complexity of time series associated to dynamical systems inferred from independent component analysis received 11 may 2005 published 24 october 2005a not trivial problem for every experimental time series associated to a natural system is to individuate thesigni cant variables to describe the dynamics i e the effective degrees of freedom the application of inde pendent component analysis ica has provided interesting results in this direction e g in the seismologicaland atmospheric eld since all natural phenomena can be represented by dynamical systems our aim is tocheck the performance of ica in this general context to avoid ambiguities when investigating an unknownexperimental system we show many examples representing linear nonlinear and stochastic processes inwhich ica seems to be an ef cacious preanalysis able to give information about the complexity of thedynamics doi 10 1103 physreve 72 046712 pacs number s 07 05 mh 05 45 tp

computing positive stable numerical solutions of moving boundary problems for concrete carbonation abstract this paper deals with the construction and computation of numerical solutions of a coupled mixed partial differential equation system arising in concrete carbonation problems the moving boundary problem under study is firstly transformed in a fixed boundary one allowing the computation of the propagation front as a new unknown that can be computed together with the mass concentrations of co 2 in air and water apart from the stability and the consistency of the numerical solution constructed by a finite difference scheme qualitative properties of the numerical solution are established in fact positivity of the concentrations increasing properties of the propagation front and monotone behavior of the solution are proved we also confirm numerically the t law of propagation results are illustrated with numerical examples

analytic hierarchy process for multi sensor data fusion based on belief function theory abstract multi sensor data fusion is an evolving technology whereby data from multiple sensor inputs are processed and combined the data derived from multiple sensors can however be uncertain imperfect and conflicting the present study is undertaken to help contribute to the continuous search for viable approaches to overcome the problems associated with data conflict and imperfection sensor readings represented by belief functions have to be fused according to their corresponding weights previous studies have often estimated the weights of sensor readings based on a single criterion mono criteria approaches for the assessment of sensor reading weights are however often unreliable and inadequate for the reflection of reality accordingly this work opts for the use of a multi criteria decision aid a modified analytical hierarchy process ahp that incorporates several criteria is proposed to determine the weights of a sensor reading set the approach relies on the automation of pairwise comparisons to eliminate subjectivity and reduce inconsistency it assesses the weight of each sensor reading and fuses the weighed readings obtained using a modified average combination rule the efficiency of this approach is evaluated in a target recognition context several tests sensitivity analysis and comparisons with other approaches available in the literature are described

constructing unconditionally time stable numerical solutions for mixed parabolic problems this paper proposes a new numerical method based on an implicit difference scheme and the fourier method which is applied to construct numerical solutions of mixed parabolic problems the method is consistent and unconditionally time stable

on the dempster shafer framework and new combination rules abstract we discuss the basic concepts of the dempster shafer approach basic probability assignments belief functions and probability functions we discuss how to represent various types of knowledge in this framework we discuss measures of entropy and specificity for belief structures we discuss the combination and extension of belief structures we introduce some concerns associated with the dempster rule of combination inherent in the normalization due to conflict we introduce two alternative techniques for combining belief structures the first uses dempster s rule while the second is based upon a modification of this rule we discuss the issue of credibility of a witness

a novel combination method for conflicting evidence based on inconsistent measurements dempster shafer d s evidence theory is a kind of effective tool for uncertain information fusion however the counter intuitive results are often obtained when the conflicting pieces of evidence are fused with dempster s combination rule in order to solve the existing counter intuitive problem more effectively and less conservatively in this paper we propose an improved combination method for the conflicting evidence based on inconsistent measurements firstly a new approach is proposed for measuring the conflict between two pieces of evidence then the conflicting evidence is revised by selecting discount coefficients moreover dempster s combination rule is significantly improved by the new conflict coefficients and the fusion results are acquired by the improved combination rule finally examples are given to illustrate the effectiveness and potential of the developed new techniques

n 1 dimensional reduced differential transform method for solving partial differential equations in this paper we study the generalization of the reduced differential transform method to n 1 dimensional case thus the partial differential equations pdes can be solved efficiently one distinctive practical feature of this method is that it is applied without using discretization or restrictive assumptions the other is that large computational work and round off errors are avoided we employ the proposed method on a few initial value problems to illustrate it is highly accurate and more efficient hence our method is a powerful method for solving the pdes and problems arising in physics engineering area and so on

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

the combination of evidence in the transferable belief model a description of the transferable belief model which is used to quantify degrees of belief based on belief functions is given the impact of open and closed world assumption on conditioning is discussed the nature of the frame of discernment on which a degree of belief will be established is discussed a set of axioms justifying dempster s rule for the combination of belief functions induced by two distinct evidences is presented

recovering the history of a groundwater contaminant plume method of quasi reversibility the method of quasi reversibility qr lattes and lions 1969 has been used previously to solve the diffusion equation with reversed time we develop a quasi reversible solution to a convection dispersion equation by solving the qr diffusion operator in a moving coordinate system the solution procedure is applied to the problem of recovering the history of a groundwater contaminant plume from observations of its present conditions this approach to the plume history problem is potentially superior to the tikhonov regularization approach used by skaggs and kabala 1994 because it is easier to implement and readily allows for space and time dependent transport parameters however our results for a few example problems suggest that the qr procedure is less accurate than the regularization technique thus the easy implementation and improved generality of the qr procedure come at the expense of accuracy this trade off will have to be weighed if the qr technique is to be used

a discrete eigenfunctions method for computing mixed hyperbolic problems based on an implicit difference scheme in this paper numerical solutions of mixed hyperbolic problems are computed using a discrete eigenfunctions method combined with an implicit difference scheme this new numerical technique preserves the qualitative properties of the analytic solution due to the sturm liouville structure of the underlying discrete linear boundary value problem and has computational stability advantages vs other methods illustrative examples are included

computing the variable coefficient telegraph equation using a discrete eigenfunctions method this paper deals with the construction of discrete numerical solutions of mixed problems for the telegraph equation after discretization the two variables partial difference mixed problem is solved by means of a discrete eigenfunctions method that mimics the advantages of the continuous eigenfunction method while eliminating its computational disadvantages the solution is based on a closed form solution of the inhomogeneous second order difference equation without increasing the problem s dimension

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

a multicriteria approach for analysis of conflicts in evidence theory we propose a new approach to model the conflict on dst as multi criteria problem we introduce a new subjective notion of conflict through a pseudo criteria analysis we present a numerical application of the proposed model based on 2 and 3 conflict measures therefore it is showed that is possible to capture conflict in dst using more that to 2 criteria dempster shafer theory dst or evidence theory is regarded as one of the leading theories for modeling uncertainty in imprecise situations the main advantage of this theory arises from the possibility of combining different bodies of evidence originally developed by using dempster s combination rule however this rule leads to counter intuitive results when the bodies of evidence conflict with each other to a high degree thus different combinations of conflict management rules have been developed over the years where regardless of the method used what should be identified first of all is the level of conflict between the bodies of evidence therefore different metrics were used to classify or quantify the conflict but no single one of these was successful because it is impracticable to represent all situations of conflict in this theory by using only one metric therefore the contribution of this article is to analyze conflict within dst by using a multi criteria analysis for which the multi criteria decision making mcdm method considered was electre tri on modeling the problem three classes of conflict low medium and high were considered to validate the model a numerical analysis was conducted that included the use of a method to point up conflict so as to infer parameters

combining various types of belief structures we first discuss the basic ideas of the dempster shafer belief structure we particularly emphasize the associated measures of plausibility and belief we discuss the cumulative distribution function associated with a belief structure we next turn to the issue of combining multiple belief structures two different types of combination of belief structures are investigated the first which we refer to as the fusion of belief structures occurs when the belief structures being combined are providing information about the same variable here we make use of the dempster rule the second type which we refer to as the joining of belief structures occurs when the belief structures being combined are providing information about different variables here we make use of a belief structures cumulative distribution function and the sklar theorem the classic belief structures typically have a finite number of focal elements here we began to look at belief structures which have a continuum of focal elements

closed form numerical solutions of variable coefficient linear second order elliptic problems abstract in this work we develop an alternative numerical technique which allows to construct a numerical solution in closed form of variable coefficient linear second order elliptic problems with dirichlet boundary conditions the elliptic partial differential equation is approximated by a consistent explicit difference scheme and using a discrete separation of the variables method we determine a closed form solution of the two resulting discrete boundary value problems with the separated variables avoiding to have to solve large algebraic systems one of these boundary value problems is a discrete sturm liouville problem which guarantees the qualitative properties of the exact solution of elliptic problem a constructive procedure for the computation of the numerical solution is given and an illustrative example is included

weighted cautious conjunctive rule for belief functions combination denoeux proposed an operator called the cautious conjunctive rule ccr to combine non dogmatic belief functions i e the frame is considered a focal element from reliable dependent sources which can occur in practice however in cases such as uncertain multiple attribute and group decision analyses belief functions may denote data that vary in importance this paper extends ccr as a weighted ccr wccr to combine belief functions in consideration of their relative weights in such situations properties of wccr are analyzed proven and demonstrated using numerical examples in particular the consideration of relative weights enables wccr to combine dogmatic belief functions the normalized wccr is further constructed and used to assess the trustworthiness of a hospital information system employed in many hospitals in anhui province china

a new combination of evidence based on compromise dempster rule of combination is the standard way of combining multiple pieces of evidence given by independent sources of information however it aroused many controversies about its validity and many alternatives have been proposed the paper examines the model of combination in dempster s original paper and indicates that handling of the independence required among multiple pieces of evidence is strange from the viewpoint of semantics where the independence among occurrences of multiple pieces of information might be confused with the consistency among contents of the information the paper then proposes a new model of combination and a new rule of combination called combination by compromise as a consensus generator the properties of the proposed combination as well as several alternative combination methods proposed so far are discussed in the light of the drawbacks and advantages of dempster rule several numerical examples which demonstrate the properties are also shown the discussion and the examples suggest that the proposed combination produces the most preferable results among them from the viewpoints of consensus generation

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

the transferable belief model abstract we describe the transferable belief model a model for representing quantified beliefs based on belief functions beliefs can be held at two levels 1 a credal level where beliefs are entertained and quantified by belief functions 2 a pignistic level where beliefs can be used to make decisions and are quantified by probability functions the relation between the belief function and the probability function when decisions must be made is derived and justified four paradigms are analyzed in order to compare bayesian upper and lower probability and the transferable belief approaches

automatic solution of sturm liouville problems using the pruess method abstract we develop algorithms based on coefficient approximation for the automatic solution of regular and singular sturm liouville problems

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

combining uncertain information of differing modalities in this paper we consider approaches for combining separately possibilistic uncertainty probabilistic uncertainty and situations where both forms of uncertainty appear an approach to probability aggregation using rational consensus with equi weighting is developed this aggregation is analyzed with information measures as one way to assess combinations and understand the impact on uncertainty the analysis is based on combinations of bounding cases of probability distributions measures of conflict and the effect on information are developed next possibility transformations are used and illustrated by three representative possibility cases the resultant transformed probabilities are aggregated with general probability distributions and the result evaluated with information measures as before finally a general approach to combining possibility distributions directly using quality criteria is described an example is provided to illustrate the basic possibility distribution aggregation fusion developed

a low computational cost numerical method for solving mixed diffusion problems in this paper a discrete eigenfunctions method for constructing numerical solutions of mixed diffusion problem with space varying properties and source term is developed after discretization instead of solving algebraically the discretized problem we propose a discrete eigenfunctions method which reduces the computational cost of standard finite difference methods

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