efficient root finding algorithm with application to list decoding of algebraic geometric codes a list decoding for an error correcting code is a decoding algorithm that generates a list of codewords within a hamming distance t from the received vector where t can be greater than the error correction bound in previous work by m shokrollahi and h wasserman see ibid vol 45 p 432 7 march 1999 a list decoding procedure for reed solomon codes was generalized to algebraic geometric codes recent work by v guruswami and m sudan see ibid vol 45 p 1757 67 sept 1999 gives improved list decodings for reed solomon codes and algebraic geometric codes that work for all rates and have many applications however these list decoding algorithms are rather complicated r roth and g ruckenstein see ibid vol 46 p 246 57 jan 2000 proposed an efficient implementation of the list decoding of reed solomon codes in this correspondence extending roth and ruckenstein s fast algorithm for finding roots of univariate polynomials over polynomial rings i e the reconstruct algorithm we present an efficient algorithm for finding the roots of univariate polynomials over function fields based on the extended algorithm we give an efficient list decoding algorithm for algebraic geometric codes

a justesen construction of binary concatenated codes that asymptotically meet the zyablov bound for low rate an explicit construction of a sequence of binary codes that asymptotically meet the zyablov bound for rates lower than 0 30 is given by using justesen s construction of concatenation the outer codes are constructed from generalized hermitian curves these outer codes can be described without any algebraic geometry terminology while the proofs of some properties deeply rely on algebraic geometry

reconstructing algebraic functions from mixed data we consider a variant of the traditional task of explicitly reconstructing algebraic functions from black box representations in the traditional setting for such problems one is given access to an unknown function f that is represented by a black box or an oracle which can be queried for the value of f at any input given a guarantee that this unknown function f is some nice algebraic function say a polynomial in its input of degree bound d the goal of the reconstruction problem is to explicitly determine the coefficients of the unknown polynomial all work on polynomial interpolation especially sparse ones are or may be presented in such a setting the work of kaltofen and trager computing with polynomials given by black boxes for their evaluations greatest common divisors factorization separation of numerators and denominators in proc 29th ann ieee symp on foundations of computer science 1988 pp 296 305 for instance highlights the utility of this setting by performing numerous manipulations on polynomials presented as black boxes the variant considered in this paper differs from the traditional setting in that our black boxes represent several algebraic functions f1 fk where at each input x the box arbitrarily chooses a subset of f1 x fk x to output and we do not know which subset it outputs we show how to reconstruct the functions f1 fk from the black box provided the black box outputs according to these functions often this allows us to group the sample points into sets such that for each set all outputs to points in the set are from the same algebraic function our methods are robust in the presence of a small fraction of arbitrary errors in the black box our model and techniques can be applied in the areas of computer vision machine learning curve fitting and polynomial approximation self correcting programs and bivariate polynomial factorization

combinatorial bounds for list decoding informally an error correcting code has nice list decodability properties if every hamming ball of large radius has a small number of codewords in it we report linear codes with nontrivial list decodability i e codes of large rate that are nicely list decodable and codes of large distance that are not nicely list decodable specifically on the positive side we show that there exist codes of rate r and block length n that have at most c codewords in every hamming ball of radius h sup 1 1 r 1 c spl middot n this answers the main open question from the work of elias 1957 this result also has consequences for the construction of concatenated codes of good rate that are list decodable from a large fraction of errors improving previous results of guruswami and sudan see ieee trans inform theory vol 45 p 1757 67 sept 1999 and proc 32nd acm symp theory of computing stoc portland or p 181 190 may 2000 in this vein specifically for every spl epsi 0 we present a polynomial time constructible asymptotically good family of binary codes of rate spl omega spl epsi sup 4 that can be list decoded in polynomial time from up to a fraction 1 2 spl epsi of errors using lists of size o spl epsi sup 2 on the negative side we show that for every spl delta and c there exists spl tau 0 and an infinite family of linear codes c sub i sub i such that if n sub i denotes the block length of c sub i then c sub i has minimum distance at least spl delta spl middot n sub i and contains more than c sub 1 spl middot n sub i sup c codewords in some hamming ball of radius spl tau spl middot n sub i while this result is still far from known bounds on the list decodability of linear codes it is the first to bound the radius for list decodability by a polynomial sized list away from the minimum distance of the code

threshold effect with stochastic fluctuation in bacteria colony like proliferation dynamics as analyzed through a comparative study of reaction diffusion equations and cellular automata we report a comparative study on pattern formation between the methods of cellular automata ca and reaction diffusion equations rd applying to a morphology of bacterial colony formation to do so we began the study with setting an extremely simple model which was designed to realize autocatalytic proliferation of bacteria denoted as x fed with nutrition n and their inactive state prespore state p1 due to starvation x n 2x and x p1 respectively it was found numerically that while the ca could successfully generate rich patterns ranging from the circular fat structure to the viscous finger like complicated one the naive rd reproduced only the circular pattern but failed to give a finger structure augmenting the rd equations by adding two physical factors i a threshold effect in the dynamics of x n 2x breaking the continuity limit of rd and ii internal noise with onset threshold breaking the inherent symmetry of rd we have found that the viscous finger like realistic patterns are indeed recovered by thus modified rd this highlights the important difference between ca and rd and at the same time clarifies the necessary factors for the complicated patterns to emerge in such a surprisingly simple model system

on determining deep holes of generalized reed solomon codes for a linear code deep holes are defined to be vectors that are further away from codewords than all other vectors the problem of deciding whether a received word is a deep hole for generalized reed solomon grs codes is proved to be co np complete by guruswami and vardy for the extended reed solomon codes rs q mathbb f q k a conjecture was made to classify deep holes by cheng and murray since then efforts have been made to prove the conjecture or its various forms in this paper we classify deep holes completely for grs codes rs p d k where p is a prime d k geqslant p 1 2 our techniques are built on the idea of deep hole trees and several results concerning the erdos heilbronn conjecture

subspace polynomials and limits to list decoding of reed solomon codes we show combinatorial limitations on efficient list decoding of reed solomon codes beyond the johnson guraswami sudan bounds in particular we show that for arbitrarily large fields fn fn n for any 0 1 and k n 1 existence there exists a received word wn fn fn that agrees with a super polynomial number of distinct degree k polynomials on n points each 2 explicit there exists a polynomial time constructible received word w n fn fn that agrees with a superpolynomial number of distinct degree k polynomials on 2 log n k points each in both cases our results improve upon the previous state of the art which was n points of agreement for the existence case proved by justesen and hoholdt and 2n points of agreement for the explicit case proved by guruswami and rudra furthermore for close to 1 our bound approaches the guruswami sudan bound which is n k and implies limitations on extending their efficient reed solomon list decoding algorithm to larger decoding radius our proof is based on some remarkable properties of sub space polynomials using similar ideas we then present a family of low rate codes that are efficiently list decodable beyond the johnson bound this leads to an optimal list decoding algorithm for the family of matrix codes

the importance of being discrete life always wins on the surface many systems in chemistry biology finance and social sciences present emerging features that are not easy to guess from the elementary interactions of their microscopic individual components in the past the macroscopic behavior of such systems was modeled by assuming that the collective dynamics of microscopic components can be effectively described collectively by equations acting on spatially continuous density distributions it turns out that to the contrary taking into account the actual individual discrete character of the microscopic components of these systems is crucial for explaining their macroscopic behavior in fact we find that in conditions in which the continuum approach would predict the extinction of all of the population respectively the vanishing of the invested capital or the concentration of a chemical substance etc the microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development in particular it is found that in two dimensions life the localized proliferating phase always prevails

limits to list decoding reed solomon codes in this paper we prove the following two results that expose some combinatorial limitations to list decoding reed solomon codes 1 given n distinct elements alpha1 alphan from a field f and n subsets s1 sn of f each of size at most l the list decoding algorithm of guruswami and sudan can in polynomial time output all polynomials p of degree at most k that satisfy p alphai isinsi for every i as long as l 0 agreement of k is trivial to achieve such a bound was known earlier only for a nonexplicit center finding explicit bad list decoding configurations is of significant interest for example the best known rate versus distance tradeoff due to xing is based on a bad list decoding configuration for algebraic geometric codes which is unfortunately not explicitly known

improved probabilistic decoding of interleaved reed solomon codes and folded hermitian codes probabilistic simultaneous polynomial reconstruction algorithm of bleichenbacher kiayias and yung is extended to the polynomials whose degrees are allowed to be distinct specifically for a finite field f positive integers n r t and distinct elements z 1 z 2 z email protected f we present a probabilistic algorithm which can recover polynomials p 1 p 2 p email protected f x of degree less than k 1 k 2 k r respectively for a given instance i 1 n satisfying p l z i y i l for all email protected 1 2 r and for all email protected email protected 1 2 n such that i t with probability at least 1 n t f and with time complexity at most o rn 4 if t max k 1 k 2 k r email protected j 1 rk jr 1 next by using this algorithm we present a probabilistic decoder for interleaved reed solomon codes it is observed that interleaved reed solomon codes over f with rate r can be decoded up to burst error rate rr 1 1 r probabilistically for an interleaving parameter r then it is proved that q folded hermitian codes over f q 2 q with rate r can be decoded up to error rate qq 1 1 r probabilistically

discreteness induced stochastic steady state in reaction diffusion systems self consistent analysis and stochastic simulations abstract a self consistent equation to derive a discreteness induced stochastic steady state is presented for reaction diffusion systems for this formalism we use the so called kuramoto length a typical distance over which a molecule diffuses in its lifetime as was originally introduced to determine if local fluctuations influence globally the whole system we show that this kuramoto length is also relevant to determine whether the discreteness of molecules is significant or not if the number of molecules of a certain species within the kuramoto length is small and discrete localization of some other chemicals is brought about which can accelerate certain reactions when this acceleration influences the concentration of the original molecule species it is shown that a novel stochastic steady state is induced that does not appear in the continuum limit a theory to obtain and characterize this state is introduced based on the self consistent equation for chemical concentrations this stochastic steady state is confirmed by numerical simulations on a certain reaction model which agrees well with the theoretical estimation formation and coexistence of domains with different stochastic states are also reported which is maintained by the discreteness relevance of our result to intracellular reactions is briefly discussed

differential and integral methods for multidimensional inverse scattering problems a layer stripping procedure for solving three dimensional schrodinger equation inverse scattering problems is developed this procedure operates by recursively reconstructing the radon transform of the potential from the jump in the radon transform of the scattered field at the wave front this reconstructed potential is then used to propagate the wave front and scattered field differentially further into the support of the potential the connections between this differential procedure and integral equation procedures are then illustrated by the derivations of two well known exact integral equation procedures using the radon transform and a generalized radon transform these procedures as well as the layer stripping procedure are then reduced to the familiar born approximation result for this problem by neglecting multiple scattering events this illustrates the central role of the radon transform in both exact and approximate inversion procedures

applications of list decoding to tracing traitors we apply results from algebraic coding theory to solve problems in cryptography by using recent results on list decoding of error correcting codes to efficiently find traitors who collude to create pirates we produce schemes for which the traceability ta traitor tracing algorithm is very fast we compare the ta and identifiable parent property ipp traitor tracing algorithms and give evidence that when using an algebraic structure the ability to trace traitors with the ipp algorithm implies the ability to trace with the ta algorithm we also demonstrate that list decoding techniques can be used to find all possible pirate coalitions finally we raise some related open questions about linear codes and suggest uses for other decoding techniques in the presence of additional information about traitor behavior

the watts strogatz network model developed by including degree distribution theory and computer simulation by using theoretical analysis and computer simulations we develop the watts strogatz network model by including degree distribution in an attempt to improve the comparison between characteristic path lengths and clustering coefficients predicted by the original watts strogatz network model and those of the real networks with the small world property good agreement between the predictions of the theoretical analysis and those of the computer simulations has been shown it is found that the developed watts strogatz network model can fit the real small world networks more satisfactorily some other interesting results are also reported by adjusting the parameters in a model degree distribution function the developed watts strogatz network model is expected to help in the future analysis of various social problems as well as financial markets with the small world property pacs numbers 89 75 hc 05 50 q 87 23 ge some figures in this article are in colour only in the electronic version

hard problems of algebraic geometry codes the minimum distance is one of the most important combinatorial characterizations of a code the maximum likelihood decoding problem is one of the most important algorithmic problems of a code while these problems are known to be hard for general linear codes the techniques used to prove their hardness often rely on the construction of artificial codes in general much less is known about the hardness of the specific classes of natural linear codes in this correspondence we show that both problems are np hard for algebraic geometry codes we achieve this by reducing a well known np complete problem to these problems using a randomized algorithm the family of codes in the reductions is based on elliptic curves they have positive rates but the alphabet sizes are exponential in the block lengths

a geometric growth model interpolating between regular and small world networks we propose a geometric growth model which interpolates between one dimensional linear graphs and small world networks the model undergoes a transition from large to small worlds we study the topological characteristics by both theoretical predictions and numerical simulations which are in good accordance with each other our geometrically growing model is a complementarity for the static ws model

recursiveness switching and fluctuations in a replicating catalytic network a protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors depending on the numbers of molecules and species and the path rate three phases are found fast switching state without recursive production recursive production and itinerancy between the above two states the number distributions of the molecules in the recursive states are shown to be log normal except for those species that form a core hypercycle and are explained with the help of a heuristic argument

a layer stripping solution of the inverse problem for a one dimensional elastic medium a fast algorithm for recovering profiles of density and lame parameters as functions of depth for the inverse seismic problem in an elastic medium is obtained the medium is probed with planar impulsive p and sv waves at oblique incidence and the medium velocity components are measured at the surface the interconversion of p and sv waves defines reflection coefficients from which the medium parameter profiles are obtained recursively the algorithm works on a layer stripping principle and it is specified in both differential and recursive forms a physical interpretation of this procedure is given in terms of a lattice filter where the first reflections of the downgoing waves in each layer yield the various reflection coefficients for that layer a computer run of the algorithm on the synthetic impulsive plane wave responses of a twenty layer medium shows that the algorithm works satisfactorily

progressive algebraic soft decision decoding of reed solomon codes the algebraic soft decision decoding asd algorithm is a polynomial time soft decoding algorithm for reed solomon rs codes it outperforms both the algebraic hard decision decoding ahd and the conventional unique decoding algorithms but with a high computational cost this paper proposes a progressive asd pasd algorithm that enables the conventional asd algorithm to perform decoding with an adjustable designed factorization output list size ols the ols is enlarged progressively leading to an incremental computation for the interpolation and an enhanced error correction capability multiple factorizations are performed in order to find out the intended message polynomial which will be validated by a cyclic redundant check crc code the incremental interpolation constraints are introduced to characterize the progressive decoding the validity analysis of the algorithm shows the pasd algorithm is a natural and computationally saving generalization of the asd algorithm delivering the same interpolation solution the average decoding complexity of the algorithm is further theoretically characterized revealing its dependence on the channel condition the simulation results further validate the analysis by showing that the average decoding complexity can be converged to the minimal level in a good channel condition finally performance evaluation shows the pasd algorithm preserves the error correction capability of the asd algorithm

a generalization of the berlekamp massey algorithm for multisequence shift register synthesis with applications to decoding cyclic codes a generalization of the berlekamp massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences a more general problem is first considered that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field which includes the multisequence problem as a special case a simple iterative algorithm the fundamental iterative algorithm fia is presented for solving this problem the generalized algorithm is then derived through a refinement of the fia application of this generalized algorithm to decoding cyclic codes up to the hartmann tzeng ht bound and roos bound making use of multiple syndrome sequences is considered conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error locator polynomial are determined with respect to decoding up to the ht bound and special cases of the roos bound

differential methods in inverse scattering this paper discusses a new set of differential methods for solving the inverse scattering problem associated to the propagation of waves in an inhomogeneous medium by writing the medium equations in the form of a two component system describing the interaction of rightward and leftward propagating waves the causality of the propagation phenomena is exploited in order to identify the medium layer by layer the recursive procedure that we obtain constitutes a continuous version of an algorithm first derived by schur in order to test for the boundedness of functions analytic inside the unit circle it recovers the local reflectivity function of the medium using similar ideas some other differential methods can also be derived to reconstruct alternative parametrizations of the layered medium in terms of the local impedance or of the potential function the differential inverse scattering methods turn out to be very efficient since in some sense they let the medium perform the inversion by itself and thus

list decoding of crisscross errors in this paper list decoding of crisscross errors in arrays over finite fields is considered for this purpose the so called cover metric is used where the cover of a matrix is a set of rows and columns which contains all non zero elements of the matrix a johnson like upper bound on the maximum list size in the cover metric is derived showing that the list of codewords has polynomial size up to a certain radius furthermore a simple list decoding algorithm for a known optimal code construction is presented which decodes errors in the cover metric up to our upper bound these results reveal significant differences between the cover metric and the rank metric and show that the cover metric is more suitable for correcting crisscross errors

application of the schur algorithm to the inverse problem for a layered acoustic medium the schur algorithm is a signal processing algorithm which works on a layer stripping principle its time domain version the fast cholesky recursion is a fast and efficient algorithm well suited for high speed data processing in this paper these algorithms are applied to the inverse problem for a continuous layered acoustic medium three different excitations of the medium are considered impulsive plane waves at normal incidence impulsive plane waves at oblique incidence and spherical waves emanating from an impulsive point source the fast algorithms obtained for each of these problems seem to be computationally superior to past work done on these problems that employed gelfand levitan theory to reconstruct the potential of a schrodinger equation

deterministic factorization of sparse polynomials with bounded individual degree in this article we study the problem of deterministic factorization of sparse polynomials we show that if f f x1 x2 xn is a polynomial with s monomials with individual degrees of its variables bounded by d then f can be deterministically factored in time spoly d log n prior to our work the only efficient factoring algorithms known for this class of polynomials were randomized and other than for the cases of d 1 and d 2 only exponential time deterministic factoring algorithms were known a crucial ingredient in our proof is a quasi polynomial sparsity bound for factors of sparse polynomials of bounded individual degree in particular we show that if f is an s sparse polynomial in n variables with individual degrees of its variables bounded by d then the sparsity of each factor of f is bounded by s 9 d2 log n this is the first non trivial bound on factor sparsity for d 2 our sparsity bound uses techniques from convex geometry such as the theory of newton polytopes and an approximate version of the classical caratheodory s theorem our work addresses and partially answers a question of von zur gathen and kaltofen 1985 who asked whether a quasi polynomial bound holds for the sparsity of factors of sparse polynomials

simple full field method for the elastic characterization of orthotropic composite plates a speckle shearing interferometer with a simple setup is designed and tested for full field characterization of the elastic properties of isotropic and orthotropic composite plates the technique is straightforward and provides comparable results obtained by standard methods the proposed method has the advantages of being noncontact and full field in nature beam specimens cut from the plate were loaded under the standard four point bending configuration gradients of bending deformation are measured by the speckle shearing interferometer directly curvature of each bended beam is calculated from the slope of the fitted line of the gradient data the elastic moduli and poisson s ratios of the plate material are determined from the curvature of the beam specimens comparing the present approach to other full field techniques reported in literature that are mostly based on deformation measurement of a specimen subjected to a complicated load field the present method is much easier to apply and the image analysis procedure is much simpler

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

inversion of acoustic material signature of layered solids the simplex inversion technique is applied to the acoustic material signature ams of layered solids to obtain thickness and material properties of layers it is shown in this paper that by careful application of the simplex technique it is possible to extract much information about a multilayered specimen from its ams a brief review of different inversion techniques is also given in the paper from which the relative advantages of using the simplex alogrithm over other techniques are derived

a parametric approach to list decoding of reed solomon codes using interpolation in this paper we present a minimal list decoding algorithm for reed solomon rs codes minimal list decoding for a code c refers to list decoding with radius l where l is the minimum of the distances between the received word r and any codeword in c we consider the problem of determining the value of l as well as determining all the codewords at distance l our approach involves a parametrization of interpolating polynomials of a minimal grobner basis g we present two efficient ways to compute g we also show that so called re encoding can be used to further reduce the complexity we then demonstrate how our parametric approach can be solved by a computationally feasible rational curve fitting solution from a recent paper by wu besides we present an algorithm to compute the minimum multiplicity as well as the optimal values of the parameters associated with this multiplicity which results in overall savings in both memory and computation

the one dimensional inverse problem of reflection seismology an impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth the ensuing particle velocity at the surface is assumed to be measured the problem of calculating the subsurface characteristic impedance from knowledge of the input pulse and the measured data is the one dimensional inverse problem of reflection seismology the problem is set up mathematically as an inverse problem for a first order 2 times 2 hyperbolic system the role of propagation of singularities is explained and the relation between the solution of the inverse problem and the cholesky factorization of certain matrices constructed from the data is elaborated for both the continuum problem and the related discrete problem it is found that recursive numerical techniques such as the levinson algorithm and certain other fast methods for cholesky factorization are intimately related to explicit finite difference schemes for solving hyperbolic systems the order of approximation between the

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

improved decoding of reed solomon and algebraic geometry codes given an error correcting code over strings of length n and an arbitrary input string also of length n the list decoding problem is that of finding all codewords within a specified hamming distance from the input string we present an improved list decoding algorithm for decoding reed solomon codes the list decoding problem for reed solomon codes reduces to the following curve fitting problem over a field f given n points x sub i spl middot y sub i sub i 1 sup n x sub i y sub i spl isin f and a degree parameter k and error parameter e find all univariate polynomials p of degree at most k such that y sub i p x sub i for all but at most e values of i spl isin 1 n we give an algorithm that solves this problem for e 1 3 where the result yields the first asymptotic improvement in four decades the algorithm generalizes to solve the list decoding problem for other algebraic codes specifically alternant codes a class of codes including bch codes and algebraic geometry codes in both cases we obtain a list decoding algorithm that corrects up to n spl radic n n d errors where n is the block length and d is the designed distance of the code the improvement for the case of algebraic geometry codes extends the methods of shokrollahi and wasserman see in proc 29th annu acm symp theory of computing p 241 48 1998 and improves upon their bound for every choice of n and d we also present some other consequences of our algorithm including a solution to a weighted curve fitting problem which may be of use in soft decision decoding algorithms for reed solomon codes

inverse calculation of material parameters for a thin layer system using transient elastic waves the inverse calculation of material parameters of a thin layer system is investigated using transient elastic waves the inverse problem is formulated as an optimization problem in which the norm of the discrepancies between the calculated and measured normal surface displacements is minimized through the simplex algorithm the theoretical result is first solved using the laplace transform and the transient response is then implemented analytically by cagniard s method in the experiment the source time function is generated by the brittle fracture of a pencil lead on the surface of the thin layer system and a national bureau of standards nbs conical transducer is used to record the surface responses to obtain reliable inverse results for material parameters a two step inverse calculation procedure is proposed the recovered material parameters of the specimens agree well with the theoretical values and experimental results

inverse evaluation of material constants for composite plates by optical interferometry method electronic speckle pattern interferometry espi is a powerful tool for the full field noncontact and real time measurement method of surface displacements for deformed bodies as compared with the conventional film recording and optical reconstruction procedures used for holographic interferometry the interferometric fringes of espi are produced instantly by a video recording system in this study the amplitude fluctuation espi af espi optical system is used for measuring the resonant frequencies and mode shapes of vibrating composite plates by making use of the resonant frequencies for free plates obtained experimentally an inverse evaluation for the material constants is developed using the rayleigh ritz technique and the simplex method for function minimization finally finite element calculation is used to construct the mode shapes from the obtained material constants by inverse evaluation and the results are compared with the experimental observations the experimental method based on optical af espi setup and the inverse algorithms proposed might become a reliable and self consistent methodology for evaluating material constants of composite plates

fast chase decoding algorithms and architectures for reed solomon codes chase decoding is a prevalent soft decision decoding method for algebraic codes where an efficient bounded distance decoder is available essentially it repeatedly applies bounded distance decoding upon combinatorially flipping certain least reliable bits or patterns for nonbinary case in this paper we devise a one pass chase decoding algorithm of reed solomon codes such that the desired error locator polynomial by flipping an error pattern is obtained in one pass when operated in parallel through utilizing the preceding results this is effectively achieved through cumulative interpolation and linear feedback shift register lfsr synthesis techniques furthermore through converting the algorithm into the transform domain exhaustive root search for each error locator polynomial is circumvented computationally the new algorithm exhibits linear complexity in attempting to determine a candidate codeword associated with each additionally flipped symbol pattern it compares favorably to quadratic complexity by straightforwardly utilizing hard decision decoding where and denote the code length and minimum distance respectively we also reveal a corrected algorithm for one pass generalized minimum distance gmd decoding for reed solomon codes from koetter s original work in addition we devise a highly efficient one pass chase decoding algorithm for binary bose chaudhuri hocquenghem bch codes by taking advantage of a key characteristic of the berlekamp algorithm finally we present a systolic very large scale integration vlsi decoder architecture through slightly compromising the proposed one pass chase decoding algorithm it takes clock cycles to complete one iteration by flipping one error pattern both circuit and memory complexities are dictated by the dimension of flipping patterns in particular they are independent of the code length or the minimum distance rendering it highly attractive for various applications

algebraic soft decision decoding of reed solomon codes using bit level soft information the performance of algebraic soft decision decoding of reed solomon codes using bit level soft information is investigated optimal multiplicity assignment strategies for algebraic soft decision decoding sdd with infinite cost are first studied over erasure channels and the binary symmetric channel the corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are derived the multiplicity assignment strategy and the corresponding performance analysis are then generalized to characterize the decoding region of algebraic sdd over a mixed error and bit level erasure channel the bit level decoding region of the proposed multiplicity assignment strategy is shown to be significantly larger than that of conventional berlekamp massey decoding as an application a bit level generalized minimum distance decoding algorithm is proposed the proposed decoding compares favorably with many other reed solomon sdd algorithms over various channels moreover owing to the simplicity of the proposed bit level generalized minimum distance decoding its performance can be tightly bounded using order statistics

layer stripping solutions of multidimensional inverse scattering problems a layer stripping procedure for solving three dimensional schrodinger equation inverse scattering problems is developed this method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region it is thus a generalization of algorithms that have been developed for one dimensional inverse scattering problems although the procedure has not yet been numerically tested the corresponding one dimensional algorithms have performed well on synthetic data the procedure is applied to a two dimensional inverse seismic problem connections between simplifications of this method and born approximation inverse scattering methods are also noted

performance of sphere decoding of block codes a sphere decoder searches for the closest lattice point within a certain search radius the search radius provides a tradeoff between performance and complexity we focus on analyzing the performance of sphere decoding of linear block codes we analyze the performance of soft decision sphere decoding on awgn channels and a variety of modulation schemes a hard decision sphere decoder is a bounded distance decoder with the corresponding decoding radius we analyze the performance of hard decision sphere decoding on binary and q ary symmetric channels an upper bound on the performance of maximum likelihood decoding of linear codes defined over fq e g reed solomon codes and transmitted over q ary symmetric channels is derived and used in the analysis we then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes the tradeoff between the performance and complexity of a sphere decoder is then discussed

complexity of decoding positive rate primitive reed solomon codes it has been proved that the maximum likelihood decoding problem of reed solomon codes is np hard however the length of the code in the proof is at most polylogarithmic in the size of the alphabet for the complexity of maximum likelihood decoding of the primitive reed solomon code whose length is one less than the size of alphabet the only known result states that it is at least as hard as the discrete logarithm in some cases where the information rate unfortunately goes to zero in this paper it is proved under a well known cryptography hardness assumption that 1 there does not exist a randomized polynomial time maximum likelihood decoder for the reed solomon code family q k q q where k x is any function in z z computable in time xo 1 satisfying x k x x x 2 there does not exist a randomized polynomial time bounded distance decoder for primitive reed solomon codes at distance 2 3 of the minimum distance for any constant 0 1 3 in particular this rules out the possibility of a polynomial time algorithm for maximum likelihood decoding problem of primitive reed solomon codes of any rate under the assumption

combinatorial properties of frameproof and traceability codes in order to protect copyrighted material codes may be embedded in the content or codes may be associated with the keys used to recover the content codes can offer protection by providing some form of traceability ta for pirated data several researchers have studied different notions of ta and related concepts in previous years strong versions of ta allow at least one member of a coalition that constructs a pirate decoder to be traced weaker versions of this concept ensure that no coalition can frame a disjoint user or group of users all these concepts can be formulated as codes having certain combinatorial properties we study the relationships between the various notions and we discuss equivalent formulations using structures such as perfect hash families we use methods from combinatorics and coding theory to provide bounds necessary conditions and constructions sufficient conditions for the objects of interest

mean field solution of the small world network model the small world network model is a simple model of the structure of social networks which possesses characteristics of both regular lattices and random graphs the model consists of a one dimensional lattice with a low density of shortcuts added between randomly selected pairs of points these shortcuts greatly reduce the typical path length between any two points on the lattice we present a mean field solution for the average path length and for the distribution of path lengths in the model this solution is exact in the limit of large system size and either a large or small number of shortcuts

efficient interpolation in the guruswami sudan algorithm a novel algorithm is proposed for the interpolation step of the guruswami sudan list decoding algorithm the proposed method is based on the binary exponentiation algorithm and can be considered as an extension of the lee o sullivan method the algorithm is shown to achieve both asymptotical and practical performance gain compared to the case of iterative interpolation algorithm further complexity reduction is achieved by employing the reencoding transformation the key contribution of the paper which enables the complexity reduction is a novel randomized ideal multiplication algorithm

linearized polynomial interpolation and its applications in this paper we first propose an interpolation algorithm in a well ordered free module of a linearized polynomial ring and then use this algorithm to decode several important families of codes gabidulin codes kotter and kschischang kk codes and mahdavifar and vardy mv codes our decoding algorithm for gabidulin codes is different from the polynomial reconstruction algorithm by loidreau when applied to decode kk codes our interpolation algorithm is equivalent to the sudan style list 1 decoding algorithm proposed by kotter and kschischang for kk codes the interpolation approach is also capable of solving the interpolation problem for the list decoding of mv codes proposed by mahdavifar and vardy and has a lower complexity than gaussian elimination an interpolator for list decoding of mv codes has also been implemented in hardware and the synthesis results show that it leads to better throughput and efficiency than gaussian elimination

noise induced order a new noise effect on chaos in one dimensional mappings is reported the transition from chaotic behavior to ordered behavior induced by external noise is observed in a certain class of one dimensional mappings this transition is clearly shown in terms of the lyapunov number entropy power spectrum and the nature of orbits

growing networks with mixed attachment mechanisms networks grow and evolve when new nodes and links are added in there are two methods to add the links uniform attachment and preferential attachment we take account of the addition of links with mixed attachment between uniform attachment and preferential attachment in proportion by using numerical simulations and analysis based on a continuum theory we obtain that the degree distribution p k has an extended power law form p k k k0 when the number of edges k of a node is much larger than a certain value k0 the degree distribution reduces to the power law form p k k and when k is much smaller than k0 the degree distribution degenerates into the exponential form it has been found that degree distribution possesses this extended power law form for many real networks such as the movie actor network the citation network of scientific papers and diverse protein interaction networks

iterative soft input soft output decoding of reed solomon codes by adapting the parity check matrix an iterative algorithm is presented for soft input soft output siso decoding of reed solomon rs codes the proposed iterative algorithm uses the sum product algorithm spa in conjunction with a binary parity check matrix of the rs code the novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the spa is applied at each iteration the proposed algorithm can be geometrically interpreted as a two stage gradient descent with an adaptive potential function this adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and therefore significantly improves the performance simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding hdd and compare favorably with other popular soft decision decoding methods

on rational interpolation based list decoding and list decoding binary goppa codes we derive the wu list decoding algorithm for generalized reed solomon grs codes by using grobner bases over modules and the euclidean algorithm as the initial algorithm instead of the berlekamp massey algorithm we present a novel method for constructing the interpolation polynomial fast we give a new application of the wu list decoder by decoding irreducible binary goppa codes up to the binary johnson radius finally we point out a connection between the governing equations of the wu algorithm and the guruswami sudan algorithm immediately leading to equality in the decoding range and a duality in the choice of parameters needed for decoding both in the case of grs codes and in the case of goppa codes

high rate codes with sublinear time decoding locally decodable codes are error correcting codes that admit efficient decoding algorithms any bit of the original message can be recovered by looking at only a small number of locations of a corrupted codeword the tradeoff between the rate of a code and the locality efficiency of its decoding algorithms has been well studied and it has widely been suspected that nontrivial locality must come at the price of low rate a particular setting of potential interest in practice is codes of constant rate for such codes decoding algorithms with locality o k were known only for codes of rate 1 where k is the length of the message furthermore for codes of rate 1 2 no nontrivial locality had been achieved in this article we construct a new family of locally decodable codes that have very efficient local decoding algorithms and at the same time have rate approaching 1 we show that for every 0 and 0 for infinitely many k there exists a code c which encodes messages of length k with rate 1 and is locally decodable from a constant fraction of errors using o k queries and time these codes which we call multiplicity codes are based on evaluating multivariate polynomials and their derivatives multiplicity codes extend traditional multivariate polynomial codes they inherit the local decodability of these codes and at the same time achieve better tradeoffs and flexibility in the rate and minimum distance

analytical sensitivities of principal components in time series analysis of dynamical systems original method for calculating the analytical sensitivities of the principal components of dynamical systems is developed methods for analytical sensitivity calculations are developed for both the singular value decomposition and eigenanalysis based approaches for principal component calculation sensitivities with respect to state initial conditions and system parameters are enabled by state transition matrix calculations for augmented state and parameter differential equations a novel approach to compute principal component sensitivities with respect to transient forcing function parameters isintroduced bytransforming nonhomogenous differential equations forced system into homogenous differential equations unforced system these new developments are applied to several example problems in dynamics analysis with an emphasis on structural dynamics analysis analytical sensitivities provide the necessary derivatives for gradient based optimization algorithms and provide an analytical framework for evaluating structural modifications based on principal components analysis

list decoding of generalized reed solomon codes over commutative rings we show that the list decoding procedure of guruswami and sudan may be used to decode generalized reed solomon rs codes defined over commutative rings with identity an algorithm for performing the first of the two phases of this decoding procedure is also given in particular we show that for generalized rs codes over chain rings the probability of picking an incorrect codeword from a given list can be reduced by increasing the size of the code alphabet while keeping the length and minimum hamming distance of the code constant

karhunen loeve decomposition approach to analyzing complex network synchronization in this paper the approach of the karhunen lo ve decomposition known also as the proper orthogonal modes poms is taken to analyze phase synchronization of various complex networks with different topologies namely the classic kuramoto model coupled chaotic maps with gaussian delays and a chain of diffusively coupled bistable oscillators in the case of the kuramoto model the poms reveal the tendency and the level of synchronization with the increase of the coupling strength for globally coupled networks and scale free networks while periodic poms are found in nearest neighbor coupled networks furthermore for cluster networks on the kuramoto model the first leading poms based on different time intervals reveal that different sub groups of nodes synchronize gradually to different levels eventually leading to the complete phase synchronization in the case of coupled chaotic maps some properties of phase synchronization change with the coupling strength value in the case of the chain of diffusively coupled bistable oscillators several main poms not only determine the network phase synchronization but also provide good reconstruction of the network responses

bounded distance 1 soft decision reed solomon decoding we present a new reed solomon decoding algorithm which embodies several refinements of an earlier algorithm some portions of this new decoding algorithm operate on symbols of length lgq bits other portions operate on somewhat longer symbols in the worst case the total number of calculations required by the new decoding algorithm is proportional to nr where n is the code s block length and r is its redundancy this worst case workload is very similar to prior algorithms but in many applications average case workload and error correcting performance are both much better the input to the new algorithm consists of n received symbols from gf q and n nonnegative real numbers each of which is the reliability of the corresponding received symbol any conceivable errata pattern has a score equal to the sum of the reliabilities of its locations with nonzero errata values a max likelihood decoder would find the minimum score over all possible errata patterns our new decoding algorithm finds the minimum score only over a subset of these possible errata patterns the errata within any candidate errata pattern may be partitioned into errors and erasures depending on whether the corresponding reliabilities are above or below an erasure threshold different candidate errata patterns may have different thresholds each chosen to minimize its corresponding errata count which is defined as 2 spl middot number of errors number of erasures the new algorithm finds an errata pattern with minimum score among all errata patterns for which errata count spl les r 1 where r is the redundancy of the rs code conventional algorithms also require that the erasure threshold be set a priori the new algorithm obtains the best answer over all possible settings of the erasure threshold conventional cyclic rs codes have length n q 1 and their locations correspond to the nonzero elements of gf q the new algorithm also applies very naturally to rs codes which have been doubly extended by the inclusion of 0 and spl infin as additional locations

achievable error exponents for the private fingerprinting game fingerprinting systems in the presence of collusive attacks are analyzed as a game between a fingerprinter and a decoder on the one hand and a coalition of two or more attackers on the other hand the fingerprinter distributes to different users different fingerprinted copies of a host data covertext drawn from a memoryless stationary source embedded with different fingerprints the coalition members create a forgery of the data while aiming at erasing the fingerprints in order not to be detected their action is modeled by a multiple access channel mac we analyze the performance of two classes of decoders associated with different kinds of error events the decoder of the first class aims at detecting the entire coalition whereas the second is satisfied with the detection of at least one member of the coalition both decoders have access to the original covertext data and observe the forgery in order to identify member s of the coalition motivated by a worst case approach we assume that the coalition of attackers is informed of the hiding strategy taken by the fingerprinter and the decoder while they are uninformed of the attacking scheme achievable single letter expressions for the two kinds of error exponents are obtained single letter lower bounds are also derived for the subclass of constant composition codes these lower and the upper bounds coincide for the error exponent of the first class further for the error of the first kind a decoder that is optimal is introduced and the worst case attack channel is characterized