gaussian multiple description coding with low density generator matrix codes it is shown that the coding problem for an arbitrary point on the dominant face of an l description el gamal cover egc region can be converted to that for a vertex of a k description egc region for some k 2l 1 where the latter problem can be solved via successive coding a practical scheme is proposed for the quadratic gaussian case by reducing each step in successive coding to a gaussian quantization operation and implementing such an operation using low density generator matrix codes the effectiveness of this scheme is verified through extensive simulation experiments

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness we demonstrate that the cumulant lattice boltzmann model with optimized parameters captures the drag crisis for flows over a sphere no sub grid model and no wall function is required and the boundary layer is only marginally resolved it is observed that in the transition regime between the high and the low drag configuration the flow switches from one state to the other state

near wall treatment for the simulation of turbulent flow by the cumulant lattice boltzmann method abstract we present a new wall function implementation for the cumulant lattice boltzmann method that sets a partial slip velocity on the wall by computing a skin frictional coefficient our approach uses local information and is particularly appropriate for implementations on general purpose graphics processing units the validation of the model has been conducted by performing numerical simulations of the turbulent channel flow test case with different grid resolutions and for different reynolds numbers the results showed encouraging agreement with direct numerical simulation data for velocity profile reynolds shear and normal stresses

global solutions to a model of structural phase transitions in shape memory alloys abstract global in time existence and uniqueness of solutions to a nonlinear system of coupled evolution equations is discussed the system represents a model of dynamical structural phase transitions martensitic transformations in shape memory alloys

frechet differentiability of the solutions of a semilinear abstract cauchy problem abstract sufficient conditions are found under which the solutions z t q of a semilinear abstract cauchy problem of the form d d t z t a q z t f q t z t are frechet differentiable with respect to the parameter q an explicit form is provided for the sensitivity equation satisfied by the frechet derivative d q z t q

n channel symmetric multiple descriptions part ii an achievable rate distortion region in this part ii of a two part paper we present a new achievable rate distortion region for the symmetric n channel multiple descriptions coding problem n 2 where the rate of every description is the same and the reconstruction distortion depends only on the number of descriptions received using a new approach for the random coding constructions along with a generalization of the technique used in the two channel el gamal and cover region to any n the rate region presented here achieves points that have not been known in the literature previously this rate region is derived from a concatenation of source channel erasure codes developed in part i of this work by deploying the framework of source coding with side information random binning the key idea is that by using the framework of source coding with side information multiple statistically identical realizations representing the coarse version of a source can be simultaneously refined by a single encoding we point out that there is an important conceptual difference in random coding construction for the multiple descriptions coding problem between the case of n 2 and n 2 to illustrate the framework we also present the important case of the gaussian source in detail

universal multiple description scalar quantization analysis and design this paper introduces a new high rate analysis of the multiple description scalar quantizer mdsq with balanced descriptions the analysis provides insight into the structure of the mdsq suggesting the nonoptimality of uniform central quantizer cell lengths as well as a method to approximate optimal cell lengths for both level constrained and entropy constrained mdsq new upper bounds on the granular distortion for sources with smooth probability density functions pdfs are derived under the mean squared error measure which are 0 4 db lower than previous results based on the insights a universal multiple description scalar quantizer umdsq is proposed which at high rate can achieve nearly the same performance as the fully optimized entropy constrained mdsq ecmdsq without requiring extensive training the proposed umdsq has only two control parameters and a continuum of tradeoff points between the central and side distortions can be achieved as the two parameters are varied

on the rate loss of multiple description source codes the rate loss of a multiresolution source code mrsc describes the difference between the rate needed to achieve distortion d sub i in resolution i and the rate distortion function r d sub i this paper generalizes the rate loss definition to multiple description source codes mdscs and bounds the mdsc rate loss for arbitrary memoryless sources for a two description mdsc 2dsc the rate loss of description i with distortion d sub i is defined as l sub i r sub i r d sub i i 1 2 where r sub i is the rate of the ith description the joint rate loss associated with decoding the two descriptions together to achieve central distortion d sub 0 is measured either as l sub 0 r sub 1 r sub 2 r d sub 0 or as l sub 12 l sub 1 l sub 2 we show that for any memoryless source with variance spl sigma sup 2 there exists a 2dsc for that source with l sub 1 spl les 1 2 or l sub 2 spl les 1 2 and a l sub 0 spl les 1 if d sub 0 spl les d sub 1 d sub 2 spl sigma sup 2 b l sub 12 spl les 1 if 1 d sub 0 spl les 1 d sub 1 1 d sub 2 1 spl sigma sup 2 c l sub 0 spl les l sub g0 1 5 and l sub 12 spl les l sub g12 1 otherwise where l sub g0 and l sub g12 are the joint rate losses of a gaussian source with variance spl sigma sup 2

broadcasting correlated vector gaussians the problem of sending two correlated vector gaussian sources over a bandwidth matched two user scalar gaussian broadcast channel is studied in this paper where each receiver wishes to reconstruct its target source under a covariance distortion constraint we derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair our derivation is based on a new bounding technique which involves the introduction of appropriate remote sources furthermore it is shown that this lower bound is achievable by a class of hybrid schemes for the special case where the weak receiver wishes to reconstruct a scalar source under the mean squared error distortion constraint

n channel asymmetric entropy constrained multiple description lattice vector quantization this paper is about the design and analysis of an index assignment ia based multiple description coding scheme for the n channel asymmetric case we use entropy constrained lattice vector quantization and restrict attention to simple reconstruction functions which are given by the inverse ia function when all descriptions are received or otherwise by a weighted average of the received descriptions we consider smooth sources with finite differential entropy rate and mse fidelity criterion as in previous designs our construction is based on nested lattices which are combined through a single ia function the results are exact under high resolution conditions and asymptotically as the nesting ratios of the lattices approach infinity for any n the design is asymptotically optimal within the class of ia based schemes moreover in the case of two descriptions and finite lattice vector dimensions greater than one the performance is strictly better than that of existing designs in the case of three descriptions we show that in the limit of large lattice vector dimensions points on the inner bound of pradhan can be achieved furthermore for three descriptions and finite lattice vector dimensions we show that the ia based approach yields in the symmetric case a smaller rate loss than the recently proposed source splitting approach

global existence for thermomechanical processes with nonconvex free energies of ginzburg landau form abstract global existence of solutions is proved for the system of partial differential equations which governs the nonlinear thermomechanical processes in a nonviscous solid under the assumption that the corresponding free energy density is of ginzburg landau type to allow for possible solid solid phase transitions in the material the stress strain interrelation is not assumed to be monotone

erasure multiple descriptions a binary erasure version of channel multiple descriptions md with symmetric descriptions i e the rates of the descriptions are equal and the distortion constraint depends only on the number of messages received is considered no excess rate for every out of descriptions i e any messages have sum rate where is shannon s rate distortion function for erasure distortion and is the distortion constraint to be met is investigated the goal is to characterize the achievable distortions reconstruction fidelity is measured using two criteria a worst case criterion which computes distortion by maximizing the per letter distortion over all source sequences and an average case criterion which computes distortion by averaging the per letter distortion over all source sequences achievability schemes are presented based on systematic maximum distance separable codes for worst case distortion and random binning for average case distortion and optimality results are proved for the corresponding distortion regions the erasure md setup is then used to propose a layered coding framework for multiple descriptions which is then applied to vector gaussian md and shown to be optimal for symmetric scalar gaussian md with two levels of receivers and no excess rate at the central receiver

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

parameter differentiability of the solution of a nonlinear abstract cauchy problem in this article an abstract nonlinear evolution equation with a parameter appearing in the nonlinear part is considered by using the theory of analytic semigroups and a generalization of gronwall s lemma for singular kernels sufficient conditions to ensure differentiability of the solution with respect to the parameter are derived in terms of the smoothness of the nonlinear part of the equation the results are applied to a nonlinear system of partial differential equations modeling the dynamics of shape memory alloys

the rate distortion region for multiple descriptions without excess rate during recent years there has been strong interest in a certain source coding problem which some authors call the problem of multiple descriptions old and new wringing techniques enable us to establish a single letter characterization of the rate distortion region in the case of no excess rate for the joint description

the gaussian many help one distributed source coding problem jointly gaussian memoryless sources are observed at n distinct terminals the goal is to efficiently encode the observations in a distributed fashion so as to enable reconstruction of any one of the observations say the first one at the decoder subject to a quadratic fidelity criterion our main result is a precise characterization of the rate distortion region when the covariance matrix of the sources satisfies a tree structure condition in this situation a natural analog digital separation scheme optimally trades off the distributed quantization rate tuples and the distortion in the reconstruction each encoder consists of a point to point gaussian vector quantizer followed by a slepian wolf binning encoder we also provide a partial converse that suggests that the tree structure condition is fundamental

asymmetric multilevel diversity coding and asymmetric gaussian multiple descriptions we consider the asymmetric multilevel diversity a mld coding problem where a set of 2k 1 information sources ordered in a decreasing level of importance is encoded into k messages or descriptions there are 2k 1 decoders each of which has access to a nonempty subset of the encoded messages each decoder is required to reproduce the information sources up to a certain importance level depending on the combination of descriptions available to it we obtain a single letter characterization of the achievable rate region for the 3 description problem in contrast to symmetric multilevel diversity coding source separation coding is not sufficient in the asymmetric case and ideas akin to network coding need to be used strategically based on the intuitions gained in treating the a mld problem we derive inner and outer bounds for the rate region of the asymmetric gaussian multiple description md problem with three descriptions both the inner and outer bounds have a similar geometric structure to the rate region template of the a mld coding problem and moreover we show that the gap between them is constant which results in an approximate characterization of the asymmetric gaussian three description rate region

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

multiple description coding for stationary gaussian sources we consider the problem of multiple description coding for stationary gaussian sources under the squared error distortion measure the rate region is characterized for the 2 description case it is shown that each supporting line of the rate region is achievable with a transform lattice quantization scheme we show the optimal coding scheme has a natural spectral domain coding interpretation which yields a reverse water filling solution with a frequency dependent water level instead of the flat water level as in the conventional single description case

asymmetric multiple description lattice vector quantizers we consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile ranging from symmetric or balanced to successively refinable we present a solution to a labeling problem which is an important part of the construction along with a general design procedure the high rate asymptotic performance of the quantizer is also studied we evaluate the rate distortion performance of the quantizer and compare it to known information theoretic bounds the high rate asymptotic analysis is compared to the performance of the quantizer

transition to turbulence small disturbances and sensitivity analysis i a motivating problem abstract for over 100 years researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized navier stokes equations however for many simple flows this approach fails to match experimental results recently new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system these new mostly linear theories have increased our understanding of the transition process but the role of nonlinearity has not been explored in detail this paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence in this part we study a highly sensitive one dimensional burgers equation as a motivating problem sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance also sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem in the second part of this work this analysis will be extended to the three dimensional navier stokes equations to show that small disturbances have great potential to trigger transition to turbulence

multiple description coding with many channels an achievable region for the l channel multiple description coding problem is presented this region generalizes two channel results of el gamal and cover 1982 and of zhang and berger 1987 it further generalizes three channel results of gray and wyner 1974 and of zhang and berger a source that is successively refinable on chains is shown to be successively refinable on trees a new outer bound on the rate distortion rd region for memoryless gaussian sources with mean squared error distortion is also derived the achievable region meets this outer bound for certain symmetric cases

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii application to flow around a sphere at drag crisis the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness

the group finite element formulation abstract the introduction of trial solutions for groups of variables within a finite element formulation is shown to provide a significant economy with no loss of accuracy for steady solutions of the two dimensional burgers equations with linear rectangular elements the application of the group finite element to the convective term produces a threefold reduction in execution time with a small improvement in accuracy operation count estimates indicate even larger economies in three dimensions or if higher order nonlinearities occur or if higher order shape functions are used applications of the group formulation are described for inviscid and viscous laminar and turbulent separated and unseparated and incompressible and compressible flows

a pde sensitivity equation method for optimal aerodynamic design the use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design a typical procedure uses a simulation scheme to evaluate the objective function from the approximate states and its gradient then passes this information to an optimization algorithm once the simulation scheme cfd flow solver has been selected and used to provide approximate function evaluations there are several possible approaches to the problem of computing gradients one popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients although this black box approach has many advantages in shape optimization problems one must compute mesh sensitivities in order to compute the design sensitivity in this paper we present an alternative approach using the pde sensitivity equation to develop algorithms for computing gradients this approach has the advantage that mesh sensitivities need not be computed moreover when it is possible to use the cfd scheme for both the forward problem and the sensitivity equation then there are computational advantages an apparent disadvantage of this approach is that it does not always produce consistent derivatives however for a proper combination of discretization schemes one can showasymptotic consistencyunder mesh refinement which is often sufficient to guarantee convergence of the optimal design algorithm in particular we show that when asymptotically consistent schemes are combined with a trust region optimization algorithm the resulting optimal design method converges we denote this approach as thesensitivity equation method the sensitivity equation method is presented convergence results are given and the approach is illustrated on two optimal design problems involving shocks

new results in binary multiple descriptions an encoder whose input is a binary equiprobable memoryless source produces one output of rate r 1 and another of rate r 2 let d 1 d 2 and d 0 respectively denote the average error frequencies with which the source data can be reproduced on the basis of the encoder output of rate r l only the encoder output of rate r 2 only and both encoder outputs the two descriptions problem is to determine the region r of all quintuples r 1 r 2 d 1 d 2 d 0 that are achievable in thc usual shannon sense let r d 1 d log 2 d 1 d log 2 1 d denote the error frequency rate distortion function of the source the no excess rate case prevails when r 1 r 2 r d 0 and the excess rate case when r 1 r 2 r d 0 denote the section of r at r 1 r 2 d 0 by d r 1 r 2 d 0 d 1 d 2 r 1 r 2 d 1 d 2 d 0 in r in the no excess rate case we show that a portion of the boundary of d r 1 r 2 d 0 coincides with the curve frac 1 2 d 1 2d 0 frac 1 2 d 2 2d 0 frac 1 2 1 2d 0 2 this curve is an extension of witsenhausen s hyperbola bound to the case d 0 0 it follows that the projection of r onto the d 1 d 2 plane at fixed d 0 consists of all d 1 geq d 0 and d 2 geq d 0 that lie on or above this hyperbola in the excess rate case we show by counterexample that the achievable region of el gamal and cover is not tight

successive refinement of vector sources under individual distortion criteria the successive refinement problem is extended to vector sources where individual distortion constraints are posed on each vector component for vector gaussian sources with squared error distortion a single letter rate distortion characterization is inherited from the previously studied gaussian multiple descriptions problem with covariance distortion constraints though this characterization is amenable to well known numerical convex optimization techniques an analytical solution is difficult to obtain in full generality even for 2 d sources in this work the special case of successive refinability is addressed analytically specifically vector gaussian sources are shown to be not successively refinable everywhere unlike scalar gaussian sources it is also shown that for 2 d gaussian sources the rate loss at the second stage can be as high as 0 5 b sample in a degenerate scenario corresponding to what is known as sequential coding of correlated sources finally analysis of 2 d binary symmetric sources with hamming distortion reveals that the behavior of these sources with respect to successive refinability exhibits remarkable similarity to their 2 d gaussian counterparts

near optimality of composite multiple description source codes in this paper new upper and lower bounds are first presented for the rate loss of multiple description source codes mdscs for a two description mdsc 2dsc the rate loss of description i with distortion di is defined as li ri r di i 1 2 where ri is the rate of the ith description and r d is the rate distortion function for the given source the joint rate loss associated with decoding the two descriptions together to achieve central distortion d0 is measured as l0 r1 r2 r d0 consider an arbitrary memoryless source with variance 2 and let the distortion measure be the mean squared error distortion measure it is shown that for any optimal 2dsc a 0 l0 0 8802 and 0 l1 l2 0 3802 if d0 d1 d2 2 b 0 l1 l2 0 4401 if d0 1 d1 1 d2 1 2 1 c 0 l1 l2 0 3802 and r max d1 d2 1 l0 r max d1 d2 0 3802 for all other d0 a tighter bound on the distance between the el gamal cover inner bound and the achievable region is also presented inspired by these new bounds a low complexity composite 2dsc design first developed by lastras montano and castelli is extended and the resulting code is shown to be near optimal for all memoryless sources and all distortions these results are also extended to mdscs with an arbitrary number of packets finally gaussian sources are analyzed in detail to verify these bounds and examine their tightness

design of entropy constrained multiple description scalar quantizers the problem of entropy constrained multiple description scalar quantizer design is posed as an optimization problem necessary conditions for optimality are derived and an iterative design algorithm is presented performance results are presented for a gaussian source along with comparisons to the multiple description rate distortion bound and a reference system

generalized entropy power inequalities and monotonicity properties of information new families of fisher information and entropy power inequalities for sums of independent random variables are presented these inequalities relate the information in the sum of n independent random variables to the information contained in sums over subsets of the random variables for an arbitrary collection of subsets as a consequence a simple proof of the monotonicity of information in central limit theorems is obtained both in the setting of independent and identically distributed i i d summands as well as in the more general setting of independent summands with variance standardized sums

optimal index assignment for multiple description scalar quantization with translated lattice codebooks we design a k description scalar quantizer whose construction is based on a structure of translated scalar lattices and a lattice in k 1 dimensional space the use of translated lattices provides a performance advantage by exploiting a so called staggering gain the use of the k 1 dimensional lattice facilitates analytic insight into the performance and significantly speeds up the computation of the index assignment compared to state of the art methods using a common decoding method the proposed index assignment is proven to be optimal for the k description case it is shown that the optimal index assignment is not unique this is illustrated for the two description case where a periodic index assignment is selected from possible optimal assignments and described in detail the performance of the proposed quantizer accurately matches theoretic analysis over the full range of operational redundancies moreover the quantizer outperforms the state of the art md scheme as the redundancy among the description increases

a lower bound on the sum rate of multiple description coding with symmetric distortion constraints we derive a single letter lower bound on the minimum sum rate of multiple description coding with symmetric distortion constraints for the binary uniform source with the erasure distortion measure or hamming distortion measure this lower bound can be evaluated with the aid of certain minimax theorems a similar minimax theorem is established in the quadratic gaussian setting which is further leveraged to analyze the special case where the minimum sum rate subject to two levels of distortion constraints with the second level imposed on the complete set of descriptions is attained in particular we determine the minimum achievable distortions at the intermediate levels

multiuser successive refinement and multiple description coding in this correspondence we consider the multiuser successive refinement msr problem where the users are connected to a central server via links with different noiseless capacities and each user wishes to reconstruct in a successive refinement fashion an achievable region is given for the two user two layer case and it provides the complete rate distortion region for the gaussian source under the mse distortion measure the key observation is that this problem includes the multiple description md problem with two descriptions as a subsystem and the techniques useful in the md problem can be extended to this case it is shown that the coding scheme based on the universality of random binning is suboptimal because multiple gaussian side informations only at the decoders do incur performance loss in contrast to the case of single side information at the decoder it is further shown that unlike the single user case when there are multiple users the loss of performance by a multistage coding approach can be unbounded for the gaussian source the result suggests that in such a setting the benefit of using successive refinement is not likely to justify the accompanying performance loss the msr problem is also related to the source coding problem where each decoder has its individual side information while the encoder has the complete set of the side informations the msr problem further includes several variations of the md problem for which the specialization of the general result is investigated and the implication is discussed

consistent lattice boltzmann modeling of low speed isothermal flows at finite knudsen numbers in slip flow regime ii application to curved boundaries gaseous flows inside microfluidic devices often fall in the slip flow regime according to this theoretical description the navier stokes model remains applicable in bulk while at solid walls a slip velocity boundary model shall be considered physically it is well established that to properly account for the wall curvature the wall slip velocity must be determined by the shear stress rather than the normal component of the velocity derivative alone as commonly applied to planar surfaces it follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics cfd techniques this paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice boltzmann method lbm to substantiate this conclusion this work undertakes the following three studies first we examine the conditions under which the generic reflection type boundary rules used by lbm become consistent models for the slip velocity boundary condition this effort makes use of the second order chapman enskog expansion method where we address both planar and curved boundaries the analysis also clarifies the capabilities and limitations behind the considered reflection type slip schemes second we revisit the family of parabolic accurate lbm slip boundary schemes originally formulated in phys rev e 96 013311 2017 2470 004510 1103 physreve 96 013311 on the basis of the multireflection framework and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate lbm slip boundary formulations such as the linearly accurate slip schemes and the widely popular kinetic based boundary schemes in addition we also discuss the numerical stability of the parabolic slip schemes previously developed providing an heuristic strategy to improve their stable range of operation third we evaluate the performance of the several slip boundary schemes debated in this paper the numerical tests correspond to two classical 2d benchmark flow problems of slip over non planar solid surfaces namely i the velocity profile of the cylindrical couette flow and ii the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles the obtained numerical results confirm the competitiveness of the lbm when equipped with slip boundary schemes of parabolic accuracy as cfd tool to simulate slippage phenomena over arbitrarily non planar surfaces indeed although operating on a simple uniform mesh discretization the lbm yields a similar or even superior level of accuracy compared to state of the art fem simulations conducted on hardworking body fitted meshes this conclusion establishes the lbm as a very appealing cfd technique for simulating microfluidic flows in the slip flow regime a result that deserves further exploration in future studies

vector gaussian multiple description with two levels of receivers the problem of l multiple descriptions of a stationary and ergodic gaussian source with two levels of receivers is investigated each of the first level receivers receive an arbitrary subset k of the l descriptions k l the second level receiver receives all l descriptions all the receivers both at the first level and the second level reconstruct the source using the subset of descriptions they receive the corresponding reconstructions are subject to quadratic distortion constraints our main result is the derivation of an outer bound on the sum rate of the descriptions so that the distortion constraints are met we show that an analog digital separation architecture involving joint gaussian vector quantizers and a binning scheme meets this outer bound with equality for several scenarios these scenarios include the case when the distortion constraints are symmetric and the case for general distortion constraints with k 2 and l 3

multiple description vector quantization with a coarse lattice a multiple description md lattice vector quantization technique for two descriptions was previously introduced in which fine and coarse codebooks are both lattices the encoding begins with quantization to the nearest point in the fine lattice this encoding is an inherent optimization for the decoder that receives both descriptions performance can be improved with little increase in complexity by considering all decoders in the initial encoding step the altered encoding relies only on the symmetries of the coarse lattice this allows us to further improve performance without a significant increase in complexity by replacing the fine lattice codebook with a nonlattice codebook that respects many of the symmetries of the coarse lattice examples constructed with the two dimensional 2 d hexagonal lattice demonstrate large improvement over time sharing between previously known quantizers

the cumulant lattice boltzmann equation in three dimensions theory and validation we propose analyze and validate a lattice boltzmann model with a cumulant collision operator the new model is analytically and numerically shown to poses smaller errors than a moment based multiple relaxation time lattice boltzmann model we demonstrate the usability of the cumulant lattice boltzmann model by simulations of flow around a sphere for reynolds numbers from 200 to 105

multiple description image coding based on delta sigma quantization with rate distortion optimization recently ostergaard and zamir revealed the connection between multiple description coding and delta sigma quantization dsq the principle has been applied to image coding with main focus on the framework where each block is processed separately in this brief we propose a two channel multiple description image coding scheme that performs inter block processing the source image is first rearranged into a block sequence then vector dsq is performed with a bank of noise shaping filters their coefficients as well as the quantization steps are chosen by a rate distortion optimization algorithm a post processing algorithm is proposed for side decoding experiment results show the improvement achieved by the proposed scheme in terms of both peak signal to noise ratio values and subjective quality

multiple description coding with prediction compensation a new multiple description coding paradigm is proposed by combining the time domain lapped transform block level source splitting linear prediction and prediction residual encoding the method provides effective redundancy control and fully utilizes the source correlation the joint optimization of all system components and the asymptotic performance analysis are presented image coding results demonstrate the superior performance of the proposed method especially at low redundancies

approximating the gaussian multiple description rate region under symmetric distortion constraints we consider multiple description md coding for the gaussian source with k descriptions under the symmetric mean squared error mse distortion constraints and provide an approximate characterization of the rate region we show that the rate region can be sandwiched between two polytopes between which the gap can be upper bounded by constants dependent on the number of descriptions but independent of the distortion constraints underlying this result is an exact characterization of the lossless multilevel diversity source coding problem a lossless counterpart of the md problem this connection provides a polytopic template for the inner and outer bounds to the rate region in order to establish the outer bound we generalize ozarow s technique to introduce a strategic expansion of the original probability space by more than one random variable for the symmetric rate case with any number of descriptions we show that the gap between the upper bound and the lower bound for the individual description rate distortion function is no larger than 0 92 bit the results developed in this work also suggest that the ldquoseparationrdquo approach of combining successive refinement quantization and lossless multilevel diversity coding is a competitive one since its performance is only a constant away from the optimum the results are further extended to general sources under the mse distortion measure where a similar but looser bound on the gap holds

design of multiple description scalar quantizers the design of scalar quantizers for communication systems that use diversity to overcome channel impairments is considered the design problem is posed as an optimization problem and necessary conditions for optimality are derived a design algorithm a generalization of s p lloyd s 1962 algorithm for quantizer design is developed unlike a single channel scalar quantizer the performance of a multiple description scalar quantizer is dependent on the index assignment the problem of index assignment is addressed good index assignments performance results and sample quantizer designs are presented for a memoryless gaussian source comparisons are made with rate distortion bounds for the multiple description problem

global solutions to the equations of a ginzburg landau theory for structural phase transitions in shape memory alloys abstract global existence of smooth solutions is proved for the system of partial differential equations governing the dynamics of martensic phase transitions in shape memory alloys the free energy is assumed in ginzburg landau form and nonconvex in the order parameter

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

the sum rate of vector gaussian multiple description coding with tree structured covariance distortion constraints a single letter lower bound on the sum rate of multiple description coding with tree structured distortion constraints is established by generalizing ozarow s celebrated converse argument through the introduction of auxiliary random variables that form a markov tree for the quadratic vector gaussian case this lower bound is shown to be achievable by an extended el gamal cover scheme yielding a complete characterization of the minimum sum rate

an improved outer bound for multiterminal source coding we prove a new outer bound on the rate distortion region for the multiterminal source coding problem this bound subsumes the best outer bound in the literature and improves upon it strictly in some cases the improved bound enables us to obtain a new conclusive result for the binary erasure version of the ceo problem the bound recovers many of the converse results that have been established for special cases of the problem including the recent one for the gaussian two encoder problem

on the exponentially slow motion of a viscous shock using formal asymptotic methods we study the internal layer behavior associated with the following viscous shock problem in the limit e 0 the convex nonlinearity f u satisfies f f for the steady problem we show that the method of matched asymptotic expansions fails to uniquely determine the location of the equilibrium shock layer solution this indeterminacy resulting from neglecting certain exponentially small effects is eliminated by using the projection method which exploits certain properties of the spectrum associated with the linearized operator for the time dependent problem we show that the viscous shock which is formed from initial data drifts towards the equilibrium solution on an exponentially long time interval of the order o ec e for some c 0 this exponentially slow behavior is analyzed by deriving an equation of motion for the location of the viscous shock for burgers equation f u u2 2 the results give an analytical characterization of the slow shock layer motion observed numerically in kreiss and kreiss see 11 we also show that the shock layer behavior is very sensitive to small changes in the boundary operator in addition using a wkb type method the slow viscous shock motion is studied numerically for small e the results comparing favorably with corresponding analytical results finally we relate the slow viscous shock motion to similar slow internal layer motion for the allen cahn equation

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

a source channel separation theorem with application to the source broadcast problem a converse method is developed for the source broadcast problem specifically it is shown that the separation architecture is optimal for a variant of the source broadcast problem and the associated source channel separation theorem can be leveraged via a reduction argument to establish a necessary condition for the original problem which unifies several existing results in the literature somewhat surprisingly this method albeit based on the source channel separation theorem can be used to prove the optimality of non separation based schemes and determine the performance limits in certain scenarios where the separation architecture is suboptimal

large eddy simulation coupled with wall models for turbulent channel flows at high reynolds numbers with a lattice boltzmann method application to coriolis mass flowmeter abstract the numerical prediction of pressure drop within wall bounded flow domains at high reynolds numbers re using a large eddy simulation les approach is a challenging task for industrial applications because the fluid domain is usually underresolved a lattice boltzmann method lbm with bhatnagar gross and krook bgk collision operator coupled with the smagorinsky lilly turbulence model is used to model these wall bounded turbulent flows the near wall region is modelled using wall functions to decrease the required mesh resolution for high re the influence of different velocity boundary approaches and wall functions is investigated for the benchmark bi periodic fully developed turbulent channel flow for friction reynolds numbers re of 1000 2000 and 5200 this benchmark case is validated against direct numerical simulation dns results for turbulent statistics of 1st and 2nd order based on this validation the pressure drop of an industrial coriolis mass flowmeter is compared to experimental data for re up to 127 800 the error of the pressure drop calculation in underresolved grids is reduced by two orders of magnitude in comparison to a no slip approach for curved boundaries

sum rate of the vacationing ceo problem the vacationing chief executive officer ceo problem combines the salient features of the so called ceo problem and the multiple description md problem in this setting noisy versions of a source are observed by two encoders as in the ceo problem in addition we require that each encoder generate mds of the source as in the md problem the vacationing ceo problem arises in asynchronous multicast networks and solving it is an essential step in developing a general theory for multiencoder and multidecoder lossy compression in this paper an achievable sum rate and two sum rate lower bounds are presented for the quadratic gaussian vacationing ceo problem these bounds exactly determine the optimal sum rate over a wide range of parameters

rate distortion theory for gaussian multiterminal source coding systems with several side informations at the decoder in this paper we consider the separate coding problem for l 1 correlated gaussian memoryless sources we deal with the case where l sources work as partial side information at the decoder for the reconstruction of the remaining source the determination problem of the rate distortion region for this system is the so called many help one problem and it has been known as a highly challenging problem for almost 20 years in this paper we give a partial solution to this problem we determine the rate distortion region in the case where the l sources working as partial side information are conditionally independent if the remaining source we wish to reconstruct is given the additive white gaussian noise ceo problem is a special case of this we also discuss the relation of the result previous results of ours

a state space approach to a one dimensional mathematical model for the dynamics of phase transitions in pseudoelastic materials abstract an abstract formulation of a general mathematical model for the dynamics of shape memory alloys is presented using a state space approach the model is written as a semilinear cauchy problem in an appropriate hilbert space it is shown that the differential operator corresponding to the linear part of the system generates an exponentially stable analytic semigroup for this semigroup explicit decay rates are given in terms of the physical constants of the system and its continuity with respect to the model parameters is proved a proof of local existence of solutions is given and open problems are discussed

multiple description vector quantization with lattice codebooks design and analysis the problem of designing a multiple description vector quantizer with lattice codebook spl lambda is considered a general solution is given to a labeling problem which plays a crucial role in the design of such quantizers numerical performance results are obtained for quantizers based on the lattices a sub 2 and z sup i i 1 2 4 8 that make use of this labeling algorithm the high rate squared error distortions for this family of l dimensional vector quantizers are then analyzed for a memoryless source with probability density function pdf p and differential entropy h p spl infin for any a spl epsiv 0 1 and rate pair r r it is shown that the two channel distortion d sub o and the channel 1 or channel 2 distortion d sub s satisfy lim sub r spl rarr spl infin d sub o 2 sup 2r 1 a 1 4 g spl lambda 2 sup 2h p and lim sub r spl rarr spl infin d sub s 2 sup 2r 1 a g s sub l 2 sup 2h p where g spl lambda is the normalized second moment of a voronoi cell of the lattice spl lambda and g s sub l is the normalized second moment of a sphere in l dimensions

asymptotic analysis of multiple description quantizers a high rate analysis of multiple description quantizers is presented for rth power distortions and general source densities both fixed length and variable length encoding of the quantizer indices are considered optimal companding functions are shown to be the same as for single channel quantizers as compared to the bound of ozarow 1980 a gap of 8 69 db and 3 07 db exists between the entropy constrained and level constrained cases respectively for a memoryless gaussian source and r 2

vector gaussian multiple description with individual and central receivers t multiple descriptions of a vector gaussian source for individual and central receivers are investigated the sum rate of the descriptions with covariance distortion measure constraints in a positive semidefinite ordering is exactly characterized for two descriptions the entire rate region is characterized the key component of the solution is a novel information theoretic inequality that is used to lower bound the achievable multiple description rates jointly gaussian descriptions are optimal in achieving the limiting rates we also show the robustness of this description scheme the distortions achieved are no larger when used to describe any non gaussian source with the same covariance matrix

new coding schemes for the symmetric k description problem we propose novel coding schemes for the k description problem with symmetric rates and symmetric distortion constraints there are two main new ingredients in these schemes the first one is akin to the method seen in the well known butterfly network of network coding literature and systematic erasure channel codes are applied on certain carefully chosen source coding component the second approach is built on the quantization splitting technique which was previously proven useful in the gaussian ceo problem we first focus on a special case of the three description problem where any two descriptions are rate distortion optimal jointly referred to as the no two description excess rate case for this special case and the quadratic gaussian source we show that the two aforementioned approaches lead to rate distortion points outside the achievable region based on the source channel erasure codes previously proposed by pradhan puri and ramchandran interestingly though only the symmetric problem is considered in our work the proposed schemes in fact benefit from time sharing several asymmetric rate distortion points the insights gained through the no two description excess rate case lead to strategic combination of the new ingredients with the existing coding scheme yielding new coding schemes for the symmetric k description problem

gaussian robust sequential and predictive coding we introduce two new source coding problems robust sequential coding and robust predictive coding for the gauss markov source model with the mean squared error distortion measure we characterize certain supporting hyperplanes of the rate region of these two coding problems our investigation also reveals an information theoretic minimax theorem and the associated extremal inequalities

investigation of the les wale turbulence model within the lattice boltzmann framework turbulence models which can perform the transition from laminar flow to fully developed turbulent flow are of key importance in industrial applications a promising approach is the les wale model which can be used without wall functions or global damping functions the model produces an efficient and fast scheme due to its algebraic character additionally its prediction of the transition from laminar to turbulent regimes has shown promising results in this work the les wale model is investigated within the lattice boltzmann framework for validation purposes various test cases are presented first a channel flow at a reynolds number of 6876 is investigated secondly the flow around a wall mounted cube at various reynolds numbers is determined the flow regime varies from laminar to transitional to fully turbulent conditions at a reynolds number of 40 000 with respect to the cube height

multireflection boundary conditions for lattice boltzmann models we present a general framework for several previously introduced boundary conditions for lattice boltzmann models such as the bounce back rule and the linear and quadratic interpolations the objectives are twofold first to give theoretical tools to study the existing link type boundary conditions and their corresponding accuracy second to design boundary conditions for general flows which are third order kinetic accurate using these new boundary conditions couette and poiseuille flows are exact solutions of the lattice boltzmann models for a reynolds number mathrm re 0 stokes limit for arbitrary inclination with the lattice directions numerical comparisons are given for stokes flows in periodic arrays of spheres and cylinders linear periodic array of cylinders between moving plates and for navier stokes flows in periodic arrays of cylinders for mathrm re l200 these results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce back reflection up to an order of magnitude on the hydrodynamics fields further improvement is achieved with the new multireflection boundary conditions reaching a level of accuracy close to the quasianalytical reference solutions even for rather modest grid resolutions and few points in the narrowest channels more important the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions finally the good stability of these schemes is highlighted by some simulations of moving obstacles a cylinder between flat walls and a sphere in a cylinder

equivalent partial differential equations of a lattice boltzmann scheme we show that when we formulate the lattice boltzmann equation with a small time step dt and an associated space scale dx a taylor expansion joined with the so called equivalent equation methodology leads to establishing macroscopic fluid equations as a formal limit we recover the euler equations of gas dynamics at the first order and the compressible navier stokes equations at the second order

combinatorial message sharing and a new achievable region for multiple descriptions this paper presents a new achievable rate distortion region for the general l channel multiple descriptions mds problem a well known general region for this problem is due to venkataramani kramer and goyal vkg their encoding scheme is an extension of the el gamal cover ec and zhang berger zb coding schemes to the l channel case and includes a combinatorial number of refinement codebooks one for each subset of the descriptions as in zb the scheme also allows for a single common codeword to be shared by all descriptions this paper proposes a novel encoding technique involving combinatorial message sharing cms where every subset of the descriptions may share a distinct common message this introduces a combinatorial number of shared codebooks along with the refinement codebooks of these shared codebooks provide a more flexible framework to tradeoff redundancy across the messages for resilience to descriptions loss we derive an achievable rate distortion region for the proposed technique and show that it subsumes the vkg region for general sources and distortion measures we further show that cms provides a strict improvement of the achievable region for any source and distortion measures for which some two description subset is such that zb achieves points outside the ec region we then show a more surprising result cms outperforms vkg for a general class of sources and distortion measures including scenarios where the zb and ec regions coincide for all two description subsets in particular we show that cms strictly improves on vkg for the l channel quadratic gaussian md problem for all l geq 3 despite the fact that the ec region is complete for the corresponding two descriptions problem consequently the correlated quantization scheme an extreme special case of vkg that has been proven to be optimal for several cross sections of the l channel quadratic gaussian md problem is strictly suboptimal in general using the encoding principles derived we show that the cms scheme achieves the complete rate distortion region for several asymmetric cross sections of the l channel quadratic gaussian md problem

wall model for large eddy simulation based on the lattice boltzmann method an original wall model for lattice boltzmann based large eddy simulation is presented it relies on either an analytical profile for the velocity profile within the first off wall cell or the solution of turbulent boundary layer equations the latter are solved thanks to a meshless approach to obtain a user friendly method the proposed method is observed to be both robust and accurate yielding very satisfactory results in plane channel flow up to re email protected 000 on uniform grids with dx email protected email protected 1000 the computed maximum error on skin friction is about 4 in most investigated cases on the coarsest grids 10 grid points across the half channel height it lies within 1 2 on finer grids with 20 60 uniformly distributed grid points in the channel half height

on the role of the refinement layer in multiple description coding and scalable coding we clarify the relationship among several existing achievable multiple description rate distortion regions by investigating the role of refinement layer in multiple description coding specifically we show that the refinement layer in the el gamal cover egc scheme and the venkataramani kramer goyal vkg scheme can be removed as a consequence the egc region is equivalent to the egc region an antecedent version of the egc region while the vkg region when specialized to the 2 description case is equivalent to the zhang berger zb region moreover we prove that for multiple description coding with individual and hierarchical distortion constraints the number of layers in the vkg scheme can be significantly reduced when only certain weighted sum rates are concerned the role of refinement layer in scalable coding a special case of multiple description coding is also studied

n channel symmetric multiple descriptions part i n k source channel erasure codes in this two part paper we present a new achievable rate region for the general n channel symmetric multiple descriptions problem in part i inspired by the concept of maximum distance separable mds erasure channel codes we consider a special case of this rate region where the source is encoded into n descriptions each with rate r these descriptions are transmitted over n bandwidth constrained and errorless channels during transmission a subset of these channels can break down thus erasing the corresponding descriptions the decoder is interested in recovering the source with the reception of at least k descriptions thus the encoder is allowed to sample only one realization of this breakdown process during the entire transmission for gaussian sources we have the following interesting result when any k descriptions arrive the achievable distortion exactly matches the optimal distortion rate performance corresponding to a source rate of kr bits with the reception of any m k descriptions the source reconstruction quality is strictly better the improvement being nearly linear in the number of descriptions received

shock layer movement for burgers equation this paper considers the motion of the shock layer exhibited by the solution of the initial boundary value problem for the equation epsilon u xx uu x u t with small values of epsilon 0 this burgers equation occurs as a model for a number of physical problems and is representative of many convection dominated evolution equations a specific example will be solved explicitly using the cole hopf transformation the result suggests a corresponding asymptotic approach which provides the shock layer location x epsilon t as the solution of an initial value problem that method which can be applied to a far wider class of equations also shows how the steady state shock location can be changed substantially by asymptotic exponentially small perturbations

identifiability of the landau ginzburg potential in a mathematical model of shape memory alloys abstract the nonlinear partial differential equations considered here arise from the conservation laws of linear momentum and energy and describe structural phase transitions in one dimensional shape memory solids with non convex landau ginzburg free energy potentials in this article the theories of analytic semigroups and real interpolation spaces for maximal accretive operators are used to show that the solutions of the model depend continuously on the admissible parameters also we show that the non physical parameters that define the free energy are identifiable from the model

high rate analysis of symmetric l channel multiple description coding this paper studies the tight rate distortion bound for l channel symmetric multiple description coding of a scalar gaussian source with two levels of receivers each of the first level receivers obtains of the l descriptions l the second level receiver obtains all l descriptions we find that if the central distortion corresponding to the second level receiver is much smaller than the side distortion corresponding to the first level receivers the product of a function of the side distortions and the central distortion is asymptotically independent of the redundancy between the descriptions using this property we analyze the asymptotic behavior of a practical multiple description lattice vector quantizer mdlvq our analysis includes the treatment of the mdlvq system from a new geometric viewpoint which results in an expression for the side distortions using the normalized second moment of a sphere of higher dimensionality than the quantization space the expression of the distortion product derived from the lower bound is then applied as a criterion to assess the performance loss of the considered mdlvq system in principle the efficiency of other practical md systems can also be evaluated using the derived distortion product

coding for the large alphabet adversarial channel we consider the problem of encoding an i i d source into a set of symbols or messages that may be altered by an adversary while en route to the decoder we focus in particular on the regime in which the number of messages is fixed while the blocklength of the source and the size of each message tend to infinity for this fixed blocklength large alphabet channel we show that combining an optimal rate distortion code with an optimal error correction code yields an optimal overall code for gaussian sources with quadratic distortion and binary uniform sources with hamming distortion but that it can be suboptimal by an arbitrarily large factor in general we also consider the scenario in which the distortion constraint that the decoder must satisfy depends on the number of errors that occur we show that the problem can be reduced operationally to one with erasures instead of errors in two special cases one involving lossless reproduction of functions of the source and one in which the encoder and decoder share common randomness

information theoretic proofs of entropy power inequalities while most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information up to now shannon s entropy power inequality epi is an exception existing information theoretic proofs of the epi hinge on representations of differential entropy using either fisher information or minimum mean square error mmse which are derived from de bruijn s identity in this paper we first present an unified view of these proofs showing that they share two essential ingredients 1 a data processing argument applied to a covariance preserving linear transformation 2 an integration over a path of a continuous gaussian perturbation using these ingredients we develop a new and brief proof of the epi through a mutual information inequality which replaces stam and blachman s fisher information inequality fii and an inequality for mmse by guo shamai and verdu used in earlier proofs the result has the advantage of being very simple in that it relies only on the basic properties of mutual information these ideas are then generalized to various extended versions of the epi zamir and feder s generalized epi for linear transformations of the random variables takano and johnson s epi for dependent variables liu and viswanath s covariance constrained epi and costa s concavity inequality for the entropy power

rate region of gaussian multiple description coding with individual and central distortion constraints the rate region of gaussian multiple description coding with individual and central distortion constraints is completely characterized specifically a lower bound and an upper bound are derived for each supporting hyperplane of the rate region where the lower bound is associated with a max min game while the upper bound is associated with a min max game furthermore it is shown that these two bounds coincide due to the existence of a saddle point