sample adaptive product quantization asymptotic analysis and examples vector quantization vq is an efficient data compression technique for low bit rate applications however the major disadvantage of vq is that its encoding complexity increases dramatically with bit rate and vector dimension even though one can use a modified vq such as the tree structured vq to reduce the encoding complexity it is practically infeasible to implement such a vq at a high bit rate or for large vector dimensions because of the huge memory requirement for its codebook and for the very large training sequence requirement to overcome this difficulty a structurally constrained vq called the sample adaptive product quantizer sapq has recently been proposed we extensively study the sapq that is based on scalar quantizers in order to exploit the simplicity of scalar quantization through an asymptotic distortion result we discuss the achievable performance and the relationship between distortion and encoding complexity we illustrate that even when sapq is based on scalar quantizers it can provide vq level performance we also provide numerical results that show a 2 3 db improvement over the lloyd max 1982 1960 quantizers for data rates above 4 b point

quasipolynomial generalization of lotka volterra mappings in recent years it has been shown that lotka volterra mappings constitute a valuable tool from both the theoretical and the applied points of view with developments in very diverse fields such as physics population dynamics chemistry and economy the purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism originally conceived for the analysis of ordinary differential equations can be extended into the mapping domain the extension of the formalism into the discrete time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case it will be demonstrated that lotka volterra mappings play a central role in the quasipolynomial formalism for the discrete time case moreover the extension of the formalism into the discrete time domain allows a significant generalization of lotka volterra mappings as well as a whole transfer of algebraic methods into the discrete time context the result is a novel and more general conceptual framework for the understanding of lotka volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of lotka volterra mappings and their generalizations but also for the development of new applications

a pyramid vector quantizer the geometric properties of a memoryless laplacian source are presented and used to establish a source coding theorem motivated by this geometric structure a pyramid vector quantizer pvq is developed for arbitrary vector dimension the pvq is based on the cubic lattice points that lie on the surface of an l dimensional pyramid and has simple encoding and decoding algorithms a product code version of the pvq is developed and generalized to apply to a variety of sources analytical expressions are derived for the pvq mean square error mse and simulation results are presented for pvq encoding of several memoryless sources for large rate and dimension pvq encoding of memoryless laplacian gamma and gaussian sources provides rose improvements of 5 64 8 40 and 2 39 db respectively over the corresponding optimum scalar quantizer although suboptimum in a rate distortion sense because the pvq can encode large dimensional vectors it offers significant reduction in rose distortion compared with the optimum lloyd max scalar quantizer and provides an attractive alternative to currently available vector quantizers

γ convergence of equi coercive nonlinear energies defined on vector valued functions with non uniformly bounded coefficients abstract the present paper deals with the asymptotic behavior of equi coercive sequences n of nonlinear functionals defined over vector valued functions in w 0 1 p m where p 1 m 1 and is a bounded open set of r n n 2 the strongly local energy density f n d u of the functional n satisfies a lipschitz condition with respect to the second variable which is controlled by a positive sequence a n which is only bounded in some suitable space l r we prove that the sequence n converges for the strong topology of l p m to a functional which has a strongly local density f d u for sufficiently regular functions u this compactness result extends former results on the topic which are based either on maximum principle arguments in the nonlinear scalar case or adapted div curl lemmas in the linear case here the vectorial character and the nonlinearity of the problem need a new approach based on a careful analysis of the asymptotic minimizers associated with the functional n the relevance of the conditions which are imposed to the energy density f n d u is illustrated by several examples including some classical hyperelastic energies

numerics of gram schmidt orthogonalization abstract the gram schmidt gs orthogonalization is one of the fundamental procedures in linear algebra in matrix terms it is equivalent to the factorization a q1r where q1 rm n with orthonormal columns and r upper triangular for the numerical gs factorization of a matrix a two different versions exist usually called classical and modified gram schmidt cgs and mgs although mathematically equivalent these have very different numerical properties this paper surveys the numerical properties of cgs and mgs a key observation is that mgs is numerically equivalent to householder qr factorization of the matrix a augmented by an n n zero matrix on top this can be used to derive bounds on the loss of orthogonality in mgs and to develop a backward stable algorithm based on mgs the use of reorthogonalization and iterated cgs and mgs algorithms are discussed finally block versions of gs are described

a structured fixed rate vector quantizer derived from a variable length scalar quantizer i memoryless sources for pt i see ibid vol 39 no 3 p 851 67 1993 the fixed rate scalar vector quantizer svq for quantizing stationary memoryless sources is extended to a specific type of vector source in which each component is a stationary memoryless scalar subsource independent of the other components algorithms for the design and implementation of the original svq are modified to apply to this case the resulting svq referred to as the extended svq esvq is then used to quantize stationary sources with memory with known autocorrelation function numerical results are presented for the quantization of first order gauss markov sources using this scheme it is shown that the esvq based scheme performs very close to entropy coded transform quantization while maintaining a fixed rate output and outperforms the fixed rate scheme that uses scalar lloyd max quantization of the transform coefficients it is also shown that this scheme performs better than implementable vector quantizers especially at high rates

oscillatory dynamics induced by time delay in an internet congestion control model with ring topology in this paper an n dimensional congestion control model with ring topology is considered to study delay induced oscillation via the hopf bifurcation the expression of the possible critical delay for the hopf bifurcation is obtained by analyzing the linear part of the system around the equilibrium and verified by the numerical simulation based on the linear analysis the method of multiple scales is employed to obtain the quantitative relation between the delay and the oscillation induced by it the analytical results agree well with those obtained by the numerical method furthermore the effects of other parameters are also studied the discussions reveal that excessive transfer times may cause the oscillation and that increasing the link capacity can control the oscillatory dynamics

structured prefix codes for quantized low shape parameter generalized gaussian sources the highly peaked wide tailed pdf s that are encountered in many image coding algorithms are often modeled using the family of generalized gaussian gg pdf s we study entropy coding of quantized gg sources using prefix codes that are highly structured and which therefore involve low computational complexity we provide bounds for the redundancy associated with applying these codes to quantized gg sources we also explore code efficiency and code choice for a wide range of gg source and quantizer parameters

analytical coding of gaussian sources several procedures for encoding a stationary gaussian source are investigated in contrast to vector quantization by the lbg algorithm coding and rate distortion performance can be described analytically due to the regular structure of the code vectors

an efficient qr based method for the computation of lyapunov exponents abstract an efficient and numerically stable method to determine all the lyapunov characteristic exponents of a dynamical system is developed numerical experiments are presented highlighting some aspects of convergence accuracy and efficiency in the computation of the lyapunov characteristic exponents

an efficient and stable approach for computation of lyapunov characteristic exponents of continuous dynamical systems this paper proposes a new approach for computing the lyapunov characteristic exponents lces for continuous dynamical systems in an efficient and numerically stable fashion the method is adapted to systems with small dimensions numerical examples illustrating the accuracy of method are presented

quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series we describe methods of estimating the entire lyapunov spectrum of a spatially extended system from multivariate time series observations provided that the coupling in the system is short range the jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions this circumvents the curse of dimensionality that prevents the accurate reconstruction of high dimensional dynamics from observed time series the technique is illustrated using coupled map lattices as prototype models for spatiotemporal chaos and is found to work even when the coupling is not strictly local but only exponentially decaying

realizable response matrices of multi terminal electrical acoustic and elastodynamic networks at a given frequency we give a complete characterization of the possible response matrices at a fixed frequency of n terminal electrical networks of inductors capacitors resistors and grounds and of n terminal discrete linear elastodynamic networks of springs and point masses both in three dimensional and two dimensional cases specifically we construct networks that realize any response matrix that is compatible with the known symmetry properties and thermodynamic constraints of response matrices owing to a mathematical equivalence we also obtain a characterization of the response matrices of discrete acoustic networks

a new div curl result applications to the homogenization of elliptic systems and to the weak continuity of the jacobian in this paper a new div curl result is established in an open set omega of mathbb r n n geq 2 for the product of two sequences of vector valued functions which are bounded respectively in l p omega n and l q omega n with 1 p 1 q 1 1 n 1 and whose respectively divergence and curl are compact in suitable spaces we also assume that the product converges weakly in w 1 1 omega the key ingredient of the proof is a compactness result for bounded sequences in w 1 q omega based on the imbedding of w 1 q s n 1 into l p s n 1 s n 1 the unit sphere of mathbb r n through a suitable selection of annuli on which the gradients are not too high in the spirit of de giorgi and manfredi the div curl result is applied to the homogenization of equi coercive systems whose coefficients are equi bounded in l rho omega for some rho n 1 over 2 if n 2 or in l 1 omega if n 2 it also allows us to prove a weak continuity result for the jacobian for bounded sequences in w 1 n 1 omega satisfying an alternative assumption to the l infty strong estimate of brezis and nguyen two examples show the sharpness of the results

rate distortion performance of dpcm schemes for autoregressive sources an analysis of the rate distortion performance of differential pulse code modulation dpcm schemes operating on discrete time auto regressive processes is presented the approach uses an iterative algorithm for the design of the predictive quantizer subject to an entropy constraint on the output sequence at each stage the iterative algorithm optimizes the quantizer structure given the probability distribution of the prediction error while simultaneously updating the distribution of the resulting prediction error different orthogonal expansions specifically matched to the source are used to express the prediction error density a complete description of the algorithm including convergence and uniqueness properties is given results are presented for rate distortion performance of the optimum dpcm scheme for first order gauss markov and laplace markov sources including comparisons with the corresponding rate distortion bounds furthermore asymptotic formulas indicating the high rate performance of these schemes are developed for both first order gaussian and laplacian autoregressive sources

large deformations of planar extensible beams and pantographic lattices heuristic homogenization experimental and numerical examples of equilibrium the aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call pantographic structures the interest in these materials was increased by the possibilities opened by the diffusion of technology of three dimensional printing they can be regarded once choosing a suitable length scale as families of beams also called fibres interconnected to each other by pivots and undergoing large displacements and large deformations there are however relatively few ready to use results in the literature of nonlinear beam theory in this paper we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by piola to formulate a continuum fully nonlinear beam model the homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems furthermore we consider pantographic structures find the corresponding homogenized second gradient deformation energies and study some planar problems numerical solutions for these two dimensional problems are obtained via minimization of energy and are compared with some experimental measurements in which elongation phenomena cannot be neglected

enumeration encoding and decoding algorithms for pyramid cubic lattice and trellis codes a pyramid source code is a code that assigns equal length binary strings to all reproduction codevectors of equal weighted spl epsiv sub 1 norm a pyramid source encoding is partitioned into two concatenated mappings the first from source word to reproduction codeword within a codebook the second from the reproduction codevector to a binary string the first mapping allows distortion and is accomplished using lattice quantization or trellis coded quantization the second mapping is noiseless and is denoted as enumeration efficient pyramid enumeration encoding and decoding algorithms are presented for use with fixed rate or variable rate pyramid lattice and trellis codes

determination of the closure of the set of elasticity functionals we determine the closure for mosco convergence in l2 3 of the set of elasticity functionals we prove that this closure coincides with the set of all non negative lower semicontinuous quadratic functionals which are objective i e which vanish for rigid motions the result is still valid if we consider only the set of isotropic elasticity functionals which have a prescribed poisson coefficient this shows that a very large family of materials can be reached when homogenizing a composite material with highly contrasted rigidity coefficients

fine coarse vector quantization a fast method for searching an unstructured vector quantization vq codebook is introduced and analyzed the method fine coarse vector quantization fcvq operates in two stages a fine structured vq followed by a table lookup coarse unstructured vq its rate distortion arithmetic complexity and storage are investigated using analytical and experimental means optimality condition and an optimizing algorithm are presented the results of experiments with both uniform scalar quantization and tree structured vq tsvq as the first stage are reported comparisons are made with other fast approaches to vector quantization especially tsvq it is found that when rate distortion arithmetic complexity and storage are all taken into account fcvq outperforms tsvq in a number of cases in comparison to full search quantization fcvq has much lower arithmetic complexity at the expense of a slight increase in distortion and a substantial increase in storage the increase in mean squared error over full search decays as a negative power of the available storage

dynamics and the periodic solutions of the delayed non smooth internet tcp red congestion control system via hb aft abstract this paper has attended to obtain the approximate analytical expressions of periodic solutions in the delayed non smooth internet tcp red congestion control system employing the semi analytical method named as the harmonic balance method with alternating frequency time hb aft domain technique for the first time the methodology presented herein provides the accurate approximate analytical expressions of periodic solutions including the non impacting periodic solutions and impacting periodic solutions in the non smooth dynamical system with time delays they agree very well with the results of numerical simulations by matlab it implies that the proposed method in this paper is accurate and effective furthermore rich dynamics of this delayed non smooth system is discovered in the present paper three kinds of bi stability i e coexistence of asymptotically stable equilibrium and equilibrium equilibrium and periodic solution periodic solution and periodic solution have been found in the system with the variation of the delay and the grazing solution the impacting solution traversing both the lower threshold tmin and the larger threshold tmax and a route to chaos i e intermittent to chaos have been also obtained by varying the delay employing numerical method

continuum and discrete models for structures including quasi inextensible elasticae with a view to the design and modeling of composite reinforcements abstract inspired by some composite fiber reinforcements used in aeronautical engineering and by the need of conceiving new metamaterials some discrete models including quasi inextensible elasticae are considered a class of continuum models approximately describing the macroscopic mechanical behavior of introduced structures is then heuristically proposed some of these continuum models can be regarded as a special kind of second gradient elastic media in which the higher gradient elasticity is conferred by the flexural stiffnesses of elasticae constituting the microscopic lattice the discrete models are studied by means of suitably tailored numerical codes designed to avoid numerical instabilities and locking and a comparison of discrete versus continuum models is attempted the obtained results show that the theory of generalized continua may be useful in some engineering applications and it plays a relevant role in the mechanics of woven composites the introduced discrete and continuum models are used to describe the so called bias extension test on woven fabrics and it is shown that a good choice to correctly reproduce the targeted phenomenology is to use a second gradient continuum theory however as discussed throughout the paper in the context of rigorous micro macro identification procedures there still remain many open problems to be solved especially when dealing with systems subjected to particular constraints such as inextensibility

dynamics of coupled nonlinear maps and its application to ecological modeling this paper investigates the behavior of coupled nonlinear dynamical systems we take two such dynamical systems or units couple them together and study the effect of coupling on the dynamics we demonstrate that coupling two chaotic units can indeed stabilize both of them several results describing the global dynamics of the coupled nonlinear system are established using them we show that by and large the presence of coupling appears to increase the orderliness of the coupled system s response producing periodicity synchronicity and quasi symmetry using exponential maps which are commonly used to simulate population dynamics we establish the applicability of our results to population dynamics

homogenization and optimal bounds in linear elasticity in their celebrated paper of 1963 hashin shtrikman 1 addressed the problem of determining optimal bounds for the bulk and shear moduli of a statistically isotropic elastic composite material with arbitrary isotropic phase geometry they derived a set of bounds for these moduli in the physically meaningful case of three dimensional elasticity in the case of a two phase composite let k 1 1 and k 2 2 respectively denote the bulk and shear moduli for the first and the second phase let k denote their analogues for the composite and let 0 stand for the volume fraction of the first phase in the composite under the ordering restriction that both

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

trellis coded quantization of memoryless and gauss markov sources trellis coded quantization tcq is developed and applied to the encoding of memoryless and gauss markov sources the theoretical justification for the approach is alphabet constrained rate distortion theory which is a dual to the channel capacity argument that motivates trellis coded modulation tcm the authors adopt the notions of signal set expansion set partitioning and branch labeling of tcm but modify the techniques to account for the source distribution to design tcq coders of low complexity with excellent mean squared error mse performance for a memoryless uniform source tcq provides an mse within 0 21 db of the distortion rate bound at all positive integral rates the performance is superior to that promised by the coefficient of quantization for all of the best lattices known in dimensions 24 or less for a memoryless gaussian source the tcq performance at rates of 0 5 1 and 2 b sample is superior to all previous results the authors found in the literature the encoding complexity of tcq is very modest tcq is incorporated into a predictive coding structure for the encoding of gauss markov sources simulation results for first second and third order gauss markov sources are presented

joint watermarking and compression using scalar quantization for maximizing robustness in the presence of additive gaussian attacks in joint watermarking and compression jwc a key process is quantization which embeds watermarks into a host signal while digitizing the host signal subject to requirements on the embedding rate compression rate quantization distortion and robustness using fixed rate scalar quantization for watermarking and compression in this paper we mainly consider how to design binary jwc systems to maximize the robustness of the systems in the presence of additive gaussian attacks under constraints on the compression rate and quantization distortion we first investigate optimum decoding of a binary jwc system and demonstrate by experiments that in the distortion to noise ratio dnr region of practical interest the minimum distance md decoder achieves performance comparable to that of the maximum likelihood decoder in addition to having advantages of low computation complexity and being independent of the statistics of the host signal we then present optimum binary jwc encoding schemes using fixed rate scalar quantization and the md decoder simulation results show that optimum binary jwc systems using nonuniform quantization are better than optimum binary jwc systems using uniform quantization furthermore in comparison with separate watermarking and compression systems optimum binary jwc systems using nonuniform quantization achieve significant dnr gains in the dnr region of practical interest finally spread transform dither modulation is applied to improving the robustness of the jwc systems at low dnrs

local bifurcation analysis of some dual congestion control algorithms we perform the necessary calculations to determine the stability and asymptotic forms of solutions bifurcating from steady state in a nonlinear delay differential equation with a single discrete delay the results are used to examine the loss of local stability in a selection of congestion control algorithms employed over a single link in particular we analyze the fair and the delay based dual algorithms explicit conditions are derived to ensure the onset of stable limit cycles as these algorithms just lose local stability further we are able to quantify the effect parameters of the system have on the amplitude of the bifurcating periodic solutions

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding

vector quantizers and predictive quantizers for gauss markov sources low rate vector quantizers are designed and simulated for highly correlated gauss markov sources and the resulting performance is compared with arnstein s optimized predictive quantizer and with huang and schultheiss optimized transform coder two implementations of vector quantizers are considered full search vector quantizers which are optimal but require large codebook searches and tree searched vector quantizers which are suboptimal but require far less searching the various systems are compared on the basis of performance complexity and generality of design techniques

extension of two stage vector quantization lattice vector quantization this paper is the extension of two stage vector quantization spherical lattice vector quantization vq s lvq recently introduced by pan and fischer see ieee trans inform theory vol 41 p 155 1995 first according to high resolution quantization theory generalized vector quantization lattice vector quantization g vq lvq is formulated in order to release the constraint of the spherical boundary for the second stage lattice vector quantization lvq which would provide possibilities of improving this kind of two stage unstructured structured quantizer by using more efficient lvq second among g vq lvq vector quantization pyramidal lattice vector quantization vq plvq is developed which is slightly superior or comparable to vq s lvq in performance but has a much lower complexity simulation results show that for memoryless sources vq plvq achieves a rate distortion performance that is among the best of the fixed rate quantization that we found in the literature therefore vq plvq is an attractive alternative to vq s lvq in practice third transform vq plvq tvq plvq is proposed for sources with memory for encoding 16 d vectors of the gauss markov source t vq plvq has an advantage of close to 1 0 db over vq plvq and is about 0 5 db better than vq s lvq

unary prefixed huffman coding for a group of quantized generalized gaussian sources we propose a coding algorithm called unary prefixed huffman uph coding for a family of infinite sources called quantized generalized gaussian gg sources compared with the existing codes for these gg sources the uph algorithm provides a more adaptive approach and its coding efficiency is upper bounded by entropy 2

duality theorems for joint source channel coding we consider joint source channel coding for a memoryless gaussian source and an additive white gaussian noise awgn channel for a given code defined by an encoder decoder pair spl alpha spl beta its dual code is obtained by interchanging the encoder and decoder spl beta spl alpha it is shown that if a code spl alpha spl beta is optimal at rate p channel uses per source sample and if it satisfies a certain uniform continuity condition then its dual code spl beta spl alpha is optimal for rate 1 spl rho channel uses per source sample further it is demonstrated that there is a code which is optimal but its dual code is not optimal finally using random coding we show that there is an optimal code which has an optimal dual the duality concept is also presented for the cases of i binary memoryless equiprobable source and binary symmetric channel bsc and ii colored gaussian source and additive colored gaussian noise acgn channel

minimum entropy quantizers and permutation codes amplitude quantization and permutation encoding are two approaches to efficient digitization of analog data it has been proven that they are equivalent in the sense that their optimum rate versus distortion performances are identical reviews of the aforementioned results and of work performed in the interim by several investigators are presented equations which must be satisfied by the thresholds of the minimum entropy quantizer that achieves a prescribed mean r th power distortion are derived and an iterative procedure for solving them is developed it is shown that these equations often have many families of solutions in the case of the laplacian distribution for which we had previously shown that quantizers with uniformly spaced thresholds satisfy the equations when r 2 other families of solutions with nonuniform spacing are exhibited what had appeared to be a discrepancy between the performances of optimum permutation codes and minimum entropy quantizers is resolved by the resulting optimum quantizers which span all entropy rates from zero to infinity

a new trellis source code for memoryless sources the trellis based scalar vector quantizer tb svq for memoryless sources combines the scalar vector quantizer svq with trellis coded quantization tcq to achieve both boundary gain and granular gain the resulting quantizer outperforms all other reasonable complexity fixed rate quantizers unfortunately the resulting code is catastrophic a single bit error within a block can propagate indefinitely into other blocks this correspondence presents a new trellis source code that can achieve essentially the same or in some cases better performance as the tb svq for error free channels but limits the propagation of channel errors

optimum quantizer performance for a class of non gaussian memoryless sources the performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources for a general distortion criterion necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer under a mean square error criterion the performance of entropy encoded uniform quantization of memoryless gaussian sources is well known to be within 0 255 bits sample of the rate distortion bound at relatively high rates despite claims to the contrary it is demonstrated that similar performance can be expected for a wide range of memoryless sources indeed for the cases considered the worst case performance is observed to be less than 0 3 bits sample from the rate distortion bound and in most cases this disparity is less at iow rates

computational explorations into the dynamics of rings of coupled oscillators this paper deals with the response of homogeneous and inhomogeneous rings of coupled oscillators where each individual oscillator when uncoupled from the others is chaotic it is shown that coupling can bring about a wide variety of global responses and that there is a significant range of coupling values when the response of the ring is periodic despite the fact that each oscillator is chaotic in fact numerous periodic solutions can be found depending on the initial conditions the response of a coupled set of homogeneous and non homogeneous rings is also investigated showing that the behavior of such coupled compartmental models can be quite counterintuitive and sensitive to the parameters that describe the extent and nature of coupling

symmetry breaking bifurcation for coupled chaotic attractors the authors consider transitions from synchronous to asynchronous chaotic motion in two identical dissipatively coupled one dimensional mappings they show that the probability density of the asymmetric component satisfies a scaling law the exponent in this scaling law varies continuously with the distance from the bifurcation point and is determined by the spectrum of local lyapunov exponents of the uncoupled map finally they show that the topology of the invariant set is rather unusual though the attractor for supercritical coupling is a line it is surrounded by a strange invariant set which is dense in a two dimensional neighbourhood of the attractor

nonlocal effects in two dimensional conductivity the paper deals with the asymptotic behaviour as e 0 of a two dimensional conduction problem whose matrix valued conductivity ae is e periodic and not uniformly bounded with respect to e we prove that only under the assumptions of equi coerciveness and l1 boundedness of the sequence ae the limit problem is a conduction problem of same nature this new result points out a fundamental difference between the two dimensional conductivity and the three dimensional one indeed under the same assumptions of periodicity equi coerciveness and l1 boundedness it is known that the high conductivity regions can induce nonlocal effects in three or greater dimensions

performance of entropy constrained block transform quantizers an analysis of the rate distortion performance of an entropy constrained block transform quantization scheme operating on first order stationary gauss markov sources is presented uniform threshold quantization is employed to quantize the transform coefficients an algorithm for optimum stepsize or equivalently entropy assignment among the quantizers is developed and a simple asymptotic formula indicating the high rate performance of the block transform quantization scheme is presented specific results determining the rate distortion performance of the entropy constrained block transform quantization scheme operating upon first order gauss markov sources are presented and comparisons are made with the huang and schultheiss 1963 block transform quantization vector quantization and predictive quantization

scalar vector quantization of medical images a new coding scheme based on the scalar vector quantizer svq is developed for compression of medical images the svq is a fixed rate encoder and its rate distortion performance is close to that of optimal entropy constrained scalar quantizers ecsqs for memoryless sources the use of a fixed rate quantizer is expected to eliminate some of the complexity of using variable length scalar quantizers when transmission of images over noisy channels is considered our coding scheme does not suffer from error propagation that is typical of coding schemes using variable length codes for a set of magnetic resonance mr images coding results obtained from svq and ecsq at low bit rates are indistinguishable furthermore our encoded images are perceptually indistinguishable from the original when displayed on a monitor this makes our svq based coder an attractive compression scheme for picture archiving and communication systems pacs pacs are currently under study for use in an all digital radiology environment in hospitals where reliable transmission storage and high fidelity reconstruction of images are desired

lyapunov exponents and transport in the zhang model of self organized criticality we discuss the role played by lyapunov exponents in the dynamics of zhang s model of self organized criticality we show that a large part of the spectrum the slowest modes is associated with energy transport in the lattice in particular we give bounds on the first negative lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time we then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites we use a finite size scaling ansatz for the lyapunov spectrum and relate the scaling exponent to the scaling of quantities such as avalanche size duration density of active sites etc

radial basis function approach to nonlinear granger causality of time series we consider an extension of granger causality to nonlinear bivariate time series in this frame if the prediction error of the first time series is reduced by including measurements from the second time series then the second time series is said to have a causal influence on the first one not all the nonlinear prediction schemes are suitable to evaluate causality indeed not all of them allow one to quantify how much knowledge of the other time series counts to improve prediction error we present an approach with bivariate time series modeled by a generalization of radial basis functions and show its application to a pair of unidirectionally coupled chaotic maps and to physiological examples

trellis based scalar vector quantization of sources with memory the trellis based scalar vector quantizer tb svq can achieve the rate distortion performance bound for memoryless sources this paper extends the scope of this quantizer to coding of sources with memory first considered is a simple extension called the predictive tb svq which applies a closed loop predictive coding operation in each survivor path of the viterbi codebook search algorithm although the predictive tb svq outperforms all other known structured fixed rate vector quantizers due to practical reasons it may not approach the rate distortion limit a new quantization scheme motivated by the precoding idea of laroia et al 1993 called the precoded tb svq is also considered the granular gain is realized by the underlying trellis code while the combination of the precoder and the svq structure provides the boundary gain this new quantization scheme is asymptotically optimal and can in principle approach the rate distortion bound for markov sources

a low complexity method for fixed rate entropy constrained vector quantization this paper describes a new approach to fixed rate entropy constrained vector quantization fevq for stationary memoryless sources where the structure of codewords are derived from a variable length scalar quantizer we formulate the quantization search operation as a zero one integer optimization problem and show that the resulting integer program can be closely approximated by solving a simple linear program the result is a lagrange formulation which adjoins the constraint on the entropy codeword length to the distortion unlike the previously known methods with a fixed lagrange multiplier we use an iterative algorithm to optimize the underlying objective function while updating the lagrange multiplier until the constraint on the overall rate is satisfied the key feature of the new method is the substantial reduction in the number of iterations in comparison with previous related methods in order to achieve some packing gain we combine the process of trellis coded quantization with that of fevq this results in an iterative application of the viterbi algorithm on the underlying trellis for selecting the lagrange multiplier numerical results are presented which demonstrate substantial improvement in comparison with the alternative methods reported in the literature

estimation of intensive quantities in spatio temporal systems from time series abstract we study multivariate time series generated by coupled map lattices exhibiting spatio temporal chaos and investigate to what extent we are able to estimate various intensive measures of the underlying system without explicit knowledge of the system dynamics using the rescaling and interleaving properties of the lyapunov spectrum of systems in a spatio temporally chaotic regime and paying careful attention to errors introduced by sub system boundary effects we develop algorithms that are capable of estimating the lyapunov spectrum from time series we analyse the performance of these and find that the choice of basis used to fit the dynamics is crucial when the local dynamics at a lattice site is well approximated by this basis we are able to accurately determine the full lyapunov spectrum however as the local dynamics moves away from the space spanned by this basis the performance of our algorithm deteriorates

strange nonchaotic attractors with wada basins a b s t r a c t we demonstrate strange nonchaotic attractors with wada basins snaswb and verify the abundance of snaswb in a quasiperiodically forced holmes map we identify the routes to the creation of the snaswb in a two parameter space the snaswb are characterized by the maximal lyapunov exponent by the estimation of the phase sensitivity exponent and by the singular continuous spectra we observe that the snas basins are totally wada basins in a large range of parameters the topological structures of the snas wada basins are distinguished by the basin cell method we investigate the underlying mechanism for the abundance of snaswb which is responsible for different types of basin cell in the absence of forcing this suggests that the snas cannot be predicted reliably for specific initial conditions these snaswb can thus be expected to occur more commonly in dynamical systems

delayed feedback based bifurcation control in an internet congestion model in this paper the control of hopf bifurcation in an internet congestion model with a single link accessed by a single source is presented by choosing the gain parameter as a bifurcation parameter it is found that the system without control cannot guarantee a stationary sending rate furthermore hopf bifurcation occurs when the positive gain parameter of the system exceeds a critical value for internet congestion model a control model based on delayed feedback is proposed and analyzed for delaying the onset of undesirable hopf bifurcation numerical simulations are given to justify the validity of delayed feedback controller in bifurcation control

composite media and asymptotic dirichlet forms we introduce a metric topology on the space of dirichlet forms and study compactness and closure properties of families of local and non local forms

learning chaotic attractors by neural networks an algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time series during training the algorithm learns to short term predict the time series at the same time a criterion developed by diks van zwet takens and de goede 1996 is monitored that tests the hypothesis that the reconstructed attractors of model generated and measured data are the same training is stopped when the prediction error is low and the model passes this test two other features of the algorithm are 1 the way the state of the system consisting of delays from the time series has its dimension reduced by weighted principal component analysis data reduction and 2 the user adjustable prediction horizon obtained by error propagation partially propagating prediction errors to the next time step the algorithm is first applied to data from an experimental driven chaotic pendulum of which two of the three state variables are known this is a comprehensive example that shows how well the diks test can distinguish between slightly different attractors second the algorithm is applied to the same problem but now one of the two known state variables is ignored finally we present a model for the laser data from the santa fe time series competition set a it is the first model for these data that is not only useful for short term predictions but also generates time series with similar chaotic characteristics as the measured data

multicavity formations and complexity modulation in a hyperchaotic discrete system abstract this paper introduces a novel and unified approach for controlling the directions and number of cavities of a two dimensional sine icmic modulation map 2d simm two controllers are added to the system for arranging the cavity fluctuations and translating the cavities respectively both the controllers can effectively redesign the dynamics of reproducing cavities in different directions with grid representations the dynamics of the proposed controlled model are investigated with bifurcation lyapunov and fuzzyen algorithms under various cavity formations in different directions a relationship is established for the complexity of the phase space with the directional control and various arrangements of the sinusoidal cavities the proposed model is overall hyperchaotic with the high complexity in the whole parameter plane the proposed scheme is effective for a dynamical model to reproduce the self phase structure in various arrangements for the optimization and modulation of complexity

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

low complexity predictive trellis coded quantization of speech line spectral frequencies low complexity block constrained trellis coded quantization bc tcq structures are studied and a predictive bc tcq encoding method is developed for quantization of line spectrum frequency lsf parameters for speech coding applications the performance is compared with the linear predictive coding lpc vector quantizers used in the amr wb itu g 722 2 and is 641 speech coding standards demonstrating reduction in spectral distortion sd and significant reduction in encoding complexity

some phase transitions in coupled map lattices we study finite coupled map lattices of size d 2 with individual maps 0 1 0 1 and constant diffuse coupling for x 2x mod 1 we give sufficient conditions that the coupled system has a continuum of ergodic components in the case d 2 we determine the number of ergodic components for all coupling strengths if is a mixing tent map close to the transition from mixing to a periodic interval with period 2 the uncoupled system is mixing whereas numerical studies suggest that coupling with a suitable strength breaks up the phase space into domains which are interchanged with period 2 in case d 2 we prove this rigorously

joint source and channel coding using punctured ring convolutional coded cpm in this paper a novel trellis source encoding scheme based on punctured ring convolutional codes is presented joint source and channel coding jscc using trellis coded continuous phase modulation cpm with punctured convolutional codes over rings is investigated the channels considered are the additive white gaussian noise awgn channel and the rayleigh fading channel optimal soft decoding for the proposed jscc scheme is studied the soft decoder is based on the a posteriori probability app algorithm for trellis coded cpm with punctured ring convolutional codes it is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal to noise ratio snr furthermore adaptive jscc approaches based on the proposed source coding scheme are investigated compared with jscc schemes with fixed source coding rates the proposed adaptive approaches can achieve much better performance in the high snr region the novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes the use of a soft decoder the app algorithm for the combined systems and the adaptive approaches to the jscc problem

stability switches bifurcation and multi stability of coupled networks with time delays abstract this paper reveals the dynamical behaviors of a network consisting of a pair of ring sub networks and two way couplings of neurons between the individual sub networks time delays are introduced into the internal connections within the individual sub networks and the couplings between the individual sub networks the stability and instability of the trivial equilibrium of the network are analyzed and the conditions for the existence of hopf bifurcation are obtained by discussing the associated characteristic equation the criterion for the global stability of the trivial equilibrium of the network is given by constructing a suitable lyapunov functional numerical simulations are performed to validate the theoretical results and rich dynamical behaviors are observed such as multiple stability switches of the network equilibrium synchronous asynchronous oscillations and multi stability

on optimal shaping of multidimensional constellations a scheme for the optimal shaping of multidimensional constellations is proposed this scheme is motivated by a type of structured vector quantizer for memoryless sources and results in n sphere shaping of n dimensional cubic lattice based constellations because n sphere shaping is optimal in n dimensions shaping gains higher than those of n dimensional voronoi constellations can be realized while optimal shaping for a large n can realize most of the 1 53 db total shaping gain it has the undesirable effect of increasing the size and the peak to average power ratio of the constituent 2d constellation this limits its usefulness for many real world channels which have nonlinearities the proposed scheme alleviates this problem by achieving optimal constellation shapes for a given limit on the constellation expansion ratio or the peak to average power ratio of the constituent 2d constellation results of calderbank and ozarow 1990 on nonequiprobable signaling are used to reduce the complexity of this scheme and make it independent of the data rate with essentially no effect on the shaping gain comparisons with forney s 1989 trellis shaping scheme are also provided

geometric source coding and vector quantization a geometric formulation is presented for source coding and vector quantizer design motivated by the asymptotic equipartition principle the authors consider two broad classes of source codes and vector quantizers elliptical codes and quantizers based on the gaussian density function and pyramid codes and quantizers based on the laplacian density function elliptical and weighted pyramid vector quantizers are developed by selecting codewords as points in a lattice that lie on or near a specified ellipse or pyramid the combination of geometric structure and lattice basis allows simple encoding and decoding algorithms

image coding using robust quantization for noisy digital transmission a robust quantizer is developed for encoding memoryless sources and transmission over the binary symmetric channel bsc the system combines channel optimized scalar quantization cosq with all pass filtering the latter performed using a binary phase scrambling descrambling method applied to a broad class of sources the robust quantizer achieves the same performance as the gaussian cosq for the memoryless gaussian source this quantizer is used in image coding for transmission over a bsc the peak signal to noise ratio psnr performance degrades gracefully as the channel bit error rate increases

chaotic attractors in the four dimensional leslie gower competition model abstract we study the occurrence of the chaotic attractor in the four dimensional classical leslie gower competition model we find that chaos can be generated by a cascade of quasiperiod doubling bifurcations starting from a supercritical neimark sacker bifurcation of the positive fixed point in this model the chaotic attractor is contained in the three dimensional carrying simplex that is a globally attracting invariant manifold biologically the result implies that the invasion attempts by an invader into a trimorphic population under the leslie gower dynamics can lead to chaos

lattice vector quantization of generalized gaussian sources many important sources of data including sub band image and speech coefficients are highly peaked and can be well modeled by the family of generalized gaussian gg pdfs parameterized by a shape parameter spl nu we present here algorithms for defining and quantizing to a z lattice in which the boundary is optimized to the characteristics of gg sources and show that these techniques lead to high performance and low complexity for bit rates and dimensions that are of interest in a number of practical coding applications we derive an analytical description of the granular and overload distortion valid for low and moderate bit rates and also provide a description of quantizer performance in the limit of high rate and dimension

the set of forces that ideal trusses or wire webs under tension can support abstract the problem of determining those multiplets of forces or sets of force multiplets acting at a set of points such that there exists a truss structure or wire web that can support these force multiplets with all the elements of the truss or wire web being under tension is considered the two dimensional problem where the points are at the vertices of a convex polygon is essentially solved each multiplet of forces must be such that the net anticlockwise torque around any vertex of the forces summed over any number of consecutive points clockwise past the vertex must be non negative and one can find a truss structure that supports under tension and only supports those force multiplets in a convex polyhedron of force multiplets that is generated by a finite number of force multiplets each satisfying the torque condition progress is also made on the problem where only a subset of the points are at the vertices of a convex polygon and the other points are inside in particular in the case where only one point is inside an explicit procedure is described for constructing a suitable truss if one exists an alternative recipe to that provided by guevara vasquez et al 2011 based on earlier work of camar eddine and seppecher 2003 is given for constructing a truss structure with elements under either compression or tension that supports an arbitrary collection of balanced forces at the vertices of a convex polygon finally some constraints are given on the forces that a three dimension truss or wire web under tension must satisfy

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

stability and hopf bifurcation analysis on a ring of four neurons with delays we consider a four neuron ring with self feedback and delays by analyzing the associated characteristic equation linear stability is investigated and hopf bifurcations are demonstrated as well as the stability and direction of the hopf bifurcation are determined by employing the normal form method and the center manifold reduction numerical simulations are presented to illustrate the results

symmetric trellis coded vector quantization we present here design techniques for trellis coded vector quantizers with symmetric codebooks that facilitate low complexity quantization as well as partitioning into equiprobable sets for trellis coding the quantization performance of this coder on the independently identically distributed i i d laplacian source matches the performance of trellis based scalar vector quantization tb svq but requires less computational complexity

duality between source coding and channel coding and its extension to the side information case we explore the information theoretic duality between source coding with side information at the decoder and channel coding with side information at the encoder we begin with a mathematical characterization of the functional duality between classical source and channel coding formulating the precise conditions under which the optimal encoder for one problem is functionally identical to the optimal decoder for the other problem we then extend this functional duality to the case of coding with side information by invoking this duality we are able to generalize the result of wyner and ziv 1976 relating to no rate loss for source coding with side information from gaussian to more arbitrary distributions we consider several examples corresponding to both discrete and continuous valued cases to illustrate our formulation for the gaussian cases of coding with side information we invoke geometric arguments to provide further insights into their duality our geometric treatment inspires the construction and dual use of practical coset codes for a large class of emerging applications for coding with side information such as distributed sensor networks watermarking and information hiding communication systems

vector quantization by companding a union of z lattices an encoding scheme is presented based on random coding theory in conjunction with companding techniques this combination provides an easy design and a low storage quantizer the groundwork of the study is gaussian sources the motivation is the attractive properties of gaussian and gaussian mixtures gms and their applications in data compression here codebooks are generated by companding a union of randomly translated cubic lattices the compander functions operate scalar wise providing an affordable encoding complexity that is rate independent for such a codebook an optimal search and the indexing of the codevectors are addressed performance close to finite dimensional random coding is achieved while the complexity is not far from scalar coding the structure of the codebook balances between complexity and performance in comparison to some other methods the advantage of the proposed scheme is more distinct for correlated sources

distributions of the two dimensional dct coefficients for images for a two dimensional discrete cosine transform dct image coding system there have been different assumptions concerning the distributions of the transform coefficients this paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a gaussian distribution for the dc coefficient and a laplacian distribution for the other coefficients furthermore from a simulation of the dct coding system it is shown that the assumption that the coefficients are laplacian yields a higher actual output signal to noise ratio and a much better agreement between theory and simulation than the gaussian assumption

a note on the computation of the largest p lces of discrete dynamical systems two efficient and numerically stable methods for the computation of the largest p lyapunov characteristic exponents of an n dimensional discrete dynamical systems are presented the efficiencies of the proposed methods are compared with the efficiencies of other methods through an operation count and illustrated with an example

theoretical performance of entropy encoded dpcm in this paper we derive simple approximate formulas for the performance of entropy encoded dpcm for a gaussian random process and a frequency weighted mean square distortion measure using these results we compare the performance of dpcm to the information theoretic rate distortion bound we study the effect on the performance of dpcm of the spectrum of the input process the frequency weight in the distortion measure and the number of prediction coefficients we also examine briefly the case of achromatic still images using line by line and two dimensional dpcm encoding with intrafield and intraframe information

error resilient pyramid vector quantization for image compression pyramid vector quantization pvq uses the lattice points of a pyramidal shape in multidimensional space as the quantizer codebook it is a fixed rate quantization technique that can be used for the compression of laplacian like sources arising from transform and subband image coding where its performance approaches the optimal entropy coded scalar quantizer without the necessity of variable length codes in this paper we investigate the use of pvq for compressed image transmission over noisy channels where the fixed rate quantization reduces the susceptibility to bit error corruption we propose a new method of deriving the indices of the lattice points of the multidimensional pyramid and describe how these techniques can also improve the channel noise immunity of general symmetric lattice quantizers our new indexing scheme improves channel robustness by up to 3 db over previous indexing methods and can be performed with similar computational cost the final fixed rate coding algorithm surpasses the performance of typical joint photographic experts group jpeg implementations and exhibits much greater error resilience

homogenization of stiff plates and two dimensional high viscosity stokes equations the paper deals with the homogenization of stiff heterogeneous plates assuming that the coefficients are equi bounded in l 1 we prove that the limit of a sequence of plate equations remains a plate equation which involves a strongly local linear operator acting on the second gradients this compactness result is based on a div curl lemma for fourth order equations on the other hand using an intermediate stream function we deduce from the plates case a similar result for high viscosity stokes equations in dimension two so that the nature of the stokes equation is preserved in the homogenization process finally we show that the l 1 boundedness assumption cannot be relaxed indeed in the case of the stokes equation the concentration of one very rigid strip on a line induces the appearance of second gradient terms in the limit problem which violates the compactness result obtained under the l 1 boundedness condition

optimal bounds and microgeometries for elastic two phase composites consider two isotropic linearly elastic materials with elasticity tensors c 1 c 2 and assume c 1 c 2 we prove that the class of effective tensors of composites built from these materials with given volume fractions that are invariant under a given symmetry group is such that each of its elements is bounded above and below by tensors in the same class corresponding to finite rank laminates this implies that for any imposed uniform strain or stress field optimal bounds on the effective strain or stress energy per unit volume are attained by finite rank laminates explicit bounds on the strain energy with no symmetry assumptions are given in dimensions 2 and 3 these bounds are more stringent than the classical voigt reuss bounds finally explicit bounds and microgeometries are given for the effective moduli of composites with cubic symmetry

multidimensional spherical coordinates quantization several investigators have considered polar coordinates quantization of a circularly symmetric source in particular the independent bivariate gaussian source their schemes quantize the polar coordinates independently in an attempt to reduce the mean square error below that of an analogous rectangular coordinates quantizer yet retain an implementation simpler than that of the optimal bivariate quantizer the design of a spherical coordinates quantizer in k dimensions with k 2 k 2 matches published results is considered examples are presented along with comparisons to the rectangular one dimensional and optimal schemes

trellis based scalar vector quantizer for memoryless sources the paper describes a structured vector quantization approach for stationary memoryless sources that combines the scalar vector quantizer svq ideas laroia and farvardin 1993 with trellis coded quantization marcellin and fischer 1990 the resulting quantizer is called the trellis based scalar vector quantizer tb svq the svq structure allows the tb svq to realize a large boundary gain while the underlying trellis code enables it to achieve a significant portion of the total granular gain for large block lengths and powerful possibly complex trellis codes the tb svq can in principle achieve the rate distortion bound as indicated by the results obtained even for reasonable block lengths and relatively simple trellis codes the tb svq outperforms all other fixed rate quantizers at reasonable complexity

routes to chaos in high dimensional dynamical systems a qualitative numerical study this paper examines the most probable route to chaos a high dimensional dynamical systems function space time delay neural networks endowed with a probability measure in a computational setting the most probable route to chaos relative to the measure we impose on the function space as the dimension is increased is observed to be a sequence of neimark sacker bifurcations into chaos the analysis is composed of the study of an example dynamical system followed by a probabilistic study of the ensemble of dynamical systems from which the example was drawn a scenario depicting the decoupling of the stable manifolds of the torus leading up to the onset of chaos in high dimensional dissipative dynamical systems is also presented c 2006 elsevier b v all rights reserved

lattice codebook enumeration for generalized gaussian source the goal of this correspondence is to propose a low complexity enumeration algorithm for lattice vectors based on a geometrical interpretation and valid for different source distributions i e for different l sub p norms in the range 0 p spl les 2 as a particular case we obtain the laplacian enumeration formula of fischer this point of view offers various advantages and particularly it enables one to make the link with the generalized theta series and to reduce the algorithm to the calculation of a few convolutional products in the special cases p 1 and p 2 using a dedicated digital signal processing dsp architecture convolutional products are easy to implement and require few arithmetic operations our algorithm developed for the z sup n lattice can be generalized to other lattices like the d sub n

uniform spherical coordinate quantization of spherically symmetric sources for signal quantization with the minimum mean square error criterion optimum spherical coordinate quantizers have been shown to outperform optimum rectangular coordinate qnantizers for many spherically symmetric sources in this paper spherical coordinate quantizers are designed and analyzed under the added constraint that each scalar quantizer is a uniform equal step size quantizer it is shown that for small block length uniform spherical coordinate quantizers outperform the uniform rectangular coordinate quantizer as well as the uniform qnantizer consisting of a tesselation of the minimum inertia space filling polytope

materials with prescribed constitutive parameters an inverse homogenization problem abstract this paper deals with the construction of materials with arbitrary prescribed positive semi definite constitutive tensors the construction problem can be called an inverse problem of finding a material with given homogenized coefficients the inverse problem is formulated as a topology optimization problem i e finding the interior topology of a base cell such that cost is minimized and the constraints are defined by the prescribed constitutive parameters numerical values of the constitutive parameters of a given material are found using a numerical homogenization method expressed in terms of element mutual energies numerical results show that arbitrary materials including materials with poisson s ratio 1 0 and other extreme materials can be obtained by modelling the base cell as a truss structure furthermore a wide spectrum of materials can be constructed from base cells modelled as continuous discs of varying thickness only the two dimensional case is considered in this paper but formulation and numerical procedures can easily be extended to the three dimensional case

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow