measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

monitoring changing dynamics with correlation integrals case study of an epileptic seizure abstract we describe a procedure and the motivation behind it which rapidly and accurately tracks the onset and progress of an epileptic seizure roughly speaking one monitors changes in the relative dispersion of a re embedded time series the results are robust with respect to variation of adjustable parameters such as embedding dimension lag time and critical distances moreover the general method is virtually unaffected when the data are significantly corrupted by external noise when the information computed for the individual channels is displayed in an appropriate space time plot the progress and geometric location of the seizure are easily seen an interpretation of these results in terms of a cloud of particles moving in an abstract phase space is examined

l 1 convergence to the barenblatt solution for compressible euler equations with damping we study the asymptotic behavior of compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in the natural l1 topology with decay rates to the barenblatt profile of the porous medium equation the density function tends to the barenblatt solution of the porous medium equation while the momentum is described by darcy s law the results are achieved through a comprehensive entropy analysis capturing the dissipative character of the problem

weak entropy boundary conditions for isentropic gas dynamics via kinetic relaxation abstract we consider a kinetic bgk model relaxing to isentropic gas dynamics previously introduced by the authors but with dirichlet boundary condition on the incoming velocities we pass to the limit as the relaxation parameter tends to zero by compensated compactness inside the domain and obtain that the limit satisfies entropy inequalities on the boundary involving weak traces of entropy fluxes our method is very general and could be applied to any entropy satisfying bgk model as soon as we have strong compactness of the macroscopic variables inside the domain

determination of weights of interacting criteria from a reference set abstract in this paper we present a model allowing to determine the weights related to interacting criteria this is done on the basis of the knowledge of a partial ranking over a reference set of alternatives prototypes a partial ranking over the set of criteria and a partial ranking over the set of interactions between pairs of criteria

kolmogorov smirnov test distinguishes attractors with similar dimensions recent advances in nonlinear dynamics have led to more informative characterizations of complex signals making it possible to probe correlations in data to which traditional linear statistical and spectral analyses were not sensitive many of these new tools require detailed knowledge of small scale structures of the attractor knowledge that can be acquired only from relatively large amounts of precise data that are not contaminated by noise not the kind of data one usually obtains from experiments there is a need for tools that can take advantage of coarse grained information but which nevertheless remain sensitive to higher order correlations in the data we propose that the correlation integral now much used as an intermediate step in the calculation of dimensions and entropies can be used as such a tool and that the kolmogorov smirnov test is a convenient and reliable way of comparing correlation integrals quantitatively this procedure makes it possible to distinguish between attractors with similar dimensions for example it can unambiguously distinguish p 10 mathrm ensuremath 8 the lorenz r ossler and mackey glass delay 17 attractors whose correlation dimensions are within 1 of each other we also show that the kolmogorov smirnov test is a convenient way of comparing a data set with its surrogates

human brain dynamics the analysis of eeg signals with tsallis information measure we undertake the study of human eeg signals by recourse to a wavelet based multiresolution analysis as adapted to an information measure scenario dierent information measures are employed it is shown that non extensive ones seem to be of particular usefulness their use opens up perspectives of building up automatic detection devices conjectures concerning general characteristics of focal epilepsy are formulated on the basis of a tsallis type of analysis c 1999 elsevier science b v all rights reserved

symmetries and global solvability of the isothermal gas dynamics equations we study the cauchy problem associated with the system of two conservation laws arising in isothermal gas dynamics in which the pressure and the density are related by the law equation p with 1 our results complete those obtained earlier for 1 we prove the global existence and compactness of entropy solutions generated by the vanishing viscosity method the proof relies on compensated compactness arguments and symmetry group analysis interestingly we make use here of the fact that the isothermal gas dynamics system is invariant modulo a linear scaling of the density this property enables us to reduce our problem to that with a small initial density

assessing a set of additive utility functions for multicriteria decision making the uta method abstract the purpose of the method presented in this paper is to assess additive utility functions which aggregate multiple criteria in a composite criterion using the information given by a subjective ranking on a set of stimuli or actions weak order comparison judgments and the multicriteria evaluations of these actions it is an ordinal regression method using linear programming to estimate the parameters of the utility function stability and sensitivity analysis leads to the assessment of a set of utility functions by means of post optimality analysis techniques in linear programming finally a simple illustrative example is presented and some extensions of the method are proposed

vanishing viscosity limit of the navier stokes equations to the euler equations for compressible fluid flow we establish the vanishing viscosity limit of the navier stokes equations to the isentropic euler equations for one dimensional compressible fluid flow for the navier stokes equations there exist no natural invariant regions for the equations with the real physical viscosity term so that the uniform sup norm of solutions with respect to the physical viscosity coefficient may not be directly controllable furthermore convex entropy entropy flux pairs may not produce signed entropy dissipation measures to overcome these difficulties we first develop uniform energy type estimates with respect to the viscosity coefficient for solutions of the navier stokes equations and establish the existence of measure valued solutions of the isentropic euler equations generated by the navier stokes equations based on the uniform energy type estimates and the features of the isentropic euler equations we establish that the entropy dissipation measures of the solutions of the navier stokes equations for weak entropy entropy flux pairs generated by compactly supported c2 test functions are confined in a compact set in h 1 which leads to the existence of measure valued solutions that are confined by the tartar murat commutator relation a careful characterization of the unbounded support of the measure valued solution confined by the commutator relation yields the reduction of the measurevalued solution to a dirac mass which leads to the convergence of solutions of the navier stokes equations to a finite energy entropy solution of the isentropic euler equations with finite energy initial data relative to the different end states at infinity 2010 wiley periodicals inc

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

assessing non additive utility for multicriteria decision aid abstract in the framework of multi attribute utility theory maut several methods have been proposed to build a decision maker s dm utility function representing his her preferences among such methods the uta method infers an additive utility function from a set of exemplary decisions using linear programming however the uta method does not guarantee to find a utility function which is coherent with the available information this drawback is due to the underlying utility model of uta viz the additive one which does not allow to include additional information such as an interaction among criteria in this paper we present a methodology for building a non additive utility function in the framework of the so called fuzzy integrals which permits to model preference structures with interaction between criteria like in the uta method we aim at searching a utility function representing the dm s preferences but unlike uta the functional form is a specific fuzzy integral choquet integral as a result we obtain weights which can be interpreted as the importance of coalitions of criteria exploiting the potential interaction between criteria as already proposed by other authors however within the same framework we obtain also the marginal utility functions relative to each one of the considered criteria that are evaluated on a common scale as a consequence of the implemented methodology finally we illustrate our approach with an example

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

a kinetic equation with kinetic entropy functions for scalar conservation laws we construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws in particular we prove that it is well posed uniformly in e the microscopic scale we also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions analogous to boltzmann s microscopich function such that they recover krushkov type entropy inequality on the macroscopic scale finally we prove by both bv compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case that the local density of kinetic particles admits a continuum limit as it converges strongly with e 0 to the unique entropy solution of the corresponding conservation law

equilibrium schemes for scalar conservation laws with stiff sources we consider a simple model case of stiff source terms in hyperbolic conservation laws namely the case of scalar conservation laws with a zeroth order source with low regularity it is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced cfl condition and refined meshes required because of the lack of accuracy on equilibrium states the source term should be taken into account in the upwinding and discretized at the nodes of the grid in order to solve numerically the problem we introduce a so called equilibrium schemes with the properties that i the maximum principle holds true ii discrete entropy inequalities are satisfied iii steady state solutions of the problem are maintained one of the difficulties in studying the convergence is that there are no bv estimates for this problem we therefore introduce a kinetic interpretation of upwinding taking into account the source terms based on the kinetic formulation we give a new convergence proof that only uses property ii in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions the computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that in comparison with an usual upwind scheme the corresponding equilibrium version is far more accurate furthermore numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients

singular limit problem of the camassa holm type equation abstract we consider a shallow water equation of camassa holm type containing nonlinear dispersive effects as well as fourth order dissipative effects we prove the strong convergence and establish the condition under which as diffusion and dispersion parameters tend to zero smooth solutions of the shallow water equation converge to the entropy solution of a scalar conservation law using methodology developed by hwang and tzavaras s hwang a e tzavaras kinetic decomposition of approximate solutions to conservation laws applications to relaxation and diffusion dispersion approximations comm partial differential equations 27 2002 1229 1254 the proof relies on the kinetic formulation of conservation laws and the averaging lemma

stability and convergence of a class of finite element schemes for hyperbolic systems of conservation laws we propose a class of finite element schemes for systems of hyperbolic conservation laws that are based on finite element discretizations of appropriate relaxation models we consider both semidiscrete and fully discrete finite element schemes and show that the schemes are stable and when the compensated compactness theory is applicable do converge to a weak solution of the hyperbolic system the schemes use piecewise polynomials of arbitrary degree and their consistency error is of high order we also prove that the rate of convergence of the relaxation system to a smooth solution of the conservation laws is of order o eps

equivalent representations of set functions this paper introduces four alternative representations of a set function the ma bius transformation the co ma bius transformation and the interactions between elements of any subset of a given set as extensions of shapley and banzhaf values the links between the five equivalent representations of a set function are emphasized in this presentation

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

assessing causality from multivariate time series in this work we propose a general nonparametric test of causality for weakly dependent time series more precisely we study the problem of attribution i e the proper comparison of the relative influence that two or more external dynamics trigger on a given system of interest we illustrate the possible applications of the proposed methodology in very different fields like physiology and climate science

a method for determining the weights of criteria the centralized weights abstract in multicriteria analysis many methods use weights to represent the relative importance of criteria the noncompensatory aggregation procedure used in outranking methods enables comparisons of subsets of criteria from this point of view an interactive method is presented which requests only ordinal comparisons from the decision maker the relation more important than is assumed to be a semiorder therefore the indifference part of this relation is not necessarily transitive the judgements can be formulated as linear inequalities which constrain the set of feasible weights and threshold values all vertices of this polyhedron are determined the threshold and the unknown real weights are estimated by the centroid some characteristics a possible refinement in the estimation and an illustrative example are also given

entropy satisfying flux vector splittings and kinetic bgk models we establish forward and backward relations between entropy satisfying bgk relaxation models such as those introduced previously by the author and the first order flux vector splitting numerical methods for general systems of conservation laws classically to a kinetic bgk model that is compatible with some family of entropies we can associate an entropy flux vector splitting we prove that the converse is true any entropy flux vector splitting can be interpreted by a kinetic model and we obtain an explicit characterization of entropy satisfying flux vector splitting schemes we deduce a new proof of discrete entropy inequalities under a sharp cfl condition that generalizes the monotonicity criterion in the scalar case in particular this gives a stability condition for numerical kinetic methods with noncompact velocity support a new interpretation of general kinetic schemes is also provided via approximate riemann solvers we deduce the construction of finite velocity relaxation systems for gas dynamics and obtain a hllc scheme for which we are able to prove positiveness of density and internal energy and discrete entropy inequalities

a note on the sobol indices and interactive criteria the choquet integral and the owen extension or multilinear extension are the most popular tools in multicriteria decision making to take into account the interaction between criteria it is known that the interaction transform and the banzhaf interaction transform arise as the average total variation of the choquet integral and multilinear extension respectively we consider in this note another approach to define interaction by using the sobol indices which are related to the analysis of variance of a multivariate model we prove that the sobol indices of the multilinear extension give the square of the fourier transform a well known concept in computer sciences we also relate the latter to the banzhaf interaction transform and compute the sobol indices for the 2 additive choquet integral

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

weak signal transmission in complex networks and its application in detecting connectivity we present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks through both theoretical analysis and numerical simulations we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses this finding can be conveniently used to detect the topology of unknown network such as the degree distribution clustering coefficient and community structure etc by repeatedly choosing different nodes as the signal source through four typical networks i e the regular one dimensional small world random and scale free networks we show that the features of network can be approximately given by investigating many fewer nodes than the network size thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size

state space reconstruction in the presence of noise takens theorem demonstrates that in the absence of noise a multidimensional state space can be reconstructed from a scalar time series this theorem gives little guidance however about practical considerations for reconstructing a good state space we extend takens treatment applying statistical methods to incorporate the effects of observational noise and estimation error we define the distortion matrix which is proportional to the conditional covariance of a state given a series of noisy measurements and the noise amplification which is proportional to root mean square time series prediction errors with an ideal model we derive explicit formulae for these quantities and we prove that in the low noise limit minimizing the distortion is equivalent to minimizing the noise amplification we identify several different scaling regimes for distortion and noise amplification and derive asymptotic scaling laws when the dimension and lyapunov exponents are sufficiently large these scaling laws show that no matter how the state space is reconstructed there is an explosion in the noise amplification from a practical point of view determinism is lost and the time series is effectively a random process in the low noise large data limit we show that the technique of local singular value decomposition is an optimal coordinate transformation in the sense that it achieves the minimum distortion in a state space of the lowest possible dimension however in numerical experiments we find that estimation error complicates this issue for local approximation methods we analyze the effect of reconstruction on estimation error derive a scaling law and suggest an algorithm for reducing estimation errors

compressible euler equations with general pressure law we study the hyperbolic system of euler equations for an isentropic compressible fluid governed by a general pressure law the existence and regularity of the entropy kernel that generates the family of weak entropies is established by solving a new euler poisson darboux equation which is highly singular when the density of the fluid vanishes new properties of cancellation of singularities in combinations of the entropy kernel and the associated entropy flux kernel are found

the riemann function singular entropies and the structure of oscillations in systems of two conservation laws we use singular entropies and the connection with the fundamental solution of the entropy equation and its adjoint operator in order to derive a new formula describing the coupling of oscillations between the two characteristic fields in systems of two conservation laws

finite correlation dimension for stochastic systems with power law spectra abstract we discuss a counter example to the traditional view that stochastic processes lead to a non convergence of the correlation dimension in computed or measured time series specifically we show that a simple class of colored random noises characterized by a power law power spectrum have a finite and predictable value for the correlation dimension these results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics we demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties the consequent exploitation of the non gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis we apply this approach to characterize several global properties of random noise

extracting qualitative dynamics from experimental data abstract we consider the notion of qualitative information and the practicalities of extracting it from experimental data our approach based on a theorem of takens draws on ideas from the generalized theory of information known as singular system analysis due to bertero pike and co workers we illustrate our technique with numerical data from the chaotic regime of the lorenz model

2 additive capacity identification methods from multicriteria correlation preference information the essential role of the particular families of capacities and the capacity identification methods is to help the decision maker to deal with the exponential complexity inherent in the construction process of the capacity the 2 additive capacities appear to be the most popular among the particular families of capacities since they permit to model interactions between criteria while preserving simplicity besides the preference with respect to the decision criteria most of the capacity identification methods also need to provide the desired overall evaluations of the decision alternatives in the learning set which is a time consuming task for the decision maker in this paper we propose some models to identify 2 additive capacities only from a kind of refined preference information with respect to the decision criteria called the multicriteria correlation preference information mccpi the mccpi is a group of 2 d preference information which can be described and obtained by the refined diamond diagram the common principle of the proposed models is to minimize the different kinds of deviations between the mccpi and the most desired 2 additive capacity ies a multicriteria decision making example is presented to show the feasibility of the proposed methods and a 2 d scale of the mccpi is also introduced in the further discussion of the illustrative example

nonlinear diffusive dispersive limits for scalar multidimensional conservation laws abstract we consider a class of multidimensional conservation laws with vanishing nonlinear diffusion and dispersion terms under a condition on the relative size of the diffusion and dispersion coefficients we show that the approximate solutions converge in a strong topology to the entropy solution of a scalar conservation law our proof is based on methodology developed in s hwang a e tzavaras kinetic decomposition of approximate solutions to conservation laws applications to relaxation and diffusion dispersion approximations comm partial differential equations 27 2002 1229 1254 which uses the averaging lemma

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

non additive robust ordinal regression a multiple criteria decision model based on the choquet integral abstract within the multicriteria aggregation disaggregation framework ordinal regression aims at inducing the parameters of a decision model for example those of a utility function which have to represent some holistic preference comparisons of a decision maker dm usually among the many utility functions representing the dm s preference information only one utility function is selected since such a choice is arbitrary to some extent recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the dm s preference information until now robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence in this paper we propose a non additive robust ordinal regression on a set of alternatives a whose utility is evaluated in terms of the choquet integral which permits to represent the interaction among criteria modelled by the fuzzy measures parameterizing our approach in our methodology besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives a a the dm is also requested to express the intensity of preference on pairs of alternatives from a and to supply pairwise comparisons on the importance of criteria and the sign and intensity of interaction among pairs of criteria the output of our approach defines a set of fuzzy measures capacities such that the corresponding choquet integral is compatible with the dm s preference information moreover using linear programming our decision model establishes two preference relations for any a b a the necessary weak preference relation if for all compatible fuzzy measures the utility of a is not smaller than the utility of b and the possible weak preference relation if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b

kinetic decomposition for singularly perturbed higher order partial differential equations abstract in this paper we consider singularly perturbed higher order partial differential equations we establish the condition under which the approximate solutions converge in a strong topology to the entropy solution of a scalar conservation laws using methodology developed in hwang and tzavaras comm partial differential equations 27 2002 1229 first we obtain the approximate transport equation for the given dispersive equations then using the averaging lemma we obtain the convergence

distinguishing between low dimensional dynamics and randomness in measured time series the success of current attempts to distinguish between low dimensional chaos and random behavior in a time series of observations is considered first we discuss stationary stochastic processes which produce finite numerical estimates of the correlation dimension and k2 entropy under naive application of correlation integral methods we then consider several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory this determines whether the methods are applicable to a given series if they are we evaluate the significance of a particular result for example by considering the results of the analysis of stochastic signals with statistical properties similar to those of observed series from the examples considered it is clear that the correlation integral should not be used in isolation but as one of a collection of tools to distinguish chaos from stochasticity

decision aid and decision making the objective of multiple criteria approaches is to help us to make better decisions but what is the meaning of better this field has developed considerably in the past twenty years the development makes us fully aware of the limitations on objectivity encountered in the field of decision aid and consequently of the virtual impossibility of providing a truly scientific foundation for an optimal decision work carried out under the rubric of mcdm multiple criteria decision making bases its claims to legitimacy on a framework in which these limitations are left aside multiple criteria decision aid mcda must be seen from a different perspective its aim is above all to enable us to enhance the degree of conformity and coherence between the evolution of a decision making process and the value systems and objectives of those involved in this process the purpose of decision aid is therefore to help us make our way in the presence of ambiguity uncertainty and an abundance of bifurcations we shall analyse multiple criteria concepts models and procedures from both these viewpoints

quantitative analysis by renormalized entropy of invasive electroencephalograph recordings in focal epilepsy invasive electroencephalograph eeg recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy introduced as a complexity measure for the different regimes of a dynamical system the feature was tested here for its spatio temporal behavior in epilep tic seizures in all patients a decrease of renormalized entropy within the ictal phase of seizure was found furthermore the strength of this decrease is monotonically related to the distance of the recording location to the fo cus the results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci 87 90 y

kinetic formulation for systems of two conservation laws and elastodynamics for scalar conservation laws the kinetic formulation makes it possible to generate all the entropies from a simple kernel we show how this concept replaces and simplifies greatly the concept of young measures avoiding the difficulties encountered when working in lp the general construction of the two kinetic functions that generate the entropies of 2 2 strictly hyperbolic systems is also developed here we show that it amounts to building a universal entropy i e one that can be truncated by a kinetic value along riemann invariants for elastodynamics this construction can be completed and specialized using the additional galilean invariance this allows a full characterization of convex entropies it yields a kinetic formulation consisting of two semi kinetic equations which as usual are equivalent to the infinite family of all the entropy inequalities

boundary conditions for scalar conservation laws from a kinetic point of view boundary conditions for multidimensional scalar conservation laws are obtained in the context of hydrodynamic limits from a kinetic point of view the initial boundary value kinetic problem is well posed since inward and outward characteristics of the domain can be distinguished the convergence of the first momentum of the distribution function to an entropy solution of the conservation law is established boundary conditions are obtained the equivalence with the bardos leroux and nedelec conditions is studied

microscopic theory of isothermal elastodynamics this paper examines random perturbations of the anharmonic chain of coupled oscillators the microscopic system has two conservation laws and its hyperbolic scaling limit results in the quasi linear wave equation p system of isothermal isentropic elasticity in the shock regime the compensated compactness method is used lastly results from j w shearer and d serre are applied

comparison of three nonlinear seizure prediction methods by means of the seizure prediction characteristic epilepsy is characterized by the spontaneous and unforeseeable occurrence of seizures during which the perception or behavior of patients is disturbed the predictability of these seizures would render novel therapeutic approaches possible several prediction methods have claimed to be able to predict seizures based on eeg recordings minutes in advance however the term seizure prediction is not unequivocally defined different criteria to assess prediction methods exist and only little attention has been paid to issues of sensitivity and false prediction rate we introduce an assessment criterion called the seizure prediction characteristicthat incorporates the assessment of sensitivity and false prediction rate within this framework three nonlinear seizure prediction methods were evaluated on a large eeg data pool of 21 patients altogether 582 h intracranial eeg data and 88 seizures were examined with a rate of 1 3 6 false predictions per day the dynamical similarity index achieves a sensitivity between 21 and 42 which was the best result of the three methods sensitivity was between 18 and 31 for the extended prospective version of the accumulated energy and between 13 and 30 for the effective correlation dimension these results still are not sufficient for clinical applications

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective abstract we consider multiple criteria decision aiding mcda in the case of interactions between criteria in dealing with interactions between criteria fuzzy measures and integrals have demonstrated great advantages nevertheless the determination of fuzzy measures has proven difficult because the capacities of not only single criterion but also all subsets of criteria need to be identified due to the value judgment essence of mcda the attitudes of the decision maker dm are typically modeled to identify fuzzy measures in this paper the tolerance attitudes of the dm which implies a direct requirement instead of partial preference are modeled with regard to the determination of fuzzy measures for the first time with two scales developed in this paper the dm can directly express the tolerance attitudes to certain criteria other than providing partial preference through pairwise comparison as a result it requires less prior knowledge and is more efficient to some extent further the inherent interacting mechanism of criteria under different tolerance attitudes is explored at last the tolerance attitudes are applied to the process of multiple criteria analysis using a choquet integral a classic student evaluation problem is given as an example the evaluation results are compared with additive models this paper not only provides a new inspiration to the determination of fuzzy measures but also improves the descriptive capacity of fuzzy measures to the real world