percolation processes in monomer polyatomic mixtures in this paper the percolation of mixtures of monomers and polyatomic species kk mers on a square lattice is studied by means of a finite size scaling analysis the critical exponents and the scaling collapsing of the fraction of percolating lattices are found a phase diagram separating a percolating from a non percolating region is determined the main features of the phase diagram are discussed in order to predict its evolution for larger kk mer sizes

brief paper design of highly synchronizable and robust networks in this paper the design of highly synchronizable sparse and robust dynamical networks is addressed better synchronizability means faster synchronization of the oscillators sparsity means a low ratio of links per nodes and robustness refers to the resilience of a network to the random failures or intentional removal of some of the nodes links golden spectral dynamical networks graphs are those for which the spectral spread the difference between the largest and smallest eigenvalues of the adjacency matrix is equal to the spectral gap the difference between the two largest eigenvalues of the adjacency matrix multiplied by the square of the golden ratio these networks display the property of small worldness are very homogeneous and have large isoperimetric expansion constant together with a very high synchronizability and robustness to failures of individual oscillators in particular the regular bipartite dynamical networks reported here by the first time have the best possible expansion and consequently are the most robust ones against node link failures or intentional attacks

finite time synchronization of discontinuous neural networks with delays and mismatched parameters this paper investigates the problem of finite time drive response synchronization for a class of neural networks with discontinuous activations time varying discrete and infinite time distributed delays and mismatched parameters in order to cope with the difficulties induced by discontinuous activations time delays as well as mismatched parameters simultaneously new 1 norm based analytical techniques are developed both state feedback and adaptive controllers with and without the sign function are designed based on differential inclusion theory and lyapunov functional method several sufficient conditions on the finite time synchronization are obtained our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon numerical examples are given to show the effectiveness of the theoretical analysis

synchronization of ts fuzzy complex dynamical networks with time varying impulsive delays and stochastic effects in this paper global exponential synchronization of takagi sugeno ts fuzzy complex dynamical networks with multiple time varying delays and stochastic perturbations is studied via delayed impulsive distributed control both impulsive and continuous parts of the fuzzy model have different multiple time varying delays which make the considered model general and practical a novel lemma on exponential stability of impulsive delayed differential equations was established in which the impulsive functions exhibit multiple time varying delays by utilizing the proposed lemma lyapunov functions the stochastic analysis techniques and the kronecker product general criteria ensuring global exponential synchronization in mean square of the addressed ts fuzzy complex networks are obtained moreover the theory of function minimum value is utilized to reduce the conservativeness of the obtained synchronization criteria which also makes them simple and easy to be verified in practical applications results of this paper improve and extend some existing ones numerical simulations including small world network coupled with time delayed lorenz system are given to show the effectiveness of the theoretical results

divergence runge phenomenon for least squares polynomial approximation on an equispaced grid and mock chebyshev subset interpolation runge showed more than a century ago that polynomial interpolation of a function f x using points evenly spaced on email protected 1 1 could diverge on parts of this interval even if f x was analytic everywhere on the interval least squares fitting of a polynomial of degree n to an evenly spaced grid with p points should improve accuracy if email protected n we show through numerical experiments that such an overdetermined fit reduces but does not eliminate the runge phenomenon more precisely define b n 1 p the least squares fit will fail to converge everywhere on 1 1 as n for fixed b if f x has a singularity inside a curve d b in the complex plane the width of the region enclosed by the convergence boundary d shrinks as b diminishes i e more points for a fixed polynomial degree but shrinks to the interval 1 1 only when b 0 we also show that the runge phenomenon can be completely defeated by interpolation on a mock chebyshev grid a subset of n 1 points from an equispaced grid with o n 2 points chosen to mimic the non uniform n 1 point chebyshev lobatto grid

on the lebesgue constant of barycentric rational interpolation at equidistant nodes recent results reveal that the family of barycentric rational interpolants introduced by floater and hormann is very well suited for the approximation of functions as well as their derivatives integrals and primitives especially in the case of equidistant interpolation nodes these infinitely smooth interpolants offer a much better choice than their polynomial analogue a natural and important question concerns the condition of this rational approximation method in this paper we extend a recent study of the lebesgue function and constant associated with berrut s rational interpolant at equidistant nodes to the family of floater hormann interpolants which includes the former as a special case

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

percolation through self affine surfaces we study the percolation transition in a long range correlated system a self affine surface for all relevant physical cases i e positive roughness exponents it is found that the onset of percolation is governed by the largest wavelength of the height distribution and thus self averaging breaks down self averaging is recovered for negative roughness exponents i e power law decay of the height pair correlation function and in this case the critical exponents that characterize the transition are explicitly dependent on the roughness exponent above a threshold value below this threshold the spatial correlations are no longer relevant the problem is analytically investigated for a hierarchical network and by means of numerical simulations in two dimensions finally we discuss the application of those properties to mercury porosimetry in cracks

observer based finite time control of time delayed jump systems abstract this paper provides the observer based finite time control problem of time delayed markov jump systems that possess randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process the observer based finite time h controller via state feedback is proposed to guarantee the stochastic finite time boundedness and stochastic finite time stabilization of the resulting closed loop system for all admissible disturbances and unknown time delays based on stochastic finite time stability analysis sufficient conditions that ensure stochastic robust control performance of time delay jump systems are derived the control criterion is formulated in the form of linear matrix inequalities and the designed finite time stabilization controller is described as an optimization one the presented results are extended to time varying delayed mjss simulation results illustrate the effectiveness of the developed approaches

sampled data synchronization of markovian coupled neural networks with mode delays based on mode dependent lkf this paper investigates sampled data synchronization problem of markovian coupled neural networks with mode dependent interval time varying delays and aperiodic sampling intervals based on an enhanced input delay approach a mode dependent augmented lyapunov krasovskii functional lkf is utilized which makes the lkf matrices mode dependent as much as possible by applying an extended jensen s integral inequality and wirtinger s inequality new delay dependent synchronization criteria are obtained which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay in addition the desired stochastic sampled data controllers can be obtained by solving a set of linear matrix inequalities finally two examples are provided to demonstrate the feasibility of the proposed method

second order global consensus in multiagent networks with random directional link failure in this paper we consider the second order globally nonlinear consensus in a multiagent network with general directed topology and random interconnection failure by characterizing the behavior of stochastic dynamical system with the corresponding time averaged system a criterion for the second order consensus is derived by constructing a lyapunov function for the time averaged network by associating the solution of random switching nonlinear system with the constructed lyapunov function a sufficient condition for second order globally nonlinear consensus in a multiagent network with random directed interconnections is also established it is required that the second order consensus can be achieved in the time averaged network and the lyapunov function decreases along the solution of the random switching nonlinear system at an infinite subsequence of the switching moments a numerical example is presented to justify the correctness of the theoretical results

synchronization in an array of linearly stochastically coupled networks with time delays abstract in this paper the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays the stochastic coupling term which can reflect a more realistic dynamical behavior of coupled systems in practice is introduced to model a coupled system and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly based on a simple adaptive feedback control scheme and some stochastic analysis techniques several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays finally an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results

on the constrained mock chebyshev least squares the algebraic polynomial interpolation on n 1 uniformly distributed nodes can be affected by the runge phenomenon also when the function f to be interpolated is analytic among all techniques that have been proposed to defeat this phenomenon there is the mock chebyshev interpolation which produces a polynomial p that interpolates f on a subset of m 1 of the given nodes whose elements mimic as well as possible the chebyshev lobatto points of order m in this work we use the simultaneous approximation theory to produce a polynomial p of degree r greater than m which still interpolates f on the m 1 mock chebyshev nodes minimizing at the same time the approximation error in a least squares sense on the other points of the sampling grid we give indications on how to select the degree r in order to obtain polynomial approximant good in the uniform norm furthermore we provide a sufficient condition under which the accuracy of the mock chebyshev interpolation in the uniform norm is improved numerical results are provided

the aspherity of random walks the asphericity a of a random walk is defined and calculated for non self avoiding walks the definition of a generalises to self avoiding walks percolating clusters and other fractal objects and thus provides a generalised quantitative measure of the departure from spherical symmetry of the gross shape of these objects

study of the shape of random walks a comprehensive study of the shape of discrete random walks considering the general case of arbitrary length and any space dimension is presented the probability distributions for several magnitudes such as the principal inertia moments the asphericity and the angle between the principal axis of inertia and the end to end vector are evaluated numerically in most cases and especially in low dimensional spaces these probability distributions spread widely and possess a non zero skewness this implies that any description of the shapes of random walks which is based only on mean values of related magnitudes is incomplete this situation does nor vary when random walks of large lengths are considered since the relative fluctuations ratio between the standard deviation and the mean value do not go to zero in that limit on the other hand when the space dimension grows the distributions become more peaked reaching the expected asymptotic limit for infinite dimension the present study also indicates that the probability distributions for the principal inertia moments have approximately the form of chi squared distributions analysing the probability distribution for the asphericity it is shown that the distributions for the different moments are not completely independent

adaptive polynomial interpolation on evenly spaced meshes the problem of oscillatory polynomial interpolants arising from equally spaced mesh points is considered it is shown that by making use of adaptive approaches the oscillations may be contained and the resulting polynomials are data bounded and monotone on each interval this is achieved at the cost of using a different polynomial on each subinterval computational results for a number of challenging functions including a number of problems similar to runge s function with as many as 511 points per interval are shown

a new stable basis for radial basis function interpolation it is well known that radial basis function interpolants suffer from bad conditioning if the basis of translates is used in the recent work by pazouki and schaback 2011 5 the authors gave a quite general way to build stable and orthonormal bases for the native space n f w associated to a kernel f on a domain w r s the method is simply based on the factorization of the corresponding kernel matrix starting from that setting we describe a particular basis which turns out to be orthonormal in n f w and in 2 w x where x is a set of data sites of the domain w the basis arises from a weighted singular value decomposition of the kernel matrix this basis is also related to a discretization of the compact operator t f n f w n f w t f f x w f x y f y dy x w and provides a connection with the continuous basis that arises from an eigendecomposition of t f finally using the eigenvalues of this operator we provide convergence estimates and stability bounds for interpolation and discrete least squares approximation

conductivity exponent and backbone dimension in 2 d percolation abstract we present high statistics simulations for 2 d percolation clusters in the bus bar geometry at the critical point for site and for bond percolation we measured their backbone sizes and electrical conductivities for all sets of measurements we find large corrections to scaling most of which do not seem to be described by single powers using single power terms for the corrections to scaling of the backbone masses we would obtain fractal dimensions which are different for site and bond percolation while the correct result is d b 1 6432 0 0008 for both for the conductivity the corrections to scaling are strongly non monotonic for bond percolation the exponent t t is measured as 0 9826 0 0008 in disagreement with the alexander orbach and other conjectures

cluster synchronization stability for stochastic complex dynamical networks with probabilistic interval time varying delays the paper investigates the cluster synchronization stability problem for a class of complex dynamical networks with stochastic nonlinearities and probabilistic interval time varying delays the stochastic nonlinearities are considered here to reflect more realistic dynamical behaviors of complex networks the delay in this paper is assumed to be random and its probability distribution is known a priori based on the stochastic analysis techniques and the properties of the kronecker product delay dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

the shapes of open and closed random walks a 1 d expansion a new technique for calculating the shapes of random walks is presented the method is used to derive an exact analytical expression for the asphericity of an unrestricted closed or ring walk embedded in d spatial dimensions a graphical procedure is developed to systematise a 1 d series expansion for the individual principal radii of gyration and their respective probability distribution functions p r2i 1 or i or d the average principal radii of gyration are calculated to o 1 d2 for both open and closed walks and selected terms in the 1 d expansion are summed to all orders in 1 d in the determination of p r2i this leads to an explicit analytical form for p r2i for open walks the distribution of the largest eigenvalue is compared with a distribution obtained from numerical simulations of walks in three dimensions the agreement between the two is extremely good other predictions for various parameters that characterise the average shape of open and closed walks in three dimensions are also found to agree remarkably well with the results of simulations the error being of the order of 5

two dimensional polymer networks near percolation we report an extensive finite size study of polymer networks near the percolation threshold using numerical techniques the polymers are modeled by random walks occupying the bonds of a two dimensional square lattice we measure the percolation threshold and critical exponents of the networks for various polymer lengths we find that the critical occupation probability is a decreasing function of the polymer length and the percolation of polymers with a fixed polymer length belongs to the same universality class as ordinary bond percolation by adding particles to the lattice cells we can study the diffusion process in polymer networks measuring the current near percolation we observe that its critical exponent is also independent of polymer length

universality and time scale invariance for the shape of planar levy processes for a broad class of planar markov processes viz l evy processes satisfying certain conditions valid e g in the case of brownian motion and l evy flights we establish an exact universal formula describing the shape of the convex hull of sample paths we show indeed that the average number of edges joining paths points separated by a time lapse ensuremath delta ensuremath tau ensuremath in left ensuremath delta ensuremath tau 1 ensuremath delta ensuremath tau 2 right is equal to 2 phantom rule 0 16em 0ex text ln left ensuremath delta ensuremath tau 2 ensuremath delta ensuremath tau 1 right regardless of the specific distribution of the process s increments and regardless of its total duration t the formula also exhibits invariance when the time scale is multiplied by any constant apart from its theoretical importance our result provides insights regarding the shape of two dimensional objects e g polymer chains modeled by the sample paths of stochastic processes generally more complex than brownian motion in particular for a total time or parameter duration t the average number of edges on the convex hull cut off to discard edges joining points separated by a time lapse shorter than some ensuremath delta ensuremath tau lt will be given by 2 phantom rule 0 16em 0ex text ln frac t ensuremath delta ensuremath tau thus it will only grow logarithmically rather than at some higher pace

critical exponents and universality for the isotropic nematic phase transition in a system of self assembled rigid rods on a lattice monte carlo simulations have been carried out for a system of monomers on square lattices that by decreasing temperature or increasing density polymerize reversibly into chains with two allowed directions and at the same time undergo a continuous isotropic nematic in transition the results show that the self assembly process affects the nature of the transition thus the calculation of the critical exponents and the behavior of binder cumulants indicate that the universality class of the in transition changes from two dimensional ising type for monodisperse rods without self assembly to q 1 potts type for self assembled rods

variance constrained state estimation for complex networks with randomly varying topologies this paper investigates the variance constrained h infty state estimation problem for a class of nonlinear time varying complex networks with randomly varying topologies stochastic inner coupling and measurement quantization a kronecker delta function and markovian jumping parameters are utilized to describe the random changes of network topologies a gaussian random variable is introduced to model the stochastic disturbances in the inner coupling of complex networks as a kind of incomplete measurements measurement quantization is taken into consideration so as to account for the signal distortion phenomenon in the transmission process stochastic nonlinearities with known statistical characteristics are utilized to describe the stochastic evolution of the complex networks we aim to design a finite horizon estimator such that in the simultaneous presence of quantized measurements and stochastic inner coupling the prescribed variance constraints on the estimation error and the desired h infty performance requirements are guaranteed over a finite horizon sufficient conditions are established by means of a series of recursive linear matrix inequalities and subsequently the estimator gain parameters are derived a simulation example is presented to illustrate the effectiveness and applicability of the proposed estimator design algorithm

study of the shape of random walks ii inertia moment ratios and the two dimensional asphericity a study of some features of the quantities used to describe the shape of random walks focusing on the probability distribution of the asphericity of discrete random walks in two dimensions is presented a connection is established between the asphericity distribution and the probability distribution corresponding to the ratio of the principal inertia moments the probability distributions of arbitrary inertia moment ratios are analysed for varying spatial dimension and an analytic expression for them is found which presents excellent agreement with monte carlo data in all the cases considered this function is then used to obtain the corresponding two dimensional asphericity distribution which also proved to be a very good approximation to the true distribution obtained from an independent monte carlo simulation

universal formulas for percolation thresholds a power law is postulated for both site and bond percolation thresholds the formula is mathit p mathit c mathit p 0 d 1 q 1 mathrm ensuremath mathit a mathit d mathit b where d is the space dimension and q the coordination number all thresholds up to d ensuremath rightarrow ensuremath infty are found to belong to only three universality classes for two classes b 0 for site dilution while b a for bond dilution the remaining class associated with high dimensions is characterized by b 2a 1 for both sites and bonds classes are defined by a set of value for mathit p 0 a deviations from available numerical estimates at d ensuremath le 7 are within ifmmode pm else textpm fi 0 008 and ifmmode pm else textpm fi 0 0004 for high dimensional hypercubic expansions at d ensuremath ge 8 the formula is found to be also valid for ising critical temperatures textcopyright 1996 the american physical society

interpolation in the limit of increasingly flat radial basis functions abstract many types of radial basis functions such as multiquadrics contain a free parameter in the limit where the basis functions become increasingly flat the linear system to solve becomes highly ill conditioned and the expansion coefficients diverge nevertheless we find in this study that limiting interpolants often exist and take the form of polynomials in the 1 d case we prove that with simple conditions on the basis function the interpolants converge to the lagrange interpolating polynomial hence differentiation of this limit is equivalent to the standard finite difference method we also summarize some preliminary observations regarding the limit in 2 d

impossibility of fast stable approximation of analytic functions from equispaced samples it is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions to avoid instability one must settle for root exponential convergence the proof combines a bernstein inequality of 1912 with an estimate due to coppersmith and rivlin in 1992

pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers pinning stabilization problem of linearly coupled stochastic neural networks lcsnns is studied in this paper a minimum number of controllers are used to force the lcsnns to the desired equilibrium point by fully utilizing the structure of the network in order to pinning control the lcsnns to a certain desired state only one controller is required for strongly connected network topology and m controllers which will be shown to be the minimum number are needed for lcsnns with m reducible coupling matrix the isolate node of the lcsnns can be stable periodic or even chaotic the coupling laplacian matrix of the lcsnns can be symmetric irreducible asymmetric irreducible or m reducible which means that the network topology can be strongly connected weakly connected or even unconnected there is no constraint on the network topology some criteria are derived to judge whether the lcsnns can be controlled in mean square by using designed controllers the given criteria are expressed in terms of strict linear matrix inequalities which can be easily checked by resorting to recently developed algorithm moreover numerical examples including small world and scale free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems

robust exponential stability of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays this paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays and known or unknown parameters the jumping parameters are determined by a continuous time discrete state markov chain and the mixed time delays under consideration comprise both time varying delays and continuously distributed delays to the best of the authors knowledge till now the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper the main objective of this paper is to fill this gap by constructing a novel lyapunov krasovskii functional and using some new approaches and techniques several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square the results presented in this paper generalize and improve many known results finally two numerical examples and their simulations are given to show the effectiveness of the theoretical results

synchronization of markovian coupled neural networks with nonidentical node delays and random coupling strengths in this paper a general model of coupled neural networks with markovian jumping and random coupling strengths is introduced in the process of evolution the proposed model switches from one mode to another according to a markovian chain and all the modes have different constant time delays the coupling strengths are characterized by mutually independent random variables when compared with most of existing dynamical network models which share common time delay for all modes and have constant coupling strengths our model is more practical because different chaotic neural network models can have different time delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors by designing a novel lyapunov functional and using some inequalities and the properties of random variables we derive several new sufficient synchronization criteria formulated by linear matrix inequalities the obtained criteria depend on mode delays and mathematical expectations and variances of the random coupling strengths as well numerical examples are given to demonstrate the effectiveness of the theoretical results meanwhile right continuous markovian chain is also presented

global synchronization for discrete time stochastic complex networks with randomly occurred nonlinearities and mixed time delays in this paper the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurred nonlinearities rons and time delays the discrete time complex networks under consideration are subject to 1 stochastic nonlinearities that occur according to the bernoulli distributed white noise sequences 2 stochastic disturbances that enter the coupling term the delayed coupling term as well as the overall network and 3 time delays that include both the discrete and distributed ones note that the newly introduced rons and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment e g internet based control systems by constructing a novel lyapunov like matrix functional the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem by employing a combination of the linear matrix inequality lmi techniques the free weighting matrix method and stochastic analysis theories several delay dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete time stochastic complex networks with time delays the criteria derived are characterized in terms of lmis whose solution can be solved by utilizing the standard numerical software a simulation example is presented to show the effectiveness and applicability of the proposed results

exponential synchronization of linearly coupled neural networks with impulsive disturbances this brief investigates globally exponential synchronization for linearly coupled neural networks nns with time varying delay and impulsive disturbances since the impulsive effects discussed in this brief are regarded as disturbances the impulses should not happen too frequently the concept of average impulsive interval is used to formalize this phenomenon by referring to an impulsive delay differential inequality we investigate the globally exponential synchronization of linearly coupled nns with impulsive disturbances the derived sufficient condition is closely related with the time delay impulse strengths average impulsive interval and coupling structure of the systems the obtained criterion is given in terms of an algebraic inequality which is easy to be verified and hence our result is valid for large scale systems the results extend and improve upon earlier work as a numerical example a small world network composing of impulsive coupled chaotic delayed nn nodes is given to illustrate our theoretical result

on the lebesgue constant of berrut s rational interpolant at equidistant nodes it is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting in this paper we confirm this observation by proving that the lebesgue constant of berrut s rational interpolant grows only logarithmically in the number of interpolation nodes moreover the numerical results suggest that the lebesgue constant behaves similarly for interpolation at chebyshev as well as logarithmically distributed nodes

universal formulas for percolation thresholds ii extension to anisotropic and aperiodic lattices in a recent paper we reported a universal power law for both site and bond percolation thresholds in any bravais lattice with q equivalent nearest neighbors in dimension d we now extend it to three different classes of lattices which are respectively anisotropic lattices without equivalent nearest neighbors non bravais lattices with two atom unit cells and quasicrystals the investigation is focused on d 2 and 3 due to the lack of experimental data at higher dimensions the extension to these lattices requires the substitution of q by an effective non integer value q mathrm eff in the universal law for each of the 17 lattices which constitute our sample we argue for the existence of one q mathrm eff which reproduces both the site and the percolation threshold with a deviation with respect to numerical estimates which does not exceed ensuremath mp 0 01

an extension of the floater hormann family of barycentric rational interpolants the barycentric rational interpolants introduced by floater and hormann in 2007 are blends of polynomial interpolants of fixed degree d in some cases these rational functions achieve approximation of much higher quality than the classical polynomial interpolants which e g are ill conditioned and lead to runge s phenomenon if the interpolation nodes are equispaced for such nodes however the condition of floater hormann interpolation deteriorates exponentially with increasing d in this paper an extension of the floater hormann family with improved condition at equispaced nodes is presented and investigated the efficiency of its applications such as the approximation of derivatives integrals and primitives of functions is compared to the corresponding results recently obtained with the original family of rational interpolants math subject classification 65d05 65l12 65d32 41a05 41a20 41a25

stability and synchronization of discrete time markovian jumping neural networks with mixed mode dependent time delays in this paper we introduce a new class of discrete time neural networks dnns with markovian jumping parameters as well as mode dependent mixed time delays both discrete and distributed time delays specifically the parameters of the dnns are subject to the switching from one to another at different times according to a markov chain and the mixed time delays consist of both discrete and distributed delays that are dependent on the markovian jumping mode we first deal with the stability analysis problem of the addressed neural networks a special inequality is developed to account for the mixed time delays in the discrete time setting and a novel lyapunov krasovskii functional is put forward to reflect the mode dependent time delays sufficient conditions are established in terms of linear matrix inequalities lmis that guarantee the stochastic stability we then turn to the synchronization problem among an array of identical coupled markovian jumping neural networks with mixed mode dependent time delays by utilizing the lyapunov stability theory and the kronecker product it is shown that the addressed synchronization problem is solvable if several lmis are feasible hence different from the commonly used matrix norm theories such as the m matrix method a unified lmi approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation where the lmis can be easily solved by using the available matlab lmi toolbox two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

monte carlo study of percolation on disordered triangular lattices abstract a simple model for amorphous solids consisting of a mixed bond triangular lattice with a fraction of attenuated bonds randomly distributed which simulate the presence of defects in the surface is studied here by using computational simulation the degree of disorder of the surface is tunable by selecting the values of 1 the fraction of regular attenuated bonds 1 0 1 and 2 the factor r which is defined as the ratio between the value of the conductivity associated to an attenuated bond and that corresponding to a regular bond 0 r 1 the results obtained show how the percolation properties of the disordered system are modified with respect to the standard random bond percolation problem r 0

bond dimer percolation on square lattices abstract percolation due to the simultaneous occupation of two neighboring bond sites namely a bond dimer is considered here by means of the renormalization cell technique providing an analytic way to obtain results such as percolation threshold jamming coverage and critical exponents this is complementary to previous numerical studies and extends the validation of the renormalization cell technique four different bond dimer depositions are considered nematic straight angular and tortuous results for each of them are given and analyzed separately size of the cells is varied these results are combined with means of finite size scaling to obtain tendencies towards the thermodynamic limit it is observed that the percolation threshold is reached at lower concentrations than for monomeric bond percolation establishing a trend for correlated bond percolation similar to the one already established for site dimer percolation two different techniques are used to obtain the percolation threshold getting results that are in good agreement with numerical simulations similarly acceptable results for jamming coverage are obtained values for critical exponents are also in good agreement with those reported by means of numerical techniques

site trimer percolation on square lattices percolation of site trimers k mers with k 3 is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem results are compared to those obtained here by means of extensive computer simulations five different deposition possibilities for site trimers are included according to shape and orientation of the depositing objects analytical results for the percolation threshold p c are all close to 0 55 while numerical results show a slight dispersion around this value a comparison with p c values previously reported for monomers and dimers establishes the tendency of p c to decrease as k increases critical exponent was also obtained both by analytical and numerical methods results for the latter give values very close to the expected value 4 3 showing that this percolation case corresponds to the universality class of random percolation

statistical properties of the set of sites visited by the two dimensional random walk we study the support i e the set of visited sites of a t step random walk on a two dimensional square lattice in the large t limit a broad class of global properties m t of the support is considered including for example the number s t of its sites the length of its boundary the number of islands of unvisited sites that it encloses the number of such islands of given shape size and orientation and the number of occurrences in space of specific local patterns of visited and unvisited sites on a finite lattice we determine the scaling functions that describe the averages on appropriate lattice size dependent time scales on an infinite lattice we first observe that the all increase with t as where k is an m dependent positive integer we then consider the class of random processes constituted by the fluctuations around average we show that to leading order as t gets large these fluctuations are all proportional to a single universal random process normalized to for the probability law of tends to that of varadhan s renormalized local time of self intersections an implication is that in the long time limit all are proportional to

six strategies for defeating the runge phenomenon in gaussian radial basis functions on a finite interval radial basis function rbf interpolation is a meshless strategy with great promise for adaptive approximation because it is meshless there is no canonical grid to act as a starting point for function adaptive grid modification uniform grids are therefore common with rbfs like polynomial interpolation which is the limit of rbf interpolation when the rbf functions are very wide the flat limit rbf interpolants are vulnerable to the runge phenomenon whether the grid is uniform or irregular the n point interpolant may diverge as n on the interval spanned by the interpolation points even for a function f x that is analytic everywhere on and near this interval in this work we discuss six strategies for defeating the runge phenomenon specializing to a uniform grid on a finite interval and one particular species of rbfs in one space dimension f x exp a 2 h 2 x 2 where h is the grid spacing three strategies fail but three are successful one good strategy is to vary a with the number of interpolation points n as n 1 4 unfortunately this gives both a subgeometric rate of convergence for the approximation error falling as exp qn for some constant q and a matrix condition number that grows as exp pn for some p 0 in order to explain why fixed a independent of n is not a convergent strategy we digress to discuss error saturation and show experimentally that the saturation error on the finite interval is about 0 6exp 0 47 a 2 f if a user chosen error tolerance d is acceptable then the optimum choice is a o p t i m u m d 1 2log d 0 06 the second good strategy is rbf extension which uses rbf functions with centers on a interval slightly larger than the target interval to approximate f x a third strategy is to split the interval into two boundary layers and a large middle interval and apply separate rbf approximations on each the slow decrease of a strategy is much cheaper but rbf extension is much more resistant to ill conditioning and therefore can achieve much lower errors the three interval method is the least accurate but is robust and inexpensive

exponential h synchronization and state estimation for chaotic systems via a unified model in this paper h synchronization and state estimation problems are considered for different types of chaotic systems a unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems such as hopfield neural networks cellular neural networks chua s circuits unified chaotic systems qi systems chaotic recurrent multilayer perceptrons etc based on the h performance analysis of this unified model using the linear matrix inequality approach novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the state estimation problem is then studied for the same unified model where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level the parameters of these controllers and filters are obtained by solving the eigenvalue problem most chaotic systems can be transformed into this unified model and h synchronization controllers and state estimators for these systems are designed in a unified way three numerical examples are provided to show the usefulness of the proposed h synchronization and state estimation conditions

the shape of self avoiding walks an exhaustive analysis of the shape properties of discrete self avoiding random walks is presented the dependence of the main parameters of the probability distributions from the length of the walk and the differences between these distributions for conventional and self avoiding walks are studied by means of high precision monte carlo simulations it is shown that the characteristics of the shape of self avoiding random walks when regarded as a function of the walk length present the expected asymptotic behaviour the differences with conventional random walks depend upon the observable considered the probability distributions of the principal inertia eigenvalues of self avoiding walks spread around the most probable value more widely than the corresponding distributions for unrestricted walks while in the cases of the asphericity or ratios of inertia eigenvalues the distributions for self avoiding walks are somewhat more peaked than their counterparts for conventional random walks analytical expressions for the probability distributions of inertia moment ratios and the two dimensional asphericity are given for common random walks there is an excellent agreement between these analytical distributions and the monte carlo data in this work it is established that this concordance is maintained if the same analytical distributions are applied to the self avoiding case this means that within the precision of the simulations the functional form of the mentioned distributions does not vary when passing from conventional to self avoiding walks

bivariate lagrange interpolation at the padua points the ideal theory approach the padua points are a family of points on the square 1 1 2 given by explicit formulas that admits unique lagrange interpolation by bivariate polynomials interpolation polynomials and cubature formulas based on the padua points are studied from an ideal theoretic point of view which leads to the discovery of a compact formula for the interpolation polynomials the lp convergence of the interpolation polynomials is also studied

monte carlo simulation of the percolation process caused by the random sequential adsorption of k mers on heterogeneous triangular lattices abstract mixed site bond percolation is studied for a random sequential adsorption process of k mers on heterogeneous lattices with variable connectivity by means of monte carlo simulation the percolation phase diagrams are built to render evidence about complex structures critical exponents are also calculated to show that the universality class corresponding to ordinary percolation in two dimensions is preserved

mode dependent stochastic synchronization for markovian coupled neural networks with time varying mode delays this paper investigates the stochastic synchronization problem for markovian hybrid coupled neural networks with interval time varying mode delays and random coupling strengths the coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric a mode dependent augmented lyapunov krasovskii functional lkf is proposed where some terms involving triple or quadruple integrals are considered which makes the lkf matrices mode dependent as much as possible this gives significant improvement in the synchronization criteria i e less conservative results can be obtained in addition by applying an extended jensen s integral inequality and the properties of random variables new delay dependent synchronization criteria are derived the obtained criteria depend not only on upper and lower bounds of mode delays but also on mathematical expectations and variances of the random coupling strengths finally two numerical examples are provided to demonstrate the feasibility of the proposed results

bounds for polynomials with a unit discrete norm let e be the set of n equidistant points in 1 1 and fn e be the set of all polynomials p of degree n with max p c c e 1 we prove that 7t kn n x max p x clog p e arctan ky s x r v 1 n2 jv2 where n n and c is an absolute constant the result is essentially sharp bounds for kn z z g c uniform for n n are also obtained the method of proof of those results is a general one it allows one to obtain sharp or sharp up to a log n factor bounds for kn under rather general assumptions on e j5 n a model result is announced for a class of sets e main components of the method are discussed in some detail in the process of investigating the case of equally spaced points

synchronization control of stochastic delayed neural networks abstract in this paper synchronization control of stochastic neural networks with time varying delays has been considered a novel control method is given using the lyapunov functional method and linear matrix inequality lmi approach several sufficient conditions have been derived to ensure the global asymptotical stability in mean square for the error system and thus the drive system synchronize with the response system also the estimation gains can be obtained with these new and effective methods synchronization can be achieved simulation results are given to verify the theoretical analysis in this paper

fixed time synchronization of markovian jump fuzzy cellular neural networks with stochastic disturbance and time varying delays abstract this paper mainly studies the fixed time synchronization of markovian jump fuzzy cellular neural networks with stochastic perturbations and time varying delays in the leakage term by designing delay dependent controllers with or without fuzzy terms constructing a suitable stochastic lyapunov functional and using matrix analysis techniques this paper derives some novel and useful sufficient conditions to guarantee the fixed time synchronization of the addressed drive response systems and the conditions are delay dependent which has less conservative results the finite time is also independent of the initial states finally numerical examples are given to illustrate the effectiveness of the proposed main results

thermal percolation for interacting monomers adsorbed on square lattices in this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies by means of a finite size scaling analysis the critical exponents and the scaling collapsing of the fraction of percolating lattice are found a phase diagram separating a percolating from a non percolating region is determined the main features of the phase diagram are discussed in terms of simple considerations related to the interactions present in the problem the influence of the phase transitions occurring in the system is reflected by the phase diagram in addition a scaling treatment maintaining constant the surface coverage and varying the temperature of the system is performed in all the considered cases the universality class of the model is found to be the same as for the random percolation model

similarity of percolation thresholds on the hcp and fcc lattices extensive monte carlo simulations were performed in order to determine the precise values of the critical thresholds for site phcpc s 0 199 255 5 0 000 001 0 and bond phcpc b 0 120 164 0 0 000 001 0 percolation on the hcp lattice to compare with previous precise measurements on the fcc lattice also exact enumeration of the hcp and fcc lattices was performed and yielded generating functions and series for the zeroth first and second moments of both lattices when these series and the values of pc are compared to those for the fcc lattice it is apparent that the site percolation thresholds are different however the bond percolation thresholds are equal within error bars and the series only differ slightly in the higher order terms suggesting the actual values are very close to each other if not identical

dependence of the percolation threshold on the size of the percolating species abstract site and bond percolation of k mers of different structures and forms deposited on 2 d regular lattices is studied in addition the percolation threshold for percolating k mers on a bethe lattice is analytically obtained by using finite size scaling theory the analysis of the results is performed in order to determine the behavior of the percolation threshold which exhibits an exponential decrease with the k mer size characteristic parameters of that function are dependent not only on the form and structure of k mers but also on the properties of the lattice where they are deposited an expression for the percolation threshold as a function of the parameters of the problem is proposed and discussed

bond percolation of polymers we study bond percolation of n non interacting gaussian polymers of l segments on a 2d square lattice of size l with reflecting boundaries through simulations we find the fraction of configurations displaying no connected cluster which span from one edge to the opposite edge from this fraction we define a critical segment density lc l and the associated critical fraction of occupied bonds plc l so that they can be identified as the percolation threshold in the l limit whereas plc l is found to decrease monotonically with l for a wide range of polymer lengths lc l is non monotonic we give physical arguments for this intriguing behaviour in terms of the competing effects of multiple bond occupancies and polymerization

repeated bond traversal probabilities for the simple random walk we consider the average number bm t of bonds traversed exactly m times by a t step simple random walk we determine bm t explicitly in the scaling limit t with m t fixed in dimension d 1 and m log t fixed in dimension d 2 the scaling function is an erfc in d 1 and an exponential in d 2

a fast algorithm for computing the mock chebyshev nodes abstract runge phenomenon which is a very well known example and published by c runge in 1901 is as follows polynomial interpolation of a function f using equidistant interpolation points on 1 1 could diverge on certain parts of this interval even if f is analytic anywhere on the interval among all the techniques that have been proposed to defeat this phenomenon in the literature of approximation theory there is the mock chebyshev interpolation on a grid a subset of n 1 points from an equispaced grid with o n 2 points chosen to mimic the non uniform n 1 point chebyshev lobatto grid 1 this study suggests a fast algorithm for computing the mock chebyshev nodes using the distance between each pair of consecutive points the complexity of the algorithm is o n where n 1 is the number of the chebyshev lobatto nodes on the interval 1 1 a discussion of bivariate generalization of the mock chebyshev nodes to the padua interpolation points in 1 1 2 is given and numerical results are also provided

adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations this paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays mixed delays as well as uncertain nonlinear external and stochastic perturbations hybrid perturbations a simple but robust adaptive controller is designed such that the response system can lag synchronize with a drive system based on the lyapunov stability theory and some suitable lyapunov krasovskii functionals several sufficient conditions ensuring the lag synchronization are developed our synchronization criteria are easily verified and do not need to solve any linear matrix inequality some existing results are improved and extended moreover the designed adaptive controller has better anti interference capacity and is more practical than the usual adaptive controller numerical simulations are exploited to show the effectiveness of the theoretical results

blinking model and synchronization in small world networks with a time varying coupling the paper proposes a new type of small world networks of cells with chaotic behavior this network consists of a regular lattice of cells with constant 2k nearest neighbor couplings and time dependent on off couplings between any other pair of cells in each time interval of duration such a coupling is switched on with probability p and the corresponding switching random variables are independent for different links and for different times at each moment the coupling structure corresponds to a small world graph but the shortcuts change from time interval to time interval which is a good model for many real world dynamical networks it is to be distinguished from networks that have randomly chosen shortcuts fixed in time here we apply the connection graph stability method developed in the companion paper connection graph stability method for synchronized coupled chaotic systems see this issue to the study of global synchronization in this network with the time varying coupling structure in the case where the on off switching is fast with respect to the characteristic synchronization time of the network the synchronization thresholds are explicitly linked with the average path length of the coupling graph and with the probability p of shortcut switchings in this blinking model we prove that for the blinking model a few random shortcut additions significantly lower the synchronization threshold together with the effective characteristic path length short interactions between cells as in the blinking model are important in practice to cite prominent examples computers networked over the internet interact by sending packets of information and neurons in our brain interact by sending short pulses called spikes the rare interaction between arbitrary nodes in the network greatly facilitates synchronization without loading the network much in this respect we believe that it is more efficient than a structure of fixed random connections