local projection stabilization for the oseen problem and its interpretation as a variational multiscale method we propose to apply the recently introduced local projection stabilization to the numerical computation of the oseen equation at high reynolds number the discretization is done by nested finite element spaces using a priori error estimation techniques we prove the convergence of the method the a priori estimates are independent of the local peclet number and give a sufficient condition for the size of the stabilization parameters in order to ensure optimality of the approximation when the exact solution is smooth moreover we show how this method may be cast in the framework of variational multiscale methods we indicate what modeling assumptions must be made to use the method for large eddy simulations

treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses finite element approximations of the stokes and navier stokes equations with in homogeneous essential boundary conditions are considered boundary conditions are enforced weakly by introducing lagrange multipliers optimal error estimates including some for the stress vector on the boundary are derived under minimal regularity assumptions on the data particular attention is paid to the analysis of a practical choice of finite element spaces for which the lagrange multiplier calculation uncouples from that for the velocity and pressure the results are also applicable to general second order elliptic systems

c 0 elements for generalized indefinite maxwell equations in this paper we develop the c 0 finite element method for a generalized curlcurl grad div indefinite maxwell problem in a lipschitz domain such as nonconvex polygon for which the solution of the problem may be nonsmooth and only have the h r regularity for some r 1 the ingredients of our method are that two mass lumping l 2 projectors are applied to curl and div operators in the problem and that c 0 linear element or isoparametric bilinear element enriched with one element bubble on every triangle element or with two element bubbles on every quadrilateral element respectively is employed for each component of the nonsmooth solution due to the fact that the element bubbles can be statically eliminated at element levels our method is essentially three nodes or four nodes c 0 lagrange element method with two fortin type interpolations established a very technical duality argument is elaborated to estimate the error for the indefinite problem for the nonsmooth solution having the h r regularity where r may vary in the interval 0 1 we obtain the error bound mathcal o h r in an energy norm some numerical experiments are performed to confirm the theoretical error bounds

unified index to quantifying heterogeneity of complex networks abstract although recent studies have revealed that degree heterogeneity of a complex network has significant impact on the network performance and function a unified definition of the heterogeneity of a network with any degree distribution is absent in this paper we define a heterogeneity index 0 h 1 to quantify the degree heterogeneity of any given network we analytically show the existence of an upper bound of h 0 5 for exponential networks thus explain why exponential networks are homogeneous on the other hand we also analytically show that the heterogeneity index of an infinite power law network is between 1 and 0 5 if and only if its degree exponent is between 2 and 2 5 we further show that for any power law network with a degree exponent greater than 2 5 there always exists an exponential network such that both networks have the same heterogeneity index this may help to explain why 2 5 is a critical degree exponent for some dynamic behaviors on power law networks

a blind approach to hammerstein model identification this paper discusses the hammerstein model identification using a blind approach by fast sampling at the output it is shown that identification of the linear part can be achieved based only on the output measurements that makes the hammerstein model identification possible without knowing the structure of the nonlinearity and the internal variables

least squares solutions as solutions of a perturbation form of the galerkin methods interior pointwise error estimates and pollution effect first order div least squares ls finite element methods for second order elliptic partial differential equations are considered the main idea of this paper is a consideration of the ls solution u h for the primary function u as the solution of a perturbation form of the galerkin methods consequently the results concerning the perturbation form of the galerkin methods can be applied for the ls methods here we use the pointwise error estimates for the perturbation form provided by schatz a h schatz pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids part ii interior estimates siam j numer anal 38 2000 1269 1293 to obtain the pointwise estimates for the ls solution the estimates consist of the local truncation error and pollution terms we provide estimates for pollution terms our process for arriving at the estimates involves obtaining the norm of a linear functional which accounts for the perturbation our estimates are valid for both smooth and nonsmooth problems for the smooth problems the pollution is weaker than the local truncation error for the nonsmooth problems we provide a criterion for determining the strength of the pollution in particular we identify superconvergent points for nonconvex polygonal domains

statistical mechanics of the international trade network analyzing real data on international trade covering the time interval 1950 2000 we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks whose directed connections bilateral trade volumes are only characterized by the product of the trading countries gdps it means that time evolution of this network may be considered as a continuous sequence of equilibrium states i e a quasistatic process this in turn allows one to apply the linear response theory to make and also verify simple predictions about the network in particular we show that bilateral trade fulfills a fluctuation response theorem which states that the average relative change in imports exports between two countries is a sum of the relative changes in their gdps yearly changes in trade volumes prove that the theorem is valid

bubble stabilization of finite element methods for the linearized incompressible navier stokes equations abstract in this paper we discuss the stabilization via bubble functions of a finite element method for stationary linearized incompressible navier stokes equations it is shown that residual free bubbles can reproduce supg

generalizations of the clustering coefficient to weighted complex networks the recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account here we focus on various generalizations of the clustering coefficient which is one of the central characteristics in the complex network theory we present a comparative study of the several suggestions introduced in the literature and point out their advantages and limitations the concepts are illustrated by simple examples as well as by empirical data of the world trade and weighted coauthorship networks

optimal isoparametric finite elements and error estimates for domains involving curved boundaries we describe a practical procedure for the triangulation of arbitrary n dimensional regular bounded domains by isoparametric simplicial elements preserving the optimal order of accuracy along similar lines we prove general error estimates for the finite element solution of second order elliptic problems various kinds of nonhomogeneous boundary conditions can be dealt with such as dirichlet neumann and robin boundary conditions

continuous time hammerstein system identification a continuous time hammerstein system i e a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one is identified the system is driven and disturbed by white random signals the a priori information about both subsystems is nonparametric which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown an algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown the impulse response of the dynamic part is recovered with a correlation method the algorithms are computationally independent results of a simulation example are given

randomizing world trade i a binary network analysis the international trade network itn has received renewed multidisciplinary interest due to recent advances in network theory however it is still unclear whether a network approach conveys additional nontrivial information with respect to traditional international economics analyses that describe world trade only in terms of local first order properties in this and in a companion paper we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher order patterns of the itn in all its possible representations binary or weighted directed or undirected aggregated or disaggregated by commodity and across several years here we show that remarkably the properties of all binary projections of the network can be completely traced back to the degree sequence which is therefore maximally informative our results imply that explaining the observed degree sequence of the itn which has not received particular attention in economic theory should instead become one the main focuses of models of trade

a modified streamline diffusion method for solving the stationary navier stokes equation recently hughes et al 11 12 proposed new finite element schemes of petrov galerkin type for solving the stokes problem which do not require the discrete version of the ladyshenskaya babuska brezzi condition lbb condition in this paper we derive a conforming finite element method for solving the stationary navier stokes equations which combines the advantages of arbitrary finite element spaces for velocity pressure with the favourable properties of the streamline diffusion method in the case of moderate and high reynolds number

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

weighted networks as randomly reinforced urn processes we analyze weighted networks as randomly reinforced urn processes in which the edge total weights are determined by a reinforcement mechanism we develop a new statistical test and a new procedure based on it to study the evolution of networks over time detecting the dominance of some edges with respect to the others and then assessing if a given instance of the network is taken at its steady state or not distance from the steady state can be considered as a measure of the relevance of the observed properties of the network our results are quite general in the sense that they are not based on a particular probability distribution or functional form of the random weights moreover the proposed tool can be applied also to dense networks which have received little attention by network community so far since they are often problematic we apply our procedure in the context of the international trade network determining a core of dominant edges

moreau yosida regularization in state constrained elliptic control problems error estimates and parameter adjustment an adjustment scheme for the regularization parameter of a moreau yosida based regularization or relaxation approach to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced the method utilizes error estimates of an associated finite element discretization of the regularized problems for the optimal selection of the regularization parameter in dependence on the mesh size of discretization and error estimates for the approximation error due to regularization the theoretical results are verified numerically

a unified analysis of mixed and stabilized finite element solutions of navier stokes equations abstract this paper performs a unified numerical analysis of mixed and stabilized finite element numerical solutions of 2d and 3d steady navier stokes equations we introduce a general internal discretization of navier stokes equations of which both mixed and stabilized methods are particular cases we prove convergence of stabilized methods with non linear stabilization coefficients in particular for flows with convection dominance we also analyze the approximation of branches of regular solutions in the case of convection dominance we introduce a stabilized post processing of galerkin finite element fe solution of convection dominated flows some numerical test for nonlinear flows show the good performances of this technique

scaling relations for diversity of languages abstract the distribution of living languages is investigated and scaling relations are found for the diversity of languages as a function of the country area and population these results are compared with data from ecology and from computer simulations of fragmentation dynamics where similar scalings appear the language size distribution is also studied and shown to display two scaling regions i one for the largest in population languages and ii another one for intermediate size languages it is then argued that these two classes of languages may have distinct growth dynamics being distributed on the sets of different fractal dimensions

optimal finite element interpolation on curved domains this paper is devoted to a general theory of approximation of functions in finite element spaces in particular the case is considered where the functions to be interpolated are on the one hand not very smooth and on the other are defined on curved domains thus a number of well known optimal interpolation results are generalized

sharply local pointwise a posteriori error estimates for parabolic problems we prove pointwise a posteriori error estimates for semi and fully discrete finite element methods for approximating the solution u to a parabolic model problem our estimates may be used to bound the finite element error u u h l d where d is an arbitrary subset of the space time domain of the definition of the given pde in contrast to standard global error estimates these estimators de emphasize spatial error contributions from space time regions removed from d our results are valid on arbitrary shape regular simplicial meshes which may change in time and also provide insight into the contribution of mesh change to local errors when implemented in an adaptive method these estimates require only enough spatial mesh refinement away from d in order to ensure that local solution quality is not polluted by global effects

world trade web topological properties dynamics and evolution this paper studies the statistical properties of the web of import export relationships among world countries using a weighted network approach we analyze how the distributions of the most important network statistics measuring connectivity assortativity clustering and centrality have coevolved over time we show that all node statistic distributions and their correlation structure have remained surprisingly stable in the last 20 years and are likely to do so in the future conversely the distribution of positive link weights is slowly moving from a log normal density towards a power law we also characterize the autoregressive properties of network statistics dynamics we find that network statistics growth rates are well proxied by fat tailed densities like the laplace or the asymmetric exponential power finally we find that all our results are reasonably robust to a few alternative economically meaningful weighting schemes

bubble finite elements for the primitive equations of the ocean we introduce in this paper two original mixed methods for the numerical resolution of the stationary primitive equations pe of the ocean the pe govern the behavior of oceanic flows in shallow domains for large time scales we use a reduced formulation lions et al 28 involving horizontal velocities and surface pressures by using bubble functions constructed ad hoc we are able to define two stable mixed methods requiring a low number of degrees of freedom the first one is based on the addition of bubbles of reduced support to inlinemediaobject not available see fulltext velocities elementwise the second one makes use of conic bubbles of extended support along the vertical coordinate the latter constitutes a genuine mini element for the pe e g it requires the least number of extra degrees of freedom to stabilize piecewise linear hydrostatic pressures both methods verify a specific inf sup condition and provide stability and convergence finally we compare several numerical features of the proposed pairs in the context of other fe methods found in the literature

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

brief estimation of an n l n hammerstein wiener model estimation of a single input single output block oriented model is studied the model consists of a linear block embedded between two static nonlinear gains hence it is called n l n hammerstein wiener model first the model structure is motivated and the disturbance model is discussed the paper then concentrates on parameter estimation a relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear in parameters this leads to a simple algorithm which minimizes the original loss function the convergence and consistency of the algorithm are studied in order to reduce the variance error the obtained linear model is further reduced using frequency weighted model reduction simulation study will be used to illustrate the method

assortativity and act degree distribution of some collaboration networks empirical investigation results on weighted and un weighted assortativity act degree distribution degree distribution and node strength distribution of nine real world collaboration networks have been presented the investigations propose that act degree distribution degree distribution and node strength distribution usually show so called shifted power law spl function forms which can continuously vary from an ideal power law to an ideal exponential decay two parameters a and z can be used for description of the distribution functions another conclusion is that assortativity coefficient and the parameter a or z is monotonously dependent on each other by the collaboration network evolution model introduced in a reference p zhang et al physica a 360 2006 599 we analytically derived the spl distributions which typically appeared in general situations where nodes are selected partially randomly with a probability p and partially by linear preferential principle with the probability 1 p the analytic discussion gives an explicit expression on the relationship between the random selection proportion p and the parameters a and z the numerical simulation results by the model show a monotonic dependence of assortativity on the random selection proportion p the empirically obtained assortativity versus a or z curve for the four collaboration networks with small maximal act size t max shows a good agreement with the model prediction according to the curves one can qualitatively judge the random selection proportion of the real world network in its evolution process r 2007 elsevier b v all rights reserved

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

adaptive control of weiner type nonlinear systems abstract this study is concerned with the problem of adaptive control of a wiener type nonlinear process it is assumed that the linear dynamic part of the process can be represented by a pulse transfer function of known order with stable inverse followed by a known time delay the memoryless nonlinearity is one to one on a compact set and belongs to one of two classes 1 piecewise linear with known breakpoints or 2 smooth function in which case an approximation is made it is represented by linear splines the output signal from the linear part is not available for measurement the global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints otherwise there will be a residual tracking error which depends on the nonlinearity approximation error but the boundedness of all signals can be assured the proposed scheme is used for adaptive control of the ph process in a continuous flow reactor

scaling behavior in economics the problem of quantifying company growth inspired by work of both widom and mandelbrot we analyze the computstat database comprising all publicly traded united states manufacturing companies in the years 1974 1993 we find that the distribution of company size remains stable for the 20 years we study i e the mean value and standard deviation remain approximately constant we study the distribution of sizes of the new companies in each year and find it to be well approximated by a log normal we find i the distribution of the logarithm of the growth rates for a fixed growth period of t years and for companies with approximately the same size s displays an exponential tent shaped form rather than the bell shaped gaussian one would expect for a log normal distribution and ii the fluctuations in the growth rates measured by the width of this distribution t decrease with company size and increase with time t we find that for annual growth rates t 1 t s and that the exponent takes the same value within the error bars for several measures of the size of a company in particular we obtain 0 20 0 03 for sales 0 18 0 03 for number of employees 0 18 0 03 for assets 0 18 0 03 for cost of goods sold and 0 20 0 03 for propert plant and equipment we propose models that may lead to some insight into these phenomena first we study a model in which the growth rate of a company is affected by a tendency to retain an optimal size that model leads to an exponential distribution of the logarithm of growth rate in agreement with the empirical results then we study a hierarchical tree like model of a company that enables us to relate to parameters of a company structure we find that 1n 1nz where z defines the mean branching ratio of the hierarchical tree and is the probability that the lower levels follow the policy of higher levels in the hierarchy we also study the output distribution of growth rates of this hierarchical model we find that the distribution is consistent with the exponential form found empirically we also discuss the time dependence of the shape of the distribution of the growth rates

finite element analysis of varitional crimes for a quasilinear elliptic problem in 3d we examine a finite element approximation of a quasilinear boundary value elliptic problem in a three dimensional bounded convex domain with a smooth boundary the domain is approximated by a polyhedron and a numerical integration is taken into account we apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains in the w 1 2 norm to the true solution without any additional regularity assumptions

postprocessing the linear finite element method we extend the idea of the postprocessing galerkin methods for dissipative evolution equations to the case of the linear finite element method the postprocessing technique has been developed earlier for spectral methods and for higher order finite element methods the analysis shows that this procedure improves the order of convergence of the piecewise linear galerkin finite element approximation in the h1 norm we show by means of numerical experiments that there is no improvement in the order of convergence in the l2 norm

auxiliary model based least squares identification methods for hammerstein output error systems abstract the difficulty in identification of a hammerstein a linear dynamical block following a memoryless nonlinear block nonlinear output error model is that the information vector in the identification model contains unknown variables the noise free true outputs of the system in this paper an auxiliary model based least squares identification algorithm is developed the basic idea is to replace the unknown variables by the output of an auxiliary model convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition the simulation results show the effectiveness of the proposed algorithms

on the coupling of mixed fem and bem for an exterior helmholtz problem in the plane this paper deals with an elliptic boundary value problem posed in the plane with variable coefficients but whose restriction to the exterior of a bounded domain reduces to a helmholtz equation we consider a mixed variational formulation in a bounded domain that contains the heterogeneous medium coupled with a boundary integral method applied to the helmholtz equation in we utilize suitable auxiliary problems duality arguments and fredholm alternative to show that the resulting formulation of the problem is well posed then we define a corresponding galerkin scheme by using rotated raviart thomas subspaces and spectral elements on the interface we show that the discrete problem is uniquely solvable and convergent and prove optimal error estimates finally we illustrate our analysis with some results from computational experiments

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

clustering in complex directed networks many empirical networks display an inherent tendency to cluster i e to form circles of connected nodes this feature is typically measured by the clustering coefficient cc the cc originally introduced for binary undirected graphs has been recently generalized to weighted undirected networks here we extend the cc to the case of binary and weighted directed networks and we compute its expected value for random graphs we distinguish between ccs that count all directed triangles in the graph independently of the direction of their edges and ccs that only consider particular types of directed triangles e g cycles the main concepts are illustrated by employing empirical data on world trade flows

numerical investigation of the regularity of the pressure for the primitive equations of the ocean abstract in this work we analyze the regularity of the pressure of the primitive equations pe of the ocean by numerical simulation and analysis this model makes use of the hydrostatic pressure assumption several authors have shown that the hydrostatic hypothesis limits the regularity of the surface pressure to ld3 2 where the weight d is the depth of the domain and is the surface domain nevertheless the same l2 regularity as in the navier stokes case can be proved when the domain has a talus we address in this paper the question whether this gap of regularity is also observable in the numerical approximation of the primitive equations specifically for the numerical solver of the primitive equations considered we prove convergence of the surface pressure in ld3 2 and in l2 for subdomains with talus this lack of regularity near the border is confirmed by numerical tests where we observe the formation of an infinite normal derivative in of the surface pressure as the size of the talus vanishes moreover we show that the ld3 2 regularity obtained in the theory for domains without talus is not far from being optimal

self organization of collaboration networks we study collaboration networks in terms of evolving self organizing bipartite graph models we propose a model of a growing network which combines preferential edge attachment with the bipartite structure generic for collaboration networks the model depends exclusively on basic properties of the network such as the total number of collaborators and acts of collaboration the mean size of collaborations etc the simplest model defined within this framework already allows us to describe many of the main topological characteristics degree distribution clustering coefficient etc of one mode projections of several real collaboration networks without parameter fitting we explain the observed dependence of the local clustering on degree and the degree degree correlations in terms of the aging of collaborators and their physical impossibility to participate in an unlimited number of collaborations

the cost of complexity in system identification frequency function estimation of finite impulse response systems in this paper we consider full order modeling i e when the true system belongs to the model set we investigate the minimum amount of input energy required to estimate a given linear system with a full order model within a prescribed degree of accuracy as a function of the model complexity this quantity we define to be the cost of complexity the degree of accuracy is measured by the inverse of the maximum variance of the discrete time frequency function estimator over a given frequency range b b it is commonly believed that the cost increases as the model complexity increases however the amount of information that is to be extracted from the system also influences the cost the objective of this paper is to quantify these dependencies for systems described by finite impulse response models it is shown that asymptotically in the model order n and sample size the cost is well approximated by o2n b where o2 is the noise variance this expression can be used as a simple rule of thumb for assessing trade offs that have to be made in a system identification project where full order models are used for example for given experiment duration excitation level and desired accuracy one can assess how the achievable frequency range depends on the required model order this type of consideration is useful when formally planning experiments in addition we establish several properties of the cost of complexity we find for example that if b is very close but not necessarily equal to the optimal input satisfies the model quality constraint for all frequencies

adaptive finite elements for a linear parabolic problem a posteriori error estimates for the heat equation in two space dimensions are presented a classical discretization is used euler backward in time and continuous piecewise linear triangular finite elements in space the error is bounded above and below by an explicit error estimator based on the residual numerical results are presented for uniform triangulations and constant time steps the quality of our error estimator is discussed an adaptive algorithm is then proposed successive delaunay triangulations are generated so that the estimated relative error is close to a preset tolerance again numerical results demonstrate the efficiency of our approach c 1998 elsevier science s a all rights reserved

a term by term stabilization algorithm for finite element solution of incompressible flow problems this paper introduces a stabilization technique for finite element numerical solution of 2d and 3d incompressible flow problems it may be applied to stabilize the discretization of the pressure gradient and also of any individual operator term such as the convection curl or divergence operators with specific levels of numerical diffusion for each one of them its computational complexity is reduced with respect to usual residual based stabilization techniques we consider piecewise affine finite elements for which we obtain optimal error bounds for steady navier stokes and also for generalized stokes equations including convection we include some numerical experiment in well known 2d test cases that show its good performances

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

a new stabilized finite element formulation for scalar convection diffusion problems the streamline and approximate upwind petrov galerkin method abstract a new stabilized and accurate finite element formulation for convection dominated problems is herein developed the basis of the new formulation is the choice of a new upwind function the upwind function chosen for the new method provokes its degeneration into the supg or cau methods depending on the approximate solution s regularity the accuracy and stability of the new formulation for the linear and scalar advection diffusion equation is demonstrated in several numerical examples

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

a stabilized space time discretization for the primitive equations in oceanography in this work we introduce and analyze a space time discretization for the primitive equations of the ocean we use a reduced formulation of these equations which only includes the 3d horizontal velocity and the 2d surface pressure cf 19 20 we use a semi implicit backward euler scheme for the time discretization the spatial discretization in each time step is carried out through a penalty stabilized method this allows to circumvent the use of pairs of spaces satisfying the inf sup condition thus attempting a large saving of degrees of freedom we prove stability estimates from which we deduce weak convergence in two steps first in space to a semi discretisation in time and then in time to the continuous problem finally we show a numerical test in a real life application specifically we simulate the wind driven circulation in the leman lake

incompressible finite element methods for navier stokes equations with nonstandard boundary conditions in r 3 application des methodes a elements finis incompressibles aux equations de navier stokes avec des conditions aux limites non standards dans r 3 utilisation du potentiel vecteur de la vorticite et de la pression estimations d erreurs

a variational multi scale method with spectral approximation of the sub scales application to the 1d advection diffusion equations abstract this paper introduces a variational multi scale method where the sub grid scales are computed by spectral approximations it is based upon an extension of the spectral theorem to non necessarily self adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted l 2 spaces this allows to element wise calculate the sub grid scales by means of the associated spectral expansion we propose a feasible vms spectral method by truncation of this spectral expansion to a finite number of modes we apply this general framework to the convection diffusion equation by analytically computing the family of eigenfunctions we perform a convergence and error analysis we also present some numerical tests that show the stability of the method for an odd number of spectral modes and an improvement of accuracy in the large resolved scales due to the adding of the sub grid spectral scales

a kind of collaboration competition networks abstract we propose describing a kind of cooperation competition systems by node weighted bipartite graphs in such systems the nodes can be divided into two types one expresses a kind of activities organizations or events named acts and another expresses the actors participating in some acts in each act the actors basically show collaboration relationship with each other however they play different roles in the cooperation usually every actor tries to play the most important role therefore the role difference can be regarded as a kind of competition the node weight usually signifies the role or importance degree of each actor we propose using some statistical properties for the description of such kind of systems the properties without considering node weight can describe the cooperation situation and configuration the properties with node weight may describe the competition results two example systems are reported to show the description method and the corresponding empirical investigation results one is the undergraduate elective network and another the library network of yangzhou university the description method may be effective for the similar systems in different fields

the growth of business firms theoretical framework and empirical evidence we introduce a model of proportional growth to explain the distribution pg g of business firm growth rates the model predicts that pg g is exponential in the central part and depicts an asymptotic power law behavior in the tails with an exponent 3 because of data limitations previous studies in this field have been focusing exclusively on the laplace shape of the body of the distribution in this article we test the model at different levels of aggregation in the economy from products to firms to countries and we find that the predictions of the model agree with empirical growth distributions and size variance relationships

parametric identification of parallel wiener hammerstein systems block oriented nonlinear models are popular in nonlinear modeling because of their advantages to be quite simple to understand and easy to use to increase the flexibility of single branch block oriented models such as hammerstein wiener and wiener hammerstein models parallel block oriented models can be considered this paper presents a method to identify parallel wiener hammerstein systems starting from input output data only in the first step the best linear approximation is estimated for different input excitation levels in the second step the dynamics are decomposed over a number of parallel orthogonal branches next the dynamics of each branch are partitioned into a linear time invariant subsystem at the input and a linear time invariant subsystem at the output this is repeated for each branch of the model the static nonlinear part of the model is also estimated during this step the consistency of the proposed initialization procedure is proven the method is validated on real world measurements using a custom built parallel wiener hammerstein test system

structure and evolution of the world trade network the world trade web wtw the network defined by the international import export trade relationships has been recently shown to display some important topological properties which are tightly related to the gross domestic product of world countries while our previous analysis focused on the static undirected version of the wtw here we address its full evolving directed description this is accomplished by exploiting the peculiar reciprocity structure of the wtw to recover the directed nature of international trade channels and by studying the temporal dependence of the parameters describing the wtw topology

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

gls and evss methods for a three field stokes problem arising from viscoelastic flows in this paper order one finite elements together with galerkin least squares gls methods are used for solving a three held stokes problem arising from the numerical study of viscoelastic hows stability and convergence results are established even when the solvent viscosity is small compared to the viscosity due to the polymer chains an iterative algorithm decoupling velocity pressure and stress calculations is proposed the link with the modified elastic viscous split stress evss method studied in m fortin r guenette r pierre comput methods appl mech engrg 143 1997 79 95 r guenette m fortin j non newtonian fluid mech 60 1995 27 52 is presented numerical results are in agreement with theoretical predictions and with those presented in m fortin r guenette r pierre comput methods appl mech engrg 143 1997 79 95 c 2001 elsevier science b v all rights reserved

nonparametric identification of wiener systems a wiener system i e a system in which a linear dynamic part is followed by a nonlinear and memoryless one is identified no parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem and a nonparametric algorithm recovering the characteristic from input output observations of the whole system is proposed its consistency is shown and the rate of convergence is given an idea for identification of the impulse response of the linear subsystem is proposed results of numerical simulation are also presented

extension of some particular interpolation operators to a triangle with one curved side abstract we extend some nielson and marshall type interpolation operators to the case of a triangle with one curved side we study the interpolation properties of the obtained operators and of their product and boolean sum operators the orders of accuracy and the remainders of the corresponding interpolation formulas finally we give some numerical examples

a local regularization operator for triangular and quadrilateral finite elements this paper develops a local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes this operator is a variant of the regularization operator of clement however ours is constructed via a local projection in a reference domain we prove in this paper that it has the same optimal approximation properties as the standard interpolation operator and we present some applications

recursive identification of mimo wiener systems stochastic approximation sa algorithms are proposed to identify a multi input and multi output mimo wiener system in which the system input is taken to be a sequence of independent and identically distributed i i d gaussian random vectors uk n 0 i the algorithm for identifying the nonlinear part is designed with multi variable kernel functions under suitable conditions we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one

error estimates in w 2 semi norms for discrete interpolating d 2 splines we derive error estimates in w 2 semi norms for multivariate discrete d 2 splines that interpolate an unknown function at the vertices of given triangulations these results are widely based on the construction of approximation operators and linear projectors onto piecewise polynomial spaces having weakly stable local bases

recursive identification for multi input multi output hammerstein wiener system abstractin this paper an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi input multi output hammerstein wiener system with process noise in the proposed identification method the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible then the auxiliary variable is constructed the parameters of the regression equations are identified and the system parameter matrices can be obtained by matrix composition of the parameter product matrix a theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance the effectiveness of the proposed method is validated through the experiments

identification of hammerstein wiener models this paper develops and illustrates a new maximum likelihood based method for the identification of hammerstein wiener model structures a central aspect is that a very general situation is considered wherein multivariable data non invertible hammerstein and wiener nonlinearities and colored stochastic disturbances both before and after the wiener nonlinearity are all catered for the method developed here addresses the blind wiener estimation problem as a special case

non reflecting boundary conditions for waveguides new non reflecting boundary conditions are introduced for the solution of the helmholtz equation in a waveguide these boundary conditions are perfectly transparent for all propagating modes they do not require the determination of these propagating modes but only their propagation constants a quasi local form of these boundary conditions is well suited as terminating boundary condition beyond finite element meshes related convergence properties to the exact solution and optimal error estimates are established

reconstructing the world trade multiplex the role of intensive and extensive biases in economic and financial networks the strength of each node has always an important economic meaning such as the size of supply and demand import and export or financial exposure constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown however several studies have proved that real economic networks and multiplexes topologically differ from configurations inferred only from node strengths here we provide a detailed analysis of the world trade multiplex by comparing it to an enhanced null model that simultaneously reproduces the strength and the degree of each node we study several temporal snapshots and almost 100 layers commodity classes of the multiplex and find that the observed properties are systematically well reproduced by our model our formalism allows us to introduce the static concept of extensive and intensive bias defined as a measurable tendency of the network to prefer either the formation of extra links or the reinforcement of link weights with respect to a reference case where only strengths are enforced our findings complement the existing economic literature on dynamic intensive and extensive trade margins more generally they show that real world multiplexes can be strongly shaped by layer specific local constraints

a microscopic study of the fitness dependent topology of the world trade network abstract previous studies have suggested that the world trade network belongs to the class of static hidden variable models in this article we investigate the microscopic structure of the world trade network that is the hidden variable correlation matrix of the network the hidden variable is defined as a rank ordering of gross domestic products this choice significantly reduces the noise in the statistical analysis found in previous studies the hidden variable correlation matrix that expresses the probability that a trade relationship between two countries of given fitness exists suggests an attachment kernel that at least partially favours trading pairs or dissimilar fitness rather than the purely multiplicative one found previously additionally we provide an in depth look at the data source and reveal that first order results such as the degree distribution exhibit significant qualitative differences depending on the data provider furthermore we shed light on the intertemporal activity of international trade and point out that fluctuations occur mostly between countries with strong dissimilarities of fitness and connectivity

an extended clique degree distribution and its heterogeneity in cooperation competition networks abstract after xiao et al w k xiao j ren f qi z w song m x zhu h f yang h y jin b h wang tao zhou empirical study on clique degree distribution of networks phys rev e 76 2007 037102 in this article we present an investigation on so called k cliques which are defined as complete subgraphs of k k 1 nodes in the cooperation competition networks described by bipartite graphs in the networks the nodes named actors are taking part in events organizations or activities named acts we mainly examine a property of a k clique called k clique act degree q defined as the number of acts in which the k clique takes part our analytic treatment on a cooperation competition network evolution model demonstrates that the distribution of k clique act degrees obeys mandelbrot distribution p q q to validate the analytical model we have further studied 13 different empirical cooperation competition networks with the clique numbers k 2 and k 3 empirical investigation results show an agreement with the analytic derivations we propose a new heterogeneity index h to describe the heterogeneous degree distributions of k clique and heuristically derive the correlation between h and and we argue that the cliques which take part in the largest number of acts are the most important subgraphs which can provide a new criterion to distinguish important cliques in the real world networks

analysis of a streamline diffusion finite element method for the stokes and navier stokes equations for the stokes equations with convection and the incompressible navier stokes equations the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure thus allowing the use of arbitrary pairs of velocity pressure spaces for the linear problem the authors obtain for all mesh peclet numbers optimal error estimates in natural norms including in particular the l 2 norm of the pressure the same holds for the nonlinear problem which close to a regular branch of solutions i e the linearized operator is an isomorphism of the norm of the inverse of which still depends on the reynolds number consequently the dependence of the error constants on the reynolds number is not completely resolved in this case

finite element approximations for the stokes equations on curved domains and their errors we construct finite element spaces for the stokes equations on curved domains which satisfy the email protected ka condition moreover we estimate the errors of the finite element approximations for the stokes equations

invariant distributions and the limiting behavior of markovian economic models equilibria in stochastic economic models are often time series which fluctuate in complex ways but it is sometimes possible to summarize the long run average characteristics of these fluctuations for example if the law of motion determined by economic interactions is markovian and if the equilibrium time series converges in a specific probabilistic sense then the long run behavior is completely determined by an invariant probability distribution this paper develops and unifies a number of results found in the probability literature which enable one to prove under very general conditions the existence of an invariant distribution and the convergence of the corresponding markov process virtually all of economic theory focuses upon the study of economic equilibrium this concept has recently undergone several subtle elaborations no longer must a system of markets in equilibrium be thought of as one at rest in a static steady state instead there is a growing body of literature e g 4 5 12 16 20 21 which defines equilibrium as a stochastic process of market clearing prices and quantities which is consistent with the self interested behavior of economic agents needless to say equilibrium stochastic processes can be very complex time series which fluctuate in irregular ways for theoretical and econometric purposes it is useful to have a convenient way of summarizing the average behavior of such processes over time this paper draws together and unifies a number of fundamental results from the probability literature which enable one to do this for discrete time markov processes on general state spaces the starting point of the analysis is a set s of economic states e g prices and or quantities the only technical restriction placed upon s is that it be a borel subset of a complete separable metric space the second datum is a transition probability p s on s the number p s a records the probability that the economic system moves from the state s to some state in the borel subset a of s during one unit of elapsed time in economic applications the transition probability is usually derived from hypotheses about market clearing and the maximizing behavior of economic agents the transition probability together with an initial probability measure on s defines a discrete time markov process one way of summarizing the dynamic behavior implied by p is to look for an invariant probability a probability measure x on s is invariant for p if for all borel subsets a of s one has the equality f p s a x ds x a an invariant probability is a kind of probabilistic steady state for the dynamics defined by p of course there may be no invariant probability for p at all and even if one exists it may convey no information about the average behavior of the process over time except under very special initial conditions there is a second way of summarizing the behavior of markov processes defined by the transition probability p let p s a denote the n step transition

empirical study on clique degree distribution of networks the community structure and motif modular network hierarchy are of great importance for understanding the relationship between structures and functions we investigate the distribution of clique degrees which are an extension of degree and can be used to measure the density of cliques in networks empirical studies indicate the extensive existence of power law clique degree distributions in various real networks and the power law exponent decreases with an increase of clique size

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100