a stochastic continuation approach to piecewise constant reconstruction we address the problem of reconstructing a piecewise constant 3 d object from a few noisy 2 d line integral projections more generally the theory developed here readily applies to the recovery of an ideal n d signal n ges 1 from indirect measurements corrupted by noise stabilization of this ill conditioned inverse problem is achieved with the potts prior model which leads to a challenging optimization task to overcome this difficulty we introduce a new class of hybrid algorithms that combines simulated annealing with deterministic continuation we call this class of algorithms stochastic continuation sc we first prove that under mild assumptions sc inherits the finite time convergence properties of generalized simulated annealing then we show that sc can be successfully applied to our reconstruction problem in addition we look into the concave distortion acceleration method introduced for standard simulated annealing and we derive an explicit formula for choosing the free parameter of the cost function numerical experiments using both synthetic data and real radiographic testing data show that sc outperforms standard simulated annealing

hitting time asymptotics for hard core interactions on grids we consider the hard core model with metropolis transition probabilities on finite grid graphs and investigate the asymptotic behavior of the first hitting time between its two maximum occupancy configurations in the low temperature regime in particular we show how the order of magnitude of this first hitting time depends on the grid sizes and on the boundary conditions by means of a novel combinatorial method our analysis also proves the asymptotic exponentiality of the scaled hitting time and yields the mixing time of the process in the low temperature limit as side result in order to derive these results we extended the model independent framework in manzo et al j stat phys 115 1 2 591 642 2004 for first hitting times to allow for a more general initial state and target subset

the convergence of stochastic algorithms solving flow shop scheduling abstract in the paper we apply logarithmic cooling schedules of simulated annealing based algorithms to flow shop scheduling in our problem setting the objective to minimize the overall completion time which is called the makespan we prove a lower bound for the number of steps that are sufficient to approach an optimum solution with a certain probability the result is related to the maximum escape depth from local minima of the underlying energy landscape in our approach we need n o log o 1 1 steps to be in an optimum solution with probability 1 where n denotes the total number of tasks the auxiliary computations are of polynomial complexity since the model cannot be approximated arbitrarily closely in the general case unless p np the approach can be used to obtain approximation algorithms that work well in the average case

a fast algorithm for computing distance spectrum of convolutional codes a fast algorithm for searching a tree fast is presented for computing the distance spectrum of convolutional codes the distance profile of a code is used to limit substantially the error patterns that have to be searched the algorithm can easily be modified to determine the number of nonzero information bits of an incorrect path as well as the length of an error event for testing systematic codes a faster version of the algorithm is given fast is much faster than the standard bidirectional search on a microvax d sub infinity 27 was verified for a rate r 1 2 memory m 25 code in 37 s of cpu time extensive tables of rate r 1 2 encoders are given several of the listed encoders have distance spectra superior to those of any previously known codes of the same rate and memory a conjecture than an r 1 2 systematic convolutional code of memory 2m will perform as well as a nonsystematic convolutional code of memory m is given strong support

on interleaved differentially encoded convolutional codes we study a serially interleaved concatenated code construction where the outer code is a standard convolutional code and the inner code is a recursive convolutional code of rate 1 we focus on the ubiquitous inner differential encoder used in particular to resolve phase ambiguities double differential encoder used to resolve both phase and frequency ambiguities and another rate 1 recursive convolutional code of memory 2 we substantiate analytically the rather surprising result that the error probabilities corresponding to a maximum likelihood ml coherently detected antipodal modulation over the additive white gaussian noise awgn channel for this construction are advantageous as compared to the stand alone outer convolutional code this is in spite of the fact that the inner code is of rate 1 the analysis is based on the tangential sphere upper bound of an ml decoder incorporating the ensemble weight distribution wd of the concatenated code where the ensemble is generated by all random and uniform interleavers this surprising result is attributed to the wd thinning observed for the concatenated scheme which shapes the wd of the outer convolutional code to resemble more closely the binomial distribution typical of a fully random code of the same length and rate this gain is maintained regardless of a rather dramatic decrease as demonstrated here in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand alone convolutional code the advantage of the examined serially interleaved concatenated code given in terms of bit and or block error probability which is decoded by a practical suboptimal decoder over the optimally decoded standard convolutional code is demonstrated by simulations and some insights into the performance of the iterative decoding algorithm are also discussed though we have investigated only specific constructions of constituent inner rate 1 and outer codes we trust hinging on the rational of the arguments here that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes

on improved bounds on the decoding error probability of block codes over interleaved fading channels with applications to turbo like codes we derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved rician fading channels coherently detected and maximum likelihood ml decoded we assume that the fading coefficients during each symbol are statistically independent due to a perfect channel interleaver and that perfect estimates of these fading coefficients are provided to the receiver the improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity and are found by generalizing some previously introduced upper bounds for the binary input additive white gaussian nose awgn channel the advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low density parity check ldpc codes and it is especially pronounced in a portion of the rate region exceeding the cutoff rate our generalization of the duman and salehi bound duman and salehi 1998 duman 1998 which is based on certain variations of gallager s 1965 bounding technique is demonstrated to be the tightest reported upper bound we therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo like codes referring to the optimal ml decoding for certain ensembles of uniformly interleaved turbo codes the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms

a distance spectrum interpretation of turbo codes the performance of turbo codes is addressed by examining the code s distance spectrum the error floor that occurs at moderate signal to noise ratios is shown to be a consequence of the relatively low free distance of the code it is also shown that the error floor can be lowered by increasing the size of the interleaver without changing the free distance of the code alternatively the free distance of the code may be increased by using primitive feedback polynomials the excellent performance of turbo codes at low signal to noise ratios is explained in terms of the distance spectrum the interleaver in the turbo encoder is shown to reduce the number of low weight codewords through a process called spectral thinning this thinned distance spectrum results in the free distance asymptote being the dominant performance parameter for low and moderate signal to noise ratios

strategies for computing goal oriented a posteriori error measures in non linear elasticity we investigate the characteristics and performance of goal oriented a posteriori error measures for a class of non linear elasticity models while restriction is made to small strain theory the chosen error measure of the displacement field can be global or local probing the chosen quantity in a specific spatial point the error is computable with the aid of the solution of a dual problem whose data depend on the error measure the main thrust of the paper is to evaluate the performance of a few different approximation strategies for computing the dual solution the chosen strategies are compared in terms of accuracy ease of implementation reliability and cost efficiency a well known numerical example the cook s membrane is used for the numerical evaluations

a proof of convergence of the map turbo detector to the awgn case in this paper we consider a coded transmission over a frequency selective channel we propose to study analytically the convergence of the turbo detector using a maximum a posteriori map equalizer and a map decoder we show that the densities of the extrinsic log likelihood ratios llrs exchanged during the iterations are e symmetric and output symmetric under the gaussian approximation this property allows to perform a one dimensional 1 d analysis of the turbo detector by deriving the analytical expressions of the extrinsic llr distributions under the gaussian approximation we prove that the bit error rate ber performance of the turbo detector converges to the ber performance of the coded additive white gaussian noise awgn channel at high signal to noise ratio snr for any frequency selective channel

natural norm a posteriori error estimators for reduced basis approximations we present a technique for the rapid and reliable prediction of linear functional outputs of coercive and noncoercive linear elliptic partial differential equations with affine parameter dependence the essential components are i rapidly convergent global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n judiciously selected points in parameter space ii a posteriori error estimation relaxations of the error residual equation that provide inexpensive yet sharp bounds for the error in the outputs of interest and iii offiine online computational procedures methods which decouple the generation and projection stages of the approximation process the operation count for the online stage in which given a new parameter value we calculate the output of interest and associated error bound depends only on n typically very small and the parametric complexity of the problem in this paper we propose a new natural norm formulation for our reduced basis error estimation framework that a greatly simplifies and improves our inf sup lower bound construction offline and evaluation online a critical ingredient of our a posteriori error estimators and b much better controls significantly sharpens our output error bounds in particular through deflation for parameter values corresponding to nearly singular solution behavior we apply the method to two illustrative problems a coercive laplacian heat conduction problem which becomes singular as the heat transfer coefficient tends to zero and a non coercive helmholtz acoustics problem which becomes singular as we approach resonance in both cases we observe very economical and sharp construction of the requisite natural norm inf sup lower bound rapid convergence of the reduced basis approximation reasonable effectivities even for near singular behavior for our deflated output error estimators and significant several order of magnitude online computational savings relative to standard finite element procedures

turbo decoding on the binary erasure channel finite length analysis and turbo stopping sets this paper is devoted to the finite length analysis of turbo decoding over the binary erasure channel bec the performance of iterative belief propagation decoding of low density parity check ldpc codes over the bec can be characterized in terms of stopping sets we describe turbo decoding on the bec which is simpler than turbo decoding on other channels we then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure apply turbo decoding until the transmitted codeword has been recovered or the decoder fails to progress further then the set of erased positions that will remain when the decoder stops is equal to the unique maximum size turbo stopping set which is also a subset of the set of erased positions furthermore we present some improvements of the basic turbo decoding algorithm on the bec the proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results finally we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption and an efficient enumeration algorithm of small size turbo stopping sets for a particular interleaver the solution is based on the algorithm proposed by garello et al in 2001 to compute an exhaustive list of all low weight codewords in a turbo code

on quasi cyclic interleavers for parallel turbo codes in this correspondence we present an interleaving scheme that yields quasi cyclic turbo codes we prove that randomly chosen members of this family yield with probability almost 1 turbo codes with asymptotically optimum minimum distance i e growing as a logarithm of the interleaver size these interleavers are also very practical in terms of memory requirements and their decoding error probabilities for small block lengths compare favorably with previous interleaving schemes

a priori model reduction through proper generalized decomposition for solving time dependent partial differential equations over the past years model reduction techniques have become a necessary path for the reduction of computational requirements in the numerical simulation of complex models a family of a priori model reduction techniques called proper generalized decomposition pgd methods are receiving a growing interest these methods rely on the a priori construction of separated variables representations of the solution of models defined in tensor product spaces they can be interpreted as generalizations of proper orthogonal decomposition pod for the a priori construction of such separated representations in this paper we introduce and study different definitions of pgd for the solution of time dependent partial differential equations we review classical definitions of pgd based on galerkin or minimal residual formulations and we propose and discuss several improvements for these classical definitions we give an interpretation of optimal decompositions as the solution of pseudo eigenproblems we also introduce a new definition of pgd called minimax pgd which can be interpreted as a petrov galerkin model reduction technique where test and trial reduced basis functions are related by an adjoint problem this new definition improves convergence properties of separated representations with respect to a chosen metric it coincides with a classical pod for degenerate time dependent partial differential equations for the numerical construction of each pgd we propose algorithms inspired from the solution of eigenproblems several numerical examples illustrate and compare the different definitions of pgd on transient advection diffusion reaction equations

theory of genetic algorithms ii models for genetic operators over the string tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling we present a theoretical framework for an asymptotically converging scaled genetic algorithm which uses an arbitrary size alphabet and common scaled genetic operators the alphabet can be interpreted as a set of equidistant real numbers and multiple spot mutation performs a scalable compromise between pure random search and neighborhood based change on the alphabet level we discuss several versions of the crossover operator and their interplay with mutation in particular we consider uniform crossover and gene lottery crossover which does not commute with mutation the vose liepins version of mutation crossover is also integrated in our approach in order to achieve convergence to global optima the mutation rate and the crossover rate have to be annealed to zero in proper fashion and unbounded power law scaled proportional fitness selection is used with logarithmic growth in the exponent our analysis shows that using certain types of crossover operators and large population size allows for particularly slow annealing schedules for the crossover rate in our discussion we focus on the following three major aspects based upon contraction properties of the mutation and fitness selection operators i the drive towards uniform populations in a genetic algorithm using standard operations ii weak ergodicity of the inhomogeneous markov chain describing the probabilistic model for the scaled algorithm iii convergence to globally optimal solutions in particular we remove two restrictions imposed in theorem 8 6 and remark 8 7 of theoret comput sci 259 2001 1 where a similar type of algorithm is considered as described here mutation need not commute with crossover and the fitness function which may come from a coevolutionary single species setting need not have a single maximum

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

interleaver design for serially concatenated convolutional codes theory and application this paper addresses the problem of interleaver design for serially concatenated convolutional codes scccs tailored to the constituent codes of the sccc configuration we present a theoretical framework for interleaver optimization based on a cost function closely tied to the asymptotic bit error rate ber of the block code c sub s resulting from proper termination of the constituent codes in the sccc code we define a canonical form of the interleaving engine denoted as the finite state permuter fsp and using its structural property develop a systematic iterative technique for construction of interleavers the core theoretical results focus on the asymptotic behavior of a class of cost functions and their martingale property which is then used to develop an order recursive interleaver optimization algorithm we address the issue of the complexity of the interleaver growth algorithm presented in the paper and demonstrate that it has polynomial complexity subsequently we provide details about the application of the proposed technique and present a modification of the algorithm that employs error pattern feedback for improved performance at a reduced complexity sample experimental results are provided for an sccc code of rate 1 3 and information block length 320 that achieves a minimum distance of d sub min 44

cross validation in principal component analysis summary this paper describes a form of cross validation in the context of principal component analysis which has a number of useful aspects as regards multivariate data inspection and description topics covered include choice of dimensionality identification of influential observations and selection of important variables the methods are motivated by and illustrated on a well known data set 1 data set and objectives jeffers 1967 described two detailed multivariate case studies one of which concerned 19 variables measured on each of 40 winged aphids alatee adelges that had been caught in a light trap the 19 variables are listed in table 1 principal component analysis pca was used to examine the structure in the data and if possible to answer the following questions i how many dimensions of the individuals are being measured ii how many distinct taxa are present in the habitat iii which variables among the 19 are redundant for distinguishing between taxa and which must be retained in future work of the 19 variables 14 are length or width measurements four are counts and one anal fold is a presence absence variable scored 0 or 1 in view of this disparity in variable type jeffers elected to standardise the data and thus effect the pca by finding the latent roots and vectors of the correlation rather than covariance matrix of the data the elements of each latent vector provide the coefficients of one of 19 linear combinations of the standardised original variables that successively maximise sample variance subject to being orthogonal with each other and the corresponding latent root is the sample variance of that linear combination the 19 observations for each aphid were subjected to each of these 19 linear transformations to form the 19 principal component scores for that aphid the above questions were then answered as follows i the latent roots of the correlation matrix were as given in table 1 the four largest comprise 73 0 12 5 3 9 and 2 6 respectively of the total variance 19 0 of the standardised variables the dimensionality of the data was therefore taken to be 2 ii when the scores of the first two principal components for the 40 aphids were plotted against orthogonal axes the resulting 40 points divided into four groups as shown in figure 1 hence four distinct species were identified for the aphids iii from consideration of the size of coefficients in the first three principal components it was concluded that only the four variables length of tibia number of ovipositor

hypocoercivity in metastable settings and kinetic simulated annealing combining classical arguments for the analysis of the simulated annealing algorithm with the more recent hypocoercive method of distorted entropy we prove the convergence for large time of the kinetic langevin annealing with logarithmic cooling schedule

convergence to global minima for a class of diffusion processes abstract we prove that there exists a gain function t t t 0 such that the solution of the sde d x t t grad u x t d t t d b t settles down on the set of global minima of u in particular the existence of a gain function t t 0 so that yt satisfying d y t t grad u y t d t d b t converges to the set of the global minima of u is verified then we apply the results to the robbins monro and the kiefer wolfowitz procedures which are of particular interest in statistics

phase transition and landscape statistics of the number partitioning problem the phase transition in the number partitioning problem npp i e the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution is investigated by examining the energy landscape of this classic optimization problem this is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure termed a barrier tree the leaves and internal nodes of which represent respectively the minima and the lowest energy saddles connecting those minima here we apply several measures of shape balance and symmetry as well as of branch lengths barrier heights to the barrier trees that result from the landscape of the npp aiming at identifying traces of the easy hard transition we find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights only the difficulty measure given by the maximum value of the ratio between the barrier height and the energy surplus of local minima succeeded in detecting traces of the phase transition in the tree in addition we show that the barrier trees associated with the npp are very similar to random trees contrasting dramatically with trees associated with the p spin glass and random energy models we also examine critically a recent conjecture on the equivalence between the npp and a truncated random energy model

differential turbo coded modulation with app channel estimation a serially concatenated coding system which can operate without channel state information csi with use of a simple channel estimation technique is presented this channel estimation technique uses the inner decoder s a posteriori probability app information about the transmitted symbols to form a channel estimate for each symbol interval and is termed app channel estimation the serially concatenated code is comprised of an outer rate 2 3 binary error control code separated by a bit interleaver from an inner code consisting of an 8 phase shift keying psk bit mapping and differential 8 psk modulation coherent decoding provides bit error rate performance 0 6 db from 8 psk capacity for large interleaver sizes app channel estimation decoding without initial csi over constant and random walk phase models shows near coherent results with fractions of a decibel performance loss for random walk and linear phase models

efficient non linear model reduction via a least squares petrov galerkin projection and compressive tensor approximations the first author acknowledges the partial support by a national science foundation graduate fellowship and the partial support by a national defense science and engineering graduate fellowship the second and third authors acknowledge the partial support by the motor sports division of the toyota motor corporation under agreement number 48737 and the partial support by a research grant from the academic excellence alliance program between king abdullah university of science and technology kaust and stanford university all authors also acknowledge the constructive comments received during the review process

the latin multiscale computational method and the proper generalized decomposition this paper deals with the synergy between the latin multiscale method and what is called the proper generalized decomposition pgd which is the key of its performances

on the asymptotic input output weight distributions and thresholds of convolutional and turbo like encoders we present a general method for computing the asymptotic input output weight distribution of convolutional encoders in some instances one can derive explicit analytic expressions in general though to determine the growth rate of the input output weight distribution for a particular normalized input weight spl kappa and output weight spl omega a system of polynomial equations has to be solved this method is then used to determine the asymptotic weight distribution of various concatenated code ensembles and to derive lower bounds on the thresholds of these ensembles under maximum likelihood ml decoding

stochastic relaxation on partitions with connected components and its application to image segmentation we present a new method of segmentation in which images are segmented in partitions with connected components we give computationally inexpensive algorithms for probability simulation and simulated annealing on the space of partitions with connected components of a general graph in particular hastings algorithms 1970 and generalized metropolis algorithms are defined to avoid heavy computation to achieve segmentation we propose a hierarchical approach which at each step minimizes a cost function on the space of partitions with connected components of a graph the algorithm is applied to segment gray level color and textured images

proper generalized decomposition of time multiscale models summary models encountered in computational mechanics could involve many time scales when these time scales cannot be separated one must solve the evolution model in the entire time interval by using the finest time step that the model implies in some cases the solution procedure becomes cumbersome because of the extremely large number of time steps needed for integrating the evolution model in the whole time interval in this paper we considered an alternative approach that lies in separating the time axis one dimensional in nature in a multidimensional time space then for circumventing the resulting curse of dimensionality the proper generalized decomposition was applied allowing a fast solution with significant computing time savings with respect to a standard incremental integration copyright 2011 john wiley sons ltd

a logarithmic upper bound on the minimum distance of turbo codes we derive new upper bounds on the minimum distance which turbo codes can maximally attain with the optimum interleaver of a given length the new bounds grow approximately logarithmically with the interleaver length and they are tighter than all previously derived bounds for medium length and long interleavers an extensive discussion highlights the impacts of the new bounds in the context of interleaver design and provides some new design guidelines

adaptive reduced basis finite element heterogeneous multiscale method an adaptive reduced basis finite element heterogeneous multiscale method rb fe hmm is proposed for elliptic problems with multiple scales the multiscale method is based on the rb fe hmm introduced in a abdulle y bai reduced basis finite element heterogeneous multiscale method for high order discretizations of elliptic homogenization problems j comput phys 231 21 2012 7014 7036 it couples a macroscopic solver with effective data recovered from the solution of micro problems solved on sampling domains unlike classical numerical homogenization methods the micro problems are computed in a finite dimensional space spanned by a small number of accurately computed representative micro solutions the reduced basis obtained by a greedy algorithm in an offline stage in this paper we present a residual based a posteriori error analysis in the energy norm as well as an a posteriori error analysis in quantities of interest for both type of adaptive strategies rigorous a posteriori error estimates are derived and corresponding error estimators are proposed in contrast to the adaptive finite element heterogeneous multiscale method fe hmm there is no need to adapt the micro mesh simultaneously to the macroscopic mesh refinement up to an offline preliminary stage the rb fe hmm has the same computational complexity as a standard adaptive fem for the effective problem two and three dimensional numerical experiments confirm the efficiency of the rb fe hmm and illustrate the improvements compared to the adaptive fe hmm c 2013 elsevier b v all rights reserved

improved upper bounds on the ml decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum the ensemble performance of parallel and serial concatenated turbo codes is considered where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time varying recursive systematic convolutional codes following the derivation of the input output weight enumeration functions of the ensembles of random parallel and serial concatenated turbo codes the tangential sphere upper bound is employed to provide improved upper bounds on the block and bit error probabilities of these ensembles of codes for the binary input additive white gaussian noise awgn channel based on coherent detection of equi energy antipodal signals and maximum likelihood decoding the influence of the interleaver length and the memory length of the component codes is investigated the improved bounding technique proposed here is compared to the conventional union bound and to a alternative bounding technique by duman and salehi 1998 which incorporates modified gallager bounds the advantage of the derived bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random recursive systematic convolutional component codes and it is especially pronounced in the region exceeding the cutoff rate where the performance of turbo codes is most appealing these upper bounds are also compared to simulation results of the iterative decoding algorithm

certification of projection based reduced order modelling in computational homogenisation by the constitutive relation error in this paper we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites the upper bound relies on the construction of a reduced model for the stress field upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense the desired bounding property is obtained the lower bound is obtained by defining a hierarchical enriched reduced model for the displacement we show that the sharpness of both error estimates can be seamlessly controlled by adapting the parameters of the corresponding reduced order model

linear programming based optimization of the distance spectrum of linear block codes we describe an approach for the identification of good distance spectra for possibly existing binary linear block codes based on linear programming and the macwilliams delsarte 1977 1972 identities specifically the linear program is defined by an expression characterizing the performance of a potential code in terms of its distance spectrum and constraints imposed by the macwilliams delsarte identities using the union bound to characterize performance our results suggest that the best distance spectrum is not a function of signal to noise ratio snr above the cutoff rate snr and also suggest the existence of several unknown good codes characterizing the performance using the maximum spectral error component of the union bound suggests spectral thinning with decreasing snr

relative frequencies of generalized simulated annealing we consider a class of nonhomogeneous markov chains arising in simulated annealing and related stochastic search algorithms using only elementary first principles we analyze the convergence and rate of convergence of the relative frequencies of visits to states in the markov chain we describe in detail three examples including the standard simulated annealing algorithm to show how our framework applies to specific stochastic search algorithmsthese examples have not previously been recognized to be sufficiently similar to share common analytical grounds our analysis though elementary provides the strongest sample path convergence results to date for simulated annealing type markov chains our results serve to illustrate that by taking a purely sample path view surprisingly strong statements can be made using only relatively elementary tools

numerical model reduction with error control in computational homogenization of transient heat flow numerical model reduction nmr is exploited for solving the finite element problem on a representative volume element rve that arises from the computational homogenization of a model problem of transient heat flow since the problem is linear an orthogonal basis is obtained via the classical method of spectral decomposition a symmetrized version of the space time variational format is adopted for estimating the error from the model reduction in i energy norm and in ii given quantities of interest this technique which was recently developed in the context of the non selfadjoint stationary diffusion convection problem is novel in the present context of nmr by considering the discrete unreduced model as exact we are able to obtain guaranteed bounds on the error while using only the reduced basis and with minor computational effort the performance of the error estimates is demonstrated via numerical results where the subscale is modeled in both one and three spatial dimensions

fluctuations of empirical means at low temperature for finite markov chains with rare transitions in the general case the integrated autocovariance and autocorrelation time are essential tools to understand the dynamical behavior of a markov chain we study here these two objects for markov chains with rare transitions with no reversibility assumption we give upper bounds for the autocovariance and the integrated autocorrelation time as well as exponential equivalents at low temperature we also link their slowest modes with the underline energy landscape under mild assumptions our proofs will be based on large deviation estimates coming from the theory of wentzell and freidlin and others 4 3 12 and on coupling arguments see 6 for a review on the coupling method

on the techniques for constructing admissible stress fields in model verification performances on engineering examples robust global goal oriented error estimation is used nowadays to control the approximate finite element solutions obtained from simulation in the context of computational mechanics the construction of admissible stress fields ie stress tensors which verify the equilibrium equations is required to set up strict and guaranteed error bounds using residual based error estimators and plays an important role in the quality of the error estimates this work focuses on the different procedures used in the calculation of admissible stress fields which is a crucial and technically complicated point the three main techniques that currently exist called the element equilibration technique eet the star patch equilibration technique spet and the element equilibration star patch technique eespt are investigated and compared with respect to three different criteria namely the quality of associated error estimators computational cost and easiness of practical implementation into commercial finite element codes the numerical results which are presented focus on industrial problems they highlight the main advantages and drawbacks of the different methods and show that the behavior of the three estimators which have the same convergence rate as the exact global error is consistent two and three dimensional experiments have been carried out in order to compare the performance and the computational cost of the three different approaches the analysis of the results reveals that the spet is more accurate than eet and eespt methods but the corresponding computational cost is higher overall the numerical tests prove the interest of the hybrid method eespt and show that it is a correct compromise between quality of the error estimate practical implementation and computational cost furthermore the influence of the cost function involved in the eet and the eespt is studied in order to optimize the estimators

near capacity turbo trellis coded modulation design based on exit charts and union bounds transactions papers bandwidth efficient parallel concatenated turbo trellis coded modulation ttcm schemes were designed for communicating over uncorrelated rayleigh fading channels a symbol based union bound was derived for analysing the error floor of the proposed ttcm schemes a pair of in phase i and quadrature phase q interleavers were employed for interleaving the i and q components of the ttcm coded symbols in order to attain an increased diversity gain the decoding convergence of the iq ttcm schemes was analysed using symbol based extrinsic information transfer exit charts the best ttcm component codes were selected with the aid of both the symbolbased union bound and non binary exit charts for designing capacity approaching iq ttcm schemes in the context of 8 psk 16 qam 32 qam and 64 qam modulation schemes

simulated annealing acceleration techniques and image restoration typically the linear image restoration problem is an ill conditioned underdetermined inverse problem here stabilization is achieved via the introduction of a first order smoothness constraint which allows the preservation of edges and leads to the minimization of a nonconvex functional in order to carry through this optimization task we use stochastic relaxation with annealing we prefer the metropolis dynamics to the popular but computationally much more expensive gibbs sampler still metropolis type annealing algorithms are also widely reported to exhibit a low convergence rate their finite time behavior is outlined and we investigate some inexpensive acceleration techniques that do not alter their theoretical convergence properties namely restriction of the state space to a locally bounded image space and increasing concave transform of the cost functional successful experiments about space variant restoration of simulated synthetic aperture imaging data illustrate the performance of the resulting class of algorithms and show significant benefits in terms of convergence speed

stochastic local search for the feature set problem with applications to microarray data we prove a m o na time bound for finding minimum solutions smin of feature set problems where n is the total size of a given feature set problem smin m equals the number of non target features a is a relatively small constant and 1 is the confidence that the solution is of minimum length in terms of parameterized complexity of np complete problems our time bound differs from an fpt type bound by the factor mo for fixed the algorithm is applied to a prominent microarray dataset the classification of gene expression data related to acute myeloid leukaemia aml and acute lymphoblastic leukaemia all from the set of potentially significant features calculated by the algorithm we can identify three genes d88422 m92287 l09209 that produce zero errors on the test set by using a simple straightforward evaluation procedure performing the test on the single gene m84526 produces only one error

the energy transformation method for the metropolis algorithm compared with simulated annealing we present and analyze a new speed up technique for monte carlo optimization the iterated energy transformation algorithm where the metropolis algorithm is used repeatedly with more and more favourable energy functions derived from the original one by increasing transformations we show that this method allows a better speed up than simulated annealing when convergence speed is measured by the probability of failure of the algorithm after a large number of iterations we study also the limit of a large state space in the special case when the energy is made of a sum of independent terms we show that the convergence time of the i e t algorithm is polynomial in the size number of coordinates of the problem but with a worse exponent than for simulated annealing this indicates that the i e t algorithm is well suited for moderate size problems but not for too large ones the independent component case is a good model for the end of many optimization processes when at low temperature a neighbourhood of a local minimum is explored by small and far apart modifications of the current solution we show that in this case both global optimization methods simulated annealing and the i e t algorithm are less efficient than repeated local stochastic optimizations using the general concept of slow stochastic optimization algorithm we show that any slow global optimization scheme should be followed by a local one to perform the last approach to a minimum

goal oriented error estimation and adaptivity for the finite element method abstract in this paper we study a new approach in a posteriori error estimation in which the numerical error of finite element approximations is estimated in terms of quantities of interest rather than the classical energy norm these so called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs we present here the theory with respect to a class of elliptic boundary value problems and in particular show how to obtain accurate estimates as well as upper and lower bounds on the error we also study the new concept of goal oriented adaptivity which embodies mesh adaptation procedures designed to control error in specific quantities numerical experiments confirm that such procedures greatly accelerate the attainment of local features of the solution to preset accuracies as compared to traditional adaptive schemes based on energy norm error estimates

asymptotical behaviour of several interacting annealing processes we prove that the optimal convergence speed exponent for parallel annealing based on periodically interacting multiple searches with time periodr is always worse than for independent multiple searches whenever the cost function has only one global minimum our proofs will be based on large deviation estimates coming from the theory of generalized simulated annealing g s a

interpolation method for adapting reduced order models and application to aeroelasticity reduced order models are usually thought of as computationally inexpensive mathematical representations that offer the potential for near real time analysis although most reduced order models can operate in near real time their construction can be computationally expensive as it requires accumulating a large number of system responses to input excitations furthermore reduced order models usually lack robustness with respect to parameter changes and therefore must often be rebuilt for each parameter variation together these two issues underline the need for a fast and robust method for adapting precomputed reduced order models to new sets of physical or modeling parameters to this effect this paper presents an interpolation method based on the grassmann manifold and its tangent space at a point that is applicable to structural aerodynamic aeroelastic and many other reduced order models based on projection schemes this method is illustrated here with the adaptation of computational fluid dynamics based aeroelastic reduced order models of complete fighter configurations to new values of the freestream mach number good correlations with results obtained from direct reduced order model reconstruction high fidelity nonlinear and linear simulations are reported thereby highlighting the potential of the proposed reduced order model adaptation method for near real time aeroelastic predictions using precomputed reduced order model databases

on the design of bit interleaved turbo coded modulation with low error floors in this paper we introduce an algorithm to optimize the performance in the error floor region of bit interleaved turbo coded modulation bitcm on the additive white gaussian noise channel the key ingredient is an exact turbo code weight distribution algorithm producing a list of all codewords in the underlying turbo code of weight less than a given threshold in bitcm the information sequence is turbo encoded bit interleaved and mapped to signal points in a signal constellation using the union bounding technique we show that a well designed bit interleaver is crucial to have a low error floor furthermore the error rate performance in the waterfall region depends on the bit interleaver since the level of protection from channel noise on the bit level depends on the bit position and the neighboring bit values within the same symbol in the transmitted sequence we observe a tradeoff between error rate performance in the waterfall and error floor regions as illustrated by an extensive case study of a high rate bitcm scheme this tradeoff is typical in iterative decoding of turbo like codes the reported case study shows that it is possible to design bit interleavers with our proposed algorithm with equal or better performance in the waterfall region and superior performance in the error floor region compared with randomly generated bit interleavers in particular we were able to design bitcm schemes with maximum likelihood decoding frame error rates of 10 12 and 10 17 at 2 6 and 3 8 db away from unconstrained channel capacity at spectral efficiencies of 3 10 and 6 20 b s hz using square 16 and 256 quadrature amplitude modulation signal constellations respectively

on the verification of model reduction methods based on the proper generalized decomposition in this work we introduce a consistent error estimator for numerical simulations performed by means of the proper generalized decomposition pgd approximation this estimator which is based on the constitutive relation error enables to capture all error sources i e those coming from space and time numerical discretizations from the truncation of the pgd decomposition etc and leads to guaranteed bounds on the exact error the specificity of the associated method is a double approach i e a kinematic approach and a unusual static approach for solving the parameterized problem by means of pgd this last approach makes straightforward the computation of a statically admissible solution which is necessary for robust error estimation an attractive feature of the error estimator we set up is that it is obtained by means of classical procedures available in finite element codes it thus represents a practical and relevant tool for driving algorithms carried out in pgd being possibly used as a stopping criterion or as an adaptation indicator numerical experiments on transient thermal problems illustrate the performances of the proposed method for global error estimation

the reduced model multiscale method r3m for the non linear homogenization of hyperelastic media at finite strains this paper presents a new multi scale method for the homogenization analysis of hyperelastic solids undergoing finite strains the key contribution is to use an incremental nonlinear homogenization technique in tandem with a model reduction method in order to alleviate the complexity of multiscale procedures which usually involve a large number of nonlinear nested problems to be solved the problem associated with the representative volume element rve is solved via a model reduction method proper orthogonal decomposition the reduced basis is obtained through pre computations on the rve the technique coined as reduced model multiscale method r3m allows reducing significantly the computation times as no large matrix needs to be inverted and as the convergence of both macro and micro problems is enhanced furthermore the r3m drastically reduces the size of the data base describing the history of the micro problems in order to validate the technique in the context of porous elastomers at finite strains a comparison between a full and a reduced multiscale analysis is performed through numerical examples involving different micro and macro structures as well as different nonlinear models neo hookean mooney rivlin it is shown that the r3m gives good agreement with the full simulations at lower computational and data storage requirements

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

optimal power rate allocation and code selection for iterative joint detection of coded random cdma iterative interference cancellation of coded code division multiple access cdma using random spreading with linear cancellation is analyzed if users are grouped into power classes and shannon bound approaching codes are used a geometric power distribution achieves the additive white gaussian noise awgn channel shannon bound as the numbers of classes becomes large the optimal distribution of the size of these classes is shown to be uniform if users are grouped into different rate classes with equal powers among equal rate users the shannon bound for awgn channels can be achieved with an arbitrary distribution of the classes sizes provided that the size of the largest rate class obeys the mild condition that its ratio of size to processing gain is much smaller than the inverse of the signal to noise ratio snr the case of equal powers and equal rates among all users is addressed as a worst case scenario it is argued that simple repetition codes provide for a larger achievable capacity than stronger codes it is shown that this capacity monotonically increases as the rate of the code decreases a density evolution analysis is used to show that the achievable rates exceed those of a minimum mean square error filter applied to the uncoded signals this lower bound is tight for small ratios of bit energy to noise power and otherwise the iterative cancellation receiver provides an appreciably larger capacity relating to recent result from the application of statistical mechanics it is shown that the repetition coded system with iterative cancellation achieves the performance of an equivalent optimal joint detector for uncoded transmission

list decoding of turbo codes list decoding of turbo codes is analyzed under the assumption of a maximum likelihood ml list decoder it is shown that large asymptotic gains can be achieved on both the additive white gaussian noise awgn and fully interleaved flat rayleigh fading channels it is also shown that the relative asymptotic gains for turbo codes are larger than those for convolutional codes finally a practical list decoding algorithm based on the list output viterbi algorithm lova is proposed as an approximation to the ml list decoder simulation results show that the proposed algorithm provides significant gains corroborating the analytical results the asymptotic gain manifests itself as a reduction in the bit error rate ber and frame error rate fer floor of turbo codes

a posteriori error estimation for numerical model reduction in computational homogenization of porous media numerical model reduction is adopted for solving the microscale problem that arizes from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields a reduced basis is obtained for the pressure field using i spectral decomposition sd and ii proper orthogonal decomposition pod this strategy has been used in previous work the main contribution of this article is the extension with an a posteriori estimator for assessing the error in i energy norm and in ii a given quantity of interest the error estimator builds on previous work by the authors the novelty presented in this article is the generalization of the estimator to a coupled problem and more importantly to accommodate the estimator for a pod basis rather than the sd basis guaranteed fully computable and low cost bounds are derived and the performance of the error estimates is demonstrated via numerical results

variance of the turbo code performance bound over the interleavers we evaluate the variance of the union performance bound for a rate 1 3 turbo code over all possible interleavers of length n under the assumption of a maximum likelihood ml decoder theoretical and simulation results for turbo codes with two memory component codes indicate that the coefficient of variation of the bound increases with the signal to noise ratio and decreases with the interleaver length theoretical analysis for large interleaver lengths shows that the coefficient of variation asymptotically approaches a constant value the results also demonstrate that the majority of the interleavers have performance bounds very close to the average value of the bound this phenomenon is more palpable for larger interleaver lengths

nonlinear model reduction via discrete empirical interpolation a dimension reduction method called discrete empirical interpolation is proposed and shown to dramatically reduce the computational complexity of the popular proper orthogonal decomposition pod method for constructing reduced order models for time dependent and or parametrized nonlinear partial differential equations pdes in the presence of a general nonlinearity the standard pod galerkin technique reduces dimension in the sense that far fewer variables are present but the complexity of evaluating the nonlinear term remains that of the original problem the original empirical interpolation method eim is a modification of pod that reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by pod we propose a discrete empirical interpolation method deim a variant that is suitable for reducing the dimension of systems of ordinary differential equations odes of a certain type as presented here it is applicable to odes arising from finite difference discretization of time dependent pdes and or parametrically dependent steady state problems however the approach extends to arbitrary systems of nonlinear odes with minor modification our contribution is a greatly simplified description of the eim in a finite dimensional setting that possesses an error bound on the quality of approximation an application of deim to a finite difference discretization of the one dimensional fitzhugh nagumo equations is shown to reduce the dimension from 1024 to order 5 variables with negligible error over a long time integration that fully captures nonlinear limit cycle behavior we also demonstrate applicability in higher spatial dimensions with similar state space dimension reduction and accuracy results

on error controlled numerical model reduction in fe2 analysis of transient heat flow numerical model reduction is exploited for solving the two scale problem that arises from the computational homogenization of a model problem of transient heat flow since the problem is linear an orthogonal basis is obtained via the method of spectral decomposition a key feature is the construction of a symmetrized version of the space time variational format by which it is possible to estimate the error from the model reduction in i energy norm and in ii a given quantity of interest in previous work by the authors this strategy has been applied to the solution of an individual representative volume element problem whereas the error transport to the macroscale problem in the finite element squared fe2 approach was ignored in this paper such transport of error is included in the error estimate it is remarkable that it is still possible to obtain guaranteed bounds on the error as compared to the fully resolved discrete finite element problem while using only the reduced basis and with minor extra computational effort the performance of the error estimates is demonstrated via numerical results whereby the subscale is modeled in three dimensions whereas the macroscale problem is either one or two dimensional

eigendeformation based reduced order homogenization for failure analysis of heterogeneous materials the manuscript presents a novel model reduction approach for periodic heterogeneous media which combines the multiple scale asymptotic msa expansion method with the transformation field analysis tfa to reduce the computational cost of a direct homogenization approach without significantly compromising on solution accuracy the evolution of failure in micro phases and interfaces is modeled using eigendeformation adaptive model improvement strategy incorporating a hierarchical sequence of computational homogenization models is employed to control the accuracy of the model we present the model formulation and the computational details along with verification with respect to direct homogenization and validation with respect to physical experiments studies

the computation of bounds for linear functional outputs of weak solutions to the two dimensional elasticity equations we present a method for the computation of upper and lower bounds for linear functional outputs of the exact solutions to the two dimensional elasticity equations the method can be regarded as a generalization of the well known complementary energy principle the desired output is cast as the supremum of a quadratic linear convex functional over an infinite dimensional domain using duality the computation of an upper bound for the output of interest is reduced to a feasibility problem for the complementary or dual problem in order to make the problem tractable from a computational perspective two additional relaxations that preserve the bounding properties are introduced first the domain is triangulated and a domain decomposition strategy is used to generate a sequence of independent problems to be solved over each triangle the lagrange multipliers enforcing continuity are approximated using piecewise linear functions over the edges of the triangulation second the solution of the adjoint problem is approximated over the triangulation using a standard galerkin finite element approach a lower bound for the output of interest is computed by repeating the process for the negative of the output reversing the sign of the computed upper bound for the negative of the output yields a lower bound for the actual output the method can be easily generalized to three dimensions however a constructive proof for the existence of feasible solutions for the outputs of interest is only given in two dimensions the computed bound gaps are found to converge optimally that is at the same rate as the finite element approximation an attractive feature of the proposed approach is that it allows for a data set to be generated that can be used to certify and document the computed bounds using this data set and a simple algorithm the correctness of the computed bounds can be established without recourse to the original code used to compute them in the present paper only computational domains whose boundary is made up of straight sided segments and polynomially varying loads are considered two examples are given to illustrate the proposed methodology

markov chains with exponentially small transition probabilities first exit problem from a general domain i the reversible case we consider general ergodic aperiodic markov chains with finite state space whose transition probabilities between pairs of different communicating states are exponentially small in a large parameter we extend previous results by m i freidlin and a d wentzell fw on the first exit problem from a general domainq in the present paper we analyze the case ofreversible markov chains the general case will be studied in a forthcoming paper we probe in a purely probabilistic way and without using the fw graphical technique some results on the first exit problem from a general domainq containing many attractors in particular we analyze the properties of special domains calledcycles and by using the new concept oftemporal entropy we obtain new results leading to a complete description of the typical tube of trajectories during the first excursion outsideq

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

landscapes on spaces of trees combinatorial optimization problems defined on sets of phylogenetic trees are an important issue in computational biology for instance the problem of reconstructing a phylogeny using maximum likelihood or parsimony approaches the collection of possible phylogenetic trees is arranged as a so called robinson graph by means of the nearest neighborhood interchange move the coherent algebra and spectra of robinson graphs are discussed in some detail as their knowledge is important for an understanding of the landscape structure we consider simple model landscapes as well as landscapes arising from the maximum parsimony problem focusing on two complementary measures of ruggedness the amplitude spectrum arising from projecting the cost functions onto the eigenspaces of the underlying graph and the topology of local minima and their connecting saddle points

linear system modelization of concatenated block and convolutional codes in this paper we characterize four models of concatenation of a block code and a convolutional code from a linear systems theory viewpoint we provide the input state output representation of these models and we give conditions in order to get a non catastrophic concatenated convolutional code with minimal representation lower bounds on the free distances of the concatenated codes are also developed

hyper reduction of mechanical models involving internal variables we propose to improve the efficiency of the computation of the reduced state variables related to a given reduced basis this basis is supposed to be built by using the snapshot proper orthogonal decomposition pod model reduction method in the framework of non linear mechanical problems involving internal variables the local integration of the constitutive laws can dramatically limit the computational savings provided by the reduction of the order of the model this drawback is due to the fact that using a galerkin formulation the size of the reduced basis has no effect on the complexity of the constitutive equations in this paper we show how a reduced basis approximation and a petrov galerkin formulation enable to reduce the computational effort related to the internal variables the key concept is a reduced integration domain where the integration of the constitutive equations is performed the local computations being not made over the entire domain we extrapolate the computed internal variable over the full domain using pod vectors related to the internal variables this paper shows the improvement of the computational saving obtained by the hyper reduction of the elasto plastic model of a simple structure

solving scheduling problems by simulated annealing we define a general methodology to deal with a large family of scheduling problems we consider the case where some of the constraints are expressed through the minimization of a loss function we study in detail a benchmark example consisting of some jigsaw puzzle problem with additional constraints we discuss some algorithmic issues typical of scheduling problems such as the apparition of small unused gaps or the representation of proportionality constraints we also carry on an experimental comparison between the metropolis algorithm simulated annealing and the iterated energy transformation method to see whether asymptotical theoretical results are a good guide towards practically efficient algorithms

rapid carrier acquisition from baud rate samples maximum likelihood estimation of phase and frequency offset involves the maximization of a nonlinear likelihood function we develop an estimator for carrier acquisition by linearizing the likelihood function and show that its performance is close to the cramer rao bound crb the estimator is then extended to blind frequency acquisition and combined with testing to eliminate unlikely hypotheses with proper modeling of the likelihood resulting from the blind search simulations show that the algorithm quickly rejects all but the correct frequency hypothesis

bridging proper orthogonal decomposition methods and augmented newton krylov algorithms an adaptive model order reduction for highly nonlinear mechanical problems this article describes a bridge between pod based model order reduction techniques and the classical newton krylov solvers this bridge is used to derive an efficient algorithm to correct on the fly the reduced order modelling of highly nonlinear problems undergoing strong topological changes damage initiation problems tackled via a corrected hyperreduction method are used as an example it is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm even when strong topological changes are involved

a nonlinear manifold based reduced order model for multiscale analysis of heterogeneous hyperelastic materials a new manifold based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented the model relies on a global geometric framework for nonlinear dimensionality reduction isomap and the macroscopic loading parameters are linked to the reduced space using a neural network the proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization to construct the manifold we perform a number of large three dimensional simulations of a statistically representative unit cell using a parallel finite strain finite element solver the manifold based reduced order model is verified using common principles from the machine learning community both homogenization and localization of the multiscale solution are demonstrated on a large three dimensional example and the local microscopic fields as well as the homogenized macroscopic potential are obtained with acceptable engineering accuracy

the effect of multiple optima on the simple ga run time complexity genetic algorithms are stochastic search algorithms that have been applied to optimization problems in this paper we analyze the run time complexity of a genetic algorithm when we are interested in one of a set of distinguished solutions one such case occurs when multiple optima exist we define the worst case scenario and derive a probabilistic worst case bound on the number of iterations required to find one of these multiple solutions of interest

interleavers for turbo codes using permutation polynomials over integer rings a class of deterministic interleavers for turbo codes tcs based on permutation polynomials over spl zopf sub n is introduced the main characteristic of this class of interleavers is that they can be algebraically designed to fit a given component code moreover since the interleaver can be generated by a few simple computations storage of the interleaver tables can be avoided by using the permutation polynomial based interleavers the design of the interleavers reduces to the selection of the coefficients of the polynomials it is observed that the performance of the tcs using these permutation polynomial based interleavers is usually dominated by a subset of input weight 2m error events the minimum distance and its multiplicity or the first few spectrum lines of this subset are used as design criterion to select good permutation polynomials a simple method to enumerate these error events for small m is presented searches for good interleavers are performed the decoding performance of these interleavers is close to s random interleavers for long frame sizes for short frame sizes the new interleavers outperform s random interleavers

model order reduction for hyperelastic materials in this paper we develop a novel algorithm for the dimensional reduction of the models of hyperelastic solids undergoing large strains unlike standard proper orthogonal decomposition methods the proposed algorithm minimizes the use of the newton algorithms in the search of non linear equilibrium paths of elastic bodies the proposed technique is based upon two main ingredients on one side the use of classic proper orthogonal decomposition techniques that extract the most valuable information from pre computed complete models this information is used to build global shape functions in a ritz like framework on the other hand to reduce the use of newton procedures an asymptotic expansion is made for some variables of interest this expansion shows the interesting feature of possessing one unique tangent operator for all the terms of the expansion thus minimizing the updating of the tangent stiffness matrix of the problem the paper is completed with some numerical examples in order to show the performance of the technique in the framework of hyperelastic kirchhoff saint venant and neo hookean solids

stochastic nonlinear image restoration using the wavelet transform the dominant methodology for image restoration is to stabilize the problem by including a roughness penalty in addition to faithfulness to the data among various choices concave stabilizers stand out for their boundary detection capabilities but the resulting cost function to be minimized is generally multimodal although simulated annealing is theoretically optimal to take up this challenge standard stochastic algorithms suffer from two drawbacks i practical convergence difficulties are encountered with second order prior models and ii it remains computationally demanding to favor the formation of smooth contour lines by taking the discontinuity field explicitly into account this work shows that both weaknesses can be overcome in a multiresolution framework by means of the 2 d discrete wavelet transform dwt we first propose to improve convergence toward global minima by single site updating on the wavelet domain for this purpose a new restricted dwt space is introduced and a theoretically sound updating mechanism is constructed on this subspace next we suggest to incorporate the smoothness of the discontinuity field via an additional penalty term defined on the high frequency subbands the resulting increase in complexity is small and the approach requires the specification of a unique extra parameter for which an explicit selection formula is derived

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes