time discretization of an integro differential equation of parabolic type the stability and convergence properties of two time discretizations of an integro differential equation of parabolic type are studied the methods reduce to the backward euler and crank nicolson methods if the integral term is absent the integral term is approximated in each case by a quadrature rule with relatively high order truncation error so that a relatively large time step can be used for the quadrature in order to reduce the memory and computational requirements of the method

sharp l 2 error estimates and superconvergence of mixed finite element methods for non fickian flows in porous media a sharper l2 error estimate is obtained for the non fickian flow of fluid in porous media by means of a mixed ritz volterra projection instead of the mixed ritz projection used in r e ewing y lin and j wang acta math univ comenian n s 70 2001 pp 75 84 moreover local l2 superconvergence for the velocity along the gauss lines and for the pressure at the gauss points is derived for the mixed finite element method via the ritz volterra projection and global l2 superconvergence for the velocity and the pressure is also investigated by virtue of an interpolation postprocessing technique on the basis of the superconvergence estimates some useful a posteriori error estimators are presented for this mixed finite element method

global stability of endemic equilibrium of an epidemic model with birth and death on complex networks abstract we study global stability of endemic equilibrium of an epidemic model with birth and death on complex networks under some conditions the local asymptotic stability of the endemic equilibrium was established by zhang and jin 2011 for correlated networks and the global asymptotic stability was obtained by chen and sun 2014 for uncorrelated networks in this work we remove those conditions and prove by constructing a lyapunov function that the endemic equilibrium is globally asymptotically stable numerical simulations are also presented to illustrate the feasibility of the result

multiobjective evolutionary optimization of type 2 fuzzy rule based systems for financial data classification classification techniques are becoming essential in the financial world for reducing risks and possible disasters managers are interested in not only high accuracy but in interpretability and transparency as well it is widely accepted now that the comprehension of how inputs and outputs are related to each other is crucial for taking operative and strategic decisions furthermore inputs are often affected by contextual factors and characterized by a high level of uncertainty in addition financial data are usually highly skewed toward the majority class with the aim of achieving high accuracies preserving the interpretability and managing uncertain and unbalanced data this paper presents a novel method to deal with financial data classification by adopting type 2 fuzzy rule based classifiers frbcs generated from data by a multiobjective evolutionary algorithm moea the classifiers employ an approach denoted as scaled dominance for defining rule weights in such a way to help minority classes to be correctly classified in particular we have extended paes rcs an moea based approach to learn concurrently the rule and data bases of frbcs for managing both interval type 2 fuzzy sets and unbalanced datasets to the best of our knowledge this is the first work that generates type 2 frbcs by concurrently maximizing accuracy and minimizing the number of rules and the rule length with the objective of producing interpretable models of real world skewed and incomplete financial datasets the rule bases are generated by exploiting a rule and condition selection rcs approach which selects a reduced number of rules from a heuristically generated rule base and a reduced number of conditions for each selected rule during the evolutionary process the weight associated with each rule is scaled by the scaled dominance approach on the fuzzy frequency of the output class in order to give a higher weight to the minority class as regards the data base learning the membership function parameters of the interval type 2 fuzzy sets used in the rules are learned concurrently to the application of rcs unbalanced datasets are managed by using in addition to complexity selectivity and specificity as objectives of the moea rather than only the classification rate we tested our approach named it2 paes rcs on 11 financial datasets and compared our results with the ones obtained by the original paes rcs with three objectives and with and without scaled dominance the frbcs fuzzy association rule based classification model for high dimensional dataset farc hd and fuzzy unordered rules induction algorithm furia the classical c4 5 decision tree algorithm and its cost sensitive version using nonparametric statistical tests we will show that it2 paes rcs generates frbcs with on average accuracy statistically comparable with and complexity lower than the ones generated by the two versions of the original paes rcs further the frbcs generated by farc hd and furia and the decision trees computed by c4 5 and its cost sensitive version despite the highest complexity result to be less accurate than the frbcs generated by it2 paes rcs finally we will highlight how these frbcs are easily interpretable by showing and discussing one of them

the analysis of an epidemic model on networks abstract the paper consider an epidemic model with birth and death on networks we derive the epidemic threshold r0 dependent on birth rate b death rate d natural death and from the infectious disease and natural death and cure rate and the stability of the equilibriums the disease free equilibrium and endemic equilibrium are analysed finally the effects of various immunization schemes are studied and compared we show that both targeted and acquaintance immunization strategies compare favorably to a proportional scheme in terms of effectiveness for active immunization the threshold is easier to apply practically to illustrate our theoretical analysis some numerical simulations are also included

adaptive discretization of fractional order viscoelasticity using sparse time history an efficient numerical method to integrate the constitutive response of fractional order viscoelasticity is developed the method can handle variable time steps to overcome the problem of the growing amount of data that has to be stored and used in each time step we introduce sparse quadrature we use an internal variable formulation of the viscoelastic equations where the internal variable is of stress type the rate equation that governs the evolution of the internal variable involves a fractional integral and can be identified as a volterra integral equation of the second kind with a weakly singular kernel for the numerical integration of the rate equation we adopt the finite element method in time in particular the discontinuous galerkin method with piecewise constant basis functions is used a priori and a posteriori error estimates are proved an adaptive strategy based on the a posteriori error estimate is developed finally the precision and effectiveness of the method are demonstrated by comparing the numerical solutions with analytical solutions

behaviors of susceptible infected epidemics on scale free networks with identical infectivity in this paper we propose a susceptible infected model with identical infectivity in which at every time step each node can only contact a constant number of neighbors we implemented this model on scale free networks and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate furthermore by numerical simulation we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible infected model finally we investigate a fast spreading strategy when only local information is available different from the extensively studied path finding strategy the strategy preferring small degree nodes is more efficient than that preferring large degree nodes our results indicate the existence of an essential relationship between network traffic and network epidemic on scale free networks

on fully discrete galerkin approximations for partial integro differential equations of parabolic type the subject of this work is the application of fully discrete galerkin finite element methods to initial boundary value problems for linear partial integro differential equations of parabolic type we investigate numerical schemes based on the pade discretization with respect to time and associated with certain quadrature formulas to approximate the integral term a preliminary error estimate is established which contains a term related to the quadrature rule to be specified in particular we consider quadrature rules with sparse quadrature points so as to limit the storage requirements without sacrificing the order of overall convergence for the backward euler scheme the crank nicolson scheme and a third order pade type scheme the specific quadrature rules analyzed are based on the rectangular the trapezoidal and simpson s rule for all the schemes studied optimal order error estimates are obtained in the case that the solution of the problem is smooth enough since this is important for our error analysis we also discuss the regularity of the exact solutions of our equations high order regularity results with respect to both space and time are given for the solution of problems with smooth enough data 17 refs

monotone iterates for solving nonlinear integro parabolic equations of volterra type the paper deals with numerical solving of nonlinear integro parabolic problems based on the method of upper and lower solutions a monotone iterative method is constructed existence and uniqueness of a solution to the nonlinear difference scheme are established an analysis of convergence rates of the monotone iterative method is given construction of initial upper and lower solutions is discussed numerical experiments are presented

fuzzy sets and type 2 under algebraic product and algebraic sum abstract the concept of fuzzy sets of type 2 has been proposed by l a zadeh as an extension of ordinary fuzzy sets a fuzzy set of type 2 can be defined by a fuzzy membership function the grade or fuzzy grade of which is taken to be a fuzzy set in the unit interval 0 1 rather than a point in 0 1 this paper investigates the algebraic properties of fuzzy grades that is fuzzy sets of type 2 under the operations of algebraic product and algebraic sum which can be defined by using the concept of the extension principle and shows that fuzzy grades under these operations do not form such algebraic structures as a lattice and a semiring moreover the properties of fuzzy grades are also discussed in the case where algebraic product and algebraic sum are combined with the well known operations of join and meet for fuzzy grades and it is shown that normal convex fuzzy grades form a lattice ordered semigroup under join meet and algebraic product

time discretization via laplace transformation of an integro differential equation of parabolic type we consider the discretization in time of an inhomogeneous parabolic integro differential equation with a memory term of convolution type in a banach space setting the method is based on representing the solution as an integral along a smooth curve in the complex plane which is evaluated to high accuracy by quadrature using the approach in recent work of lopez fernandez and palencia this reduces the problem to a finite set of elliptic equations with complex coefficients which may be solved in parallel the method is combined with finite element discretization in the spatial variables to yield a fully discrete method the paper is a further development of earlier work by the authors which on the one hand treated purely parabolic equations and on the other an evolution equation with a positive type memory term

some new error estimates of a semidiscrete finite volume element method for a parabolic integro differential equation with nonsmooth initial data a semidiscrete finite volume element fve approximation to a parabolic integro differential equation pide is analyzed in a two dimensional convex polygonal domain an optimal order l 2 error estimate for smooth initial data and nearly the same optimal order l 2 error estimate for nonsmooth initial data are obtained more precisely for homogeneous equations an elementary energy technique and a duality argument are used to derive an error estimate of order o left t 1 h 2 ln h right in the l 2 norm for positive time when the given initial function is only in l 2

type 2 fuzzy markov random fields and their application to handwritten chinese character recognition in this paper we integrate type 2 t2 fuzzy sets with markov random fields mrfs referred to as t2 fmrfs which may handle both fuzziness and randomness in the structural pattern representation on the one hand the t2 membership function mf has a 3 d structure in which the primary mf describes randomness and the secondary mf evaluates the fuzziness of the primary mf on the other hand mrfs can represent patterns statistical structurally in terms of neighborhood system and clique potentials and thus have been widely applied to image analysis and computer vision in the proposed t2 fmrfs we define the same neighborhood system as that in classical mrfs to describe uncertain structural information in patterns we derive the fuzzy likelihood clique potentials from t2 fuzzy gaussian mixture models the fuzzy prior clique potentials are penalties for the mismatched structures based on prior knowledge because chinese characters have hierarchical structures we use t2 fmrfs to model character structures in the handwritten chinese character recognition system the overall recognition rate is 99 07 which confirms the effectiveness of the proposed method

global stability and attractivity of a network based sis epidemic model with nonmonotone incidence rate abstract in this paper we study the global stability and attractivity of the endemic equilibrium for a network based sis epidemic model with nonmonotone incidence rate the model was introduced in li 2015 we prove that the endemic equilibrium is globally asymptotically stable if a parameter of this model is sufficiently large and is globally attractive if the transmission rate satisfies c 1 2 where c is the epidemic threshold some numerical experiments are also presented to illustrate the theoretical results

a self evolving interval type 2 fuzzy neural network with online structure and parameter learning this paper proposes a self evolving interval type 2 fuzzy neural network seit2fnn with online structure and parameter learning the antecedent parts in each fuzzy rule of the seit2fnn are interval type 2 fuzzy sets and the fuzzy rules are of the takagi sugeno kang tsk type the initial rule base in the seit2fnn is empty and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space to avoid generating highly overlapping fuzzy sets in each input variable an efficient fuzzy set reduction method is also proposed this method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated for parameter learning the consequent part parameters are tuned by the rule ordered kalman filter algorithm for high accuracy learning performance detailed learning equations on applying the rule ordered kalman filter algorithm to the seit2fnn consequent part learning with rules being generated online are derived the antecedent part parameters are learned by gradient descent algorithms the seit2fnn is applied to simulations on nonlinear plant modeling adaptive noise cancellation and chaotic signal prediction comparisons with other type 1 and type 2 fuzzy systems in these examples verify the performance of the seit2fnn

a note on global stability of the virose equilibrium for network based computer viruses epidemics abstract it has been recently conjectured in yang et al 2013 27 that the unique virose equilibrium of a network based model is globally asymptotically stable in the feasible region the aim of this paper is to investigate the global stability of the virose equilibrium by using the direct lyapunov method and appropriate grouping techniques for lyapunov function derivatives some sufficient conditions are established which improves the relevant results moreover we provide a new brief proof for global stability of the virus free equilibrium by using comparison method and discuss quantitatively the effect of various immunization schemes including uniform immunization targeted immunization and high risk immunization on the viruses spread which suggests promising strategy to halt viruses spread in computer networks

higher level fuzzy numbers arising from fuzzy regression consider a fuzzy random variable y with expectation symbol b x where b is an unknown fuzzy number and an unknown real number for n observations yi xi there is a model yi b xi ei i 1 2 n where ei are fuzzy valued errors independently and identically distributed in some sense the aim is to obtain estimates of b when all fuzzy numbers are triangular and the ei are uniformly distributed maximum likelihood estimators emerge naturally as a special form of higher level fuzzy number thus mle can be interpreted as an estimation procedure which transforms randomness into higher levels of fuzziness

epidemic dynamics on scale free networks with piecewise linear infectivity and immunization we examine epidemic thresholds for disease spread using susceptible infected susceptible models on scale free networks with variable infectivity infectivity between nodes is modeled as a piecewise linear function of the node degree rather than the less realistic linear transformation considered previously with this nonlinear infectivity we derive conditions for the epidemic threshold to be positive the effects of various immunization schemes including ring and targeted vaccination are studied and compared we find that both targeted and ring immunization strategies compare favorably to a proportional scheme in terms of effectiveness

infection dynamics on scale free networks we discuss properties of infection processes on scale free networks relating them to the node connectivity distribution that characterizes the network considering the epidemiologically important case of a disease that confers permanent immunity upon recovery we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual s degree of connectivity within the population as in an earlier study r pastor satorras and a vesipignani phys rev lett 86 3200 2001 phys rev e 63 006117 2001 for an infection that did not confer immunity upon recovery the epidemic process in contrast with many traditional epidemiological models does not exhibit threshold behavior and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale free network finally we discuss effects that arise from finite population sizes showing that networks of finite size do exhibit threshold effects infections cannot spread for arbitrarily low transmission probabilities

dynamics for an seirs epidemic model with time delay on a scale free network abstract a new seirs epidemic model with time delay on a scale free network is introduced the basic reproduction number r 0 is defined and it does not depend on time delay by analyzing the characteristic equation of equilibria and constructing suitable lyapunov functionals the stability of steady states is proved system does not occur hopf bifurcation around disease free equilibrium e 0 uniform immunization and targeted immunization are investigated numerical simulations and sensitivity analysis are performed results indicate that time delay plays a significant part in propagation process of epidemics on a scale free network

data based system modeling using a type 2 fuzzy neural network with a hybrid learning algorithm we propose a novel approach for building a type 2 neural fuzzy system from a given set of input output training data a self constructing fuzzy clustering method is used to partition the training dataset into clusters through input similarity and output similarity tests the membership function associated with each cluster is defined with the mean and deviation of the data points included in the cluster then a type 2 fuzzy takagi sugeno kang if then rule is derived from each cluster to form a fuzzy rule base a fuzzy neural network is constructed accordingly and the associated parameters are refined by a hybrid learning algorithm which incorporates particle swarm optimization and a least squares estimation for a new input a corresponding crisp output of the system is obtained by combining the inferred results of all the rules into a type 2 fuzzy set which is then defuzzified by applying a refined type reduction algorithm experimental results are presented to demonstrate the effectiveness of our proposed approach

interval valued fuzzy sets representation on multiple antecedent fuzzy s implications and reasoning abstract interval valued fuzzy sets are used to represent multiple antecedent s implications based on normal forms where linguistic connectives antecedents and consequents are assumed to be fuzzy these intervals are represented equivalently with their lower and upper bounds general forms are given for the bounds of multiple antecedent fuzzy s implications bounds for multiple antecedent reasoning are also investigated based on the bounds of multiple antecedent s implications it is suggested that modification functions utilized in approximation analogical reasoning aar be determined in such a way that consequents deduced by aar fall within the bounds of the reasoning an example is given to show how the bounds might be used to choose a modification scheme in aar

quasi wavelet based numerical method for a class of partial integro differential equation abstract in this paper we study the numerical solution of initial boundary problem for a class of partial integro differential equations the quasi wavelet method is proposed to handle the spatial derivatives while the forward euler method is used to discretize the temporal derivatives detailed discrete schemes are given and some numerical experiments are included to demonstrate the effectiveness of the discrete technique the comparisons of the present numerical results with the exact analytical solutions show that the quasi wavelet based numerical method has distinctive local property and can achieve accurate results

a fractional order model for ebola virus infection with delayed immune response on heterogeneous complex networks abstract most of the biological systems have long range temporal memory and modeling of such systems by fractional order differential equations has more advantages than classical models with integer orders in this paper we provide a fractional order ebola virus epidemic model with delayed immune response on heterogeneous complex networks the time delay is introduced in the cytotoxic t lymphocyte ctls term based on fractional laplace transform some conditions on stability are derived for the model the analysis shows that the fractional order time delay can effectively enrich the dynamics and strengthen the stability condition of fractional order infection model finally the derived theoretical results are justified by some numerical simulations

on the naturality of the iteration and recursive specifications abstract in 5 the naturality of level of sentence control structures concatenation conditional and iterative recursion is given in the present article we emphasize from a categorical semantics point of view following 11 the iteration and some of its relations with general recursion at the unit level

discontinuous galerkin finite element approximation of nonlinear non fickian diffusion in viscoelastic polymers we consider discrete schemes for a nonlinear model of non fickian diffusion in viscoelastic polymers the model is motivated by but not the same as that proposed by cohen et al in siam j appl math 55 pp 348 368 1995 the spatial discretisation is effected with both the symmetric and non symmetric interior penalty discontinuous galerkin finite element method and the time discretisation is of crank nicolson type we also discuss two means of handling the nonlinearity either implicitly which requires the solution of nonlinear equations at each time level or through a linearisation based on extrapolating from previous time levels the same optimal orders of convergence are proven in both cases and to verify this some numerical results are also given for the linearised scheme

footprint of uncertainty for type 2 fuzzy sets in the paper a new and comprehensible definition is proposed for type 2 fuzzy sets t2 fss and the primary and secondary memberships function are defined respectively by using multi valued mapping a new definition and formula for the footprint of uncertainty fou is presented and based on the new definitions the relation between fou and the original definition of t2 fs is discussed finally the partition method of fou is provided to represent the primary membership grade the fou and the interval type 2 fuzzy sets it2 fs when the upper and lower membership functions umf lmf of fou are given

numerical methods for treating problems of viscoelastic isotropic solid deformation mathematical models for treating problems of linear viscoelasticity involving hereditary constitutive relations for compressible solids are discussed and their discretization using finite element methods in space together with quadrature rules in time to treat the hereditary integrals is described the range of applicability of this type of formulation is reviewed in the context of geometric and constitutive linearity nonlinearity and the limitations imposed by the availability of physical data are discussed one of the above models is a volterra integral equation of the second kind in this when the kernel is separable an established technique due to goursat 1933 can be exploited to reformulate the problem as a system of ordinary differential equations this approach will be described for the special case of a linear viscoelastic isotropic homogeneous synchronous constant poisson s ratio solid this method results in a complete decoupling of the space and time dependence in this case the problem can be solved at each time level by solving first a problem of linear elasticity and then a system of ordinary differential equations for each point in the spatial mesh at which the viscoelastic displacements are required the advantages disadvantages and limitations offered by this and various other schemes for solving problems of viscoelasticity as outlined below are discussed

numerical solution of parabolic integro differential equations by the discontinuous galerkin method the numerical solution of a parabolic equation with memory is considered the equation is first discretized in time by means of the discontinuous galerkin method with piecewise constant or piecewise linear approximating functions the analysis presented allows variable time steps which as will be shown call then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data the combination with finite element discretizat in space is also studied

on the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel ii nonsmooth initial data abstract backward euler methods are considered for a parabolic integrodifferential equation with a memory term containing a weakly singular kernel the integral term is treated by means of a convolution quadrature suggested by lubich some results from lubich s discretized fractional calculus play a crucial role in error analyses the stability and convergence properties of the time discretizations are derived and are applied to the semidiscrete equations built by the galerkin finite element methods in the space variables

an enhanced type reduction algorithm for type 2 fuzzy sets karnik and mendel proposed an algorithm to compute the centroid of an interval type 2 fuzzy set efficiently based on this algorithm liu developed a centroid type reduction strategy to carry out type reduction for type 2 fuzzy sets a type 2 fuzzy set is decomposed into a collection of interval type 2 fuzzy sets by cuts then the karnik mendel algorithm is called for each interval type 2 fuzzy set iteratively however the initialization of the switch point in each application of the karnik mendel algorithm is not a good one in this paper we present an improvement to liu s algorithm we employ the previously obtained result to construct the starting values in the current application of the karnik mendel algorithm convergence in each iteration except the first one can then speed up and type reduction for type 2 fuzzy sets can be carried out faster the efficiency of the improved algorithm is analyzed mathematically and demonstrated by experimental results

effect of infection age on an sir epidemic model with demography on complex networks abstract for the long term population behavior demography is a very important factor impacting the disease spread infection age also helps us better understand the process of the disease transmission in this paper we incorporate these two factors in an sir epidemic model on complex networks through mathematical analysis the basic reproduction number r 0 is shown to be a sharp threshold to determine whether or not the disease spreads precisely if r 0 is less than 1 then the disease free equilibrium is globally asymptotically stable while if r 0 is larger than 1 then the endemic equilibrium is globally asymptotically stable some simulations are carried out to illustrate the theoretical results

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

adaptive discretization of an integro differential equation with a weakly singular convolution kernel an integro differential equation involving a convolution integral with a weakly singular kernel is considered the kernel can be that of a fractional integral the integro differential equation is discretized using the discontinuous galerkin method with piecewise constant basis functions sparse quadrature is introduced for the convolution term to overcome the problem with the growing amount of data that has to be stored and used in each time step a priori and a posteriori error estimates are proved an adaptive strategy based on the a posteriori error estimate is developed finally the precision and effectiveness of the algorithm are demonstrated in the case that the convolution is a fractional integral this is done by comparing the numerical solutions with analytical solutions

application of fuzzy sets of type 2 to the solution of fuzzy equation systems abstract the present paper continues the authors investigation on fuzzy equation systems with tolerances we consider the situation that the outputs of an object are modelled by fuzzy sets of type 2 for special membership functions this problem can be attributed to a problem with tolerances moreover this concept enables us to define solutions for fuzzy outputs of type 1 when classical solution concepts may fail

designing of a type 2 fuzzy logic filter for improving edge preserving restoration of interlaced to progressive conversion this paper focuses on recently advanced fuzzy models and the application of type 2 fuzzy sets in video deinterlacing the final goal of the proposed deinterlacing algorithm is to exactly determine an unknown pixel value while preserving the edges and details of the image to begin we will discuss some artefacts of spatial temporal and spatio temporal domain deinterlacing methods in order to address the aforementioned issues we adopted type 2 fuzzy sets concepts to design a weight evaluating approach in the proposed method the upper and lower fuzzy membership functions of the type 2 fuzzy logic filters are derived from the type 1 or primary fuzzy membership function the weights from upper and lower membership functions are considered to be multiplied with the candidate deinterlaced pixels experimental results proved that the performance of the proposed method was superior both objectively and subjectively to other different conventional deinterlacing methods moreover the proposed method preserved the smoothness of the original image edges and produced a high quality progressive image

impulse noise removal from digital images by a detail preserving filter based on type 2 fuzzy logic a novel image filter based on type 2 fuzzy logic techniques is proposed for detail preserving restoration of digital images corrupted by impulse noise the performance of the proposed filter is evaluated for different test images corrupted at various noise densities and also compared with representative conventional as well as state of the art impulse noise filters from the literature experimental results show that the proposed filter exhibits superior performance over the competing operators and is capable of efficiently suppressing the noise in the image while at the same time effectively preserving thin lines edges texture and other useful information within the image

dynamics of an saits alcoholism model on unweighted and weighted networks abstract a novel saits alcoholism model on networks is introduced in which alcoholics are divided into light problem alcoholics and heavy problem alcoholics susceptible individuals can enter into the compartment of heavy problem alcoholics directly by contacting with light problem alcoholics or heavy problem alcoholics and the heavy problem alcoholics who receive treatment can relapse into the compartment of heavy problem alcoholics are also considered first the dynamics of our model on unweighted networks including the basic reproduction number existence and stability of equilibria are studied second the models with fixed weighted and adaptive weighted networks are introduced and investigated at last some simulations are presented to illustrate and extend our results our results show that it is very important to treat alcoholics to quit the drinking

on clarifying some definitions and notations used for type 2 fuzzy sets as well as some recommended changes this paper is about some important changes in type 2 fuzzy set t2 fs definitions and notations that have occurred during the past 16 years it summarizes the evolution of how the primary membership jx has been used in both the mathematical descriptions of a t2 fs and its footprint of uncertainty fou discusses notational problems associated with the secondary membership function explains why and when one should distinguish between the fou and the domain of uncertainty dou explains why no errors have been introduced into t2 fs computations because of notation and it provides recommendations notational changes that can be used by all authors

neuro fuzzy clustering of radiographic tibia image data using type 2 fuzzy sets abstract this paper presents the results of using type 2 fuzzy sets to assist in the pre processing of data for use with neuro fuzzy clustering for classification of sports injuries in the lower leg this research is concerned with the analysis of bone scans from stress related injuries to the tibia of particular interest is whether neural network based clustering techniques can help the consultant in classifying the images the work was motivated by the situation where there is a relatively small amount of relevant data and difficulties are faced by consultants in classifying the various types of injuries for this particular problem the consultant s interpretation of the image lends itself to representation using type 2 fuzzy sets this research sets out to address whether with fuzzy neuro clustering techniques some insights may be provided to the consultant that they can use along with their experience and knowledge the results of this approach indicate that the use of neural clustering using a type 2 representation can improve the classification of shin images

an a priori error estimate for a temporally discontinuous galerkin space time finite element method for linear elasto and visco dynamics the work of shaw was supported in part by the engineering and physical sciences research council ep h011072 1 this support is gratefully acknowledged

stability of an sairs alcoholism model on scale free networks abstract a new sairs alcoholism model with birth and death on complex heterogeneous networks is proposed the total population of our model is partitioned into four compartments the susceptible individual the light problem alcoholic the heavy problem alcoholic and the recovered individual the spread of alcoholism threshold r 0 is calculated by the next generation matrix method when r 0 1 the alcohol free equilibrium is globally asymptotically stable then the alcoholics will disappear when r 0 1 the alcoholism equilibrium is global attractivity then the number of alcoholics will remain stable and alcoholism will become endemic furthermore the modified sairs alcoholism model on weighted contact network is introduced dynamical behavior of the modified model is also studied numerical simulations are also presented to verify and extend theoretical results our results show that it is very important to treat alcoholics to control the spread of the alcoholism

discontinuous galerkin method for an integro differential equation modeling dynamic fractional order viscoelasticity an integro differential equation modeling dynamic fractional order viscoelasticity with a mittag leffler type convolution kernel is considered a discontinuous galerkin method based on piecewise constant polynomials is formulated for temporal semidiscretization of the problem stability estimates of the discrete problem are proved that are used to prove optimal order a priori error estimates the theory is illustrated by a numerical example

on type 2 fuzzy relations and interval valued type 2 fuzzy sets this paper introduces new operations on the algebra of fuzzy truth values extended supremum and extended infimum which are generalizations of the extended operations of maximum and minimum between fuzzy truth values for type 2 fuzzy sets respectively using these new operations the properties of type 2 fuzzy relations are discussed especially the compositions of type 2 fuzzy relations on this basis this paper introduces interval valued type 2 fuzzy sets and interval valued type 2 fuzzy relations and discusses their properties

epidemic dynamics in finite size scale free networks many real networks present a bounded scale free behavior with a connectivity cutoff due to physical constraints or a finite network size we study epidemic dynamics in bounded scale free networks with soft and hard connectivity cutoffs the finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes the induced epidemic threshold is very small even at a relatively small cutoff showing that the neglection of connectivity fluctuations in bounded scale free networks leads to a strong overestimation of the epidemic threshold we provide the expression for the infection prevalence and discuss its finite size corrections the present paper shows that the highly heterogeneous nature of scale free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes

dynamics of a competing two strain sis epidemic model on complex networks with a saturating incidence rate this paper studies a two strain sis epidemic model with a competing mechanism and a saturating incidence rate on complex networks this type of incidence rate can be used to reflect the crowding effect of the infective individuals we first obtain the associated reproduction numbers for each of the two strains which determine the existence of the boundary equilibria the stability of the disease free and boundary equilibria are further examined besides this we also show that the two competing strains can coexist under certain conditions interestingly the saturating incidence rate can have specific effects on not only the stability of the boundary equilibria but also the existence of the coexistence equilibrium numerical simulations are presented to support the theoretical results

finite element approximation of diffusion equations with convolution terms approximation of solutions to diffusion equations with memory represented by convolution integral terms is considered such problems arise from modeling of flows in fissured media convergence of the method is proved and results of numerical experiments confirming the theoretical results are presented the advantages of implementation of the algorithm in a multiprocessing environment are discussed

an alternating direction implicit galerkin finite element method for the distributed order time fractional mobile immobile equation in two dimensions abstract in this paper we shall present the alternating direction implicit adi galerkin finite element method fem for solving the distributed order time fractional mobile immobile equation in two dimensions in the time direction the backward euler method is used to deal with the temporal first order derivative and the weighted and shifted grunwald formula is employed to discretize the distributed order time fractional derivative galerkin fem is used for discretization of the spatial direction and then an adi galerkin finite element scheme is constructed the stability and l 2 norm convergence are proved several numerical experiments are provided to verify our theoretical analysis

global stability of endemic equilibrium for a siqrs epidemic model on complex networks abstract we study the global stability of endemic equilibrium of a siqrs epidemic model on complex networks this model was proposed by li et al 2014 the local asymptotic stability of disease free equilibrium and the permanence of the disease were proved by them by use of a combination of lyapunov function method and a monotone iterative technique we prove that the endemic equilibrium is globally asymptotically stable numerical simulations indicate that quarantine strategy is an effective measure in preventing and controlling epidemic spreading

nonstationary fuzzy sets in this paper the notion termed a ldquononstationary fuzzy setrdquo is introduced and the concept of a perturbation function that is used for generating nonstationary fuzzy sets is presented definitions of the basic set operators the union the intersection and the complement for nonstationary fuzzy sets are given together with proofs of selected properties of these operators two case studies were carried out in order to illustrate the use of nonstationary fuzzy sets in a nonstationary fuzzy inference and to provide an initial insight into the relationships between nonstationary and interval type 2 fuzzy sets

a triangular type 2 multi objective linear programming model and a solution strategy abstract we consider a multi objective linear programming model with type 2 fuzzy objectives the considered model has the flexibility for the user to specify the more general membership functions for objectives to reflect the inherent fuzziness while being simple and practical we develop two solution strategies with reasonable computing costs the additional cost as compared to the type 1 fuzzy model is indeed insignificant these two algorithms compute pareto optimal solutions of the type 2 problems one being based on a maxmin approach and the other on aggregating the objectives finally applying the proposed algorithms we work out two illustrative examples

analysis of data generated from multidimensional type 1 and type 2 fuzzy membership functions due to the numerous applications that utilize different types of fuzzy membership functions mfs it may sometimes be difficult to choose an appropriate mf for a particular application in this paper we establish preliminary guidelines to direct this selection by proposing a three stage method in the forward stage different mfs such as crisp mfs type 1 t1 fuzzy mfs and type 2 t2 fuzzy mfs are generated from multidimensional data sets next in the reverse stage data is generated back from these mfs by considering different bin sizes in doing so various data sets may be generated for different applications which require fuzzy data finally for the similarity analysis stage we propose an iterative algorithm that makes use of the results of wilcoxon signed rank wsr and wilcoxon rank sum wrs tests to compare the original data and the generated data from the results of these tests recommendations concerning the suitability of mfs for a specific application may be suggested by observing the accuracy of representation and the requirements of the application with this analysis the objective is to gain insight on when t2 fuzzy sets may be considered to outperform t1 fuzzy sets and vice versa several examples are provided using synthetic and real data to validate the iterative algorithm for data sets in various dimensions

a survey of recent advances in the numerical treatment of volterra integral and integro differential equations abstract the present survey paper samples recent advances in the numerical analysis of volterra integral equations of the first and second kind and of integro differential equations including equations with weakly singular kernels except for some important earlier references the discussion focuses on the development which has taken place during the last dozen years a fairly extensive bibliography selected to be representative rather than comprehensive complements the paper

stability analysis of an sis epidemic model with feedback mechanism on networks abstract in this paper an epidemic model with feedback mechanism on networks is investigated we obtain the basic reproductive number r 0 and analyze the stability behaviors of disease free equilibrium e 0 and endemic equilibrium e when r 0 1 the disease free equilibrium is globally asymptotically stable and when r 0 1 the endemic equilibrium is asymptotically stable although the feedback mechanism cannot change the basic reproductive number r 0 as we prove it should be indicated that it can weaken the spreading of diseases and reduce the endemic level finally the results of the stability and the effectiveness of the feedback mechanism are illustrated by some numerical simulations

discontinuous galerkin method with a posteriori l_p 0 t_i error estimate for second kind volterra problems we consider a discontinuous galerkin finite element method applied in time to a model volterra equation of the second kind a residual based computable l p 0 t i galerkin error estimate is derived for 1 le p le infty this estimate does not explicitly contain the time step and therefore the time step control must be based on a heuristic criterion the estimate can then be used to demonstrate the integrity or otherwise of the finite element solution after performing some numerical experiments we conclude that this approach is at least competetive with classical discretizations since it is computationally simple to implement but has the added advantage of reliable error feedback

generalized and extended fuzzy sets with applications abstract this paper introduces generalized fuzzy sets extended fuzzy sets and generalized extended fuzzy sets and shows how these fuzzy sets may arise naturally in some applications the applications presented are chosen from the areas of decision theory hierarchical analysis and expert systems zadeh s method of reducing a level 2 fuzzy set to a regular fuzzy set is generalized to reduce some of these new fuzzy sets to simpler fuzzy sets what is needed then for applications is an algebra of irreducible generalized extended fuzzy sets

a comparison of fuzzy strategies for corporate acquisition analysis analysing all prospective companies for acquisition in large market sectors is an onerous task a strategy that results in a shortlist of companies that meet certain basic criteria is required the short listed companies can then be further investigated in more detail later if desired fuzzy logic systems flss imbued with the expertise of a focal organisation s financial experts can be of great assistance in this process in this paper an investigation into the suitability of flss for acquisition analysis is presented the nuances of training and tuning are discussed in particular the difficulty of obtaining suitable amounts of expert data is a recurring theme throughout the paper a strategy for circumventing this issue is presented that relies on the design of a conventional fuzzy logic rule base with the assistance of a financial expert with the rule base created various scenarios such as the simulation of multiple experts and the creation of expert training data are investigated in particular two scenarios for the creation of simulated expert data are presented in the first the responses from the different experts are averaged and in the second scenario the responses from all the different experts are preserved in the training data this paper builds on previous work with scalable membership functions however the use of fuzzy c means clustering and backpropagation training are new developments additionally a type 2 fls is developed and its potential advantages are discussed for this application the type 2 system facilitates the inclusion of the opinions of multiple experts both the type 1 and type 2 flss were trained using the backpropagation algorithm with early stopping and verified with five fold cross validation multiple runs of the five fold method were conducted with different random orderings of the data for this particular application the type 1 system performed comparably with the type 2 system despite the considerable amount of variation in the expert training data the training results have proven the methods to be capable of efficient tuning of parameters and of reliable ranking of prospective companies

error estimates for semidiscrete finite element methods for parabolic integro differential equations application des methodes d elements finis aux equations integro differentielles de type parabolique avec un noyau integral forme par un operateur aux derivees partielles d ordre 2

applications and numerical analysis of partial differential volterra equations a brief survey this article contains a concise survey of the numerical analysis of volterra equations and leads up to some recent results on a posteriori error estimation for finite element approximations

an analysis of transmission dynamics of drug resistant disease on scale free networks in this paper we present an sir drug resistant model on scale free networks the model has a disease free equilibrium which is globally asymptotically stable when a threshold quantity is less than one the model has a wild strain equilibrium and a resistant strain equilibrium which are asymptotically stable when their respective reproduction number is great than one when treatment leads to resistance development the model can have a unique coexistence equilibrium and we also prove the persistence of infection the effects of two immunization schemes including proportional immunization scheme and targeted immunization scheme are studied and compared we find that targeted strategy compare favorably to a proportional immunization has prominent effect to control the disease spread on scale free networks

design of interval type 2 fuzzy sliding mode controller in this paper an interval type 2 fuzzy sliding mode controller it2fsmc is proposed for linear and nonlinear systems the proposed it2fsmc is a combination of the interval type 2 fuzzy logic control it2flc and the sliding mode control smc which inherits the benefits of these two methods the objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed loop system the lyapunov stability method is adopted to verify the stability of the interval type 2 fuzzy sliding mode controller system the design procedure of the it2fsmc is explored in detail a typical second order linear interval system with 50 parameter variations an inverted pendulum with variation of pole characteristics and a duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method the simulation results show that the it2fsmc achieves the best tracking performance in comparison with the type 1 fuzzy logic controller t1flc the it2flc and the type 1 fuzzy sliding mode controller t1fsmc

the finite element numerical analysis for a class nonlinear evolution equations a complete stability and convergence analysis is given for two level scheme for the approximate solution of a class generalized nerve conduction equation defining a kind of truncation error and using a kind of technique optimal order estimates in l 2 is constructively obtained

time discretization of fractional subdiffusion equations via fractional resolvent operators abstract in this work we study time discretization of subdiffusion equations that is fractional differential equations of order 0 1 assuming that a is the generator of a fractional resolvent family s t t 0 which allows to write the solution to the subdiffusion equation t u t a u t f t as a variation of constants formula we find an interesting connection between s t t 0 and a discrete resolvent family s n n n and then by using the properties of s t t 0 we study the existence of solutions to the discrete subdiffusion equation c u n a u n f n n n where based on the backward euler method for a 0 given c u n is an approximation of t u t at time t n n we study simultaneously the fractional derivative in the caputo and riemann liouville sense we also provide error estimates and some experiments to illustrate the results

finite element approximation of a parabolic integro differential equation with a weakly singular kernel we give error estimates for the numerical solution by means of the galerkin finite element method of an integro differential equation of parabolic type with a memory term containing a weakly singular kernel optimal order estimates are shown for spatially semidiscrete and completely discrete methods special attention is paid to the regularity of the exact solution

global stability analysis of an sir epidemic model with demographics and time delay on networks abstract in this paper a susceptible infected recovery sir epidemic model is governed with demographics and time delay on networks firstly the basic reproduction number r 0 is derived dependent on birth rate death rate recovery rate and transmission rate the disease free equilibrium of the model is stable when r 0 1 and unstable when r 0 1 secondly based on a jacobian matrix calculated along with the disease free equilibrium we find that the system does not occur hopf branch under the disease free equilibrium thirdly the global asymptotic stability of a disease free equilibrium and a unique endemic equilibrium are proved by structuring two lyapunov functions finally numerical simulations are performed to illustrate the analysis results

numerical solving nonlinear integro parabolic equations by the monotone weighted average method the paper deals with numerical solving nonlinear integro parabolic problems of volterra type based on the weighted average method a monotone iterative method is presented construction of initial upper and lower solutions is given existence and uniqueness of a solution to the nonlinear difference scheme are established an analysis of convergence rates of the monotone iterative method is given numerical experiments are presented

a meshless method on non fickian flows with mixing length growth in porous media based on radial basis functions a comparative study the present study aims to introduce a solution for parabolic integro differential equations arising in heat conduction in materials with memory which naturally occur in many applications two radial basis functions rbfs collocation schemes are employed for solving this equation the first method tested is an unsymmetric method and the second one which appears to be more efficient is a symmetric one the convergence of these two schemes is accelerated as we use the cartesian nodes as the center nodes

mixed si r epidemic dynamics in random graphs with general degree distributions analytical description of disease propagation on random networks has become one of the most productive fields in recent years yet more complex contact patterns and dynamics have been resorted to numerical study in this paper an epidemic model is defined in which each individual once infected has chances to recover from infection at certain rate the chance is represented by a parameter email protected 0 1 this model can be viewed as an interpolation between classical si model q 0 and sir model q 1 we develop a low dimensional system of non linear ordinary differential equations to model the mixed susceptible infected recovered si r epidemics on random network with general degree distributions both the final size of epidemics and the time dependent behaviors are derived within this simple framework in addition we present the exact transmissibility and the epidemic threshold for this model

finite difference approximation of a nonlinear integro differential system finite difference approximation of the nonlinear integro differential system associated with the penetration of a magnetic field into a substance is studied the convergence of the finite difference scheme is proved the rate of convergence of the discrete scheme is given the decay of the numerical solution is compared with the analytical results proven earlier

fuzzy normal forms abstract linguistic expressions of a natural language are transformed at least three times before they are expressed in computational formulas between the linguistic and the computational expressions there are the meta linguistic and propositional expressions under various interpretations and assumptions fuzzy normal forms are canonical expressions derived at the propositional level with particular assumptions the fuzzy normal forms can be generated from fuzzy truth tables with a normal form derivation algorithm and an orthodox interpretation of conjunction disjunction and complementation operations it is shown that these fuzzy normal forms display a unique structure for certain general classes of crisp operators over fuzzy sets the fuzzy normal forms generated by crisp operators over fuzzy sets that correspond to max min standard complement de morgan triple are shown to be equivalent to the classical normal forms of two valued logic i e disjunctive and conjunctive normal forms known as dnf and cnf with a particular property i e the crisp containment fdnf 3 fcnf 3 whereas the fuzzy normal forms generated by crisp operators that correspond to non idempotent t norms t conorms and standard complement de morgan triples do not have in general a similar crisp containment property i e fdnf 2 fcnf 2 neither do the fuzzy normal forms generated by crisp operators over fuzzy sets that correspond to non idempotent and non commutative and non associative conjunction disjunction and standard complement de morgan triples have a crisp containment property i e fdnf 1 fcnf 1 however they still provide bounds on the combination of concepts

dynamics of a network based sis epidemic model with nonmonotone incidence rate abstract this paper studies the dynamics of a network based sis epidemic model with nonmonotone incidence rate this type of nonlinear incidence can be used to describe the psychological effect of certain diseases spread in a contact network at high infective levels we first find a threshold value for the transmission rate this value completely determines the dynamics of the model and interestingly the threshold is not dependent on the functional form of the nonlinear incidence rate furthermore if the transmission rate is less than or equal to the threshold value the disease will die out otherwise it will be permanent numerical experiments are given to illustrate the theoretical results we also consider the effect of the nonlinear incidence on the epidemic dynamics

long time numerical solution of a parabolic equation with memory long time stability and convergence properties of two time discreti zation methods for an integro differential equation of parabolic type are studied the methods are based on the standard backward euler and second order back ward differencing methods the memory term is approximated by a quadrature rule with emphasis on such rules with reduced computational memory require ments discretization of the spatial partial differential operators by the finite element method is also considered

type 2 fuzzy hidden markov models and their application to speech recognition this paper presents an extension of hidden markov models hmms based on the type 2 t2 fuzzy set fs referred to as type 2 fuzzy hmms t2 fhmms membership functions mfs of t2 fss are three dimensional and this new third dimension offers additional degrees of freedom to evaluate the hmms fuzziness therefore t2 fhmms are able to handle both random and fuzzy uncertainties existing universally in the sequential data we derive the t2 fuzzy forward backward algorithm and viterbi algorithm using t2 fs operations in order to investigate the effectiveness of t2 fhmms we apply them to phoneme classification and recognition on the timit speech database experimental results show that t2 fhmms can effectively handle noise and dialect uncertainties in speech signals besides a better classification performance than the classical hmms

behavior of susceptible infected susceptible epidemics on heterogeneous networks with saturation we investigate saturation effects in susceptible infected susceptible models of the spread of epidemics in heterogeneous populations the structure of interactions in the population is represented by networks with connectivity distribution p k including scale free sf networks with power law distributions p k approximately k gamma considering cases where the transmission of infection between nodes depends on their connectivity we introduce a saturation function c k which reduces the infection transmission rate lambda across an edge going from a node with high connectivity k a mean field approximation with the neglect of degree degree correlation then leads to a finite threshold lambda c 0 for sf networks with 2 gamma 3 we also find in this approximation the fraction of infected individuals among those with degree k for lambda close to lambda c we investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean field theory with and without neglect of degree degree correlations

fuzzy artmap a neural network architecture for incremental supervised learning of analog multidimensional maps a neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors which may represent fuzzy or crisp sets of features the architecture called fuzzy artmap achieves a synthesis of fuzzy logic and adaptive resonance theory art neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and art category choice resonance and learning four classes of simulation illustrated fuzzy artmap performance in relation to benchmark backpropagation and generic algorithm systems these simulations include finding points inside versus outside a circle learning to tell two spirals apart incremental approximation of a piecewise continuous function and a letter recognition database the fuzzy artmap system is also compared with salzberg s nge systems and with simpson s fmmc system

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

an hp version discontinuous galerkin method for integro differential equations of parabolic type we study the numerical solution of a class of parabolic integro differential equations with weakly singular kernels we use an hp version discontinuous galerkin dg method for the discretization in time we derive optimal hp version error estimates and show that exponential rates of convergence can be achieved for solutions with singular temporal behavior near t 0 caused by the weakly singular kernel moreover we prove that by using nonuniformly refined time steps optimal algebraic convergence rates can be achieved for the h version dg method we then combine the dg time stepping method with a standard finite element discretization in space and present an optimal error analysis of the resulting fully discrete scheme our theoretical results are numerically validated in a series of test problems

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

finite element methods of the two nonlinear integro differential equations abstract transformation of dependent variables such as the kirchhoff transformation is a classical tool for solving nonlinear partial differential equations in larsson et al this approach was used in connection with the finite element method zlamal used it in galerkin approximation in space the euler method in time and applied it to the solution of nonlinear heat equations here we give justification of the methods for the two nonlinear integro heat equations in the case that the discretization is carried through by piecewise linear polynomials in space and by the implicit euler method in time with quadrature rules which require the storage of relatively few values of the solution the estimate of the discretization error in the maximum norm is introduced the results depend on superconvergence in the gradient for a related elliptic problem which is shown to hold only for very special meshes

the analysis of an epidemic model with time delay on scale free networks abstract a new epidemic s i s model with time delay on scale free networks is presented we give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive number is less than unity and the disease is uniformly persistent when the basic reproductive number is more than unity the effects of various immunization schemes are studied numerical simulations are given to demonstrate the main results