a finite element spectral method for approximating the time harmonic maxwell system in r 3 we describe and analyze a method for computing an approximation to the time harmonic electromagnetic field scattered by a bounded inhomogeneity the method is to couple a finite element scheme on a bounded domain with a series solution outside the bounded domain the main result of the paper is to show that the proposed numerical scheme possesses a unique solution with quasi optimal approximation properties we do this by verifying the conditions of the babuska brezzi theory for saddle point problems in analyzing the continuous problem we also provide a new variational proof of the existence of solutions of the continuous maxwell problem

inverse medium scattering problems for electromagnetic waves consider a time harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in mathbb r 3 in this paper existence and uniqueness of the variational problem for forward scattering are established an energy estimate for the scattered field with a uniform bound with respect to the wavenumber is obtained in the case of low frequency on which the born approximation is based a continuation method for the inverse medium scattering problem which reconstructs the scatterer of an inhomogeneous medium from boundary measurements of the scattered wave is developed the algorithm requires multifrequency scattering data using an initial guess from the born approximation each update is obtained via recursive linearization on the wavenumber k by solving one forward problem and one adjoint problem of maxwell s equations

corrigendum a finite element spectral method for approximating the time harmonic maxwell system in r 3 in our paper siam j appl math 55 1995 pp 1234 1344 theorem 4 2 b is incorrect this note shows how to avoid the use of theorem 4 2 b in the remainder of the paper we emphasize that the main results of the paper theorems 4 6 and 5 3 are correct but that the proofs must be modified as shown in this note

on learning multicategory classification with sample queries consider the pattern recognition problem of learning multicategory classification from a labeled sample for instance the problem of learning character recognition where a category corresponds to an alphanumeric letter the classical theory of pattern recognition assumes labeled examples appear according to the unknown underlying pattern class conditional probability distributions where the pattern classes are picked randomly according to their a priori probabilities in this paper we pose the following question can the learning accuracy be improved if labeled examples are independently randomly drawn according to the underlying class conditional probability distributions but the pattern classes are chosen not necessarily according to their a priori probabilities we answer this in the affirmative by showing that there exists a tuning of the sub sample proportions which minimizes a loss criterion the tuning is relative to the intrinsic complexity of the bayes classifier as this complexity depends on the underlying probability distributions which are assumed to be unknown we provide an algorithm which learns the proportions in an on line manner utilizing sample querying which asymptotically minimizes the criterion in practice this algorithm may be used to boost the performance of existing learning classification algorithms by apportioning better sub sample proportions

learning by canonical smooth estimation i simultaneous estimation this paper examines the problem of learning from examples in a framework that is based on but more general than valiant s probably approximately correct pac model for learning in our framework the learner observes examples that consist of sample points drawn and labeled according to a fixed unknown probability distribution based on this empirical data the learner must select from a set of candidate functions a particular function or hypothesis that will accurately predict the labels of future sample points the expected mismatch between a hypothesis prediction and the label of a new sample point is called the hypothesis generalization error following the pioneering work of vapnik and chervonenkis others have attacked this sort of learning problem by finding hypotheses that minimize the relative frequency based empirical error estimate we generalize this approach by examining the simultaneous estimation problem we demonstrate how one can learn from such a simultaneous error estimate and propose a new class of estimators called smooth estimators we characterize the class of simultaneous estimation problems solvable by a smooth estimator

empirical processes typical sequences and coordinated actions in standard borel spaces this paper proposes a new notion of typical sequences on a wide class of abstract alphabets so called standard borel spaces which is based on approximations of memoryless sources by empirical distributions uniformly over a class of measurable test functions in the finite alphabet case we can take all uniformly bounded functions and recover the usual notion of strong typicality or typicality under the total variation distance for a general alphabet however this function class turns out to be too large and must be restricted with this in mind we define typicality with respect to any glivenko cantelli function class i e a function class that admits a uniform law of large numbers and demonstrate its power by giving simple derivations of the fundamental limits on the achievable rates in several source coding scenarios in which the relevant operational criteria pertain to reproducing empirical averages of a general alphabet stationary memoryless source with respect to a suitable function class

marching schemes for inverse acoustic scattering problems for the numerical solution of inverse helmholtz problems the boundary value problem for a helmholtz equation with spatially variable wave number has to be solved repeatedly for large wave numbers this is a challenge in the paper we reformulate the inverse problem as an initial value problem and describe a marching scheme for the numerical computation that needs only n2 log n operations on an n n grid we derive stability and error estimates for the marching scheme we show that the marching solution is close to the low pass filtered true solution we present numerical examples that demonstrate the efficacy of the marching scheme

donsker classes of sets we study the central limit theorem clt and the law of large numbers lln for empirical processes indexed by a countable class of sets c the main result of purely measure theoretical nature relates different ways to measure the size of c it relies on a new rearrangement inequality that has been inspired by techniques used in the local theory of banach spaces as an application we give sharp necessary conditions for the clt that are in some sense the best possible we also obtain a way to compute the rate of convergence in the lln

stability for the multifrequency inverse medium problem abstract the solution of a multi frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies in this paper rigorous stability estimates are derived when the frequency takes value in a bounded interval it is showed that the ill posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger more precisely under certain regularity assumptions on the refractive index the estimates indicate that the power in holder stability is an increasing function of the largest value in the frequency band finally a lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula

numerical resolution of an electromagnetic inverse medium problem at fixed frequency the aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency the governing equations are the time harmonic maxwell equations formulated in electric field in a two dimensional bounded domain we express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields our numerical reconstruction algorithm combines the bfgs method and an iterative process called the adaptive eigenspace inversion the unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator both the eigenspace and the mesh are iteratively adapted during the minimization procedure numerical experiments illustrate the performance of the reconstruction for various configurations

numerical solution of inverse scattering problems with multi experimental limited aperture data in this paper a regularized homotopy continuation method is presented for numerical solution of nonlinear ill posedness inverse problems two major difficulties for solving these inverse problems by an optimization method are the ill posedness and the presence of many local minima classic iterative methods such as gauss newton or levenberg marquardt algorithms offer fast local convergence but might not be able to compute the global minimum based on a natural concept of multi experimental data a regularized homotopy continuation method is constructed to compute the global minimum as the experimental index t increases continuously the global minimizer can be computed continuously by using local optimization methods by discretizing the continuous homotopy method various recursive linearization algorithms are developed these algorithms are applied to numerical solution of an inverse medium scattering problem which reconstructs the refractive index of an inhomogeneous medium from limited aperture measurements of the far field pattern of the scattered fields it is assumed that the data is measured at multiple frequencies the inverse scattering problem with limited aperture is challenging since without full aperture measurements the ill posedness and nonlinearity of the inverse problem become more severe an efficient regularized iterative linearization method recursive linearization with respect to the wave number is developed for solving the inverse problem the convergence of the iterative method is examined by numerical examples

probably approximate learning of sets and functions probably approximate learning is the inference of a set also called a concept from a small number of sample points under the probabilistic measure of success proposed in l g valiant proc acm symposium on theory of computing 1984 pp 436 445 within this model necessary and sufficient conditions are identified for efficient learning of a class of concepts defined on the strings of the binary alphabet these results are with respect to both time and information complexity measures and are in terms of the asymptotic behaviour of the vapnik chervonenkis dimension of the class corresponding results are also obtained for the case when the error in the learning process is to be one sided in that the inferred concept is required to be a subset of the concept to be learned the scope of the learning model is then widened to include the inference of functions the vapnik chervonenkis dimension is also extended to obtain a measure called the generalized dimension of a class of functions using this m

dynamics of directed graphs the world wide web we introduce and simulate a growth model of the world wide web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real web to update outgoing links re directing them towards constantly changing selected nodes emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the web the growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links we obtain quantitative agreement with the recent empirical data in the real web for the distributions of in and out links and for the size of the connected component in a fully grown network of n nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node the distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior by decreasing the control parameter average fraction of updated and added links per time step towards c n 10 the web can resume a critical structure with no giant component in it we find a different universality class when the updates of links are not allowed i e for 0 corresponding to the network of science citations

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

the generalized polarization tensors for resolved imaging part ii shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements this paper deals with the problem of reconstructing the electromagnetic parameters and the shape of a target from multi static response matrix measurements at a single frequency the target is of characteristic size less than the operating wavelength using long wavelength asymptotic expansions of the measurements of high order we show how the electromagnetic parameters and the equivalent ellipse of the target can be reconstructed the asymptotic expansions of the measurements are written in terms of the new concept of frequency dependent polarization tensors moreover we extend the optimization approach proposed in part i 9 to image geometric details of an electromagnetic target that are finer than the equivalent ellipse the equivalent ellipse still provides a good initial guess for the optimization procedure however compared to the conductivity case in 9 the cost functional measures the discrepancy between the computed and measured high order frequency dependent polarization tensors rather than between the generalized polarization tensors the main reason for such a modification of the cost functional is the fact that the measured frequency dependent polarization tensors can be easily obtained from multistatic measurements by solving a linear system while the derivation of the generalized polarization tensors from measurements requires more delicate treatment the proposed methods are numerically implemented to demonstrate their validity and efficiency mathematics subject classification msc2000 35r30 35b30

robustness of the in degree exponent for the world wide web we consider a stochastic model for directed scale free networks following power laws in the degree distributions in both incoming and outgoing directions in our model the number of vertices grow geometrically with time with a growth rate p at each time step i each newly introduced vertex is connected to a constant number of already existing vertices with the probability linearly proportional to in degree distribution of a selected vertex and ii each existing vertex updates its outgoing edges through a stochastic multiplicative process with mean growth rate of outgoing edges g and its variance ensuremath sigma 2 using both analytic treatment and numerical simulations we show that while the out degree exponent ensuremath gamma mathrm out depends on the parameters the in degree exponent ensuremath gamma mathrm in has two distinct values ensuremath gamma mathrm in 2 for pgg and 1 for plg independent of different parameters values the latter case has logarithmic correction to the power law since the vertex growth rate p is larger than the degree growth rate g for the world wide web www nowadays the in degree exponent appears robust as ensuremath gamma mathrm in 2 for the www

learning by canonical smooth estimation ii learning and choice of model complexity this paper analyzes the properties of a procedure for learning from examples this canonical learner is based on a canonical error estimator developed in part i in learning problems one can observe data that consists of labeled sample points and the goal is to find a model or hypothesis from a set of candidates that will accurately predict the labels of new sample points the expected mismatch between a hypothesis prediction and the actual label of a new sample point is called the hypothesis generalization error we compare the canonical learner with the traditional technique of finding hypotheses that minimize the relative frequency based empirical error estimate it is shown that for a broad class of learning problems the set of cases for which such empirical error minimization works is a proper subset of the cases for which the canonical learner works we derive bounds to show that the number of samples required by these two methods is comparable we also address the issue of how to determine the appropriate complexity for the class of candidate hypotheses

a finite element method for approximating electromagnetic scattering from a conducting object we provide an error analysis of a fully discrete finite element fourier series method for approximating maxwell s equations the problem is to approximate the electromagnetic field scattered by a bounded inhomogeneous and anisotropic body the method is to truncate the domain of the calculation using a series solution of the field away from this domain we first prove a decomposition for the poincare steklov operator on this boundary into an isomorphism and a compact perturbation this is proved using a novel argument in which the scattering problem is viewed as a perturbation of the free space problem using this decomposition and edge elements to discretize the interior problem we prove an optimal error estimate for the overall problem

an improved imaging method for extended targets when we use direct imaging methods for solving inverse scattering problems we observe artificial lines which make it hard to determine the shape of targets we propose a signal space test to study the cause of the artificial lines and we use multiple frequency data to reduce the effect from them finally we use the active contour without edges acwe method to further improve the imaging results the final reconstruction is accurate and robust the computational cost is lower than iterative imaging methods which need to solve the forward problem in each iteration

inverse scattering by a continuation method with initial guesses from a direct imaging algorithm a novel continuation method is presented for solving the inverse medium scattering problem of the helmholtz equation which is to reconstruct the shape of the inhomogeneous medium from boundary measurements of the scattered field the boundary data is assumed to be available at multiple frequencies initial guesses are chosen from a direct imaging algorithm multiple signal classification music along with a level set representation at a certain wavenumber where the born approximation may not be valid each update via recursive linearization on the wavenumbers is obtained by solving one forward and one adjoint problem of the helmholtz equation

relationship between the in degree and out degree of www abstract in this paper the relationship between the in degree and out degree of world wide web is studies at each time step a new node with out degree k out is added where k out obeys the power law distribution and its mean value is m the analytical and simulation results suggest that the exponent of in degree distribution would be i 2 1 m depending on the average out degree this finding is supported by the empirical data which has not been emphasized by the previous studies on directed networks

microwave imaging by elastic deformation in this paper we show that by using microwave measurements at different frequencies and ultrasound localized perturbations to create local changes in the medium it is possible to extend the method developed by ammari et al in siam j appl math 68 2008 pp 1557 1573 to problems of the form nabla cdot a nabla u k 2 qu 0 in omega u varphi on partial omega and to reliably reconstruct both the real valued functions a and q from the internal energies a nabla u 2 and q u 2

a convergence analysis of the landweber iteration for nonlinear ill posed problems in this paper we prove that the landweber iteration is a stable method for solving nonlinear ill posed problems for perturbed data with noise level delta we propose a stopping rule that yields the convergence rate o delta 1 2 under appropriate conditions we illustrate these conditions for a few examples

automatic pattern recognition a study of the probability of error a test sequence is used to select the best rule from a class of discrimination rules defined in terms of the training sequence the vapnik chervonenkis and related inequalities are used to obtain distribution free bounds on the difference between the probability of error of the selected rule and the probability of error of the best rule in the given class the bounds are used to prove the consistency and asymptotic optimality for several popular classes including linear discriminators nearest neighbor rules kernel based rules histogram rules binary tree classifiers and fourier series classifiers in particular the method can be used to choose the smoothing parameter in kernel based rules to choose k in the k nearest neighbor rule and to choose between parametric and nonparametric rules

reconstruction of two dimensional permittivity distribution using the distorted born iterative method the distorted born iterative method dbim is used to solve two dimensional inverse scattering problems thereby providing another general method to solve the two dimensional imaging problem when the born and the rytov approximations break down numerical simulations are performed using the dbim and the method proposed previously by the authors int j imaging syst technol vol 1 no 1 p 100 8 1989 called the born iterative method bim for several cases in which the conditions for the first order born approximation are not satisfied the results show that each method has its advantages the dbim shows faster convergence rate compared to the bim while the bim is more robust to noise contamination compared to the dbim

recent developments in the qualitative approach to inverse electromagnetic scattering theory we consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the measured electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency we shall discuss the linear sampling method for solving the inverse scattering problem which does not require any a priori knowledge of the geometry and the physical properties of the scatterer included in our discussion is the case of partially coated objects and inhomogeneous background we give references for numerical examples for each problem discussed in this paper

a multi frequency inverse source problem this paper is concerned with an inverse source problem that determines the source from measurements of the radiated fields away at multiple frequencies rigorous stability estimates are established when the background medium is homogeneous it is shown that the ill posedness of the inverse problem decreases as the frequency increases under some regularity assumptions on the source function it is further proven that by increasing the frequency the logarithmic stability converts to a linear one for the inverse source problem

generation of scale free networks using a simple preferential rewiring dynamics abstract we propose a simple dynamical process for non growing networks where steady states in the long time limit exhibit power law degree distributions with the exponent 2 at each time step two nodes i and j are randomly selected and one incoming link to i is redirected to j with the rewiring probability r determined only by degrees of two nodes k i and k j while higher degree nodes are preferred to get another link this is an application of the general model introduced earlier s ree phys rev e 73 2006 026115 to take the structure of networks into account we also consider three possible distinctions for the model i how we choose a rewiring link out of all incoming links to i three cases ii whether links are directed or not two cases iii types of networks considering the existence of self loops and multiple links two cases as a result we specify the total of 12 different cases of the model we then observe numerically that networks will evolve to steady states with power law degree distributions when parameters of the model satisfy certain conditions this work is from an effort to find a simple model of the network dynamics generating scale free networks and has a potential to become an underlying mechanism for wide range of scale free non growing networks

equivalence of models for polynomial learnability abstract in this paper we consider several variants of valiant s learnability model that have appeared in the literature we give conditions under which these models are equivalent in terms of the polynomially learnable concept classes they define these equivalences allow comparisons of most of the existing theorems in valiant style learnability and show that several simplifying assumptions on polynomial learning algorithms can be made without loss of generality we also give a useful reduction of learning problems to the problem of finding consistent hypotheses and give comparisons and equivalences between valiant s model and the prediction learning models of haussler littlestone and warmuth in 29th annual ieee symposium on foundations of computer science 1988

the glivenko cantelli problem we give a new type of characterization of the glivenko cantelli classes in the case of a class mathscr l of sets the characterization is closely related to the configuration that the sets of mathscr l can have it allows one to decide simply whether a given class is a glivenko cantelli class the characterization is based on a new measure theoretic analysis of sets of measurable functions this analysis also gives an approximation theorem for glivenko cantelli classes sharpenings of the vapnik cervonenkis criteria and the value of the asymptotic discrepancy for classes that are not glivenko cantelli an application is given to the law of large numbers in a banach space for functions that need not be random variables

some contributions to fixed distribution learning theory we consider some problems in learning with respect to a fixed distribution we introduce two new notions of learnability these are probably uniformly approximately correct puac learnability which is a stronger requirement than the widely studied pac learnability and minimal empirical risk mer learnability which is a stronger requirement than the previously defined notions of solid or potential learnability it is shown that although the motivations for defining these two notions of learnability are entirely different these two notions are in fact equivalent to each other and in turn equivalent to a property introduced here referred to as the shrinking width property it is further shown that if the function class to be learned has the property that empirical means converge uniformly to their true values then all of these learnability properties hold in the course of proving conditions for these forms of learnability we also obtain a new estimate for the vc dimension of a collection of sets obtained by performing boolean operations on a given collection this result is of independent interest we consider both the case in which there is an underlying target function as well as the case of model free or agnostic learning finally we consider the issue of representation of a collection of sets by its subcollection of equivalence classes it is shown by example that by suitably choosing representatives of each equivalence class it is possible to affect the property of uniform convergence of empirical probabilities

extension of the pac framework to finite and countable markov chains we consider a model of learning in which the successive observations follow a certain markov chain the observations are labeled according to a membership to some unknown target set for a markov chain with finitely many states we show that if the target set belongs to a family of sets with a finite vapnik chervonenkis 1995 dimension then probably approximately correct pac learning of this set is possible with polynomially large samples specifically for observations following a random walk with a state space spl xscr and uniform stationary distribution the sample size required is no more than spl omega t sub 0 1 spl lambda sub 2 log t sub 0 spl chi 1 spl delta where spl delta is the confidence level spl lambda sub 2 is the second largest eigenvalue of the transition matrix and t sub 0 is the sample size sufficient for learning from independent and identically distributed i i d observations we then obtain similar results for markov chains with countably many states using lyapunov function technique and results on mixing properties of infinite state markov chains

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

a transpose free quasi minimal residual algorithm for non hermitian linear systems the biconjugate gradient method bcg for solving general non hermitian linear systems ax b and its transpose free variant the conjugate gradients squared algorithm cgs both typically exhib

decision theoretic generalizations of the pac model for neural net and other learning applications we describe a generalization of the pac learning model that is based on statistical decision theory in this model the learner receives randomly drawn examples each example consisting of an instance x in x and an outcome y in y and tries to find a hypothesis h x a where h in h that specifies the appropriate action a in a to take for each instance x in order to minimize the expectation of a loss l y a here x y and a are arbitrary sets l is a real valued function and examples are generated according to an arbitrary joint distribution on x times y special cases include the problem of learning a function from x into y the problem of learning the conditional probability distribution on y given x regression and the problem of learning a distribution on x density estimation we give theorems on the uniform convergence of empirical loss estimates to true expected loss rates for certain hypothesis spaces h and show how this implies learnability with bounded sample size disregarding computational complexity as an application we give distribution independent upper bounds on the sample size needed for learning with feedforward neural networks our theorems use a generalized notion of vc dimension that applies to classes of real valued functions adapted from pollard s work and a notion of capacity and metric dimension for classes of functions that map into a bounded metric space supersedes 89 30 and 90 52 also in information and computation vol 100 no 1 september 1992

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

fast numerical solution of the electromagnetic medium scattering problem and applications to the inverse problem we propose a method for computing the scattering of a time harmonic electromagnetic wave in a medium with a locally perturbed refractive index we prove that it converges of arbitrarily high order depending on the smoothness of the refractive index and that the time complexity is o n 3log n as an application we solve the corresponding inverse problem using a preconditioned newton method and discuss how to compute the frechet derivative of the solution operator and its adjoint by the proposed method the performance of both the forward and the inverse solver is illustrated in a number of numerical experiments

fluctuation driven dynamics of the internet topology we study the dynamics of the internet topology based on empirical data on the level of the autonomous systems it is found that the fluctuations occurring in the stochastic process of connecting and disconnecting edges are important features of the internet dynamics the network s overall growth can be described approximately by a single characteristic degree growth rate g eff approximately 0 016 and the fluctuation strength sigma eff approximately 0 14 together with the vertex growth rate alpha approximately 0 029 a stochastic model which incorporates these values and an adaptation rule newly introduced reproduces several features of the real internet topology such as the correlations between the degrees of different vertices

numerical solution of an inverse medium scattering problem for maxwell s equations at fixed frequency consider a time harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in r 3 in this paper well posedness of the variational problem for the direct scattering is examined an energy estimate for the scattered field is obtained on which the born approximation is based a regularized recursive linearization method for the inverse medium scattering which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered field is developed the algorithm requires only single frequency data using an initial guess from the born approximation each update is obtained via continuation on the spatial frequency of a two parameter family of plane waves by solving one direct problem and one adjoint problem of the maxwell equation

the inverse electromagnetic scattering problem for a mixed boundary value problem for screens we consider the inverse scattering problem of determining the shape of mixed perfectly conducting impedance screens from a knowledge of the incident time harmonic electromagnetic plane wave and the electric far field pattern of the scattered wave we adapt the linear sampling method invented by colton and kirsch inverse problems 12 1996 383 for the case of scattering by obstacles with nonempty interior numerical examples are given for mixed screens in r3

learning dynamical systems in a stationary environment abstract we consider the problem of learning the input output relation of a dynamical system from noisy data our method rests on the use of a smooth simultaneous estimator which generalizes the standard empirical estimator in a stationary environment our algorithm is shown to select a model which exhibits the probably approximately correct pac property under very mild conditions this contribution should be thought of as a first attempt to extend concepts developed in learning theory to the field of system identification where due to the presence of the system dynamics the typical i i d assumption on the data made in learning theory is not satisfied

computational limitations on learning from examples the computational complexity of learning boolean concepts from examples is investigated it is shown for various classes of concept representations that these cannot be learned feasibly in a distribution free sense unless r np these classes include a disjunctions of two monomials b boolean threshold functions and c boolean formulas in which each variable occurs at most once relationships between learning of heuristics and finding approximate solutions to np hard optimization problems are given

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

application of the fem with adaptivity for electromagnetic inverse medium scattering problems abstract the paper presents a study of solution of inverse medium scattering problems for 3d time harmonic electromagnetics the solution is based on minimization of the misfit function between the observed scattered fields and trial solutions of direct problems for the sought approximate distribution of electric permittivity the sources of illuminating waves and the observation points of the scattered fields are located in the nearfield the scatterer the simulations of the direct problems are performed with the finite element method application of adaptive mesh refinement to improve accuracy of solutions is illustrated tests with real and complex valued distributions of electric permittivity and with complete and incomplete measurement data are presented