on simple oversampled a d conversion in shift invariant spaces it has been found that the quantization error e for a conventional oversampled analog to digital a d conversion behaves like spl par e spl par sup 2 o spl tau sup 2 with respect to the sampling rate spl tau recently conventional a d conversion has been extended to a d conversion based on shift invariant spaces as consequences of such extension it offers rich choices to build a nonideal a d conversion system of high accuracy and low computational complexity as well as reduces the noise sensitivity and computational complexity in digital to analog d a conversion therefore it is necessary to establish the estimate of quantization error for the extended a d conversion based on shift invariant spaces in this paper we introduce a constructive method to establish an estimate of the quantization error as e sup 2 o spl tau sup 2 for oversampled a d conversion in shift invariant spaces meanwhile we demonstrate that the bit rate required to encode the converted digital signal in such a d conversion scheme only increases as the logarithm of the sampling ratio therefore the quantization error is an exponentially decaying function of the bit rate in order to establish such an estimate we need the nonuniform sampling theorem for shift invariant spaces which as the necessary preparation is studied prior to introducing the constructive method

randomized local search evolutionary algorithms and the minimum spanning tree problem randomized search heuristics among them randomized local search and evolutionary algorithms are applied to problems whose structure is not well understood as well as to problems in combinatorial optimization the analysis of these randomized search heuristics has been started for some well known problems and this approach is followed here for the minimum spanning tree problem after motivating this line of research it is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms

reversibility of general 1d linear cellular automata over the binary field z 2 under null boundary conditions the reversibility of cellular automata ca has long been studied but there are still many problems untouched this paper tackles the reversibility problem of the general case concerning 1d ca under null boundary conditions defined by linear rules over the binary field z 2 although transition matrix has been widely used for some special linear ca lca rules it has severe limitations its complexity depends on the number of cells and determining its reversibility becomes another unsolved tough problem for general rules by constructing deterministic finite automata dfa of the de bruijn graph presentation of ca we conclude the reversibility problem of all 1d linear rules over z 2 under null boundary conditions it turns out that any 1d lca except for some unilateral rules over z 2 under null boundary conditions can be reversible once having a proper number of cells and dfa provides an efficient way to find those numbers moreover the complexity of the dfa solution is independent of the number of cells in addition the relative low complexity of dfa can be further significantly reduced by using only a small part of it

peak value estimation of bandlimited signals from their samples noise enhancement and a local characterization in the neighborhood of an extremum the paper addresses the problem of estimating the peak value of bandlimited signals from their samples with and without oversampling this problem has significant relevance to orthogonal frequency division multiplexing ofdm signal processing and system design in particular an upper bound on the peak value is established given the peak value of the samples and the oversampling rate moreover it is shown that the bounds are sharp for all practical rates by constructing bandlimited signals taking on this bound the proof also provides a local characterization of bandlimited signals in the neighborhood of an extremum a different analysis examines the effect of small errors in the samples it is shown that oversampling can provide robust recovery in the sense that small errors in the samples lead to small errors in the reconstructed signal again an upper bound is derived relating the peak error in the samples and the peak error in the signals furthermore both problems are shown to be coupled and put in a unifying context the bounds are compared and applied to problems concerning ofdm

efficient exhaustive listings of reversible one dimensional cellular automata this paper looks at an algebraic formulation of one dimensional cellular automata using the formulation connections to combinatorial structures and graph theory become clear strong results about uniqueness and isomorphism allows us to outline effective algorithms for the generation of exhaustive lists of reversible one dimensional cellular automata and to count the number of distinct examples that exist these algorithms use the orderly algorithm methods to avoid the pitfalls of brute force searches

face recognition by using characteristic matrix and ring rotation invariant transform abstract in this research the characteristic matrix is employed to generate the various discriminators by employing these newly created discriminators one can identify the different faces the ring rotation invariant transform technique can cope with the face rotation problem and the ring rotation invariant transform technique will also generate the various transform signals by these newly created transformed signals the algorithm can also identify different faces in this research the transformed signals which are generated by the ring rotation invariant transform will be treated as the input signals and these transformed signals will be fed to the characteristic matrix to generate the various discriminators for coping with the image shifting problem one pixel in the sample image is compared with the surrounding pixels of the corresponding pixel in the unknown image the comparison approaching in this research is by the basis of pixel to pixel comparison

inverse rules of eca with rule number 150 the explicit expressions of local transition functions of the inverse cellular automata of elementary cellular automata with rule number 150 and periodic boundary conditions are given the procedure to obtain such local transition functions is based on the algebraic properties of elementary cellular automata

σ automata and chebyshev polynomials a automaton is an additive binary cellular automaton on a graph for product graphs such as a grids and cylinders reversibility and periodicity properties of the corresponding automaton can be expressed in terms of a binary version of chebyshev polynomials we will give a detailed analysis of the divisibility properties of these polynomials and apply our results to the study of automata

on simple oversampled a d conversion in l sup 2 r the accuracy of oversampled analog to digital a d conversion the dependence of accuracy on the sampling interval spl tau and on the bit rate r are characteristics fundamental to a d conversion but not completely understood these characteristics are studied for oversampled a d conversion of band limited signals in l sup 2 r we show that the digital sequence obtained in the process of oversampled a d conversion describes the corresponding analog signal with an error which tends to zero as spl tau sup 2 in energy provided that the quantization threshold crossings of the signal constitute a sequence of stable sampling in the respective space of band limited functions further we show that the sequence of quantized samples can be represented in a manner which requires only a logarithmic increase in the bit rate with the sampling frequency r o log spl tau and hence that the error of oversampled a d conversion actually exhibits an exponential decay in the bit rate as the sampling interval tends to zero

single bit oversampled a d conversion with exponential accuracy in the bit rate a scheme for simple oversampled analog to digital a d conversion using single bit quantization is presented the scheme is based on recording positions of zero crossings of the input signal added to a deterministic dither function this information can be represented in a manner such that the bit rate increases only logarithmically with the oversampling factor r the input band limited signal can be reconstructed from this information locally with o 1 r pointwise error resulting in an exponentially decaying distortion rate characteristic in the course of studying the accuracy of the proposed a d conversion scheme some new results are established about reconstruction of band limited signals from irregular samples using linear combination of functions with fast decay schemes for local interpolation of band limited signals from quantized irregular samples are also proposed

oversampled a d conversion and error rate dependence of nonbandlimited signals with finite rate of innovation we study the problem of a d conversion and error rate dependence of a class of nonbandlimited signals with finite rate of innovation in particular we analyze a continuous periodic stream of diracs characterized by a finite set of time positions and weights previous research has only considered sampling of this type of signals ignoring the presence of quantization necessary for any practical implementation to this end we first define the concept of consistent reconstruction and introduce corresponding oversampling in both time and frequency high accuracy in a consistent reconstruction is achieved by enforcing the reconstructed signal to satisfy three sets of constraints related to low pass filtering quantization and the space of continuous periodic streams of diracs we provide two schemes to reconstruct the signal for the first one we prove that the estimation mean squared error of the time positions is o 1 r sub t sup 2 r sub f sup 3 where r sub t and r sub f are the oversampling ratios in time and frequency respectively for the second scheme it is experimentally observed that at the cost of higher complexity the estimation accuracy lowers to o 1 r sub t sup 2 r sub f sup 5 our experimental results show a clear advantage of consistent over nonconsistent reconstruction regarding the rate we consider a threshold crossing based scheme where as opposed to previous research both oversampling in time and in frequency influence the coding rate we compare the error rate behavior resulting on the one hand from increasing the oversampling in time and or frequency and on the other hand from decreasing the quantization stepsize

entropy of highly correlated quantized data this paper considers the entropy of highly correlated quantized samples two results are shown the first concerns sampling and identically scalar quantizing a stationary continuous time random process over a finite interval it is shown that if the process crosses a quantization threshold with positive probability then the joint entropy of the quantized samples tends to infinity as the sampling rate goes to infinity the second result provides an upper bound to the rate at which the joint entropy tends to infinity in the case of an infinite level uniform threshold scalar quantizer and a stationary gaussian random process specifically an asymptotic formula for the conditional entropy of one quantized sample conditioned on the previous quantized sample is derived at high sampling rates these results indicate a sharp contrast between the large encoding rate in bits sec required by a lossy source code consisting of a fixed scalar quantizer and an ideal sampling rate adapted lossless code and the bounded encoding rate required by an ideal lossy source code operating at the same distortion

invertible behavior in elementary cellular automata with memory elementary cellular automata ecas have been studied for their ability to generate complex global behavior despite their simplicity one variation of ecas is obtained by adding memory to each cell in a neighborhood this process generates a provisional configuration in which the application of an evolution rule establishes the dynamics of the system this version is known as an eca with memory ecam most previous work on ecams analyzed the complex behavior taking chaotic ecas however the present paper investigates reversible ecams as obtained from reversible and permutative ecas these ecas have at least one ancestor for every configuration thus the correct permutation of states may specify the memory function to obtain reversible ecams for permutative ecas which are often irreversible we demonstrate that the use of a quiescent state and the correct manipulation of de bruijn blocks produce reversible ecams

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

welch sets for random generation and representation of reversible one dimensional cellular automata abstract reversible one dimensional cellular automata are studied from the perspective of welch sets this paper presents an algorithm to generate random welch sets that define a reversible cellular automaton then properties of welch sets are used in order to establish two bipartite graphs describing the evolution rule of reversible cellular automata the first graph gives an alternative representation for the dynamics of these systems as block mappings and shifts the second graph offers a compact representation for the evolution rule of reversible cellular automata both graphs and their matrix representations are illustrated by the generation of random reversible cellular automata with 6 and 18 states

high resolution distributed sampling of bandlimited fields with low precision sensors the problem of sampling a discrete time sequence of spatially bandlimited fields with a bounded dynamic range in a distributed communication constrained processing environment is studied a central unit having access to the data gathered by a dense network of low precision sensors is required to reconstruct the field snapshots to maximum accuracy both deterministic and stochastic field models are considered for stochastic fields results are established in the almost sure sense the feasibility of having a flexible tradeoff between the oversampling rate sensor density and the analog to digital converter adc precision while achieving an exponential accuracy in the number of bits per nyquist interval per snapshot is demonstrated this exposes an underlying conservation of bits principle the bit budget per nyquist interval per snapshot the rate can be distributed along the amplitude axis sensor precision and space sensor density in an almost arbitrary discrete valued manner while retaining the same exponential distortion rate characteristics

procedures for calculating reversible one dimensional cellular automata we describe two algorithms for calculating reversible one dimensional cellular automata of neighborhood size 2 we explain how this kind of automaton represents all the other cases using two basic properties of reversible automata such as uniform multiplicity of ancestors and welch indices these algorithms only require matrix products and transitive closures of binary relations to classify all the possible reversible automata of neighborhood size 2 we expose the features advantages and differences with other well known methods finally we present results for reversible automata from three to six states and neighborhood size 2

face recognition using ipca ica algorithm in this paper a fast incremental principal non gaussian directions analysis algorithm called ipca ica is introduced this algorithm computes the principal components of a sequence of image vectors incrementally without estimating the covariance matrix so covariance free and at the same time transforming these principal components to the independent directions that maximize the non gaussianity of the source two major techniques are used sequentially in a real time fashion in order to obtain the most efficient and independent components that describe a whole set of human faces database this procedure is done by merging the runs of two algorithms based on principal component analysis pca and independent component analysis ica running sequentially this algorithm is applied to face recognition problem simulation results on different databases showed high average success rate of this algorithm compared to others

complete characterization of stable bandlimited systems under quantization and thresholding in this paper we analyze the approximation behavior of sampling series where the sample values taken equidistantly at nyquist rate are disturbed either by the nonlinear threshold operator or the nonlinear quantization operator we perform the analysis for several spaces of bandlimited signals and completely characterize the spaces for which an approximation is possible additionally we study the approximation of outputs of stable linear time invariant systems by sampling series with disturbed samples for signals in pw pi 1 we show that there exist stable systems that become unstable under thresholding and quantization and that the approximation error is unbounded irrespective of how small the quantization step size is chosen further we give a necessary and sufficient condition for the pointwise and the uniform convergence of the series surprisingly this condition is the well known condition for bounded input bounded output bibo stability finally we discuss the special case of finite impulse response fir filters and give an upper bound for the approximation error

a closed formula for the inverse of a reversible cellular automaton with 2r 1 cyclic rule abstract reversibility of cellular automata ca has been an extensively studied problem from both a theoretical and a practical point of view it is known when a 2 r 1 cyclic cellular automaton with periodic boundary conditions p b c is reversible see siap et al 2013 but as far as we know no explicit expression is given for its inverse cellular automaton apart from the case r 1 see encinas and del rey 2007 in this paper we give a closed formula for the inverse rule of a reversible 2 r 1 cyclic cellular automaton with p b c over the finite field f 2 for any value of the neighbourhood radius r it turns out that the inverse of a reversible 2 r 1 cyclic ca with p b c is again a cyclic ca with p b c but with a different neighbourhood radius and this radius depends on certain numbers which need to be computed by a new algorithm we introduce finally we apply our results to the case r 1 which is the eca with wolfram rule number 150 to introduce an alternative and improved expression for the inverse transition dipolynomial formulated in encinas and del rey 2007 we also illustrate these results by giving explicit computations for the inverse transition dipolynomial of a reversible cellular automaton with penta cyclic rule

behavior of the quantization operator for bandlimited nonoversampled signals the process of quantization generates a loss of information and thus the original signal cannot be reconstructed exactly from the quantized samples in general however it is desirable to keep the error as small as possible in this paper the quantization error is quantified in terms of several distortion measures all these measures employ the difference between the original signal and the reconstructed signal which is obtained by bandlimited interpolation of the quantized samples we assume that the signals are bandlimited and that the samples are taken at nyquist rate it is shown that for signals in the paley wiener space pw 1 the supremum of the reconstructed signal and hence the quantization error cannot be bounded in the sense that there exists a bounded subset of pw 1 on which both quantities can increase unboundedly this unexpected behavior is due to the nonlinearity of the quantization operator and the slow decay of the sinc function the nonlinearity is essential for this behavior because every linear operator that fulfills a certain property of the quantization operator would otherwise have to be bounded furthermore it is proven that for a fixed signal the possible quantization error increases as the quantization step size tends to zero the treatment of the quantization error in this paper is completely deterministic

efficient quantization for overcomplete expansions in spl ropf sup n we study construction of structured regular quantizers for overcomplete expansions in spl ropf sup n our goal is to design structured quantizers which allow simple reconstruction algorithms with low complexity and which have good performance in terms of accuracy most related work to date in quantized redundant expansions has assumed that the same uniform scalar quantizer was used on all the expansion coefficients several approaches have been proposed to improve the reconstruction accuracy with some of these methods having significant complexity instead we consider the joint design of the overcomplete expansion and the scalar quantizers allowing different step sizes in such a way as to produce an equivalent vector quantizer evq with periodic structure the construction of a periodic quantizer is based on lattices in spl ropf sup n and the concept of geometrically scaled similar sublattices the periodicity makes it possible to achieve good accuracy using simple reconstruction algorithms e g linear reconstruction or a small lookup table

reconstruction of oversampled band limited signals from spl sigma spl delta encoded binary sequences considers the application of spl sigma spl delta modulators to analog to digital conversion the authors have previously shown that for constant input signals optimal nonlinear decoding can achieve large gains in signal to noise ratio snr over linear decoding the present paper shows a similar result for band limited input signals the new nonlinear decoding algorithm is based on projections onto convex sets pocs and alternates between a time domain operation and a band limitation to find a signal invariant under both the time domain operation results in a quadratic programming problem the band limitation can be based on singular value decomposition of a certain matrix the authors show simulation results for the snr performance of a pocs based decoder and a linear decoder for the single loop double loop and two stage spl sigma spl delta modulators and for a specific fourth order interpolative modulator depending on the modulator and the oversampling ratio improvements in snr of up to 10 20 db can be achieved

reduction of the mse in r times oversampled a d conversion o 1 r to o 1 r sup 2 in oversampled analog to digital conversion the usual reconstruction method using lowpass filtering leads to a mean squared error mse inversely proportional to the oversampling ratio r the authors prove under certain assumptions and with periodic analog input signals that optimal reconstruction achieves an mse with an oversampling ratio dependence order of at least o 1 r sup 2 that is an mse slope of spl minus 6 db per octave of oversampling is obtained rather than the conventional spl minus 3 db octave slope of classical schemes