moment preserving quantization signal processing the general solution to the moment preserving mp quantizer problem is presented it is shown that the moment preserving quantizer is related to the gauss jacobi mechanical quadrature the output levels of the n level mp quantizer are the n zeros of an nth degree orthogonal polynomial associated with the input probability distribution function and the n 1 thresholds of the mp quantizer are related to the christoffel numbers through the chebyshev markov stieltjes separation theorem the statistical convergence of the mp quantizer is investigated mp quantizer tables are presented for the uniform gaussian and laplacian density functions the moment preserving quantizer is shown to be related to block truncation coding

image compression by variable block truncation coding with optimal threshold a variable block truncation coding btc algorithm is proposed for image compression it is shown that there exists an optimal threshold for the quantization in btc algorithms fixed and variable that minimizes the errors compared to the fixed btc fbtc the variable btc vbtc gives better performance on all the tested images the use of vbtc with optimal threshold leads to a reduction of the error in the reconstructed images by almost 40 of the error in the reconstructed images obtained by fbtc this enhanced performance suggests that the vbtc with optimal threshold is a better alternative to the fixed block truncation coding

btc vq dct hybrid coding of digital images a hybrid btc vq dct block truncation coding vector quantization and discrete cosine transform image coding algorithm is presented the algorithm combines the simple computation and edge preservation properties of btc and the high fidelity and high compression ratio of adaptive dct with the high compression ratio and good subjective performance of vq and can be implemented with significantly lower coding delays than either vq or dct alone the bit map generated by btc is decomposed into a set of vectors which are vector quantized since the space of the btc bit map is much smaller than that of the original 8 b image a lookup table based vq encoder has been designed to fast encode the bit map adaptive dct coding using residual error feedback is implemented to encode the high mean and low mean subimages the overall computational complexity of btc vq dct coding is much less than either dct and vq while the fidelity performance is competitive the algorithm has strong edge preserving ability because of the implementation of btc as a precompress decimation the total compression ratio is about 10 1

locating resonances for axiom a dynamical systems for a class of differentiable dynamical systems called axiom a systems it has been shown by pollicott and the author that correlation functions have fourier transforms which are meromorphic in a strip the poles or resonances are however not easy to locate this note reviews the results which are known and discusses a simple model where the position of resonances can be estimated the effect of noise is also discussed

btc image coding using vector quantization this paper describes source encoding of the outputs of a block truncation coder btc namely the overhead statistical information and the truncated block the statistical overhead and the truncated block exhibit properties which can be effectively used for their quantization as vectors vector quantization of these btc outputs results into reduction of the bit rate of the coder the bit rate reduces up to 1 5 bits pel if vector quantization is used on one of the outputs i e either the overhead information or the truncated block by vector quantizing both the btc outputs the bit rate can he reduced up to 1 0 bits pel without introducing many perceivable errors in the reconstructed output

statistics of finite time lyapunov exponents in a random time dependent potential the sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite time lyapunov exponent lambda obtained from the elements m ij of the stability matrix m for globally chaotic dynamics lambda tends to a unique value the usual lyapunov exponent lambda infinity for almost all trajectories as t is sent to infinity but for finite t it depends on the initial conditions of the trajectory and can be considered as a statistical quantity we compute for a particle moving in a randomly time dependent one dimensional potential how the distribution function p lambda t approaches the limiting distribution p lambda infinity delta lambda lambda infinity our method also applies to the tail of the distribution which determines the growth rates of moments of m ij the results are also applicable to the problem of wave function localization in a disordered one dimensional potential

correlations of periodic area preserving maps abstract a simple analytical decay law for correlation functions of periodic area preserving maps is obtained this law is compared with numerical experiments on the standard map the agreement between experiment and theory is good when islands are absent but poor when islands are present when islands are present the correlations have a long slowly decaying tail

statistics of stretching fields in experimental fluid flows exhibiting chaotic advection stretching fields and their statistical properties are studied experimentally for four distinct two dimensional time periodic confined fluid flows exhibiting chaotic advection a random vortex array for two different reynolds numbers a set of parallel shear layers and a vortex lattice the flows are driven electromagnetically and they are studied by means of precise particle velocimetry we find that for a given flow the probability distributions of log s where s is the local stretching in n cycles can be nearly superimposed for different n when log s is rescaled using the geometrical mean of the stretching distribution the rescaled stretching fields for a given flow at various n are highly correlated spatially when n is large finally the scaled distributions for different flows are similar though there are some differences connected to the degree of spatial symmetry and time reversibility of the flows

asymptotic stability of solitary waves we show that the family of solitary waves 1 solitons of the korteweg de vries equation partial t u u partial x u partial x 3 u 0 is asymptotically stable our methods also apply for the solitary waves of a class of generalized korteweg de vries equations partial t u partial x f u partial x 3 u 0 in particular we study the case wheref u up 1 p 1 p 1 2 3 and 3 0 withf c4 the same asymptotic stability result for kdv is also proved for the casep 2 the modified korteweg de vries equation we also prove asymptotic stability for the family of solitary waves for all but a finite number of values ofp between 3 and 4 the solitary waves are known to undergo a transition from stability to instability as the parameterp increases beyond the critical valuep 4 the solution is decomposed into a modulating solitary wave with time varying speedc t and phase t bound state part and an infinite dimensional perturbation radiating part the perturbation is shown to decay exponentially in time in a local sense relative to a frame moving with the solitary wave asp 4 the local decay or radiation rate decreases due to the presence of aresonance pole associated with the linearized evolution equation for solitary wave perturbations

multilevel block truncation coding using a minimax error criterion for high fidelity compression of digital images an encoding technique called multilevel block truncation coding that preserves the spatial details in digital images while achieving a reasonable compression ratio is described an adaptive quantizer level allocation scheme which minimizes the maximum quantization error in each block and substantially reduces the computational complexity in the allocation of optimal quantization levels is introduced a 3 2 1 compression can be achieved by the multilevel block truncation coding itself the truncated or requantized data are further compressed in a second pass using combined predictive coding entropy coding and vector quantization the second pass compression can be lossless or lossy the total compression ratios are about 4 1 1 for lossless second pass compression and 6 2 1 for lossy second pass compression the subjective results of the coding algorithm are quite satisfactory with no perceived visual degradation

statistical properties of lorentz gas with periodic configuration of scatterers in our previous paper markov partitions for some classes of dispersed billiards were constructed using these partitions we estimate the decay of velocity auto correlation function and prove the central limit theorem of probability theory and donsker s invariance principle for lorentz gas with periodic configuration of scatterers

block truncation coding with entropy coding block truncation coding btc is a simple and fast image compression algorithm which achieves a constant bit rate of 2 0 bits per pixel the method is however suboptimal we propose a modification of btc in which the compression ratio is improved by coding the quantization data and the bit plane by arithmetic coding with an adaptive modelling scheme the results compare favorable with other btc variants the bit rate for test image lena is 1 53 bits per pixel with a mean square error of 16 51

long range correlation properties of area preserving chaotic systems abstract this article shows numerically that the variance of the stretching exponents for two dimensional chaotic area preserving systems grows asymptotically as a linear function of time although an intermediate anomalous power law scaling may occur this implies that the autocorrelation function of the stretching exponents is integrable this result is a generic property of 2 d mixing systems generated by diffeomorphisms the physical significance of the non persistent anomalous behavior in the decay of fluctuations is briefly addressed

a generalized block truncation coding algorithm for image compression block truncation coding is a recently developed approach to image compression whose design is specified by the appropriate moment preserving quantizer in this paper we show how the basic block truncation coding algorithm can be generalized to include a family of moment preserving quantizers with the potential for improved performance we then illustrate by way of example that such improvement is indeed possible from the standpoint of peak signal to noise ratio there is a subclass of this family of moment preserving quantizers for which practical difficulties in implementation exist however we show that frequently we can avoid this subclass and still obtain good performance

stability of incoherence in a population of coupled oscillators we analyze a mean field model of coupled oscillators with randomly distributed frequencies this system is known to exhibit a transition to collective oscillations for small coupling the system is incoherent with all the oscillators running at their natural frequencies but when the coupling exceeds a certain threshold the system spontaneously synchronizes we obtain the first rigorous stability results for this model by linearizing the fokker planck equation about the incoherent state an unexpected result is that the system has pathological stability properties the incoherent state is unstable above threshold butneutrally stable below threshold we also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise

improved block truncation coding using optimized dot diffusion block truncation coding btc has been considered a highly efficient compression technique for decades however its inherent artifacts blocking effect and false contour caused by low bit rate configuration are the key problems to deal with these an improved btc namely dot diffused btc ddbtc is proposed in this paper moreover this method can provide excellent processing efficiency by exploiting the nature parallelism advantage of the dot diffusion and excellent image quality can also be offered through co optimizing the class matrix and diffused matrix of the dot diffusion according to the experimental results the proposed ddbtc is superior to the former error diffused btc in terms of various objective image quality assessment methods as well as processing efficiency in addition the ddbtc also shows a significant image quality improvement comparing with that of the former ordered dither btc

moment preserving pattern matching abstract an accurate template matching algorithm of low computational complexity that facilitates low cost hardware design and vlsi implementation is highly desired by many image processing applications this paper describes a template matching method called moment preserving pattern matching mppm which reduces the computational complexity of template matching significantly and provides several advantages in hardware implementation the methodology is based on the concepts of pairing function and moment preserving quantization the experimental results show that it is computationally fast and accurate in locating the template if noise corruption is not too severe for obtaining a template matching algorithm of high accuracy and robustness against noise and low computational cost mppm is applied to a two stage matching scheme a statistical model for estimating the correlation threshold is also given

image representation using block pattern models and its image processing applications an image representation scheme using a set of block pattern models bpms consisting of three categories constant oriented and irregular is introduced algorithms for model classification model parameter estimation and image reconstruction from model parameters are presented and these provide the necessary vehicles for applying the proposed representation scheme to various image processing tasks the applications of the proposed models in image coding image zooming and image smoothing are described satisfactory coded images have been obtained at bit rates between 0 5 approximately 0 6 b p p bits per pixel with a high rate realization and between 0 3 approximately 0 5 b p p with a low rate realization the high rate realization has a simple structure suitable for real time implementation the methods for image zooming and smoothing are similar where both adapt the processing for each pixel according to the model of its neighborhood by using directional filters in oriented regions edges and lines are rendered sharper in a smoother manner than with conventional linear filtering approaches which leads to significant improvement in perceived image quality

contractivity of transport distances for the kinetic kuramoto equation we present synchronization and contractivity estimates for the kinetic kuramoto model obtained from the kuramoto phase model in the mean field limit for identical kuramoto oscillators we present an admissible class of initial data leading to time asymptotic complete synchronization that is all measure valued solutions converge to the traveling dirac measure concentrated on the initial averaged phase in the case of non identical oscillators we show that the velocity field converges to the average natural frequency proving that the oscillators move asymptotically with the same frequency under suitable assumptions on the initial configuration if two initial radon measures have the same natural frequency density function and strength of coupling we show that the wasserstein p distance between corresponding measure valued solutions is exponentially decreasing in time this contraction principle is more general than previous l 1 contraction properties of the kuramoto phase model

scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors the analysis of dynamical systems in terms of spectra of singularities is extended to higher dimensions and to nonhyperbolic systems prominent roles in our approach are played by the generalized partial dimensions of the invariant measure and by the distribution of effective liapunov exponents for hyperbolic attractors the latter determines the metric entropies and provides one constraint on the partial dimensions for nonhyperbolic attractors there are important modifications we discuss them for the examples of the logistic and henon map we show in particular that the generalized dimensions have singularities with noncontinuous derivative similar to first order phase transitions in statistical mechanics

markov tree model of transport in area preserving maps abstract transport in an area preserving map with a mixture of regular and chaotic regions is described in terms of the flux through invariant cantor sets called cantori a model retaining a discrete set of cantori approaching a boundary circle gives the markov chain description of hanson cary and meiss the inclusion of cantori surrounding island chains and islands about islands etc gives a markov tree model with a slower decay rate the survival probability distribution is shown to decay asymptotically as a power law the decay exponent agrees reasonably well with the computations of karney and of chirikov and shepelyanski

joint compression watermarking scheme using majority parity guidance and halftoning based block truncation coding in this paper a watermarking scheme called majority parity guided error diffused block truncation coding mpg edbtc is proposed to achieve high image quality and embedding capacity edbtc exploits the error diffusion to effectively reduce blocking effect and false contour which inherently exhibit in traditional btc in addition the coding efficiency is significantly improved by replacing high and low means evaluation with extreme values substitution the proposed mpg edbtc embeds a watermark simultaneously during compression by evaluating the parity value in a predefined parity check region pcr as documented in the experimental results the proposed scheme can provide good robustness image quality and processing efficiency finally the proposed mpg edbtc is extended to embed multiple watermarks and achieves excellent image quality robustness and capacity nowadays most multimedia is compressed before it is stored it is more appropriate to embed information such as watermarks during compression the proposed method has been proved to solve effectively the inherent problems in traditional btc and provide excellent performance in watermark embedding