simplification of packet symbol decoding with errors deletions misordering of packets and no sequence numbers in this paper a new method is described which builds on mitzenmacher s idea of adding a different pseudorandom number to each packet to help decode packet symbol low density codes with deletions errors and out of order reception without sequence numbers the new method has lower decoding complexity than the original method the most basic form of the new method applies to any parity check code structure but is limited to a rather small number of packets in the code decoding success is slightly inferior to an ideal erasure channel which would require sequence numbering and error detection in each packet error detection is needed only for the whole code amounting to usually less than one bit per packet symbol moreover if error detection can resolve one of a small number of alternatives the ordered case performs almost as well as the ideal erasure channel ways are shown to modify the basic algorithm for use with long codes possibly approaching the erasure channel capacity limit

a reduced finite volume element formulation and numerical simulations based on pod for parabolic problems a proper orthogonal decomposition pod method is applied to a usual finite volume element fve formulation for parabolic equations such that it is reduced to a pod fve formulation with lower dimensions and high enough accuracy the error estimates between the reduced pod fve solution and the usual fve solution are analyzed it is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions moreover it is also shown that the reduced pod fve formulation based on pod method is both feasible and highly efficient

a reduced order extrapolation central difference scheme based on pod for two dimensional fourth order hyperbolic equations the reduced order extrapolating fd schemes are just developed by luo s research team since 2013 see 47 52 and a very new technique the reduced order extrapolation central difference scheme based on pod for two dimensional fourth order hyperbolic equations is first built by us we provide theoretical analysis and examples to show the advantage of our method this paper is concerned with establishing the reduced order extrapolation central difference roecd scheme based on proper orthogonal decomposition pod for two dimensional 2d fourth order hyperbolic equations for this purpose we first develop the classical central difference cd scheme for the 2d fourth order hyperbolic equations and analyze its stability and convergence then by making use of the pod method we build the roecd scheme with fewer degrees of freedom and sufficiently high accuracy and furnish the error estimates of the roecd solutions and the algorithm procedure for solving the roecd scheme finally we employ some numerical examples to confirm the correctness of theoretical conclusions this implies that roecd scheme is feasible and efficient for seeking the numerical solutions of the 2d fourth order hyperbolic equations

pod and cvt based reduced order modeling of navier stokes flows abstract a discussion of reduced order modeling for complex systems such as fluid flows is given to provide a context for the construction and application of reduced order bases reviews of the pod proper orthogonal decomposition and cvt centroidal voronoi tessellation approaches to reduced order modeling are provided including descriptions of pod and cvt reduced order bases their construction from snapshot sets and their application to the low cost simulation of the navier stokes system some concrete incompressible flow examples are used to illustrate the construction and use of pod and cvt reduced order bases and to compare and contrast the two approaches to reduced order modeling

on the capacity of duplication channels the i i d duplication channel which duplicates each symbol independently with a certain probability is studied the contribution is twofold first a tight lower bound on the capacity of such channels is introduced second the capacity is computed for the small values of the duplication probability using a series expansion representation

insertion deletion correction with spectral nulls levenshtein 1966 proposed a class of single insertion deletion correcting codes based on the number theoretic construction due to varshamov and tenengolt s 1965 we present several interesting results on the binary structure of these codes and their relation to constrained codes with nulls in the power spectral density function one surprising result is that the higher order spectral null codes of immink and beenker 1987 are sub codes of balanced levenshtein codes other spectral null sub codes with similar coding rates may also be constructed we furthermore present some coding schemes and spectral shaping markers which alleviate the fundamental restriction on levenshtein s codes that the boundaries of each codeword should be known before insertion deletion correction can be effected

level set topology optimization for mechanical metamaterials under hybrid uncertainties abstract this paper proposes a level set based robust topology optimization rto method for computational design of metamaterials under hybrid uncertainties e g auxetics with negative poisson s ratio where the young s modulus of the solid is described as a random variable while the poisson s ratio is regarded as an interval variable firstly the robust objective function is formulated by a combination of interval mean and interval variance of the deterministic objective function secondly the interval mean and interval variance are computed by a hybrid uncertain analysis approach termed as polynomial chaos chebyshev interval pcci method thirdly the design sensitivities of the robust objective function are obtained after the implementation of the pcci method finally a powerful parametric level set method plsm in conjunction with the numerical homogenization method is applied to achieve the robust topological design for the auxetic microstructure several numerical cases are used to demonstrate the effectiveness of the proposed method for the robust topology optimization problems this method is non intrusive and general and can be easily extended to a range of design problems of micro structured metamaterials

a self contained automated methodology for optimal flow control this paper describes a self contained automated methodology for active flow control which couples the time dependent navier stokes system with an adjoint navier stokes system and optimality conditions from which optimal states i e unsteady flow fields and controls e g actuators may be determined the problem of boundary layer instability suppression through wave cancellation is used as the intital validation case to test the methodology here the objective of control is to match the stress vector along a portion of the boundary to a steady base flow control is effected through the injection or suction of fluid through a single orifice on the boundary the results demonstrate that instability suppression can be achieved without any a priori knowledge of the flow unsteadiness such as frequencies instability type etc the present methodology has been extended to three dimensions and may potentially be applied to separation control relaminarization and turbulence control applications using one to many sensors and actuators

spectral stochastic isogeometric analysis for linear stability analysis of plate abstract a spectral stochastic isogeometric analysis ssiga scheme is proposed for the stochastic linear stability analysis of plate with uncertain material properties within the proposed ssiga scheme the first order shear deformation theory of plate is adopted for modelling the kinematic relationship both homogeneous and functionally graded material fgm models can be incorporated the considered spatially dependent uncertainties i e young s modulus and poisson s ratio are modelled as random fields with gaussian and lognormal distributions and the spatially independent uncertainty i e gradient index of fgm is modelled as random variable the generalized isogeometric basis function is adopted for both the random field geometry representation and random field discretization through the karhunen loeve k l expansion an extended support vector regression x svr with a new generalized gegenbauer polynomial kernel is developed to model the nonlinear relationship between the structural uncertainties and the buckling load by further implementing various nonparametric statistical inference methods the mean standard deviation probability density function pdf and cumulative distribution function cdf of the buckling load can be effectively established to determine the strength limit of the plate the accuracy efficiency and applicability of the proposed approach are illustrated through two numerical examples

rates of dna sequence profiles for practical values of read lengths a recent study by one of the authors has demonstrated the importance of profile vectors in dna based data storage we provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size q read length ell and word length n consequently we demonstrate that for q ge 2 and n le q ell 2 1 the number of profile vectors is at least q kappa n with kappa very close to 1 in addition to enumeration results we provide a set of efficient encoding and decoding algorithms for certain families of profile vectors

random vibration of the functionally graded laminates in thermal environments this work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change taking into account the randomness in a number of independent input variables such as young s modulus poisson s ratio and thermal expansion coefficient of each constituent material based on third order shear deformation theory the mixed type formulation and a semi analytical approach are employed to derive the standard eigenvalue problem in terms of deflection mid plane rotations and stress function a mean centered first order perturbation technique is adopted to obtain the second order statistics of vibration frequencies a detailed parametric study is conducted and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia showing the effects of scattering in thermo elastic material constants temperature change edge support condition side to thickness ratio and plate aspect ratio on the stochastic characteristics of natural frequencies

analysis and application of finite volume element methods to a class of partial differential equations abstract the finite volume element fve methods for a class of partial differential equations are discussed and analyzed in this paper the new initial values are introduced in the finite volume element schemes and we obtain optimal error estimates in l p and w 1 p 2 p as well as some superconvergence estimates in w 1 p 2 p the main results in this paper perfect the theory of the finite volume element methods

mixed finite element formulation and error estimates based on proper orthogonal decomposition for the nonstationary navier stokes equations in this paper proper orthogonal decomposition pod is used for model reduction of mixed finite element mfe for the nonstationary navier stokes equations and error estimates between a reference solution and the pod solution of reduced mfe formulation are derived the basic idea of this reduction technique is that ensembles of data are first compiled from transient solutions computed equation system derived with the usual mfe method for the nonstationary navier stokes equations or from physics system trajectories by drawing samples of experiments and interpolation or data assimilation and then the basis functions of the usual mfe method are substituted with the pod basis functions reconstructed by the elements of the ensemble to derive the pod reduced mfe formulation for the nonstationary navier stokes equations it is shown by considering numerical simulation results obtained for the illustrating example of cavity flows that the error between pod solution of reduced mfe formulation and the reference solution is consistent with theoretical results moreover it is also shown that this result validates the feasibility and efficiency of the pod method

lee metric bch codes and their application to constrained and partial response channels shows that each code in a certain class of bch codes over gf p specified by a code length n spl les p sup m 1 and a runlength r spl les p 1 2 of consecutive roots in gf p sup m has minimum lee distance spl ges 2r for the very high rate range these codes approach the sphere packing bound on the minimum lee distance furthermore for a given r the length range of these codes is twice as large as that attainable by berlekamp s 1984 extended negacyclic codes the authors present an efficient decoding procedure based on euclid s algorithm for correcting up to r 1 errors and detecting r errors that is up to the number of lee errors guaranteed by the designed minimum lee distance 2r bounds on the minimum lee distance for r spl ges p 1 2 are provided for the reed solomon case i e when the bch code roots are in gf p the authors present two applications first lee metric bch codes can be used for protecting against bitshift errors and synchronization errors caused by insertion and or deletion of zeros in d k constrained channels second the code construction with its decoding algorithm can be formulated over the integer ring providing an algebraic approach to correcting errors in partial response channels where matched spectral null codes are used

a stochastic scaled boundary finite element method abstract by extending the existing scaled boundary finite element method sbfem into the random field problem a stochastic scaled boundary finite element method ssbfem is developed in this paper to predict the structural responses with randomly distributed material properties the analyzed domain is discretized into a number of polygons modeled as sub domains of the sbfem so that the non homogeneous material properties are possible to be considered in establishment of the constitutive equation the random field represented by the karhunen loeve kl expansion is then directly incorporated into both the equilibrium equation of the sbfem and its sensitivity analysis formulation the perturbation method is employed to calculate the statistical moments of the structural responses and a semi analytical sensitivity analysis method is used to efficiently calculate the gradients involved particularly the proposed method is successfully applied to the stochastic fracture analysis with spatially varying random material properties four numerical examples are investigated to demonstrate the validity of the proposed method

bounds on the capacity of discrete memoryless channels corrupted by synchronization and substitution errors we study the capacity of discrete memoryless channels with synchronization errors and additive noise we first show that with very large alphabets their capacity can be achieved by independent and identically distributed input sources and establish proven tight lower and upper capacity bounds we also derive tight numerical capacity bounds for channels where the synchronization between the input and output is partly preserved for instance using incorruptible synchronization markers such channels include channels with duplication errors channels that only insert or delete zeros and channels with bitshift errors studied in magnetic recording channels with small alphabets and corrupted by synchronization errors have an infinite memory revisiting the theoretical work of dobrushin and adapting techniques used to compute capacity bounds for finite state source channel models we compute improved numerical capacity lower bounds for discrete memoryless channels with small alphabets synchronization errors and memoryless noise an interesting and some what surprising result is that as long as the input sequences are not completely deleted the capacity of channels corrupted by discrete timing errors is always nonzero even if all the symbols are corrupted

stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness abstract the paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties the isogeometric analysis method is employed in the new stochastic analysis scheme which is called stochastic isogeometric analysis siga the elastic modulus and mass density are modeled as homogeneous gaussian random fields along the plane of structure the governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues in order to verify proposed method the brute force monte carlo simulation is employed the mean variance and cov coefficient of variation predicted by siga and those predicted by monte carlo simulation show good agreement the numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates the correlation between elastic modulus and mass density is also observed to have significant effect on the response cov of eigenvalue

a reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for burgers equation in this article a reduced optimizing finite difference scheme fds based on singular value decomposition svd and proper orthogonal decomposition pod for burgers equation is presented also the error estimates between the usual finite difference solution and the pod solution of reduced optimizing fds are analyzed it is shown by considering the results obtained for numerical simulations of cavity flows that the error between the pod solution of reduced optimizing fds and the solution of the usual fds is consistent with theoretical results moreover it is also shown that the reduced optimizing fds is feasible and efficient

a sequential nonlinear interval number programming method for uncertain structures a sequential nonlinear interval number programming sninp method is suggested to deal with the uncertain optimization problems a general uncertain optimization model is investigated in which the objective function and constraints are both nonlinear and uncertain a nonlinear interval number programming ninp method is employed to transform the uncertain optimization problem into a deterministic two objective optimization problem then using the linear combination method and the constraint penalty function method a deterministic single objective and non constraint optimization problem is formulated in terms of a penalty function combining this ninp method with a modified approximation management framework amf an efficient sninp method is then constructed at each iterative step an approximation optimization problem is created based on the latin hypercube design lhd and the quadratic polynomial response surface approximation rsa and it can then be solved by the ninp method efficiently the trust region method is used to manage the sequence of the approximation optimization problems based on a reliability index an efficient method is suggested to calculate the actual penalty function and whereby the reliability index and based on it the current design space can be updated two numerical examples are presented to demonstrate the effectiveness of the present method

a reduced order extrapolation technique for solution coefficient vectors in the mixed finite element method for the 2d nonlinear rosenau equation abstract this study focuses mainly on a reduced order method for the coefficient vectors in the crank nicolson mixed finite element cnmfe solutions for the two dimensional nonlinear rosenau equation we first provide a cnmfe method for the rosenau equation and give relative theoretical results as well as rewrite the cnmfe method in matrix form we then produce two sets of proper orthogonal decomposition pod bases by means of the first few coefficient vectors of the cnmfe solutions and set up a reduced order extrapolating cnmfe roecnmfe model with the pod bases as well as discuss the existence and stability as well as errors of the roecnmfe solutions by means of the matrix tool resulting in the theoretical analysis becoming very succinct lastly we present some numerical experiments to validate the correctness of the theoretical results finding that the superiority of the roecnmfe method is further verified

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

algorithms for subsequence combinatorics a subsequence is obtained from a string by deleting any number of characters thus in contrast to a substring a subsequence is not necessarily a contiguous part of the string counting subsequences under various constraints has become relevant to biological sequence analysis to machine learning to coding theory to the analysis of categorical time series in the social sciences and to the theory of word complexity we present theorems that lead to efficient dynamic programming algorithms to count 1 distinct subsequences in a string 2 distinct common subsequences of two strings 3 matching joint embeddings in two strings 4 distinct subsequences with a given minimum span and 5 sequences generated by a string allowing characters to come in runs of a length that is bounded from above

stochastic finite element analysis of shells in the present paper the stochastic formulation of the triangular composite tric facet shell element is presented using the weighted integral and local average methods the elastic modulus of the structure is considered to be a two dimensional homogeneous stochastic field which is represented via the spectral representation method as a result of the proposed derivation and the special features of the element the stochastic stiffness matrix is calculated in terms of a minimum number of random variables of the stochastic field giving a cost effective stochastic matrix under the assumption of a pre specified power spectral density function of the stochastic field it is possible to compute the response variability of the shell structure numerical tests are provided to demonstrate the applicability of the proposed methodologies

simultaneous classification and feature selection via convex quadratic programming with application to hiv associated neurocognitive disorder assessment abstract support vector machines svms that utilize a mixture of the l 1 norm and the l 2 norm penalties are capable of performing simultaneous classification and selection of highly correlated features these svms typically set up as convex programming problems are re formulated here as simple convex quadratic minimization problems over non negativity constraints giving rise to a new formulation the pq svm method solutions to our re formulation are obtained efficiently by an extremely simple algorithm computational results on a range of publicly available datasets indicate that these methods allow greater classification accuracy in addition to selecting groups of highly correlated features these methods were also compared on a new dataset assessing hiv associated neurocognitive disorder in a group of 97 hiv infected individuals

mreklm a fast multiple empirical kernel learning machine abstract multiple empirical kernel learning mekl explicitly maps samples into different empirical feature spaces in which the kernel features of the mapped samples can be directly provided thus mekl is much easier than the conventional multiple kernel learning mkl in terms of processing and analyzing the structure of mapped feature spaces however the computational complexity of mekl with m empirical feature spaces is o mn 3 where n is the number of training samples the dimensions of the generated empirical feature spaces are approximate to n when dealing with large scale problems mekl cannot handle them properly due to the severe computation and memory burden moreover most existing mekl utilizes the gradient decent optimization to learn classifiers but it is time consuming for training therefore this paper proposes a multiple random empirical kernel learning machine mreklm to overcome these problems the proposed mreklm adopts the random projection idea to map samples into multiple low dimensional empirical feature spaces with lower computational complexity o mp 3 where p n is the number of the randomly selected samples after that mreklm adopts an analytical optimization approach to directly deal with multi class problems the computational complexity of mreklm is o m 3 p 3 experimental results also validate both efficiency and effectiveness of the proposed mreklm the contributions of this work are 1 proposing a fast mekl algorithm named mreklm 2 introducing an efficient random empirical kernel mapping approach and 3 extending the capability of mekl to handle large scale problems

maximum likelihood failure diagnosis in finite state machines under unreliable observations in this paper we develop a probabilistic methodology for failure diagnosis in finite state machines based on a sequence of unreliable observations given prior knowledge of the input probability distribution but without actual knowledge of the applied input sequence the core problem we consider is to choose from a pool of known deterministic finite state machines fsms the one that most likely matches the given sequence of observations the problem becomes challenging because of sensor failures which may corrupt the observed sequence by inserting deleting and transposing symbols with certain probabilities that are assumed known we propose an efficient recursive algorithm for obtaining the most likely underlying fsm given the possibly erroneous observed sequence the proposed algorithm essentially allows us to perform online maximum likelihood failure diagnosis and is applicable to more general settings where one is required to choose the most likely underlying hidden markov model hmm based on a sequence of observations that may get corrupted with known probabilities the algorithm generalizes existing recursive algorithms for likelihood calculation in hmms by allowing loops in the associated trellis diagram we illustrate the proposed methodology using an example of diagnosis in the context of communication protocols

moment balancing templates constructions to add insertion deletion correction capability to error correcting or constrained codes templates are constructed to extend arbitrary additive error correcting or constrained codes i e additional redundant bits are added in selected positions to balance the moment of the codeword the original codes may have error correcting capabilities or constrained output symbols as predetermined by the usual communication system considerations which are retained after extending the code using some number theoretic constructions in the literature insertion deletion correction can then be achieved if the template is carefully designed the number of additional redundant bits for the insertion deletion correction can be kept small in some cases of the same order as the number of parity bits in a hamming code of comparable length

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

polynomial time low density parity check codes with rates very close to the capacity of the q ary random deletion channel for large q we demonstrate polynomial time deletion codes based on the verification based decoding paradigm that come arbitrarily close to capacity the random deletion channel takes n symbols from a q ary alphabet and each symbol is deleted independently with probability p taking advantage of recent improvements on the results of luby and mitzenmacher for verification based decoding by shokrollahi and wang we show how to design for any epsi 0 and sufficiently large n and q deletion codes with the following properties the rate is 1 p 1 epsi the failure probability is no 1 epsi2 q and the computational complexity for encoding and decoding is no 1 epsi2 log q we also extend these schemes to obtain the same results even if the undeleted symbols are also transposed arbitrarily and if a sufficiently small number of random symbols are inserted

spectral stochastic isogeometric analysis of linear elasticity abstract the stochastic isogeometric analysis of linear elasticity problem is investigated in this study the spectral stochastic analysis is introduced into isogeometric analysis iga and a novel yet robust stochastic analysis framework namely the spectral stochastic isogeometric analysis ssiga is freshly proposed unlike traditional numerical solutions of the karhunen loeve k l expansion the non uniform rational b spline nurbs and t spline basis functions are employed within the proposed framework of ssiga so the random fields acting on a continuous physical medium with complex geometry can be handled in an appropriate physically feasible and efficient fashion the polynomials chaos expansion pce is implemented to represent the stochastic structural response e g displacement strain and stress such that all corresponding statistical characteristics e g mean and standard deviation can be robustly acquired furthermore by utilizing the nonparametric statistical analysis both probability density functions pdfs and cumulative distribution functions cdfs of concerned structural displacements and stresses can be effectively established within the framework of iga by meticulously implementing the concept of the higher order k refinement the proposed ssiga provides a more legitimate and efficient stochastic computational approach for modern engineering structures which are complicated by both spatially dependent uncertainties and complex geometries

modified sub interval perturbation finite element method for 2d acoustic field prediction with large uncertain but bounded parameters abstract based on the sub interval perturbation analysis a modified sub interval perturbation finite element method is proposed to determine the bounds of sound pressure in the 2d acoustic field with large uncertain but bounded parameters in the proposed method the inversion of the invertible sub interval dynamic stiffness matrix is approximated by a modified approximate interval value sherman morrison woodbury formula to overcome the drawbacks arising from the dependency phenomenon of parameters and the unpredictable effect of neglecting the higher order terms in neumann series the modified sub interval perturbation procedures are implemented in a numerical finite element framework numerical results on a 2d acoustic tube and a 2d acoustic cavity of a car with large uncertain but bounded parameters evidence the remarkable accuracy and effectiveness of the proposed method

new multiple insertion deletion correcting codes for non binary alphabets we generalize helberg s number theoretic construction of binary multiple insertion deletion correcting codes to non binary alphabets and describe a linear decoding algorithm for correcting multiple deletions

using reed muller hbox rm 1 m codes over channels with synchronization and substitution errors we analyze the performance of a reed muller rm 1 m code over a channel that in addition to substitution errors permits either the repetition of a single bit or the deletion of a single bit the latter feature is used to model synchronization errors we first analyze the run length structure of this code we enumerate all pairs of codewords that can result in the same sequence after the deletion of a single bit and propose a simple way to prune the code by dropping one information bit such that the resulting linear subcode has good post deletion and post repetition minimum distance a bounded distance decoding algorithm is provided for the use of this pruned code over the channel this algorithm has the same order of complexity as the usual fast hadamard transform based decoder for the rm 1 m code

interval and random analysis for structure acoustic systems with large uncertain but bounded parameters abstract for the response analysis of the structure acoustic system with uncertain but bounded parameters three bounded uncertain models are introduced one is the bounded random model in which all of the uncertain but bounded parameters are described as bounded random variables with well defined probability distribution the second one is the interval model in which all of the uncertain but bounded parameters are described as interval variables due to the limited information the third one is the bounded hybrid uncertain model in which the interval variables and the bounded random variables exist simultaneously based on the parametric gegenbauer polynomial which is formulated for bounded random model recently the gegenbauer series expansion method gsem is developed for the response prediction of the structure acoustic system under these three bounded uncertain models within gsem the response of these three bounded uncertain models of the structure acoustic system can be approximated by the unified gegenbauer series with different values of polynomial parameter then the interval and random analysis for these three bounded uncertain models of the structure acoustic system are conducted on the basis of gegenbauer series owing to the orthogonal property of gegenbauer polynomial the analytical solution of the expectation and variance of gegenbauer series with respect to the bounded random variables can be readily obtained the bounds of gegenbauer series with respect to the interval variables are determined by the monte carlo simulation the gsem is applied to solve a shell structure acoustic system under these three bounded uncertain models inspired by the convergence behavior of gsem the relative improvement criterion is established to estimate the required retained order of gegenbauer series for large uncertain problems the results on numerical examples show that gsem with the estimated retained order can achieve a prescribed accuracy and good efficiency for structure acoustic systems with large uncertain but bounded parameters

a priori l 2 error estimates for finite element methods for nonlinear diffusion equations with memory this paper studies finite element approximations to the solutions of the nonlinear diffusion equations with memory an elliptic projection with memory associated with our equations is defined and then used in the derivations of optimal error estimates for semidiscrete and crank nicolson finite element approximations

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

computing the error linear complexity spectrum of a binary sequence of period 2 sup n binary sequences with high linear complexity are of interest in cryptography the linear complexity should remain high even when a small number of changes are made to the sequence the error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed we present an algorithm which computes the error linear complexity for binary sequences of period spl lscr 2 sup n using o spl lscr log spl lscr sup 2 bit operations the algorithm generalizes both the games chan 1983 and stamp martin 1993 algorithms which compute the linear complexity and the k error linear complexity of a binary sequence of period spl lscr 2 sup n respectively we also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of reed muller codes

capacity bounds and concatenated codes over segmented deletion channels we develop an information theoretic characterization and a practical coding approach for segmented deletion channels compared to channels with independent and identically distributed i i d deletions where each bit is independently deleted with an equal probability the segmentation assumption imposes certain constraints i e in a block of bits of a certain length only a limited number of deletions are allowed to occur this channel model has recently been proposed and motivated by the fact that for practical systems when a deletion error occurs it is more likely that the next one will not appear very soon we first argue that such channels are information stable hence their channel capacity exists then we introduce several upper and lower bounds with two different methods in an attempt to understand the channel capacity behavior the first scheme utilizes certain information provided to the transmitter and or receiver while the second one explores the asymptotic behavior of the bounds when the average bit deletion rate is small in the second part of the paper we consider a practical channel coding approach over a segmented deletion channel specifically we utilize outer ldpc codes concatenated with inner marker codes and develop suitable channel detection algorithms for this scenario different maximum a posteriori map based channel synchronization algorithms operating at the bit and symbol levels are introduced and specific ldpc code designs are explored simulation results clearly indicate the advantages of the proposed approach in particular for the entire range of deletion probabilities less than unity our scheme offers a significantly larger transmission rate compared to the other existing solutions in the literature

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

a reduced order extrapolated crank nicolson finite spectral element method based on pod for the 2d non stationary boussinesq equations abstract in this paper we mainly utilize proper orthogonal decomposition pod to reduce the order for the coefficient vector of the classical crank nicolson finite spectral element ccnfse method of the two dimensional 2d non stationary boussinesq equations about vorticity stream functions so that the reduced order method maintains all the advantages of the ccnfse method toward this end we first establish a ccnfse format with the second order time accuracy for the two dimensional 2d non stationary boussinesq equations about vorticity stream functions and analyze the existence stability and convergence of the ccnfse solutions and then by pod we establish a reduced order extrapolated crank nicolson finite spectral element roecnfse method and analyze the existence stability and convergence of the roecnfse solutions as well as offer the flowchart for seeking roecnfse solutions finally we use two sets of numerical experiments to validate that the numerical computational consequences are accorded with the theoretical ones such that the effectiveness and feasibility of the roecnfse method are further verified both theory and method in this paper is new and completely different from the existing reduced order methods

efficient reconstruction of sequences we introduce and solve some new problems of efficient reconstruction of an unknown sequence from its versions distorted by errors of a certain type these erroneous versions are considered as outputs of repeated transmissions over a channel either a combinatorial channel defined by the maximum number of permissible errors of a given type or a discrete memoryless channel we are interested in the smallest n such that n erroneous versions always suffice to reconstruct a sequence of length n either exactly or with a preset accuracy and or with a given probability we are also interested in simple reconstruction algorithms complete solutions for combinatorial channels with some types of errors of interest in coding theory namely substitutions transpositions deletions and insertions of symbols are given for these cases simple reconstruction algorithms based on majority and threshold principles and their nontrivial combination are found in general for combinatorial channels the considered problem is reduced to a new problem of reconstructing a vertex of an arbitrary graph with the help of the minimum number of vertices in its metrical ball of a given radius a certain sufficient condition for solution of this problem is presented for a discrete memoryless channel the asymptotic behavior of the minimum number of repeated transmissions which are sufficient to reconstruct any sequence of length n within hamming distance d with error probability spl epsiv is found when d n and spl epsiv tend to 0 as n spl rarr spl infin a similar result for the continuous channel with discrete time and additive gaussian noise is also obtained

hybrid uncertain natural frequency analysis for structures with random and interval fields abstract this paper presents a robust non deterministic free vibration analysis for engineering structures involving hybrid yet spatially dependent uncertain system parameters distinguished from the conventional hybrid uncertain eigenvalue problem the concept of interval field is enclosed with random field model such that both the stochastic and non stochastic representations of the spatial dependency of the uncertainties are simultaneously incorporated within a unified non deterministic free vibration analysis in order to determine the probabilistic characteristics i e means and standard deviations of the extremities of structural natural frequencies an extended unified interval stochastic sampling x uiss method is implemented for the purpose of effective hybrid uncertain free vibration analysis by meticulously blending sharpness promised interval eigenvalue analysis with stochastic sampling techniques the stochastic profiles i e probability density functions pdfs and the cumulative distribution functions cdfs of the extreme bounds of the structural natural frequencies can be rigorously established by utilizing the adequate statistical inference methods the applicability and effectiveness of the proposed computational framework are evidently demonstrated through the numerical investigations on various practically motivated engineering structures

reduced order modeling of the upper tropical pacific ocean model using proper orthogonal decomposition the proper orthogonal decomposition pod is shown to be an efficient model reduction technique for simulating physical processes governed by partial differential equations in this paper we make an initial effort to investigate problems related to pod reduced modeling of a large scale upper ocean circulation in the tropic pacific domain we construct different pod models with different choices of snapshots and different number of pod basis functions the results from these different pod models are compared with that of the original model the main findings are 1 the large scale seasonal variability of the tropic pacific obtained by the original model is well captured by a low dimensional system of order 22 which is constructed using 20 snapshots and 7 leading pod basis functions 2 the rms errors for the upper ocean layer thickness of the pod model of order 22 are less than 1m that is less than 1 of the average thickness and the correlation between the upper ocean layer thickness with that from the pod model is around 0 99 3 retaining modes that capture 99 energy is necessary in order to construct pod models yielding a high accuracy

optimizing the kernel in the empirical feature space in this paper we present a method of kernel optimization by maximizing a measure of class separability in the empirical feature space an euclidean space in which the training data are embedded in such a way that the geometrical structure of the data in the feature space is preserved employing a data dependent kernel we derive an effective kernel optimization algorithm that maximizes the class separability of the data in the empirical feature space it is shown that there exists a close relationship between the class separability measure introduced here and the alignment measure defined recently by cristianini extensive simulations are carried out which show that the optimized kernel is more adaptive to the input data and leads to a substantial sometimes significant improvement in the performance of various data classification algorithms

reliable communication over channels with insertions deletions and substitutions a new block code is introduced which is capable of correcting multiple insertion deletion and substitution errors the code consists of nonlinear inner codes which we call watermark codes concatenated with low density parity check codes over nonbinary fields the inner code allows probabilistic resynchronization and provides soft outputs for the outer decoder which then completes decoding we present codes of rate 0 7 and transmitted length 5000 bits that can correct 30 insertion deletion errors per block we also present codes of rate 3 14 and length 4600 bits that can correct 450 insertion deletion errors per block

on the number of subsequences when deleting symbols from a string we consider the problem of finding the number of subsequences when deleting symbols from a string we present a framework to find closed form expressions for the number of subsequences and use it to prove the first explicit formulas for and the first formulas for nonbinary alphabets we also present the first efficient algorithm to compute the number of subsequences for any string number of deletions and alphabet size

improving the computational efficiency in finite element analysis of shells with uncertain properties this work is concerned with improving the computational efficiency of the most time consuming tasks performed in monte carlo simulation based finite element analysis fea of shell structures with uncertain properties for this purpose stochastic field values are generated on a coarse mesh and then interpolated onto the fine mesh used for the standard fea computations the cost effective tric shell element is used to ensure the formation of stiffness matrices in reasonable processing times the solution of finite element equations is efficiently handled with hybrid schemes combining both iterative and direct solution concepts additional computational gains are achieved with the use of parallel computing through the straightforward partitioning of the overall monte carlo simulation process the adoption of such advanced computational approaches allows simulation based probabilistic or stochastic fea of shells to be performed in affordable computing times and therefore become more tractable in structural engineering practice the computational procedures described in this work are evaluated on a cluster of 16 networked pcs using three linear elastic test problems with uncertain material and or geometric parameters a the scordelis lo shell b a pinched cylinder and c a 3d steel frame discretized with shell elements

bounds on the capacity of channels with insertions deletions and substitutions we present novel bounds on the capacity of binary channels with independent and identically distributed insertions deletions and substitutions the proposed bounds are obtained by exploiting an auxiliary system where the channel is the same as the one in the system of interest but the receiver is provided with partial genie aided information on the insertion deletion process in particular we show that when this information is revealed we obtain a memoryless channel whose capacity evaluated by means of the blahut arimoto algorithm gives an upper bound on the capacity of interest we also show that capacity lower bounds can be derived as well by exploiting the same auxiliary system and resorting to suitable information theoretical inequalities in most scenarios the proposed bounds improve the existing ones and significantly narrow the region to which the actual capacity can belong

reliable communication over non binary insertion deletion channels we consider the problem of reliable communication over non binary insertion deletion channels where symbols are randomly deleted from or inserted in the received sequence and all symbols are corrupted by additive white gaussian noise to this end we utilize the inherent redundancy achievable in non binary symbol sets by first expanding the symbol set and then allocating part of the bits associated with each symbol to watermark symbols the watermark sequence known at the receiver is then used by a forward backward algorithm to provide soft information for an outer code which decodes the transmitted sequence through numerical results and discussions we evaluate the performance of the proposed solution and show that it leads to significant system ability to detect and correct insertions deletions we also provide estimates of the maximum achievable information rates of the system compare them with the available bounds and construct practical codes capable of approaching these limits

a set of new chebyshev kernel functions for support vector machine pattern classification in this study we introduce a set of new kernel functions derived from the generalized chebyshev polynomials the proposed generalized chebyshev polynomials allow us to derive different kernel functions by using these polynomial functions we generalize recently introduced chebyshev kernel function for vector inputs and as a result we obtain a robust set of kernel functions for support vector machine svm classification thus in this study besides clarifying how to apply the chebyshev kernel functions on vector inputs we also increase the generalization capability of the previously proposed chebyshev kernels and show how to derive new kernel functions by using the generalized chebyshev polynomials the proposed set of kernel functions provides competitive performance when compared to all other common kernel functions on average for the simulation datasets the results indicate that they can be used as a good alternative to other common kernel functions for svm classification in order to obtain better accuracy moreover test results show that the generalized chebyshev kernel approaches to the minimum support vector number for classification in general

hybrid uncertain static analysis with random and interval fields abstract uncertain static analysis of an engineering structure with diverse type of non deterministic system parameter is investigated in this study unlike the traditional hybrid uncertain static analysis involving random and interval variables the concept of random and interval fields has been implemented to model the spatially dependent uncertainties associated with the system inputs a novel computational approach namely the extended unified interval stochastic sampling x uiss method is proposed to calculate the statistical characteristics i e mean and standard deviation of the extreme bounds i e lower and upper bounds of the concerned responses e g displacement and stress of engineering structure involving hybrid spatially dependent uncertainties subsequently by utilizing either parametric or nonparametric statistical analysis the probability density functions pdfs as well as the cumulative distribution functions cdfs of the extreme bounds of the concerned structural responses can be effectively established consequently the upper and lower bounds of either the concerned responses of the engineering structure at any particular percentile of probability or the structural reliability against any specified capacities can be effectively secured the applicability and effectiveness of the proposed computational analysis framework are illustrated through the numerical investigations on various examples

construction of fixed length insertion deletion correcting runlength limited codes an algorithm is presented for the construction of fixed length insertion deletion correcting runlength limited rll codes in this construction binary d k constrained codewords are generated by codewords of a q ary lee metric based code it is shown that this new construction always yields better codes than known constructions the use of a q ary lee 1987 metric code q odd is based on the assumption that an error insertion deletion or peak shift has maximal size q 1 2 it is shown that a decoding algorithm for the lee metric code can be extended so that it can also be applied to insertion deletion correcting rll codes furthermore such an extended algorithm can also correct some error patterns containing errors of size more than q 1 2 as a consequence if s denotes the maximal size of an error then in some cases the alphabet size of the generating code can be s 1 instead of 2 spl middot s 1

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical pacific ocean reduced gravity model in this paper the tropical pacific ocean reduced gravity model is studied using the proper orthogonal decomposition pod technique of mixed finite element mfe method and an error estimate of pod approximate solution based on mfe method is derived pod is a model reduction technique for the simulation of physical processes governed by partial differential equations e g fluid flows or other complex flow phenomena it is shown by numerical examples that the error between pod approximate solution and reference solution is consistent with theoretical results thus validating the feasibility and efficiency of pod method

a pod reduced order finite difference time domain extrapolating scheme for the 2d maxwell equations in a lossy medium abstract this paper is concerned with establishing a reduced order finite difference time domain fdtd extrapolating scheme based on proper orthogonal decomposition pod method for the two dimensional 2d maxwell equations in a lossy medium for this purpose we first review the classical fdtd scheme and associated results for the 2d maxwell equations in a lossy medium and then we formulate three sets of pod bases by means of the solutions obtained from the classical fdtd scheme on the very short time interval establish the pod reduced order fdtd extrapolating scheme and furnish the error estimates among the pod reduced order fdtd solutions and the classical fdtd solutions as well as the accuracy solution for the 2d maxwell equations in a lossy medium finally we enumerate two numerical examples to confirm that the pod reduced order fdtd extrapolating scheme is feasible and efficient for simulating the phenomena for the electric and magnetic fields in a lossy medium

asymptotically good codes correcting insertions deletions and transpositions we present simple polynomial time encodable and decodable codes which are asymptotically good for channels allowing insertions deletions and transpositions as a corollary they achieve exponential error probability in a stochastic model of insertion deletion

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data

a characterization of the number of subsequences obtained via the deletion channel motivated by the study of deletion channels this paper presents improved bounds on the number of subsequences obtained from a binary string x of length n under t deletions it is known that the number of subsequences in this setting strongly depends on the number of runs in the string x where a run is a maximal substring of the same character our improved bounds are obtained by a structural analysis of the family of r run strings x an analysis in which we identify the extremal strings with respect to the number of subsequences specifically for every r we present r run strings with the minimum respectively maximum number of subsequences under any t deletions we perform an exact analysis of the number of subsequences of these extremal strings and show that this number can be calculated in polynomial time

dynamic response analysis of structure under time variant interval process model abstract due to the aggressiveness of the environmental factor the variation of the dynamic load the degeneration of the material property and the wear of the machine surface parameters related with the structure are distinctly time variant typical model for time variant uncertainties is the random process model which is constructed on the basis of a large number of samples in this work we propose a time variant interval process model which can be effectively used to deal with time variant uncertainties with limit information and then two methods are presented for the dynamic response analysis of the structure under the time variant interval process model the first one is the direct monte carlo method dmcm whose computational burden is relative high the second one is the monte carlo method based on the chebyshev polynomial expansion mcm cpe whose computational efficiency is high in mcm cpe the dynamic response of the structure is approximated by the chebyshev polynomials which can be efficiently calculated and then the variational range of the dynamic response is estimated according to the samples yielded by the monte carlo method to solve the dependency phenomenon of the interval operation the affine arithmetic is integrated into the chebyshev polynomial expansion the computational effectiveness and efficiency of mcm cpe is verified by two numerical examples including a spring mass damper system and a shell structure

some errors estimates for the box method we define and analyze several variants of the box method for discretizing elliptic boundary value problems in the plane our estimates show the error to be comparable to a standard galerkin finite element method using piecewise linear polynomials

a reduced order discontinuous galerkin method based on pod for electromagnetic simulation this paper is concerned with the design of a reduced order discontinuous galerkin dg method based on the proper orthogonal decomposition pod method for electromagnetic simulation a centered flux approximation for surface integral and a second order leap frog scheme for advancing in time are applied in the classical dg method the pod basis is created by the eigensystem of the correlation matrix which is generated by the snapshot matrix whose columns are the snapshot vectors extracted from the high fidelity dg simulation the pod discontinuous galerkin time domain formulation with lower dimension and sufficiently high accuracy is established by applying a galerkin projection for the semidiscrete dg scheme the overall goal is to reduce the computational cost while maintaining an acceptable level of accuracy numerical experiments for electromagnetic problems illustrate the performance of the proposed reduction method

a note on double insertion deletion correcting codes by using a run length representation of sequences ways to determine suband supersequences are discussed this is then used in determining the number of sub and supersequences of a sequence after double insertions or deletions it is also used in creating subsequence supersequence books that are searched to find new double insertion deletion correcting code books with higher cardinalities than those already known

lagrangian support vector machines an implicit lagrangian for the dual of a simple reformulation of the standard quadratic program of a linear support vector machine is proposed this leads to the minimization of an unconstrained differentiable convex function in a space of dimensionality equal to the number of classified points this problem is solvable by an extremely simple linearly convergent lagrangian support vector machine lsvm algorithm lsvm requires the inversion at the outset of a single matrix of the order of the much smaller dimensionality of the original input space plus one the full algorithm is given in this paper in 11 lines of matlab code without any special optimization tools such as linear or quadratic programming solvers this lsvm code can be used as is to solve classification problems with millions of points for example 2 million points in 10 dimensional input space were classified by a linear surface in 82 minutes on a pentium iii 500 mhz notebook with 384 megabytes of memory and additional swap space and in 7 minutes on a 250 mhz ultrasparc ii processor with 2 gigabytes of memory other standard classification test problems were also solved nonlinear kernel classification can also be solved by lsvm although it does not scale up to very large problems it can handle any positive semidefinite kernel and is guaranteed to converge a short matlab code is also given for nonlinear kernels and tested on a number of problems

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

optimization based on reliability and confidence interval design for the structural acoustic system with interval probabilistic variables abstract in practice the uncertain parameters whose unique distributions cannot be identified on the basis of limited data existed in the structural acoustic system extensively the uncertain parameters with limited data can be modeled as interval probabilistic variables whose distribution parameters are expressed as interval variables instead of unique values for the optimization of the structural acoustic system with interval probabilistic variables a new optimization technique named as the optimization based on reliability and confidence interval design o rcid is developed o rcid is a nested loop optimization whose computational cost during the evaluation of the confidence interval of sound pressure response and the system reliability is considerable to improve the computational efficiency of o rcid a change of variable interval probabilistic perturbation method cv ippm which is based on the perturbation approach and change of variable technique is proposed to calculate the confidence interval of sound pressure response and the system reliability by introducing cv ippm the nested loop o rcid is converted into an approximate single loop one which can be efficiently solved numerical examples demonstrate the effectiveness and efficiency of o rcid based on cv ippm for the optimization of the structural acoustic system with interval probabilistic variables

convergence of finite volume schemes for poisson s equation on nonuniform meshes an error analysis of a family of cell center finite volume schemes for poisson s equation on cartesian product nonuniform meshes in two dimensions is presented optimal order error estimates are derived in the discrete h 1 norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh on quasi uniform meshes analogous estimates are obtained in the maximum norm

deletion codes in the high noise and high rate regimes the noise model of deletions poses significant challenges in coding theory with basic questions like the capacity of the binary deletion channel still being open in this paper we study the harder model of worst case deletions with a focus on constructing efficiently decodable codes for the two extreme regimes of high noise and high rate specifically we construct polynomial time decodable codes with the following tradeoffs for any varepsilon 0 1 codes that can correct a fraction 1 varepsilon of deletions with rate mathop mathrm poly nolimits varepsilon over an alphabet of size mathop mathrm poly nolimits 1 varepsilon 2 binary codes of rate 1 tilde o sqrt varepsilon that can correct a fraction varepsilon of deletions and 3 binary codes that can be list decoded from a fraction 1 2 varepsilon of deletions with rate mathop mathrm poly nolimits varepsilon this paper gives the first efficient constructions which meet the qualitative goals of correcting a deletion fraction approaching 1 over bounded alphabets and correcting a constant fraction of bit deletions with rate approaching 1 over a fixed alphabet the above mentioned results bring our understanding of deletion code constructions in these regimes to a similar level as worst case errors

galerkin proper orthogonal decomposition methods for parabolic problems in this work error estimates for galerkin proper orthogonal decomposition pod methods for linear and certain non linear parabolic systems are proved the resulting error bounds depend on the number of pod basis functions and on the time discretization numerical examples are included

unified polynomial expansion for interval and random response analysis of uncertain structure acoustic system with arbitrary probability distribution abstract for structure acousticsystem with uncertainties the interval model the random model and the hybrid uncertain model have been introduced in the interval model and the random model the uncertain parameters are described as either the random variable with well defined probability density function pdf or the interval variable without any probability information whereas in the hybrid uncertain model both interval variable and random variable exist simultaneously for response analysis of these three uncertain models of structure acoustic problem involving arbitrary pdfs a unified polynomial expansion method named as the interval and random arbitrary polynomial chaos method irapcm is proposed in irapcm the response of the structure acoustic system is approximated by apc expansion in a unified form particularly only the weight function of polynomial basis is required to be changed to construct the apc expansion for the response of different uncertain models through the unified apc expansion the uncertain properties of the response of three uncertain models can be efficiently obtained as the apc expansion can provide a free choice of the polynomial basis the optimal polynomial basis for the random variable with arbitrary pdfs can be obtained by using the proposed irapcm the irapcm has been employed to solve a mathematical problem and a structure acoustic problem and the effectiveness of the unified irapcm for response analysis of three uncertain models is demonstrated by fully comparing it with the hybrid first order perturbation method and several existing polynomial chaos methods

an improvement to levenshtein s upper bound on the cardinality of deletion correcting codes we consider deletion correcting codes over a q ary alphabet it is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions to obtain asymptotic upper bounds on code size we apply a packing argument to channels that perform different mixtures of insertions and deletions even though the set of codes is identical for all of these channels the bounds that we obtain vary prior to this paper only the bounds corresponding to the all insertion case and the all deletion case were known we recover these as special cases the bound from the all deletion case due to levenshtein has been the best known for more than 45 years our generalized bound is better than levenshtein s bound whenever the number of deletions to be corrected is larger than the alphabet size

analysis of the cell centred finite volume method for the diffusion equation abstract this paper presents a rigorous theoretical analysis of the cell centred finite volume method for poisson s equation we review the traditional taylor series expansion technique which suggests that the cell centred method is inconsistent on nonuniform grids which is not confirmed by numerical experiments we then present an analysis of the method which confirms that the solution error does indeed reduce as the cell size is reduced this is supported by numerical calculations

on the accuracy of the finite volume element method for diffusion equations on composite grids this paper develops the finite volume element fve method which is similar to the so called control volume finite element method but tailored to composite grid applications fve is described for the general two dimensional diffusion equation in divergence form o h 3 2 discretization error estimates are then developed for the case of triangular elements these results are improved to o h 2 using a special modification involving rectilinear elements at the grid interface

stochastic simulation of non gaussian non stationary properties in a functionally graded plate abstract composites with a graded profile between two distinct phases titled functionally graded materials fgm s have been proposed for a variety of applications many current numerical models of fgm s overlook the inherent randomness observed in actual specimens which arises due to the complexity and difficulty in tailoring the gradients to exact specifications during manufacturing processes the effect of random variations in both the component volume fractions and the porosity on the response of a functionally graded metal ceramic plate subjected to constant thermal boundary conditions is investigated in this work these random variations are introduced into the fgm model via stochastic simulation of interest is the fact that the volume fraction and the porosity are both non gaussian and non stationary the non stationarity is present due to the fact that the non gaussian probability density function describing both properties changes with location sample simulations are performed using a translation mapping from a stationary standard gaussian process to a non stationary non gaussian process the results are used to quantify the effects of variations in the micromechanical configuration on the temperature thermal stresses and safety factor within a functionally graded plate

nonasymptotic upper bounds for deletion correcting codes explicit nonasymptotic upper bounds on the sizes of multiple deletion correcting codes are presented in particular the largest single deletion correcting code for q ary alphabet and string length is shown to be of size at most qn q q 1 n 1 an improved bound on the asymptotic rate function is obtained as a corollary upper bounds are also derived on sizes of codes for a constrained source that does not necessarily comprise of all strings of a particular length and this idea is demonstrated by application to sets of run length limited strings the problem of finding the largest deletion correcting code is modeled as a matching problem on a hypergraph this problem is formulated as an integer linear program the upper bound is obtained by the construction of a feasible point for the dual of the linear programming relaxation of this integer linear program the nonasymptotic bounds derived imply the known asymptotic bounds of levenshtein and tenengolts and improve on known nonasymptotic bounds numerical results support the conjecture that in the binary case the varshamov tenengolts codes are the largest single deletion correcting codes

a mixed type boundary problem describing the propagation of disturbances in viscous media i weak solutions for quasi linear equations abstract the mixed type boundary problem utt aijuxi xj t bijuxi xj f x t u ux t in n dimensional spaces has been studied the existence uniqueness and stability of the weak solution are discussed for the first boundary value case

structural reliability analysis using non probabilistic convex model abstract by using the convex model approach the bounds of the uncertain parameters are only required rather than their precise probability distributions based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information in this paper a non probabilistic reliability model is given for structures with convex model uncertainty which is defined as a ratio of the multidimensional volume falling into the reliability domain to the one of the whole convex model a monte carlo simulation is then formulated for the reliability model to obtain a reference solution a first order approximation method foam is proposed to solve the reliability model based on a linear approximation of the failure surface a second order approximation method soam is further formulated to improve the reliability analysis precision for limit state functions with relatively strong nonlinearity by introducing the suggested reliability model a convex model based system reliability method is also formulated eight numerical examples are provided to demonstrate the effectiveness of the present methods

a reduced fve formulation based on pod method and error analysis for two dimensional viscoelastic problem abstract proper orthogonal decomposition pod method has been successfully used in the reduced order modeling of complex systems in this paper we extend the applications of pod method i e combine a classical finite volume element fve method with pod method to establish a reduced fve formulation with lower dimensions and sufficiently high accuracy for two dimensional viscoelastic problem with real practical applied background and analyze the errors between the reduced pod fve solution and the classical fve solution so as to provide scientific theoretic basis for service applications some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions moreover it is also shown that the reduced fve formulation based on pod method is feasible and efficient for solving two dimensional viscoelastic problem

guess check codes for deletions insertions and synchronization we consider the problem of constructing codes that can correct delta deletions occurring in an arbitrary binary string of length n bits varshamov tenengolts vt codes dating back to 1965 are zero error single deletion delta 1 correcting codes and have an asymptotically optimal redundancy finding similar codes for delta geq 2 deletions remains an open problem in this paper we relax the standard zero error i e worst case decoding requirement by assuming that the positions of the delta deletions or insertions are independent of the code word our contribution is a new family of explicit codes that we call guess check gc codes that can correct with high probability up to a constant number of delta deletions or insertions gc codes are systematic and have deterministic polynomial time encoding and decoding algorithms we also describe the application of gc codes to file synchronization