrete time systems we convert the proposed odla problem into an equivalent constrained optimization problem and then derive a solvable fixed structure convex optimization problem

new approach to the stability of chemical reaction networks piecewise linear in rates lyapunov functions piecewise linear in rates pwlr lyapunov functions are introduced for a class of chemical reaction networks crns in addition to their simple structure these functions are robust with respect to arbitrary monotone reaction rates of which mass action is a special case the existence of such functions ensures the convergence of trajectories towards equilibria and can be used to establish their asymptotic stability with respect to the corresponding stoichiometric compatibility class we give the definition of these lyapunov functions prove their basic properties and provide algorithms for constructing them examples are provided relationship with consensus dynamics are discussed and future directions are elaborated

polyhedral lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the jacobian is non singular for a vast class of dynamical networks including chemical reaction networks crns with monotonic reaction rates the existence of a polyhedral lyapunov function plf implies structural i e parameter free local stability global structural stability is ensured under the additional assumption that each of the variables chemical species concentrations in crns is subject to a spontaneous infinitesimal dissipation this paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation showing that the existence of a plf structurally ensures global convergence if and only if the system jacobian passes a structural non singularity test it is also shown that if the jacobian is structurally non singular under positivity assumptions for the system partial derivatives the existence of an equilibrium is guaranteed for systems subject to positivity constraints it is shown that if the system admits a plf under structural non singularity assumptions global convergence within the positive orthant is structurally ensured while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise linear in rate lyapunov function

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

return distributions in dog flea model revisited abstract a recent study of coherent noise model for the system size independent case provides an exact relation between the exponent of avalanche size distribution and the q value of the appropriate q gaussian that fits the return distribution of the model this relation is applied to ehrenfest s historical dog flea model by treating the fluctuations around the thermal equilibrium as avalanches we provide a clear numerical evidence that the relation between the exponent of fluctuation length distribution and the q value of the appropriate q gaussian obeys this exact relation when the system size is large enough this allows us to determine the value of the q parameter a priori from one of the well known exponents of such dynamical systems furthermore it is shown that the return distribution in dog flea model gradually approaches q gaussian as the system size increases and this tendency can be analyzed by a well defined analytical expression

global asymptotic stability for a class of nonlinear chemical equations we consider a class of nonlinear differential equations that arises in the study of chemical reaction systems known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable more specifically we will consider chemical reaction systems that are weakly reversible have a deficiency of zero and are equipped with mass action kinetics we show that if for each c in mathbb r 0 m the intersection of the stoichiometric compatibility class c s with the subsets on the boundary that could potentially contain equilibria l w are at most discrete then global asymptotic stability follows previous global stability results for the systems considered in this paper required c s cap l w emptyset for each c in mathbb r m 0

the deficiency zero theorem and global asymptotic stability for a class of chemical reaction networks with arbitrary time delays abstract the deficiency zero theorem dzt is extended to be applied to chemical reaction networks crns with time delays the time evolution of concentrations of species in which networks is described by delay differential equations ddes the extended dzt provides a sufficient condition for a positive equilibrium point of ddes to exist and be locally asymptotically stable furthermore it is proven that the absence of boundary equilibria is a sufficient condition for the positive equilibrium point to be globally asymptotically stable these results are natural analogues of theorems proven for crns without time delays

reflections on the q fourier transform and the q gaussian function abstract the standard q fourier transform qft of a constant diverges which begs for a better treatment in addition hilhorst has conclusively proved that the ordinary qft is not of a one to one character for an infinite set of functions h j hilhorst j stat mech 2010 p10023 generalizing the ordinary qft analyzed in s umarov c tsallis s steinberg milan j math 76 2008 307 we appeal here to a complex q fourier transform and show that the problems above mentioned are overcome

spectral conditions for stability and stabilization of positive equilibria for a class of nonlinear cooperative systems nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication biological economical and neural network applications for this class of positive systems we provide conditions that guarantee existence uniqueness and stability of strictly positive equilibria these conditions can be formulated directly in terms of the spectral radius of the jacobian of the system if control inputs are available then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant

stability of nonnegative lur e systems a stability instability trichotomy for a class of nonnegative continuous time lur e systems is derived asymptotic exponential and input to state stability concepts are considered the presented trichotomy rests on perron frobenius theory absolute stability theory and recent input to state stability results for lur e systems applications of the results derived arise in various fields including density dependent population dynamics and two examples are discussed in detail

of dogs and fleas the dynamics of n uncoupled two state systems the historical ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium this approach represents a special case in the dynamics of n uncoupled two state systems in this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change analytical solutions for the probability distribution of the system s state as well as the fluctuation distribution are derived interestingly close inspection of the fluctuation distribution reveals an intrinsic time scale sampling the system s state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes for faster measurements a power law extends roughly over log10 n orders of magnitude followed by an exponential tail at some point further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind since the generic solution is rather unwieldy we derive and discuss simple and intuitive analytical solutions in the limit of small p and large n furthermore we relax the quantization of time by considering a complementary approach in continuous time finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features

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

from time series to superstatistics complex nonequilibrium systems are often effectively described by a statistics of a statistics in short a superstatistics we describe how to proceed from a given experimental time series to a superstatistical description we argue that many experimental data fall into three different universality classes chi2 superstatistics tsallis statistics chi2 inverse superstatistics and log normal superstatistics we discuss how to extract the two relevant well separated superstatistical time scales tau and t the probability density of the superstatistical parameter beta and the correlation function for beta from the experimental data we illustrate our approach by applying it to velocity time series measured in turbulent taylor couette flow which is well described by log normal superstatistics and exhibits clear time scale separation

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

local dissipative hamiltonian description of reversible reaction networks in this letter we show that closed reversible chemical reaction networks with independent elementary reactions admit a global pseudo hamiltonian structure which is at least locally dissipative around any equilibrium point the structure matrix of the hamiltonian description reflects the graph topology of the reaction network and it is a smooth function of the concentrations of the chemical species in the positive orthant the physical interpretation of the description is briefly explained and two illustrative examples are presented for global and local dissipative hamiltonian description respectively

input to state stability of rate controlled biochemical networks in this paper the study of the class of biochemical systems known as zero deficiency networks is extended to the case of time varying kinetic parameters we show that the resulting class of nonlinear systems with inputs satisfies a notion of input to state stability uniformly over a set of parameters in particular the input to state stability estimates allow us to characterize the robustness of zero deficiency networks with respect to perturbations in the parameters as well as study their stability when the reaction rates are controlled by an independent process

piecewise linear lyapunov functions for structural stability of biochemical networks we consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values we investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral lyapunov function proper to the considered network structure a numerical recursive procedure is devised to test stability for a wide class of mono and bimolecular reaction networks which we name unitary the procedure is shown to be very efficient since due to the particular structure of the problem it requires iterations in the space of integer valued matrices we also consider a similar less conservative procedure that allows us to test even when the lyapunov function cannot be found whether the system evolution is structurally bounded in this case we absorb the equations in a positive linear differential inclusion to show the effectiveness of the proposed procedure we report the outcomes of both a stability and a boundedness test for many non trivial biochemical reaction networks and we analyze well established models in the literature

skewness and kurtosis analysis for non gaussian distributions abstract in this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the gaussian we treat kurtosis in both its standard definition and that which arises in q statistics namely q kurtosis we have recently shown that the relation proposed by cristelli et al 2012 between skewness and kurtosis can only be verified for relatively small data sets independently of the type of statistics chosen however it fails for sufficiently large data sets if the fourth moment of the distribution is finite for infinite fourth moments kurtosis is not defined as the size of the data set tends to infinity for distributions with finite fourth moments the size n of the data set for which the standard kurtosis saturates to a fixed value depends on the deviation of the original distribution from the gaussian nevertheless using kurtosis as a criterion for deciding which distribution deviates further from the gaussian can be misleading for small data sets even for finite fourth moment distributions going over to q statistics we find that although the value of q kurtosis is finite in the range of 0 q 3 this quantity is not useful for comparing different non gaussian distributed data sets unless the appropriate q value which truly characterizes the data set of interest is chosen finally we propose a method to determine the correct q value and thereby to compute the q kurtosis of q gaussian distributed data sets

reconstruction families of possibilistic structure systems abstract a method is presented for characterizing the family of overall systems reconstructable from a given possibilistic structure system the technique is elaborated in terms of fuzzy relation equations it is demonstrated that the reconstruction family of a given structure system is equivalent to the set of solutions of a special type of fuzzy relation equation the solution set is partially ordered and contains both minimal solutions and a unique maximum solution when these elements are identified all members of the reconstruction family are determined another characteristic of the reconstruction family is its reconstruction uncertainty a measure of which is also developed in this paper this measure is used to define an identifiability quotient that expresses the degree of confidence with which we may identify a single overall system given a particular structure system

a shannon tsallis transformation we determine a general link between two different solutions of the maxent variational problem namely the ones that correspond to using either shannon s or tsallis entropies in the concomitant variational problem it is shown that the two variations lead to equivalent solutions that take different appearances but contain the same information these solutions are linked by our transformation

a network dynamics approach to chemical reaction networks abstracta treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics in particular of consensus dynamics by starting from the complex balanced assumption the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory and which directly relates to the thermodynamics and port hamiltonian formulation of the system central in this formulation is the definition of a balanced laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality this immediately leads to the characterisation of the set of equilibria and their stability furthermore the assumption of complex balancedness is revisited from the point of view of kirchhoff s matrix tree theorem both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics and provide additional perspectives to the latte

upper and lower fuzzy measures puri and ralescu 5 showed that a possibility measure is not in the general case a fuzzy measure this paper deals with determining a general framework where both possibility and fuzzy measures are included in order to do that the upper lower fuzzy measures which need not be lower upper continuous are considered the possibility necessity measures will be examples of such upper lower fuzzy measures finally the extensions of these concepts to fuzzy sets are also considered

random walks on the bethe lattice we obtain random walk statistics for a nearest neighbor polya walk on a bethe lattice infinite cayley tree of coordination numberz and show how a random walk problem for a particular inhomogeneous bethe lattice may be solved exactly we question the common assertion that the bethe lattice is an infinite dimensional system

the glansdorff prigogine stability criterion for biochemical reaction networks local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology the second variation of the gibbs energy around a steady state is a positive definite function and a candidate for a lyapunov function a sufficient condition for the local stability is the local negative definiteness of the time derivative of this function this is expressed by the glansdorff prigogine stability criterion previously the criterion was criticized to be overly conservative and difficult to check here we derive an easily testable form of the criterion for models of biochemical networks the criterion can be evaluated with incomplete knowledge of the parameters for ideal mass action kinetics it depends only on the steady state fluxes for reaction systems in ideal solutions the glansdorff prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the glansdorff prigogine criterion whenever these criteria are indefinite there exist parameter values such that the steady state is unstable by means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology

a generalization of the cumulant expansion application to a scale invariant probabilistic model as well known cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist if this is not the case the so called escort mean values or q moments have been proposed to characterize probability densities with divergent moments c tsallis et al j math phys 50 043303 2009 we introduce here a new mathematical object namely the q cumulants which in analogy to the cumulants provide an alternative characterization to that of the q moments for the probability densities to illustrate the technical details of the procedure we apply this new scheme to further study a recently proposed family of scale invariant discrete probabilistic models a rodriguez et al j stat mech theory exp 2008 p09006 r hanel et al eur phys j b 72 263 2009 having q gaussians as limiting probability distributions

1 f α spectra in elementary cellular automata and fractal signals we systematically compute the power spectra of the one dimensional elementary cellular automata introduced by wolfram on the one hand our analysis reveals that one automaton displays 1 f spectra though considered as trivial and on the other hand that various automata classified as chaotic or complex display no 1 f spectra we model the results generalizing the recently investigated sierpinski signal to a class of fractal signals that are tailored to produce 1 f ensuremath alpha spectra from the widespread occurrence of elementary cellular automata patterns in chemistry physics and computer sciences there are various candidates to show spectra similar to our results

predictability of the coherent noise model and its applications we study the threshold distribution function of the coherent noise model for the case of infinite number of agents this function is piecewise constant with a finite number of steps n the latter exhibits a 1 f behavior as a function of the order of occurrence of an avalanche and hence versus natural time an analytic expression of the expectation value mathcal e s for the size s of the next avalanche is obtained and used for the prediction of the next avalanche apart from mathcal e s the number of steps n can also serve for this purpose this enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data

a heuristic simulated annealing algorithm of learning possibility measures for multisource decision making abstract in multisource decision making non normalized possibility measures are used to gauge the credibilities of each subset of information sources in order to reduce the uncertainty introduced by the sources and minimize decision error the credibility of individual information source i e the possibility density is objectively learned from subjectively chosen training data a learning algorithm of the possibility measures is constructed based on the ideas of simulated annealing and feasible direction the algorithm is designed for large training data set two multifeature image segmentation experiments and a comparison of learning speed are presented

where do we stand on measures of uncertainty ambiguity fuzziness and the like abstract it is argued in this paper that the theory of fuzzy sets involves at least four fundamentally different types of uncertainty each of these types requires a measure by which the degree of uncertainty of that type can be determined two main categories of uncertainty are connected with the terms vagueness or fuzziness and ambiguity in general vagueness is associated with the difficulty of making sharp or precise distinctions in the world ambiguity on the other hand is associated with one to many relations i e situations with two or more alternatives that are left unspecified while the concept of a fuzzy set represents a basic mathematical framework for dealing with vagueness the concept of a fuzzy measure is a general framework for dealing with ambiguity several classes of measures of vagueness usually referred to as measures of fuzziness have been proposed in the literature each class is based on some underlying conception of the degree of fuzziness a general set of requirements for measures of fuzziness is formulated followed by an overview of the measures proposed in the literature measures of ambiguity are discussed within the framework of plausibility and belief measures although it does not cover all fuzzy measures this framework is sufficiently broad for most practical purposes and represents a generalization of both probability theory and possibility theory it is argued that three complementary measures of ambiguity should be employed one of them is obtained by generalizing the hartley measure of uncertainty it measures the degree of nonspecificity in individual situations described by the various belief and plausibility measures the other two are obtained by generalizing the well known shannon measure of uncertainty they measure the degree of dissonance and the degree of confusion in evidence respectively basic mathematical properties of these measures are overviewed it is also argued that each of the four types of uncertainty measures which are fundamentally different from each other can be used for measuring structural syntactic information in the same sense as the hartley and shannon measures have been used in this respect as such these measures are potentially powerful tools for dealing with systems problems such as systems modelling analysis simplification or design

nontangency based lyapunov tests for convergence and stability in systems having a continuum of equilibria this paper focuses on the stability analysis of systems having a continuum of equilibria two notions that are of particular relevance to such systems are convergence and semistability convergence is the property whereby every solution converges to a limit point that may depend on the initial condition semistability is the additional requirement that all solutions converge to limit points that are lyapunov stable we give new lyapunov function based results for convergence and semistability of nonlinear systems these results do not make assumptions of sign definiteness on the lyapunov function instead our results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite lyapunov functions to illustrate our results we deduce convergence and semistability of the kinetics of the michaelis menten chemical reaction and the closed loop dynamics of a scalar system under a universal adaptive stabilizing feedback controller

semistability of complex balanced kinetic systems with arbitrary time delays abstract in this letter we introduce a class of delayed kinetic systems derived from mass action type reaction network models we define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed kinetic systems we prove the uniqueness of equilibrium solutions within the time delayed positive stoichiometric compatibility classes for such models in our main result we prove the semistability of the equilibrium solutions for complex balanced systems with arbitrary time delays using an appropriate lyapunov krasovskii functional and lasalle s invariance principle as a consequence we obtain that every positive complex balanced equilibrium solution is locally asymptotically stable relative to its positive stoichiometric compatibility class

correction to structure and stability of certain chemical networks and applications to the kinetic proofreading model of t cell receptor signal transduction deals with the theory of structure stability robustness and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks the results given here extend but are also heavily based upon certain previous work by feinberg 1977 1979 1987 1995 and horn and jackson 1972 of which a self contained and streamlined exposition is included the theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by mckeithan 1995 for t cell receptor signal transduction

random walk on the bethe lattice and hyperbolic brownian motion we give the exact solution to the problem of a random walk on the bethe lattice through a mapping on an asymmetric random walk on the half line we also study the continuous limit of this model and discuss in detail the relation between the random walk on the bethe lattice and brownian motion on a space of constant negative curvature

inversion of umarov tsallis steinberg s q fourier transform and the complex plane generalization we introduce a complex q fourier transform as a generalization of the real one analyzed in s umarov c tsallis s steinberg milan j math 307 2008 by recourse to tempered ultradistributions we show that this complex plane generalization overcomes all the troubles that afflict its real counterpart

reconstruction of possibilistic behavior systems abstract reconstructability analysis is viewed as a process of investigating the possibilities of reconstructing desirable properties of overall systems from the knowledge of the corresponding properties of their various subsystems the reconstructability analysis consists of procedures for generating meaningful reconstruction hypotheses procedures for the evaluation of the reconstruction hypotheses and procedures for making various decisions regarding the acceptance of evaluated reconstruction hypotheses generation of additional reconstruction hypotheses termination of the analysis and the like the paper discusses the evaluation of reconstruction hypotheses when the systems under consideration are possibilistic behavior systems it is shown that a principle of maximum ambiguity similar to the principle of maximum entropy for probabilistic systems can be used for possibilistic systems it is also shown that the unbiased maximum ambiguity reconstruction can be determined by a simple join procedure in a similar fashion as for probabilistic systems the join procedure for possibilistic systems turns out to be computationally simpler than the one for probabilistic systems the paper also describes a general procedure for determining the reconstruction family

the dynamics of weakly reversible population processes near facets this paper concerns the dynamical behavior of weakly reversible deterministically modeled population processes near the facets codimension one faces of their invariant manifolds and proves that the facets of such systems are repelling it has been conjectured that any population process whose network graph is weakly reversible has strongly connected components is persistent we prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets or siphons an important application of this work pertains to chemical reaction systems that are complex balancing for these systems it is known that within the interior of each invariant manifold there is a unique equilibrium the global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies our results pertaining to weakly reversible systems imply that thi

exact results for the barabasi queuing model previous works on the queuing model introduced by barabasi to account for the heavy tailed distributions of the temporal patterns found in many human activities mainly concentrate on the extremal dynamics case and on lists of only two items here we obtain exact results for the general case with arbitrary values of the list length l and of the degree of randomness that interpolates between the deterministic and purely random limits the statistically fundamental quantities are extracted from the solution of master equations from this analysis scaling features of the model are uncovered

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

theoretical studies of self organized criticality these notes are intended to provide a pedagogical introduction to the abelian sandpile model of self organized criticality and its related models the abelian group the algebra of particle addition operators the burning test for recurrent states equivalence to the spanning trees problem are described the exact solution of the directed version of the model in any dimension is explained the model s equivalence to scheidegger s model of river basins takayasu s aggregation model and the voter model is discussed for the undirected case the solution for one dimensional lattices and the bethe lattice is briefly described known results about the two dimensional case are summarized generalization to the abelian distributed processors model is discussed time dependent properties and the universality of critical behavior in sandpiles are briefly discussed i conclude by listing some still unsolved problems

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

a continuous time ehrenfest model with catastrophes and its jump diffusion approximation we consider a continuous time ehrenfest model defined over the integers from n to n and subject to catastrophes occurring at constant rate the effect of each catastrophe istantaneously resets the process to state 0 we investigate both the transient and steady state probabilities of the above model further the first passage time through state 0 is discussed we perform a jump diffusion approximation of the above model which leads to the ornstein uhlenbeck process with catastrophes the underlying jump diffusion process is finally studied with special attention to the symmetric case arising when the ehrenfest model has equal upward and downward transition rates

generalization of an invertible mapping between probability and possibility a discrete bijective mapping between probability and possibility is generalized to the continuous case in n dimensions the mapping contains a parametrical function which can be chosen such that the probability possibility consistency relation and the uncertainty invariance principle are fulfilled simultaneously

nonextensivity and natural time the case of seismicity nonextensive statistical mechanics pioneered by tsallis has recently achieved a generalization of the gutenberg richter law for earthquakes this remarkable generalization is combined here with natural time analysis which enables the distinction of two origins of self similarity i e the process memory and the process increments infinite variance by using also detrended fluctuation analysis for the detection of long range temporal correlations we demonstrate the existence of both temporal and magnitude correlations in real seismic data of california and japan natural time analysis reveals that the nonextensivity parameter q in contrast to some published claims cannot be considered as a measure of temporal organization but the tsallis formulation does achieve a satisfactory description of real seismic data for japan for q 1 66 when supplemented by long range temporal correlations

analysis of return distributions in the coherent noise model return distributions of the coherent noise model are studied for the system size independent case it is shown that in this case these distributions are in the shape of q gaussians which are the standard distributions obtained in nonextensive statistical mechanics moreover an exact relation connecting the exponent of avalanche size distribution and the q value of appropriate q gaussian has been obtained as q 2 making use of this relation one can easily determine q parameter values of the appropriate q gaussians a priori from one of the well known exponents of the system since the coherent noise model has the advantage of producing different t values by varying a model parameter clear numerical evidences on the validity of the proposed relation have been achieved for various cases finally the effect of the system size has also been analyzed and an analytical expression has been proposed which is corroborated by the numerical results

q exponential relaxation of the expected avalanche size in the coherent noise model abstract recently sarlis and christopoulos 2012 the threshold distribution function p t h r e s k x of the coherent noise model for infinite number of agents after the k th avalanche has been studied as a function of k and hence natural time an analytic expression of the expectation value e s k 1 for the size s k 1 of the next avalanche has been obtained in the case that the coherent stresses are exponentially distributed with an average value here by using a statistical ensemble of initially identical systems we investigate the relaxation of the average e s k 1 versus k for k values smaller than k max f the numerical results indicate that e s k 1 collapses to the q exponential tsallis 1988 as a function of k for larger k values the ensemble average can be effectively described by the time average threshold distribution function obtained by newman and sneppen 1996 an estimate k 0 f k max f of this transition is provided this ensemble of coherent noise models may be considered as a simple prototype following q exponential relaxation the resulting q values are compatible with those reported in the literature for the coherent noise model

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators