very large scale linear programming a case study in combining interior point and simplex methods experience with solving a 12 753 313 variable linear program is described this problem is the linear programming relaxation of a set partitioning problem arising from an airline crew scheduling application a scheme is described that requires successive solutions of small subproblems yielding a procedure that has little growth in solution time in terms of the number of variables experience using the simplex method as implemented in cplex an interior point method as implemented in obi and a hybrid interior point simplex approach is reported the resulting procedure illustrates the power of an interior point simplex combination for solving very large scale linear programs

on the role of pattern matching in information theory in this paper the role of pattern matching in information theory is motivated and discussed we describe the relationship between a pattern s recurrence time and its probability under the data generating stochastic source we show how this relationship has led to great advances in universal data compression we then describe nonasymptotic uniform bounds on the performance of data compression algorithms in cases where the size of the training data that is available to the encoder is not large enough so as to yield the asymptotic compression the shannon entropy we then discuss applications of pattern matching and universal compression to universal prediction classification and entropy estimation

a general chebyshev complex function approximation procedure and an application to beamforming a new computational technique is described for the chebyshev or minimax approximation of a given complex valued function by means of linear combinations of given complex valued basis functions the domain of definition of all functions can be any finite set whatever neither the basis functions nor the function approximated need satisfy any special hypotheses beyond the requirement that they be defined on a common domain theoretical upper and lower bounds on the accuracy of the computed chebyshev error are derived these bounds permit both a priori and a posteriori error assessments efforts to extend the method to functions whose domain of definition is a continuum are discussed an application is presented involving re shading a 50 element antenna array to minimize the effects of a 10 element failure rate while maintaining full steering capability and mainlobe beamwidth

optimal design of fir filters with the complex chebyshev error criteria we present an improved algorithm for an established filter design problem the design of an fir filter that best approximates in the complex chebyshev sense a desired complex valued frequency response the algorithm is a variant of the simplex algorithm of linear programming which has an interpretation as an implicit multiple exchange it is iterative robust and exhibits good convergence speed global optimum convergence is guaranteed both complex and real valued impulse responses can be designed with it the design of complex coefficient filters is new an example is given for each case the design of noncausal filters is new in addition to these new applications we conjecture that this new algorithm may have important advantages over existing techniques with respect to the maximum filter length possible speed and stability of convergence accuracy and memory requirements the ability to design long filters is among the more significant improvements over previous work filters of length 1000 have been designed with the new method

efficient computation of the dft with only a subset of input or output points ways of efficiently computing the discrete fourier transform dft when the number of input and output data points differ are discussed the two problems of determining whether the length of the input sequence or the length of the output sequence is reduced can be found to be duals of each other and the same methods can to a large extent be used to solve both the algorithms utilize the redundancy in the input or output to reduce the number of operations below those of the fast fourier transform fft algorithms the usual pruning method is discussed and an efficient algorithm called transform decomposition is introduced it is based on a mixture of a standard fft algorithm and the horner polynomial evaluation scheme equivalent to the one in goertzel s algorithms it requires fewer operations and is more flexible than pruning the algorithm works for power of two and prime factor algorithms as well as for real input data

design of fir digital phase networks the problem of the minimax design of fir digital filters with prescribed phase characteristics and unit magnitude is a nonlinear optimization problem in this paper it is approximated by a linear programming problem and it is shown that the solution of this linear program is optimal to first order that is if 0 and e 0 are optimal deviations of magnitude and phase characteristics then the actual deviations obtained from the linear program solution satisfy delta leq delta 0 epsilon min 0 max 2 and epsilon leq epsilon 0 1 delta 0 1 delta 0 numerical examples are given including design results for full band m term chirp filters which like linear phase filters can be implemented with m 1 2 multiplications per point

optimal design of nonlinear phase fir filters with prescribed phase error constrained least squares design and constrained chebyshev design of one and two dimensional nonlinear phase fir filters with prescribed phase error are considered in this paper by a unified semi infinite positive definite quadratic programming approach in order to obtain unique optimal solutions we propose to impose constraints on the complex approximation error and the phase error by introducing a sigmoid phase error constraint bound function the group delay error can be greatly reduced a goldfarb idnani based algorithm is presented to solve the semi infinite positive definite quadratic program resulting from the constrained least squares design problem and then applied after some modifications to the constrained chebyshev design problem which is proved in this paper to be equivalent also to a semi infinite positive definite quadratic program through design examples the proposed method is compared with several existing methods simulation results demonstrate the effectiveness and efficiency of the proposed method

universal multiterminal source coding algorithms with asymptotically zero feedback fixed database case consider a source network in which a finite alphabet source x xi i 0 infin is to be encoded and transmitted and another finite alphabet source y xi i 0 infin correlated with x is available only to the decoder as side information traditionally the channel between the encoder and decoder in the source network is assumed to be one way this together with the fact that the encoder does not have access to y implies that the encoder has to know the achievable rates before encoding in this paper we consider universal source coding for a feedback source network in which the channel between the encoder and decoder is two way and asymmetric assume that the encoder and decoder share a random database that is independent of both x and y a string matching based variable rate block coding algorithm with simple progressive encoding and joint typicality decoding is first proposed for the feedback source network the simple progressive encoder does not need to know the achievable rates at the beginning of encoding it is proven that for any x y in a large class of sources satisfying some mixing conditions the average number of bits per letter transmitted from the encoder to the decoder compression rate goes to the conditional entropy h x y of x given y asymptotically and at the same time the average number of bits per letter transmitted from the decoder to the encoder feedback rate goes to 0 asymptotically the algorithm and the corresponding analysis results are then extended to the case where both x and y are to be encoded separately but decoded jointly finally a universal decoding algorithm is proposed to replace the joint typicality decoding and the resulting universal compression algorithm consisting of the simple progressive encoder and the universal decoding algorithm is further shown to be asymptotically optimal for the class of all jointly memoryless source side information pairs x y

rotationally symmetric biharmonic maps between models abstract the main aim of this paper is to study existence and stability properties of rotationally symmetric proper biharmonic maps between two m dimensional models in the sense of greene and wu we obtain a complete classification of rotationally symmetric proper biharmonic conformal diffeomorphisms in the special case that m 4 and the models have constant sectional curvature then by introducing the hamiltonian associated to this problem we also obtain a complete description of conformal proper biharmonic solutions in the case that the domain model is r 4 in the second part of the paper we carry out a stability study with respect to equivariant variations equivariant stability in particular we prove that i the inverse of the stereographic projection from the open 4 dimensional euclidean ball to the hyperbolic space is equivariant stable ii the inverse of the stereographic projection from the closed 4 dimensional euclidean ball to the sphere is equivariant stable with respect to variations which preserve the boundary data

an on line universal lossy data compression algorithm via continuous codebook refinement ii optimality for phi mixing source models for pt i see ibid vol 42 no 3 p 803 21 1996 two versions of the gold washing data compression algorithm one with codebook innovation interval and the other with finitely many codebook innovations are considered the version of the gold washing algorithm with codebook innovation interval k is a variant of the gold washing algorithm such that the codebook is innovated once every k 1 source words during the process of encoding the entire source it is demonstrated that when this version of the gold washing algorithm is applied to encode a stationary spl phi mixing source the expected distortion performance converges to the distortion rate function of the source as the codebook length goes to infinity furthermore if the source to be encoded is a markov source or a finite state source then the corresponding sample distortion performance converges almost surely to the distortion rate function the version of the gold washing algorithm with finitely many codebook innovations is a variant of the gold washing algorithm in which after finitely many codebook innovations the codebook is held fixed and reused to encode the forthcoming source sequence block by block similar results are shown for this version of the gold washing algorithm in addition the convergence speed of the algorithm is discussed

an on line universal lossy data compression algorithm via continuous codebook refinement iii redundancy analysis for pt ii see ibid vol 42 p 822 36 1996 the gold washing data compression algorithm is an adaptive vector quantization algorithm with vector dimension n in this paper a redundancy problem of the gold washing data compression algorithm is considered it is demonstrated that for any memoryless source with finite alphabet a and generic distribution p and for any r 0 the redundancy of the gold washing data compression algorithm with dimension n defined as the difference between the average performance of the algorithm and the distortion rate function d p r of p is upper bounded by sub spl delta r sup spl delta d p r a 2 spl xi 4 log n 2n spl sigma logn n where sub spl delta r sup spl delta d p r is the partial derivative of d p r with respect to r a is the cardinality of a and spl xi 0 is a parameter used to control the threshold in the gold washing algorithm in connection with the results of zhang yang and wei see ibid vol 43 no 1 p 71 91 1997 on the redundancy of lossy source coding this shows that the gold washing algorithm has the optimal convergence rate among all adaptive finite state vector quantizers

the performance of universal encoding universal coding theory is surveyed from the viewpoint of the interplay between delay and redundancy the price for universality turns out to be acceptably small

proper r harmonic submanifolds into ellipsoids and rotation hypersurfaces abstract the study of r harmonic maps was proposed by eells sampson in 1965 and by eells lemaire in 1983 these maps are a natural generalization of harmonic maps and are defined as the critical points of the r energy functional e r 1 2 m d d r 2 d v m where m n denotes a smooth map between two riemannian manifolds if an r harmonic map m n is an isometric immersion and it is not minimal then we say that m is a proper r harmonic submanifold of n in this paper we prove the existence of several new proper r harmonic submanifolds into ellipsoids and rotation hypersurfaces

on the asymptotic behavior of rotationally symmetrical harmonic maps abstract we study a second order ordinary differential equation which is the euler lagrange equation of the energy functional for maps with prescribed rotational symmetry we obtain liouville s type theorems for symmetric harmonic maps into ellipsoids euclidean and hyperbolic spaces and existence results as well

a fast algorithm for linear complex chebyshev approximations we propose a new algorithm for finding best minimax polynomial approximations in the complex plane the algorithm is the first satisfactory generalization of the well known remez algorithm for real approximations among all available algorithms ours is the only quadratically convergent one numerical examples are presented to illustrate rapid convergence

reduction of symmetric complex filters due to their linear phase property symmetric filters are an interesting class of finite impulse response fir filters moreover symmetric fir filters allow an efficient implementation in this paper we extend the classical definition of hermitian symmetry to a more general symmetry that is also applicable to complex filters this symmetry is called generalized hermitian symmetry we show the usefulness of this definition as it allows for a unified treatment of even and odd length filters central in this paper is a theorem on the reduction of generalized hermitian symmetric filters to hermitian symmetric filters both with finite precision coefficients a constructive proof of this theorem is presented and an associated procedure for reducing generalized hermitian symmetric filters is derived two of the examples show the application of the reduction procedure and the achieved savings on arithmetic costs finally all three examples show that a special instance of the generalized hermitian symmetric filters with finite precision coefficients may have lower arithmetic costs than the hermitian symmetric filter from which it is derived

almost sure optimality of sliding window lempel ziv algorithm and variants revisited the sliding window lempel ziv swlz algorithm has been studied extensively in the information theory literature and has been used in several commercial compression packages the asymptotic behavior of this algorithm has been studied by wyner and ziv and by shields using different approaches shields results proving asymptotic optimality for all individual sequences with respect to the class of all finite state encoders is known to imply the almost sure asymptotic optimality for the class of stationary and ergodic sources we establish the almost sure asymptotic optimality without any mixing conditions by extending the ideas of wyner and ziv using results on recurrence times from ergodic theory a nonuniversal fixed shift version of the algorithm is introduced to gain more insight into its behavior pointwise optimality results are also obtained for several variants based on match length functions introduced by gavish and lempel we also propose variants of the algorithm for sources with countable alphabet and demonstrate their pointwise optimality

a generalized suffix tree and its un expected asymptotic behaviors suffix trees find several applications in computer science and telecommunications most notably in algorithms on strings data compressions and codes despite this very little is known about their typical behaviors in a probabilistic framework a family of suffix trees further called b suffix trees built from the first n suffixes of a random word is considered in this family a noncompact suffix tree i e such that every edge is labeled by a single symbol is represented by b 1 and a compact suffix tree i e without unary nodes is asymptotically equivalent to b to infty as n to infty several parameters of b suffix trees are studied namely the depth of a given suffix the depth of insertion the height and the shortest feasible path some new results concerning typical i e almost sure behaviors of these parameters are established these findings are used to obtain several insights into certain algorithms on words molecular biology and universal data compression schemes

on match lengths zero entropy and large deviations with application to sliding window lempel ziv algorithm the sliding window lempel ziv swlz algorithm that makes use of recurrence times and match lengths has been studied from various perspectives in information theory literature in this paper we undertake a finer study of these quantities under two different scenarios 1 zero entropy sources that are characterized by strong long term memory and 2 the processes with weak memory as described through various mixing conditions for zero entropy sources a general statement on match length is obtained it is used in the proof of almost sure optimality of fixed shift variant of lempel ziv fslz and swlz algorithms given in literature through an example of stationary and ergodic processes generated by an irrational rotation we establish that for a window of size n w a compression ratio given by o log n w n w a where a depends on n w and approaches 1 as n w is obtained under the application of fslz and swlz algorithms in addition we give a general expression for the compression ratio for a class of stationary and ergodic processes with zero entropy next we extend the study of ornstein and weiss on the asymptotic behavior of the normalized version of recurrence times and establish the large deviation property for a class of mixing processes in addition an estimator of entropy based on recurrence times is proposed for which large deviation principle is proved for sources satisfying similar mixing conditions

linear programming algorithms for sparse filter design in designing discrete time filters the length of the impulse response is often used as an indication of computational cost in systems where the complexity is dominated by arithmetic operations the number of nonzero coefficients in the impulse response may be a more appropriate metric to consider instead and computational savings are realized by omitting arithmetic operations associated with zero valued coefficients this metric is particularly relevant to the design of sensor arrays where a set of array weights with many zero valued entries allows for the elimination of physical array elements resulting in a reduction of data acquisition and communication costs however designing a filter with the fewest number of nonzero coefficients subject to a set of frequency domain constraints is a computationally difficult optimization problem this paper describes several approximate polynomial time algorithms that use linear programming to design filters having a small number of nonzero coefficients i e filters that are sparse specifically we present two approaches that have different computational complexities in terms of the number of required linear programs the first technique iteratively thins the impulse response of a non sparse filter until frequency domain constraints are violated the second minimizes the 1 norm of the impulse response of the filter using the resulting design to determine the coefficients that are constrained to zero in a subsequent re optimization stage the algorithms are evaluated within the contexts of array design and acoustic equalization

a method for the optimal pattern synthesis of linear arrays with prescribed nulls a new l sub spl infin optimal method for the synthesis of equispaced linear array functions with asymmetrical far field pattern functions is proposed this iterative method provides for the exact specification of the beam width while at the same time allowing for the specification of the relative levels of individual sidelobes by index or as a function of bearing e g angularly extended nulls as well as the realization of specified narrowband nulls the resulting array factors are optimal in the weighted l sub spl infin sense and in general have complex coefficients this new remez type method employs multiple objective functions to provide the degrees of freedom that are required for exact null placement examples which demonstrate the design flexibility offered by the method are included for various sum and difference patterns including superdirective and shaped beam arrays

design of fir filters in the complex domain the design of fir digital filters with a complex valued desired frequency response using the chebyshev error is investigated the complex approximation problem is converted into a real approximation problem which is nearly equivalent to the complex problem a standard linear programming algorithm for the chebyshev solution of overdetermined equations is used to solve the real approximation problem additional constraints are introduced which allow weighting of the phase and or group delay of the approximation digital filters are designed which have nearly constant group delay in the passbands the desired constant group delay which gives the minimum chebyshev error is found to be smaller than that of a linear phase filter of the same length these filters in addition to having a smaller approximately constant group delay have better magnitude characteristics than exactly linear phase filters with the same length the filters have nearly equiripple magnitude and group delay

on certain pathwise properties of the sliding window lempel ziv algorithm we derive several almost sure results related to the sliding window lempel ziv swlz algorithm a principal result is a path wise lower bound to the redundancy equal to 1 2hlog2log 2nw log2nw in the main term where nw is the sliding window size this bound is off by a factor of two from the main term in the lower bound of a j wyner and the work of yang and kieffer which hold in the expected sense for the fixed database lempel ziv algorithm fdlz another aspect of the present work studies the asymptotic behavior of the ratio of the number of phrases to the length of the parsed string for any finite sliding window size in here we exploit the theory of asymptotic mean stationary processes of gray and kieffer and some results of kieffer and rahe in all cases it is assumed that the source is stationary and that in the most restrictive case it is an irreducible and aperiodic markov chain some of the results hold for sources that have exponential rates for entropy and more generally for the ergodic setting

chebyshev optimization of sparse fir filters using linear programming with an application to beamforming sparse fir filter design where some tap weights are zero is of interest as a means of reducing the expense or enhancing the performance of a filter as a result of fewer or more efficiently placed multipliers we show that for certain classes of filters with moderately wide passbands it is possible to increase the stopband suppression by up to 20 db without increasing the number of multipliers simply by increasing the number of delay elements zeroing the appropriate taps and optimizing the other taps using linear programming another use for sparse fir filters is for the case where multipliers have failed graceful degradation can be achieved in some types of fir filters by optimally adjusting the functional elements to compensate for the failed multipliers this approach can also be used to minimize the peak sidelobe level for beamformers that may have failed elements for the beamforming cases considered the peak sidelobe level was decreased by as much as 5 db

design and characterization of optimal fir filters with arbitrary phase an algorithm for designing a chebyshev optimal fir filter that approximates an arbitrary complex valued frequency response is presented this algorithm computes the optimal filter by solving the dual to the filter design problem it is guaranteed to converge theoretically and requires o n sup 2 computations per iteration for a filter of length n for the first time properties of the optimal filter are derived and the case where the desired filter has arbitrary constant group delay is studied in detail

on the performance of data compression algorithms based upon string matching lossless and lossy data compression algorithms based on string matching are considered in the lossless case a result of wyner and ziv 1989 is extended in the lossy case a data compression algorithm based on approximate string matching is analyzed in the following two frameworks 1 the database and the source together form a markov chain of finite order 2 the database and the source are independent with the database coming from a markov model and the source from a general stationary ergodic model in either framework it is shown that the resulting compression rate converges with probability one to a quantity computable as the infimum of an information theoretic functional over a set of auxiliary random variables the quantity is strictly greater than the rate distortion function of the source except in some symmetric cases in particular this result implies that the lossy algorithm proposed by steinberg and gutman 1993 is not optimal even for memoryless or markov sources

optimal design of complex fir filters with arbitrary magnitude and group delay responses this paper presents a method for the frequency domain design of digital finite impulse response filters with arbitrary magnitude and group delay responses the method can deal with both the equiripple design problem and the peak constrained least squares pcls design problem consequently the method can also be applied to the equiripple passbands and pcls stopbands design problem as a special case of the pcls design both the equiripple and the pcls design problems are converted into weighted least squares optimization problems they are then solved iteratively with appropriately updated error weighting functions a novel scheme for updating the error weighting function is developed to incorporate the design requirements design examples are included in order to compare the performance of the filters designed using the proposed scheme and several other existing methods

on the average redundancy rate of the lempel ziv code in this paper we settle a long standing open problem concerning the average redundancy r sub n of the lempel ziv 78 lz78 code we prove that for a memoryless source the average redundancy rate attains asymptotically er sub n a spl delta n log n o log log n log sup 2 n where a is an explicitly given constant that depends on source characteristics and spl delta x is a fluctuating function with a small amplitude we also derive the leading term for the kth moment of the number of phrases we conclude by conjecturing a precise formula on the expected redundancy for a markovian source the main result of this paper is a consequence of the second order properties of the lempel ziv algorithm obtained by jacquet and szpankowski 1995 these findings have been established by analytical techniques of the precise analysis of algorithms we give a brief survey of these results since they are interesting in their own right and shed some light on the probabilistic behavior of pattern matching based data compression

a practical method for designing fir digital filters in the complex domain a new method is presented for the design of fir fillers in the complex domain the method converts the complex approximation problem into an equivalent real nonlinear optimization problem which is solved by successive linearization using an effective geometrical linearization technique the method converges rapidly and the solution has a guaranteed accuracy it also has the flexibility of allowing addition of extra constraints such as constant group delay constraints and transition band magnitude overshoot constraints numerical examples are presented to illustrate the performance of the method

the redundancy of source coding with a fidelity criterion ii coding at a fixed rate level with unknown statistics the redundancy problem of universal lossy source coding at a fixed rate level is considered under some condition on the single letter distortion measure which implies that the cardinality k of the reproduction alphabet is not greater than the cardinality j of the source alphabet it is shown that the redundancy of universally coding memoryless sources p by nth order block codes of rate r goes like spl part spl part r d p r kln n 2n o ln n n for all memoryless sources p except a set whose volume goes to 0 as the block length n goes to infinity where d p r denotes the distortion rate function of p specifically for any sequence c sub n sub n 1 sup spl infin of block codes where c sub n is an nth order block code at the fixed rate r and any spl epsiv 0 the redundancy d sub n c sub n p of c sub n for p is greater than or equal to spl part spl part r d p r k spl epsiv ln n 2n for all p satisfying some regular conditions except a set whose volume goes to 0 as n spl rarr spl infin on the other hand there exists a sequence c sub n sub n 1 sup spl infin of block codes at the rate r such that for any p satisfying some regular conditions the super limit of d sub n c sub n p ln n n is less than or equal to spl part spl part r d p r k 2

the shortest common superstring problem average case analysis for both exact and approximate matching the shortest common superstring problem and its extension to approximate matching are considered in the probability model where each string in a given set has the same length and letters of strings are drawn independently from a finite set in the exact matching case several algorithms proposed in the literature are shown to be asymptotically optimal in the sense that the ratio of the savings resulting from the superstring constructed by each of these algorithms that is the difference between the total length of the strings in the given set and the length of the superstring to the optimal savings from the shortest superstring approaches in probability to 1 as the number of strings in the given set increases in the approximate matching case a modified version of the shortest common approximate matching superstring problem is analyzed it is demonstrated that the optimal savings in this case is given approximately by nlogn i sub l q q 2d where n is the number of strings in the given set q is the probability distribution governing the selection of letters of strings i sub l q q 2d is the lower mutual information between q and q with respect to 2d and d spl ges 0 is the distortion allowed in approximate matching in addition an approximation algorithm is proposed and proved asymptotically optimal

2d pattern matching image and video compression theory algorithms and experiments we propose a lossy data compression framework based on an approximate two dimensional 2d pattern matching 2d pmc extension of the lempel ziv 1977 1978 lossless scheme this framework forms the basis upon which higher level schemes relying on differential coding frequency domain techniques prediction and other methods can be built we apply our pattern matching framework to image and video compression and report on theoretical and experimental results theoretically we show that the fixed database model used for video compression leads to suboptimal but computationally efficient performance the compression ratio of this model is shown to tend to the generalized entropy for image compression we use a growing database model for which we provide an approximate analysis the implementation of 2d pmc is a challenging problem from the algorithmic point of view we use a range of techniques and data structures such as k d trees generalized run length coding adaptive arithmetic coding and variable and adaptive maximum distortion level to achieve good compression ratios at high compression speeds we demonstrate bit rates in the range of 0 25 0 5 bpp for high quality images and data rates in the range of 0 15 0 5 mbps for a baseline video compression scheme that does not use any prediction or interpolation we also demonstrate that this asymmetric compression scheme is capable of extremely fast decompression making it particularly suitable for networked multimedia applications

linear periodic systems and multirate filter design we present a systematic procedure for the design of filters intended for multirate systems this procedure is motivated by viewing the equiripple design of filters in linear time invariant systems as a process of obtaining optimum minimax filters for a class of bounded energy input signals the philosophy of designing optimum minimax filters for classes of input signals is extended to multirate systems which are not time invariant we develop a generalized fourier analysis appropriate for linear periodic systems and use it to derive new error criteria for multirate filter design using such criteria yields optimum minimax multirate filters for the input signal class the utility of our method is demonstrated by using it to analyze several multirate systems we give numerical results on the design of a multirate implementation of a narrowband filter and compare our work to previous work on multirate filter design our numerical analysis is based upon a new formulation of the design as a semi infinite linear programming problem

on the redundancy of lossy source coding with abstract alphabets the redundancy problem of lossy source coding with abstract source and reproduction alphabets is considered for coding at a fixed rate level it is shown that for any fixed rate r 0 and any memoryless abstract alphabet source p satisfying some mild conditions there exists a sequence c sub n sub n 1 sup spl infin of block codes at the rate r such that the distortion redundancy of c sub n defined as the difference between the performance of c sub n and the distortion rate function d p r of p is upper bounded by spl part d p r spl part r ln n 2n o ln n n for coding at a fixed distortion level it is demonstrated that for any d 0 and any memoryless abstract alphabet source p satisfying some mild conditions there exists a sequence c sub n sub n 1 sup spl infin of block codes at the fixed distortion d such that the rate redundancy of c sub n defined as the difference between the performance of c sub n and the rate distortion function r p d of p is upper bounded by 7ln n 6n o ln n n these results strengthen the traditional berger s 1968 1971 abstract alphabet source coding theorem and extend the positive redundancy results of zhang yang and wei see ibid vol 43 no 1 p 71 91 1997 and ibid vol 42 p 803 21 1996 on lossy source coding with finite alphabets and the redundancy result of wyner see ibid vol 43 p 1452 64 1997 on block coding of memoryless gaussian sources

higher order energy functionals abstract the study of higher order energy functionals was first proposed by eells and sampson in 1965 and later by eells and lemaire in 1983 these functionals provide a natural generalization of the classical energy functional more precisely eells and sampson suggested the investigation of the so called e s r energy functionals e r e s 1 2 m d d r 2 d v where m n is a map between two riemannian manifolds in the initial part of this paper we shall clarify some relevant issues about the definition of an e s r harmonic map i e a critical point of e r e s that seems important to us because in the literature other higher order energy functionals have been studied by several authors and consequently some recent examples need to be discussed and extended this shall be done in the first two sections of this work where we obtain the first examples of proper critical points of e r e s when n s m r 4 m 3 and we also prove some general facts which should be useful for future developments of this subject next we shall compute the euler lagrange system of equations for e r e s for r 4 we shall apply this result to the study of maps into space forms and to rotationally symmetric maps in particular we shall focus on the study of various family of conformal maps in section 4 we shall also show that even if 2 r dim m the functionals e r e s may not satisfy the classical palais smale condition c in the final part of the paper we shall study the second variation and compute index and nullity of some significant examples

sample converses in source coding theory the rate and distortion performance of a sequence of codes along a sample sequence of symbols generated by a stationary ergodic information source are studied two results are obtained 1 the source sample sequence is encoded by an arbitrary sequence of block codes which operate at a fixed rate level r and a sample converse is obtained which states that with probability one the lower limit of the code sample distortions is lower bounded by d r the value of the distortion rate function at r 2 the source sample sequence is encoded by an arbitrary sequence of variable rate codes which operate at a fixed distortion level d and a sample converse is obtained which states that with probability one the lower limit of the code sample rates is lower bounded by r d the value of the rate distortion function at d a novel ergodic theorem is used to obtain both sample converses

a note on equivariant biharmonic maps and stable biharmonic maps abstract in this note we generalize biharmonic equation for rotationally symmetric maps 4 20 12 to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from a 4 dimensional space form into a 4 dimensional model space we also give an improved second variation formula for biharmonic maps into a space form and use it to prove that there exists no stable proper biharmonic map with constant square norm of tension field from a compact riemannian manifold without boundary into a space form of positive sectional curvature

on the design of fir filters by complex chebyshev approximation the long standing problem of approximating a complex valued desired function with a finite impulse response fir filter is considered it is formulated as an equalization to be solved using complex valued filters the proposed algorithm deals directly with the complex error function which depends linearly on the coefficients of the filter to be designed the magnitude of this error function is minimized in the chebshev sense using a generalization of the remez exchange algorithm the method can be used to design complex or real valued selective systems as well the well known design of optimal fir filters with linear phase is included here as a special case

on polynomial approximation in the complex plane with application to conformal mapping we consider the selection of polynomial bases for polynomial approximation of analytic functions on bounded simply connected regions in the complex plane while a monomial basis may be very ill conditioned we show that a basis of lagrange polynomials with fejer points as nodes is well conditioned numerical examples where we compute polynomial approximations of conformal mappings conclude the paper

application of infinite dimensional linear programming to iir filter design with time domain constraints previously developed infinite dimensional linear programming techniques are used for the design of recursive filters with complex chebyshev error criteria and time domain constraints the approach is applied to a numerical example that deals with the design of a laguerre network as an equalization filter for a digital transmission channel

on the redundancy of the fixed database lempel ziv algorithm for spl phi mixing sources the redundancy problem of the fixed database lempel ziv 1977 algorithm is considered it is demonstrated that for a class of spl phi mixing sources which includes markov sources unifilar sources and finite state sources as special cases the redundancy of the fixed database lempel ziv algorithm with database size n is lower bounded by h loglogn logn o logloglogn logn and upper bounded by 2h loglogn logn o logloglogn logn where h is the entropy rate of the source the method of proof is new and uses the concept of variable length to variable length codes