quantization of multiple sources using nonnegative integer bit allocation asymptotically optimal real valued bit allocation among a set of quantizers for a finite collection of sources was derived in 1963 by huang and schultheiss and an algorithm for obtaining an optimal nonnegative integer valued bit allocation was given by fox in 1966 we prove that for a given bit budget the set of optimal nonnegative integer valued bit allocations is equal to the set of nonnegative integer valued bit allocation vectors which minimize the euclidean distance to the optimal real valued bit allocation vector of huang and schultheiss we also give an algorithm for finding optimal nonnegative integer valued bit allocations the algorithm has lower computational complexity than fox s algorithm as the bit budget grows finally we compare the performance of the huang schultheiss solution to that of an optimal integer valued bit allocation specifically we derive upper and lower bounds on the deviation of the mean squared error mse using optimal integer valued bit allocation from the mse using optimal real valued bit allocation it is shown that for asymptotically large transmission rates optimal integer valued bit allocations do not necessarily achieve the same performance as that predicted by huang schultheiss for optimal real valued bit allocations

a bit allocation method for sparse source coding in this paper we develop an efficient bit allocation strategy for subband based image coding systems more specifically our objective is to design a new optimization algorithm based on a rate distortion optimality criterion to this end we consider the uniform scalar quantization of a class of mixed distributed sources following a bernoulli generalized gaussian distribution this model appears to be particularly well adapted for image data which have a sparse representation in a wavelet basis in this paper we propose new approximations of the entropy and the distortion functions using piecewise affine and exponential forms respectively because of these approximations bit allocation is reformulated as a convex optimization problem solving the resulting problem allows us to derive the optimal quantization step for each subband experimental results show the benefits that can be drawn from the proposed bit allocation method in a typical transform based coding application

analysis and further results on adaptive entropy coded quantization buffer underflow and overflow problems associated with entropy coding are completely eliminated by effectively imposing reflecting walls at the buffer endpoints synchronous operation of the aecq adaptive entropy coded quantizer encoder and decoder is examined in detail and it is shown that synchronous operation is easily achieved without side information a method is developed to explicitly solve for the buffer state probability distribution and the resulting average distortion when memoryless buffer state feedback is used as well as when the source is stationary and memoryless this method is then used as a tool in the design of low distortion aecq systems with particular attention given to developing source scale invariant distortion performance it is shown that the introduction of reflecting buffer walls in a properly designed aecq system results in a very small rate distortion performance penalty and that the resulting aecq system can be an extremely simple and effective solution to the stationary memoryless source coding problem for a wide range of source types operation with nonstationary sources is also examined

invertible temporal subband wavelet filter banks with half pixel accurate motion compensation three dimensional 3 d subband wavelet coding with motion compensation has been demonstrated to be an efficient technique for video coding applications in some recent research works when motion compensation is performed with half pixel accuracy images need to be interpolated in both temporal subband analysis and synthesis stages the resulting subband filter banks developed in these former algorithms were not invertible due to image interpolation in this paper an invertible temporal analysis synthesis system with half pixel accurate motion compensation is presented we look at temporal decomposition of image sequences as a kind of down conversion of the sampling lattices the earlier motion compensated mc interlaced progressive scan conversion scheme is extended for temporal subband analysis synthesis the proposed subband wavelet filter banks allow perfect reconstruction of the decomposed video signal while retaining high energy compaction of subband transforms the invertible filter banks are then utilized in our 3 d subband video coder this video coding system does not contain the temporal dpcm loop employed in the conventional hybrid coder and the earlier mc 3 d subband coders the experimental results show a significant psnr improvement by the proposed method the generalization of our algorithm for mc temporal filtering at arbitrary subpixel accuracy is also discussed

the oseen drag on a sphere and the method of induced forces abstract the method of induced forces which was used previously to derive a scheme for the evaluation of the oseen drag exerted on a circular cylinder is applied now to the problem of the oseen drag experienced by a sphere by taking into account the zeroth and first force multipole alone very satisfactory values for the drag coefficient are obtained for reynolds numbers up to order 10 2

a variety of period doubling universality classes in multi parameter analysis of transition to chaos abstract in multi parameter analysis of the onset of chaos non feigenbaum period doubling behavior may occur at some special paths in the parameter space there are two possibilities i the dynamics at the onset of chaos remains essentially one dimensional but the one dimensional map is distorted in such a way that leaves feigenbaum s universality class ii a new mode comes to the threshold of instability and increases the effective dimension of the dynamics we submit a list of one dimensional and two dimensional maps which represent distinct classes of the period doubling universality discuss the properties of the associated types of critical behavior at the border of chaos and demonstrate pictures of the universal parameter space arrangement near the critical points

generalized synchronization a modified system approach the universal mechanism resulting in the generalized synchronization regime arising in the chaotic oscillators with the dissipative coupling has been described the reasons for the generalized synchronization occurrence may be clarified by means of a modified system approach the main results are illustrated by unidirectionally coupled rossler systems rossler and lorenz systems and logistic maps

forcing an entire bifurcation diagram case studies in chemical oscillators abstract we study the finite amplitude periodic forcing of chemical oscillators in particular we examine systems that when autonomous i e for zero forcing amplitude exhibit a single stable oscillation using one of the system parameters as a forcing variable by varying it periodically we show through extensive numerical work how the bifurcation diagram of the autonomous system with respect to this parameter affects the qualitative response of the full forced system as the forcing variable oscillates around its midpoint its instantaneous values may cross points such as hopf bifurcation poiints of the autonomous bifurcation diagram so that the characterization of the system as a simple forced oscillator is no longer valid such a neighboring hopf bifurcation of the unforced system is found to set the scene for the interaction of resonance horns and the loss of tori in the full forced system as the amplitude of the forcing grows our test case presented here is the continuous stirred tank reactor cstr with periodically forced coolant temperature

multiparameter critical situations universality and scaling in two dimensional period doubling maps we review critical situations linked with period doubling transition to chaos which require using at least two dimensional maps as models representing the universality classes each of them corresponds to a saddle solution of the two dimensional generalization of feigenbaum cvitanovic equation and is characterized by a set of distinct universal constants analogous to feigenbaum s and one type of criticality designated h was discovered by several authors in 80 th in the context of period doubling in conservative dynamics but occurs as well in dissipative dynamics as a phenomenon of codimension 2 second is bicritical behavior which takes place in systems allowing decomposition onto two dissipative period doubling subsystems each of which is brought by parameter tuning onto a threshold of chaos types of criticality designated as fq and c occur in non invertible two dimensional maps we present and discuss a number of realistic systems manifesting those types of critical behavior and point out some relevant conditions of their potential observation in physical systems in particular we indicate a possibility for realization of the h type criticality without vanishing dissipation but with its compensation in a self oscillatory system next we present a number of examples coupled henon like maps coupled driven oscillators coupled chaotic self oscillators which manifest bicritical behavior for fq type we indicate possibility to arrange it in non symmetric systems of coupled period doubling subsystems e g in henon like maps and in chua s circuits for c type we present examples of its appearance in a driven rossler oscillator at the period doubling accumulation on the edge of syncronization tongue and in a model map with the neimark sacker bifurcation

a geometrical method for the approximation of invariant tori we consider a numerical method based on the so called orthogonality condition for the approximation and continuation of invariant tori under flows the basic method was originally introduced by moore computation and parameterization of invariant curves and tori siam j numer anal 15 1991 245 263 but that work contained no stability or consistency results we show that the method is unconditionally stable and consistent in the special case of a periodic orbit however we also show that the method is unstable for two dimensional tori in three dimensional space when the discretization includes even numbers of points in both angular coordinates and we point out potential difficulties when approximating invariant tori possessing additional invariant sub manifolds e g periodic orbits we propose some remedies to these difficulties and give numerical results to highlight that the end method performs well for invariant tori of practical interest

distortion policy of buffer constrained rate control for real time vbr coders with a rate policy we can achieve buffer constrained rate control for variable bit rate coder since the rate policy emphasizes the stability of the state of the buffer we can loose the advantage of variable bit rate coders i e a nearly constant quality distortion to overcome the difficulty the distortion policy is considered in this paper based on both the state of the buffer and the distortion we can formulate the distortion policy by choosing a proper weighting factor of the cost function in the distortion policy the state of the buffer can be stable and or the variation of the distortion sequence can be kept small in addition the properties of the distortion policy are obtained we also consider switching and adaptive methods for the weighting factor to adjust time varying characteristics of blocks of images using a jpeg like image coder the distortion policy is applied to buffer constrained rate control

bifurcation structure of the c type period doubling transition abstract the period doubling transition to chaos along the edge of an arnold tongue is known to display unusual organization and scaling behavior kuznetsov et al 2005 7 it is also known that forced period doubling systems may be associated with the appearance of so called period doubled tori arneodo et al 1983 15 using the rossler system as an example we present a detailed analysis of the bifurcation structure associated with the forcing of a three dimensional period doubling system we explain how this structure is related to the recently discovered phenomenon of multi layered tori and discuss different bifurcation scenarios that transform a resonance torus into a period doubled ergodic torus similar bifurcation phenomena have recently been observed in a biologically relevant model of kidney blood flow regulation in response to fluctuations in arterial pressure

weakly convergent expansions of a plane wave and their use in fourier integrals the fourier transform of an irreducible spherical tensor is normally computed with the help of the rayleigh expansion of a plane wave in terms of spherical bessel functions and spherical harmonics the angular integrations are then trivial however the remaining radial integral containing a spherical bessel function may be so complicated that the applicability of fourier transformation is severely restricted as an alternative the use of weakly convergent expansions of a plane wave in terms of complete orthonormal sets of functions is suggested the weakly convergent expansions of a plane wave are constructed in such a way that their application in fourier integrals leads to expansions of the fourier or inverse fourier transform that converge with respect to the norm of either the hilbert space l2 r3 or the sobolev space w 1 2 r3 accordingly these weakly convergent expansions may be viewed as distributions that are defined on either l2 r3 or w 1 2 r3 the properties of some complete orthonormal se

complexity in biological systems and hamiltonian dynamics it is well known that in biology and the life sciences in general there are numerous instances of complex behaviour arising from apparently deterministic processes one is familiar with the fractal nature of the shapes of leaves and snowflakes such shapes may be described as the outcome of simple deterministic evolutionary dynamics in another area the stochastic or chaotic response of stimulated cardiac nerve cells is well known and can be modelled by nonlinear deterministic systems of ordinary differential or difference equations in most examples describing complex behaviour in biological systems the underlying models are either ordinary differential or difference equations leading to an analysis of temporal behaviour and its dependence on certain parameter values such as growth rates generation times or reaction constants in this paper we explore both the temporal and spatial nature of complex phenomena in biological systems the examples involve partial dif ferential or partial difference equations and are drawn from models of population genetics mollusc shell patterning and excitable systems in each situation we demonstrate aspects of complexity and show that non integrable hamiltonian dynamical systems play a crucial role this brings into the realms of biology such concepts as structural stability and kolmogorov arnold moser kam theory which lie at the heart of current developments in the theory of dynamical systems

subband coding systems incorporating quantizer models a new method for dealing with the effects of quantization in a subband system is proposed it uses the gain plus additive noise linear model for the lloyd max quantizer based on this it is demonstrated how by an appropriate choice of synthesis filters one can cancel all signal dependent errors at the output of the system the only remaining error is random in nature and not correlated with the input signal we therefore have a tradeoff between the error being only random or having signal dependent components as well since the error variances in both cases are comparable as a result of having only a random error it is possible to reduce this error using for example a noise removal technique the result is then extended to the case where the input is a multidimensional signal and arbitrary sampling lattices are used as well as to the qmf alias cancellation case to demonstrate the validity of the proposed approach two types of experiments on images are carried out in a toy example it is shown that using noise removal could be beneficial for a more realistic coding scheme however it is demonstrated that even in the case when the model is no longer valid when some of the subbands are discarded the output error is still much less correlated with the input signal as opposed to the commonly used subband system while visually the reconstructed images look very similar

a stable feedback control of the buffer state using the controlled lagrange multiplier method we propose a stable feedback control algorithm of the buffer state using the controlled lagrange multiplier in combined rate distortion characteristics for a buffer constrained adaptive quantization the proposed algorithm is established using feedback control theory and is described by the state equation with nonlinearity in the feedback path the nonlinearity of the state equation comes from the average distortion rate curve of the information source the stability of this buffer control algorithm is shown using lyapunov stability theory it is shown that the stability of the algorithm depends on average distortion rate curve and buffer size and sufficient conditions for the algorithm to be stable are obtained from the usual average distortion rate curve in addition it is observed from experimental results that the performance of the proposed algorithm and the optimal algorithm is not significantly different although the proposed algorithm does not provide optimal performance the algorithm can be implemented easily with quite low computational complexity as compared with others

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

an embedded still image coder with rate distortion optimization it is well known that the fixed rate coder achieves optimality when all coefficients are coded with the same rate distortion r d slope in this paper we show that the performance of the embedded coder can be optimized in a rate distortion sense by coding the coefficients with decreasing r d slope we denote such a coding strategy as rate distortion optimized embedding rde rde allocates the available coding bits first to the coefficient with the steepest r d slope i e the largest distortion decrease per coding bit the resultant coding bitstream can be truncated at any point and still maintain an optimal r d performance to avoid the overhead of coding order transmission we use the expected r d slope which can be calculated from the coded bits and is available in both the encoder and the decoder with the probability estimation table of the qm coder the calculation of the r d slope can be just a lookup table operation experimental results show that the rate distortion optimization significantly improves the coding efficiency in a wide bit rate range

computation of invariant tori by the method of characteristics in this paper we present a technique for the numerical approximation of a branch of invariant tori of finite dimensional ordinary differential equations systems our approach is a discrete version of the graph transform technique used in analytical work by fenichel indiana univ math j 21 1971 pp 193 226 in contrast to our previous work l dieci j lorenz and r d russell siam j sci statist comput 12 1991 pp 607 647 the method presented here does not require a priori knowledge of a suitable coordinate system for the branch of invariant tori but determines and updates such a coordinate system during a continuation process we give general convergence results for the method and present its algorithmic description we also show how the method performs on two physically important nonlinear problems a system of two coupled oscillators and the forced van der pol oscillator in the latter case we discuss some modifications needed to approximate an invariant curve for the poincare map

an optimal quadtree based motion estimation and motion compensated interpolation scheme for video compression we propose an optimal quadtree qt based motion estimator for video compression it is optimal in the sense that for a given bit budget for encoding the displacement vector field dvf and the qt segmentation the scheme finds a dvf and a qt segmentation which minimizes the energy of the resulting displaced frame difference dfd we find the optimal qt decomposition and the optimal dvf jointly using the lagrangian multiplier method and a multilevel dynamic program we introduce a new very fast convex search for the optimal lagrangian multiplier spl lambda which results in a very fast convergence of the lagrangian multiplier method the resulting dvf is spatially inhomogeneous since large blocks are used in areas with simple motion and small blocks in areas with complex motion we also propose a novel motion compensated interpolation scheme which uses the same mathematical tools developed for the qt based motion estimator one of the advantages of this scheme is the globally optimal control of the tradeoff between the interpolation error energy and the dvf smoothness another advantage is that no interpolation of the dvf is required since we directly estimate the dvf and the qt segmentation for the frame which needs to be interpolated we present results with the proposed qt based motion estimator which show that for the same dfd energy the proposed estimator uses about 25 fewer bits than the commonly used block matching algorithm we also experimentally compare the interpolated frames using the proposed motion compensated interpolation scheme with the reconstructed original frames

o k floquet multipliers in the determination of the asymptotic stability and bifurcation behaviour of periodic orbits it is necessary to accurately compute the floquet multipliers having modulus nearly 1 and to determine the number of multipliers that lie well inside and well outside the unit circle current numerical methods for computing floquet multipliers suffer a loss of accuracy in two cases of importance namely when the multiplier at 1 is nearly defective and when there are large multipliers an alternative approach is proposed which can be derived from a reexamination of the underlying algebraic eigenvalue problem and which is suitable for systems of ordinary differential equations numerical results indicate that avoiding the explicit construction of a matrix commonly called the circuit matrix and using known properties of a fixed floquet multiplier at 1 will circumvent the difficulties mentioned above convergence results are given

lossless image compression by quantization feedback in a content driven enhanced laplacian pyramid in this paper the effects of quantization noise feedback on the entropy of laplacian pyramids are investigated this technique makes it possible for the maximum absolute reconstruction error to be easily and strongly upper bounded near lossless coding and therefore allows reversible compression the entropy minimizing optimum quantizer is obtained by modeling the first order distributions of the differential signals as laplacian densities and by deriving a model for the equivalent memoryless entropy a novel approach based on an enhanced laplacian pyramid is proposed for the compression either lossless or lossy of gray scale images major details are prioritized through a content driven decision rule embedded in a uniform threshold quantizer with noise feedback lossless coding shows improvements over reversible joint photographers expert group jpeg and the reduced difference pyramid schemes while lossy coding outperforms jpeg with a significant peak signal to noise ratio psnr gain also subjective quality is higher even at very low bit rates due to the absence of the annoying impairments typical of jpeg moreover image versions having resolution and snr that are both progressively increasing are made available at the receiving end from the earliest retrieval stage on as intermediate steps of the decoding procedure without any additional cost

two types of phase synchronization destruction in this paper we report that there are two different types of destruction of the phase synchronization ps regime of chaotic oscillators depending on the parameter mismatch as well as in the case of the classical synchronization of periodic oscillators when the parameter mismatch of the interacting chaotic oscillators is small enough the ps breaking takes place without the destruction of the phase coherence of chaotic attractors of oscillators alternatively due to the large frequency detuning the ps breaking is accomplished by loss of the phase coherence of the chaotic attractors

detecting synchronization of self sustained oscillators by external driving with varying frequency we propose a method for detecting the presence of a synchronization of a self sustained oscillator by external driving with linearly varying frequency the method is based on a continuous wavelet transform of the signals of the self sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals we apply the method to a driven van der pol oscillator and to experimental data of human heart rate variability and respiration

framing pyramids burt and adelson 1983 introduced the laplacian pyramid lp as a multiresolution representation for images we study the lp using the frame theory and this reveals that the usual reconstruction is suboptimal we show that the lp with orthogonal filters is a tight frame and thus the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric with the forward transform in more general cases we propose an efficient filterbank fb for the reconstruction of the lp using projection that leads to a proved improvement over the usual method in the presence of noise setting up the lp as an oversampled fb we offer a complete parameterization of all synthesis fbs that provide perfect reconstruction for the lp finally we consider the situation where the lp scheme is iterated and derive the continuous domain frames associated with the lp

entropy based distortion measure and bit allocation for wavelet image compression quality criteria for image coding are often based on mean square error however this is not always a relevant measure of visual quality at low bit rates here we investigate the properties of a distortion measure based on the conditional differential entropy of the input signal given its quantized value the proposed measure appears to be a correct representation of the amount of information lost by quantization an adaptive bit allocation algorithm is proposed in order to take advantage of this criterion experimental results illustrate the behavior of the proposed distortion measure and exhibit interesting visual properties for low bit rate subband image coding

the analytic structure of oseen flow past a sphere as a function of reynolds number the feasibility of van dyke s 28 proposal that one go from zero to infinite reynolds number r by computer extension of a stokes series in powers of r depends on the analytic structure of the flow as a function of r this structure is investigated in detail for oseen flow past a sphere we find that there is a doubly infinite array of simple pole singularities in the left half complex r plane each of which lies close to one of the n zeros of the modified bessel functions k n 1 2 r for some positive integer n consequently r infty is an accumulation point of poles and hence a nonisolated singularity we have extended the stokes series for the drag coefficient c d r to 66 terms in double precision and have sought the asymptotic behavior of c d r as r to infty neither pade approximants nor an euler transformation formed from our long series give good convergence we suggest that the asymptotic behavior of c d r is primarily as an expansion in powers of r 2 3 though

smooth schur factorizations in the continuation of separatrices numerical computation of separatrices as general connecting orbits in dynamical systems is performed and their continuation as problem parameters vary is approached via a direct application of smooth block schur factorizations of jacobians and monodromy matrix functions several numerical examples are presented to illustrate the effectiveness of the algorithms used

optimal trellis based buffered compression and fast approximations the authors formalize the description of the buffer constrained adaptive quantization problem for a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer constrained environment they formulate the optimal solution they also develop slightly suboptimal but much faster approximations these solutions are valid for any globally minimum distortion criterion which is additive over the individual elements of the sequence as a first step they define the problem as one of constrained discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming forward dynamic programming using the viterbi algorithm is shown to provide a way of computing the optimal solution then they provide a heuristic algorithm based on lagrangian optimization using an operational rate distortion framework that with computing complexity reduced by an order of magnitude approaches the optimally achievable performance the algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays video encoding for cd roms and buffered jpeg coding environments where processing delay is not a concern but decoding buffer size has to be minimized

synchronization stability and duration time we consider the problem of stability and duration of the synchronization process between self excited oscillators both in their regular and chaotic states making use of the properties of hill equation describing the deviation between the slave and the master we derive the stability conditions and expressions of the synchronization time a fairly good agreement is obtained between the analytical and numerical results

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

length distribution of laminar phases for type i intermittency in the presence of noise we consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type i intermittency and random dynamics we analytically deduce the laws for the distribution of the laminar phases with the law for the mean length of the laminar phases versus the critical parameter deduced earlier w h kye and c m kim phys rev e 62 6304 2000 being the corollary fact of the developed theory we find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations we discuss also how this mechanism is expected to take place in other relevant physical circumstances

iterative rate distortion optimization of h 264 with constant bit rate constraint in this paper we apply the primal dual decomposition and subgradient projection methods to solve the rate distortion optimization problem with the constant bit rate constraint the primal decomposition method enables spatial or temporal prediction dependency within a group of picture gop to be processed in the master primal problem as a result we can apply the dual decomposition to minimize independently the lagrangian cost of all the mbs using the reference software model of h 264 furthermore the optimal lagrange multiplier is iteratively derived from the solution of the dual problem as an example we derive the optimal bit allocation condition with the consideration of temporal prediction dependency among the pictures experimental results show that the proposed method achieves better performance than the reference software model of h 264 with rate control

an optimal polygonal boundary encoding scheme in the rate distortion sense in this paper we present fast and efficient methods for the lossy encoding of object boundaries that are given as eight connect chain codes we approximate the boundary by a polygon and consider the problem of finding the polygon which leads to the smallest distortion for a given number of bits we also address the dual problem of finding the polygon which leads to the smallest bit rate for a given distortion we consider two different classes of distortion measures the first class is based on the maximum operator and the second class is based on the summation operator for the first class we derive a fast and optimal scheme that is based on a shortest path algorithm for a weighted directed acyclic graph for the second class we propose a solution approach that is based on the lagrange multiplier method which uses the above mentioned shortest path algorithm since the lagrange multiplier method can only find solutions on the convex hull of the operational rate distortion function we also propose a tree pruning based algorithm that can find all the optimal solutions finally we present results of the proposed schemes using objects from the miss america sequence

motion compensated 3 d subband coding of video this paper describes a video coding system based on motion compensated three dimensional 3 d subband wavelet coding mc 3dsbc which can overcome the limits of both 3 d sbc and mc prediction based coding in this new system spatio temporal subbands are generated by mc temporal analysis and a spatial wavelet transform and then encoded by 3 d subband finite state scalar quantization 3dsb fssq the rate allocation from the gop level to each class of subbands is optimized by utilizing the structural property of mc 3dsbc that additive superposition approximately holds for both rate and distortion the proposed video coding system is applied to several test video clips its performance exceeds that of both a known mpeg 1 implementation and a similar subband mc predictive coder while maintaining modest computational complexity and memory size

role of saddle tori in the mutual synchronization of periodic oscillations we show that in the mutual synchronization of periodic oscillators besides an attracting torus there is also a saddle torus that plays an equally important role we demonstrate that the saddle and stable tori form an elegant structure allowing for a variety of phenomena both known and new related to the origin and evolution of coexisting synchronous regimes phase multistability

image coding using adaptive recursive interpolative dpcm a predictive image coder having minimal decoder complexity is presented the image coder utilizes recursive interpolative dpcm in conjunction with adaptive classification entropy constrained trellis coded quantization and optimal rate allocation to obtain signal to noise ratios snrs in the range of those provided by the most advanced transform coders

finding nondegenerate hopf bifurcation points for four dimensional two parametric systems we establish a numerically feasible algorithm to find a simplicial approximation a to a certain part h41 of the boundary of the set h4 r4 of stable or hurwitz polynomials of degree 4 moreover we have that a hn using this we build an algorithm to find a piecewise linear approximation to the intersection curve of a given surface contained in r4 with h41 we have also devised an efficient computer program to perform all these operations the main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2 parametric hopf bifurcation problem of dimension 4

on the oseen drag on a sphere the method of induced forces is employed to evaluate the oseen drag on a sphere the accuracy of the values obtained for the drag coefficient for large reynolds numbers is increased by application of shanks s transformation on the basis of the improved values we obtain as numerical approximations for the exponent of the first term in the asymptotic expansion values approaching 0 660 for reynolds numbers between 10 2 and 10 6

adaptive data distribution for concurrent continuation continuation methods compute paths of solutions of nonlinear equations that depend on a parameter this paper examines some aspects of the multicomputer implementation of such methods the computations are done on a mesh connected multicomputer with 64 nodes one of the main issues in the development of concurrent programs is load balancing achieved here by using appropriate data distributions in the continuation process many linear systems have to be solved for nearby points along the solution path the corresponding system matrices are closely related to each other therefore pivots which are good for thelu decomposition of one matrix are likely to be acceptable for a whole segment of the solution path this suggests to choose certain data distributions that achieve good load balancing in addition if these distributions are used the resulting code is easily vectorized to test this technique the invariant manifold of a system of two identical nonlinear oscillators is computed as a function of the coupling between them this invariant manifold is determined by the solution of a system of nonlinear partial differential equations that depends on the coupling parameter a symmetry in the problem reduces this system to one single equation which is discretized by finite differences the solution of the discrete nonlinear system is followed as the coupling parameter is changed

coupling leads to chaos abstract the main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two brusselators linearly coupled by diffusion we will show that such a family contains a generic unfolding of a 4 dimensional nilpotent singularity of codimension 4 on the other hand we will prove that in any generic unfolding x of an n dimensional nilpotent singularity of codimension n there are bifurcation curves of n 1 dimensional nilpotent singularities of codimension n 1 which are in turn generically unfolded by x arguments conclude recalling that any generic unfolding of the 3 dimensional nilpotent singularity of codimension 3 exhibits strange attractors

bit allocation for dependent quantization with applications to multiresolution and mpeg video coders we address the problem of efficient bit allocation in a dependent coding environment while optimal bit allocation for independently coded signal blocks has been studied in the literature we extend these techniques to the more general temporally and spatially dependent coding scenarios of particular interest are the topical mpeg video coder and multiresolution coders our approach uses an operational rate distortion r d framework for arbitrary quantizer sets we show how a certain monotonicity property of the dependent r d curves can be exploited in formulating fast ways to obtain optimal and near optimal solutions we illustrate the application of this property in specifying intelligent pruning conditions to eliminate suboptimal operating points for the mpeg allocation problem for which we also point out fast nearly optimal heuristics additionally we formulate an efficient allocation strategy for multiresolution coders using the spatial pyramid coder as an example we then extend this analysis to a spatio temporal 3 d pyramidal coding scheme we tackle the compatibility problem of optimizing full resolution quality while simultaneously catering to subresolution bit rate or quality constraints we show how to obtain fast solutions that provide nearly optimal typically within 0 3 db full resolution quality while providing much better performance for the subresolution layer typically 2 3 db better than the full resolution optimal solution

amplitude response of coupled oscillators abstract we investigate the interaction of a pair of weakly nonlinear oscillators eg each near a hopf bifurcation when the coupling strength is comparable to the attraction of the limit cycles changes in amplitude cannot then be ignored and there are new phenomena we show that even for simple forms of these equations there are parameter regimes in which the interaction causes the system to stop oscillating and the rest state at zero stabilized by the interaction is the only stable solution when the uncoupled oscillators have a local frequency that is independent of amplitude zero shear and the coupling is scalar we give a complete description of the behavior we then analyze more complicated equations to show the effects of amplitude dependent frequency in the uncoupled equations nonzero shear and nonscalar coupling for example when there is shear there can be bistability between a phase locked solution and an unlocked drift solution in which the oscillators go at different average frequencies there can also be bistability between a phase locked solution and an equilibrium nonoscillatory solution the equations for the zero shear case have a pair of degenerate bifurcation points and the new phenomena in the nonzero shear case arise from a partial unfolding of these singularities when the coupling is nonscalar there are a variety of new behaviors including bistability of an in phase and an anti phase solution for two identical oscillators parameters for which only the anti phase solution is stable and phase trapping i e nonlocked solutions in which the oscillators still have the same average frequency it is shown that whether the coupling is diffusive or direct has many effects on the behavior of the system

an analytical and numerical study of the bifurcations in a system of linearly coupled oscillators abstract we study a two parameter family of ordinary differential equations in r 4 that governs the dynamics of two coupled planar oscillators each oscillator has a unique periodic solution that is attracting and the uncoupled product system has a unique invariant torus that is attracting the torus persists for weak coupling and contains two periodic solutions when the coupling is linear and conservative one of these in which the oscillators are synchronized persists and is stable for all coupling strengths the other in which the oscillators are radiant out of phase disappears either in a hopf bifurcation or when fixed points appear on the orbit at a critical ratio of the coupling strength to the frequency the out of phase oscillation is unstable except on an open set in the frequency coupling strength plane which contains moderate values of both parameters furthermore there are tori bifurcating from the out of phase solution which means according to the arnol d theory for hopf bifurcations in maps that there may be periodic solutions of arbitrarily large period and chaotic solutions as well numerous other bifurcations occur and there are a number of higher codimension singularities in a large region of the frequency coupling parameter plane stable steady states coexist with stable periodic solutions

bifurcation analysis of a periodically forced relaxation oscillator differential model versus phase resetting map we compare the dynamics of the periodically forced fitzhugh nagumo oscillator in its relaxation regime to that of a one dimensional discrete map of the circle derived from the phase resetting response of this oscillator the phase resetting map the forcing is a periodic train of gaussian shaped pulses with the width of the pulses much shorter than the intrinsic period of the oscillator using numerical continuation techniques we compute bifurcation diagrams for the periodic solutions of the full differential equations with the stimulation period being the bifurcation parameter the period 1 solutions which belong either to isolated loops or to an everywhere unstable branch in the bifurcation diagram at sufficiently small stimulation amplitudes merge together to form a single branch at larger stimulation amplitudes as a consequence of the fast slow nature of the oscillator this merging occurs at virtually the same stimulation amplitude for all the period 1 loops again using continuation we show that this stimulation amplitude corresponds in the circle map to a change of topological degree from one to zero we explain the origin of this coincidence and also discuss the translational symmetry properties of the bifurcation diagram

synchronization of spectral components and its regularities in chaotic dynamical systems the chaotic synchronization regime in coupled dynamical systems is considered it has been shown that theonset of a synchronous regime is based on the appearance of a phase relation between the interacting chaoticoscillator frequency components of fourier spectra the criterion of synchronization of spectral components aswell as the measure of synchronization has been discussed the universal power law has been described themain results are illustrated by coupled rossler systems van der pol and van der pol duf ng oscillators doi 10 1103 physreve 71 056204 pacs numberssd 05 45 xt 05 45 tpi introduction

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

on overflow and underflow problems in buffer instrumented variable length coding of fixed rate memoryless sources corresp it is well known that variable length coding schemes can be employed in entropy encoding of finite alphabet sources to transmit these codes over a synchronous channel however requires a buffer since in practice this buffer is of finite size it is subject to both overflow and undertow the buffer behavior is studied with particular application to huffman coding of the outputs of an optimum uniform threshold quantizer driven by a memoryless gaussian source fairly general upper and lower bounds on the average terminal time are developed under certain conditions the tightness of these bounds is verified and asymptotic formulas are developed as an example an encoding scheme employing huffman codes in conjunction with uniform quantization of memoryless gaussian sources is considered and the buffer behavior as a function of the buffer size and output rate is studied

motion vector optimization of control grid interpolation and overlapped block motion compensation using iterated dynamic programming the application of advanced motion compensation techniques control grid interpolation cgi and overlapped block motion compensation obmc to video coding systems provides significant performance advantages terms of compression ratio and visual quality over traditional block matching motion compensation however the two dimensional 2 d interdependence among motion vectors introduced by these compensation frameworks makes the problem of finding rate distortion optimal motion vectors computationally prohibitive thus iterative optimization techniques are often used to achieve good compensation performance while most reported optimization algorithms adopt an approach that uses a block matching algorithm to obtain an initial estimate and then successively optimize each motion vector the over relaxed motion vector dependency relations often result in considerable performance degradation in view of this problem we present a new optimization scheme for dependent motion vector optimization problems one based on dynamic programming our approach efficiently decomposes 2 d dependency problems into a series of one dimensional 1 d dependency problems we show that a reliable initial estimate of motion vectors can be obtained efficiently by only considering the dependency in the rate term we also show that at the iterative optimization stage an effective logarithmic search strategy can be used with dynamic programming to reduce the necessary complexity involved in distortion computation compared to conventional iterative approaches our experimental results demonstrate that our algorithm provides superior rate and distortion performance while maintaining reasonable complexity

optimal buffered compression and coding mode selection for mpeg 4 shape coding we propose an optimal buffered compression algorithm for shape coding as defined in the forthcoming mpeg 4 international standard the mpeg 4 shape coding scheme consists of two steps first distortion is introduced by down and up scaling then context based arithmetic encoding is applied since arithmetic coding is lossless the down up scaling step is considered as a virtual quantizer we first formulate the buffer constrained adaptive quantization problem for shape coding and then propose an algorithm for the optimal solution under buffer constraints previously the fact that a conversion ratio cr of 1 4 makes a coded image irritating to human observers for qcif size was reported for mpeg 4 shape coding therefore careful consideration for small size images such as qcif should be given to prevent coded images from being unacceptable to this end a low bit rate tuned algorithm is proposed in this paper as well experimental results are given using an mpeg 4 shape codec

generalized analytic functions in axially symmetric oseen flows a class of generalized analytic functions arising from the oseen equations in the axially symmetric case has been identified for this class of functions the generalized cauchy integral formula has been obtained and a series representation for the region exterior to a sphere has been constructed the velocity field of the axially symmetric oseen flow has been represented in terms of two generalized analytic functions and it has been shown that for an exterior oseen flow problem those functions are uniquely determined provided that they both vanish at infinity also the pressure and vorticity have been determined as the real and imaginary parts of the two functions representing the velocity field and the drag exerted on a solid body of revolution in the axially symmetric oseen flow has been expressed in terms of one of the involved generalized analytic functions the problem of the axially symmetric oseen flow past a solid body of revolution has been reduced to an integral equation based on the gener

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

bifurcations from an invariant circle for two parameter families of maps of the plane a computer assisted study we consider a two parameter family of maps of the plane to itself each map has a fixed point in the first quadrant and is a diffeomorphism in a neighborhood of this point for certain parameter values there is a hopf bifurcation to an invariant circle which is smooth for parameter values in a neighborhood of the bifurcation point however computer simulations show that the corresponding invariant set fails to be even topologically a circle for parameter values far from the bifurcation point this paper is an attempt to elucidate some of the mechanisms involved in this loss of smoothness and alteration of topological type

on dependent bit allocation for multiview image coding with depth image based rendering the encoding of both texture and depth maps of multiview images captured by a set of spatially correlated cameras is important for any 3 d visual communication system based on depth image based rendering dibr in this paper we address the problem of efficient bit allocation among texture and depth maps of multiview images more specifically suppose we are given a coding tool to encode texture and depth maps at the encoder and a view synthesis tool to construct intermediate views at the decoder using neighboring encoded texture and depth maps our goal is to determine how to best select captured views for encoding and distribute available bits among texture and depth maps of selected coded views such that the visual distortion of desired constructed views is minimized first in order to obtain at the encoder a low complexity estimate of the visual quality of a large number of desired synthesized views we derive a cubic distortion model based on basic dibr properties whose parameters are obtained using only a small number of viewpoint samples then we demonstrate that the optimal selection of coded views and quantization levels for corresponding texture and depth maps is equivalent to the shortest path in a specially constructed 3 d trellis finally we show that using the assumptions of monotonicity in the predictor s quantization level and distance suboptimal solutions can be efficiently pruned from the feasible space during solution search experiments show that our proposed efficient selection of coded views and quantization levels for corresponding texture and depth maps outperforms an alternative scheme using constant quantization levels for all maps commonly used in video standard implementations by up to 1 5 db moreover the complexity of our scheme can be reduced by at least 80 over the full solution search

on a variational principle for the drag in linear hydrodynamics it has been demonstrated several times that the method of induced forces is a suitable tool to calculate the drag on a submerged body in various linear approximations of the navier stokes equation in this paper we show that this method may be derived from a variational principle the stationary value of the appropriate functional is the drag the derivation of the set of equations for the induced force moments is given explicitly for two hydrodynamically relevant problems namely a sphere moving slowly along the axis of a rotating viscous fluid and a sphere in oseen flow moreover the variational scheme is employed to study the influence of momentum convection on the drag on a sphere for small reynolds and taylor numbers already with a simple approximation for the induced force density the results are in reasonably good agreement with experimental data

optimization of mpeg 2 snr scaleable codecs it is shown how the signal to noise snr scaleable coder can benefit from optimizing quantified discrete cosine transform dct coefficients in a rate distortion context in order to reduce bit rate overheads the technique is based on adjusting the quantized coefficients rather than dropping them since the former gives finer control over rate distortion trade offs the widely used lagrangian optimization technique is then applied to arrive at the optimally adjusted coefficients block we show that such an optimization is very efficient for the second layer but has little effect on the base layer

compression of laplacian pyramids through orthogonal transforms and improved prediction scalable representation of visual signals such as image and video signals has become a subject of active research since early 1980s scalability allows the adaptation of the bit rate and or the resolution of the transmitted data to the network bandwidth and or the rendering capability of the receiving device for many years spatial scalability has been achieved through wavelets but recently the laplacian pyramid lp has become an alternative choice because of reduced aliasing in the lower resolutions in this paper we focus on the coding efficiency of the lp with a view to transmitting it over a communication channel in particular we aim to improve the compression efficiency of the lp detail layers through improved interlayer prediction and orthogonal spatial transforms first we consider an lp in the open loop configuration and propose to improve its rate distortion performance by compressing it to a critically sampled representation we derive four different orthogonal spatial transforms from the upsampling and downsampling filters that can achieve this representation and apply them on the detail layers the application of these transforms to the detail layers renders a fixed number of transform coefficients either zero or redundant thus making their transmission unnecessary then we consider the compression of an lp in the closed loop configuration through similar spatial transforms because of the introduction of quantization in the prediction loop these spatial transforms applied on the detail layers do not produce the same number of zero or redundant transform coefficients as in the open loop case nevertheless the insight obtained from the open loop coding leads us to enhance the interlayer prediction and the subsequent application of the spatial transforms to the new detail layers aims to achieve better energy compaction

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

an operational rate distortion optimal single pass snr scalable video coder we introduce a new methodology for signal to noise ratio snr video scalability based on the partitioning of the dct coefficients the dct coefficients of the displaced frame difference dfd for inter blocks or the intensity for intra blocks are partitioned into a base layer and one or more enhancement layers thus producing an embedded bitstream subsets of this bitstream can be transmitted with increasing video quality as measured by the snr given a bit budget for the base and enhancement layers the partitioning of the dct coefficients is done in a way that is optimal in the operational rate distortion sense the optimization is performed using lagrangian relaxation and dynamic programming dp experimental results are presented and conclusions are drawn

consistent picture quality control strategy for dependent video coding typically a video rate control algorithm minimizes the average distortion denoted as minave at the cost of large temporal quality variation especially for videos with high motion and frequent scene changes to alleviate the negative effect on subjective video quality another criterion that restricts a small amount of quality variation among adjacent frames is preferred for practical applications as pointed out by although some existing proposals can produce consistent quality videos they often fail to fully utilize the available bits to minimize the global total distortion in this paper we would like to achieve the triple goal of consistent quality video minimizing the total distortion and meeting the bit budget strictly all at the same time on the interframe dependent coding structure two approaches are taken to accomplish this goal in the first algorithm a trellis based framework is proposed one of our contributions is to derive an equivalent condition between the distortion minimization problem and the budget minimization problem second our trellis state tree node is defined in terms of distortion which facilitates the consistent quality control third by adjusting one key parameter in our algorithm a solution in between the minave and the constant quality criteria can be obtained the second approach is to combine the lagrange multipliers method together with the consistent quality control the psnr performance is degraded slightly but the computational complexity is significantly reduced simulation results show that both our approaches produce a much smaller psnr variation at a slight average psnr loss as compared to the mpeg jm rate control when they are compared to the other consistent quality proposals only the proposed algorithms can strictly meet the target bit budget requirement no more no less and produce the largest average psnr at a small psnr variation

dynamical behavior in linearly coupled oregonators abstract tyson ann ny acad sci 316 1979 279 conjectured that the stable homogeneous positive steady state may coexist with stable echo wave meaning anti phase wave in linearly coupled oregonators and thus gave a conjecture on the bifurcation diagram of this system in this paper we rigorously prove stability of the in phase wave and existence of the anti phase wave our proof procedure actually gives a general method or line to deal with the analogous problem for instance to prove stability of the in phase wave following our line one may decompose the corresponding variational equations a four dimensional system into two independent planar systems also for instance existence of the anti phase wave can be concluded as existence and uniqueness of limit cycle of the associate oscillator in addition according to parameter regimes of existence of the anti phase wave and the stable homogeneous positive steady state we give their coexistence regime and specify it and in particular give the regime of the coupled coefficient the specified results show that the theoretical results are in good accord with tyson s numerical results

novel routes to chaos through torus breakdown in non invertible maps the paper describes a number of new scenarios for the transition to chaos through the formation and destruction of multilayered tori in non invertible maps by means of detailed numerically calculated phase portraits we first describe how three and five layered tori arise through period doubling and or pitchfork bifurcations of the saddle cycle on an ordinary resonance torus we then describe several different mechanisms for the destruction of five layered tori in a system of two linearly coupled logistic maps one of these scenarios involves the destruction of the two intermediate layers of the five layered torus through the transformation of two unstable node cycles into unstable focus cycles followed by a saddle node bifurcation that destroys the middle layer and a pair of simultaneous homoclinic bifurcations that produce two invariant closed curves with quasiperiodic dynamics along the sides of the chaotic set other scenarios involve different combinations of local and global bifurcations including bifurcations that lead to various forms of homoclinic and heteroclinic tangles we finally demonstrate that essentially the same scenarios can be observed both for a system of nonlinearly coupled logistic maps and for a couple of two dimensional non invertible maps that have previously been used to study the properties of invariant sets

two parameter analysis of the scaling behavior at the onset of chaos tricritical and pseudo tricritical points abstract we discuss the so called tricritical points at the border of the period doubling transition to chaos and examine to what extent the associated universality applies to 2d dissipative maps as a concrete example the ikeda map is studied together with its 1d analog for the approximate 1d map the tricritical points appear as the terminal points of feigenbaum s critical curves in the parameter plane for the 2d map the same type of critical behavior does not occur in a rigorous sense it may be observed as a kind of intermediate asymptotics however when one considers a finite number of period doublings we refer to the associated points in the parameter plane as pseudo tricritical for the ikeda map we present estimates of the number of period doublings after which the departure from the tricritical universality becomes essential

zero lyapunov exponent in the vicinity of the saddle node bifurcation point in the presence of noise we consider a behavior of the zero lyapunov exponent in the vicinity of the bifurcation point that occurs as the result of the interplay between dynamical mechanisms and random dynamics we analytically deduce the laws for the dependence of this lyapunov exponent on the control parameter both above and below the bifurcation point the developed theory is applicable both to the systems with the random force and to the deterministic chaotic oscillators we find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations we also discuss how the revealed regularities are expected to take place in other relevant physical circumstances

rate distortion optimization for h 264 interframe coding a general framework and algorithms rate distortion rd optimization for h 264 interframe coding with complete baseline decoding compatibility is investigated on a frame basis using soft decision quantization sdq rather than the standard hard decision quantization we first establish a general framework in which motion estimation quantization and entropy coding in h 264 for the current frame can be jointly designed to minimize a true rd cost given previously coded reference frames we then propose three rd optimization algorithms a graph based algorithm for near optimal sdq in h 264 baseline encoding given motion estimation and quantization step sizes an algorithm for near optimal residual coding in h 264 baseline encoding given motion estimation and an iterative overall algorithm to optimize h 264 baseline encoding for each individual frame given previously coded reference frames with them embedded in the indicated order the graph based algorithm for near optimal sdq is the core given motion estimation and quantization step sizes it is guaranteed to perform optimal sdq if the weak adjacent block dependency utilized in the context adaptive variable length coding of h 264 is ignored for optimization the proposed algorithms have been implemented based on the reference encoder jm82 of h 264 with complete compatibility to the baseline profile experiments show that for a set of typical video testing sequences the graph based algorithm for near optimal sdq the algorithm for near optimal residual coding and the overall algorithm achieve on average 6 8 and 12 respectively rate reduction at the same psnr ranging from 30 to 38 db when compared with the rd optimization method implemented in the h 264 reference software

analytical approach to the oseen drag on a sphere at infinite reynolds number this paper analytically evaluates the oseen drag coefficient c d of a sphere at infinite reynolds number for this purpose the method of induced forces is used this method enables the obtainment of a series of rationale converging to the desired value for c d the best value for c d on the basis of this series truncated to its first 50 terms has only a three decimal accuracy the use of the shanks transformation in accelerated form on the truncated rational series improves the accuracy to nine decimals yielding c d 1 058250936

robust adaptive buffer instrumented entropy coded quantization of stationary sources an investigation is conducted of the effects of various source statistics and buffer management algorithms for a buffer of fixed size and an algorithm that provides particularly robust rate distortion performance for a wide range of stationary sources is described the performance of this scheme which is referred to as the adaptive entropy coded quantizer aecq is compared to that of conventional adaptive pulse code modulation apcm operating at the same fixed channel transmission rate experimental results indicate that the aecq can provide considerably improved performance and more robust operation than apcm the relative sensitivity of the aecq to scale mismatch is directly related to the rather simple memoryless feedback control strategy employed this might be remedied by alternative choices of the memoryless feedback control function or by introducing memory the former is much easier to implement and or analyze than the latter

a video compression scheme with optimal bit allocation among segmentation motion and residual error we present a theory for the optimal bit allocation among quadtree qt segmentation displacement vector field dvf and displaced frame difference dfd the theory is applicable to variable block size motion compensated video coders vbsmcvc where the variable block sizes are encoded using the qt structure the dvf is encoded by first order differential pulse code modulation dpcm the dfd is encoded by a block based scheme and an additive distortion measure is employed we derive an optimal scanning path for a qt that is based on a hilbert curve we consider the case of a lossless vbsmcvc first for which we develop the optimal bit allocation algorithm using dynamic programming dp we then consider a lossy vbsmcvc for which we use lagrangian relaxation and show how an iterative scheme which employs the dp based solution can be used to find the optimal solution we finally present a vbsmcvc which is based on the proposed theory which employs a dct based dfd encoding scheme we compare the proposed coder with h 263 the results show that it outperforms h 263 significantly in the rate distortion sense as well as in the subjective sense

entropy constrained trellis coded quantization trellis coded quantization is generalized to allow noiseless coding of the trellis branch reproduction symbols an entropy constrained trellis coded quantization ectcq design algorithm is presented based on the generalized lloyd algorithm for trellis code design and the entropy constrained vector quantization design algorithm ectcq systems are designed for memoryless gaussian and laplacian sources and for first and second order gauss markov sources with an 8 state trellis the mean squared error ectcq encoding performance for memoryless sources with smooth densities is within about 0 5 db of the rate distortion function small additional improvements are achieved with larger trellises similar though not quite as good performance is achieved for the gauss markov sources by using the ectcq in a predictive coding structure