strong universal source coding subject to a rate distortion constraint the following problem in universal source coding is explored some members of a class of sources have various constraints on the maximum rate at which they may be encoded and thc remainder have various constraints on the maximum distortion that may result from encoding it is desired to find a universal code that will adapt its performance so that whatever source in the class is encoded the resulting performance meets the constraint and is optimal in the rate distortion function sense for that particular source it is shown that such codes exist when the class is totally bounded and the constraints are uniformly continuous in an appropriate sense a key result shows that the value of any uniformly continuous function on a totally bounded class can be uniformly well estimated from observations of the output of any source in

natural type selection in adaptive lossy compression consider approximate lossy matching of a source string spl sim p with a random codebook generated from reproduction distribution q at a specified distortion d previous work determined the minimum coding rate r sub 1 r p q d for this setting we observe that for a large word length and with high probability the matching codeword is typical with a distribution q sub 1 which is different from q if a new random codebook is generated spl sim q sub 1 then the source string will favor codewords which are typical with a new distribution q sub 2 resulting in a minimum coding rate r sub 2 r p q sub 1 d and so on we show that the sequences of distributions q sub 1 q sub 2 and rates r sub 1 r sub 2 generated by this procedure converge to an optimum reproduction distribution q and the rate distortion function r p d respectively we also derive a fixed rate distortion slope version of this natural type selection process in the latter case an iteration of the process stochastically simulates an iteration of the blahut arimoto 1972 algorithm for rate distortion function computation without recourse to prior knowledge of the underlying source distribution to strengthen these limit statements we also characterize the steady state error of these procedures when iterating at a finite string length implications of the main results provide fresh insights into the workings of lossy variants of the lempel ziv algorithm for adaptive compression

an affine scaling interior trust region method for lc1 minimization subject to bounds on variables in this literature we extend the classical affine scaling interior trust region algorithm for smooth bounded constrained nonlinear programming to the nonsmooth case where the objective function is only locally lipschitzian we propose and analyze a new affine scaling trust region method in association with nonmonotonic interior backtracking line search technique for solving the linear equality constrained lc 1 optimization subject to bounds on variables at each iteration the trust region subproblem is defined by minimizing a quadratic function which is required both first and second order information of the objective function and a quadratic affine scaling matrix model subject only to an ellipsoidal constraint in a null space of the affine scaling linear equality constraints the second order derivative of the objective function is explicitly required to be lipschitzian each iterate switches to a very general setting of computing trial backtracking steps generated by the general trust region subproblem and then the line search technique projects the trial backtracking steps onto the strictly feasible set of the bounded constraints on variables the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required a nonmonotonic criterion should bring about speeding up the convergence progress in some ill conditioned cases applications of the algorithm to various nonsmooth optimization problems are discussed

line search filter methods for nonlinear programming local convergence a line search method is proposed for nonlinear programming using fletcher and leyffer s filter method which replaces the traditional merit function a simple modification of the method proposed in a companion paper siam j optim 16 2005 pp 1 31 introducing second order correction steps is presented it is shown that the proposed method does not suffer from the maratos effect so that fast local convergence to second order sufficient local solutions is achieved

a continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints in this paper it is shown that given a nonlinear programming problem with inequality constraints it is possible to construct a continuously differentiable exact penalty function whose global or local unconstrained minimizers correspond to global or local solutions of the constrained problem

entropy constrained vector quantization an iterative descent algorithm based on a lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed these entropy constrained vector quantizers ecvqs can be used in tandem with variable rate noiseless coding systems to provide locally optimal variable rate block source coding with respect to a fidelity criterion experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates about 1 bit sample under the squared error distortion measure about 1 6 db improvement in the signal to noise ratio can be expected over the best scalar and lattice quantizers when block entropy coded with block length 4 even greater gains are made over other forms of entropy coded vector quantizers for pattern recognition it is shown that the ecvq algorithm is a generalization of the k means and related algorithms for estimating cluster means in that the ecvq algorithm estimates the prior cluster probabilities as well experiments on multivariate gaussian distributions show that for clustering problems involving classes with widely different priors the ecvq outperforms the k means algorithm in both likelihood and probability of error

representations of non splittable extension algebras let a be an algebra over a field k and d a self duality d mod a 2 mod aop where aop is the opposite algebra of a and mod a the category of finitely generated left a modules by an extension for short we understand an extension algebra t over a with kernel da in the sense of cartan eilenberg 3 0 da t p a 0 where p is an algebra epimorphism in the case where a is hereditary by means of the heller function qaxda the auslander reiten quiver rawda of the trivial extension a k da is completely determined by ra lo moreover for any extension t tr is isomorphic to rawda it seems that this fact suggests the existence of a closer connection between some categories of modules over t and over a 1x da though mod t is not in general equivalent to mod a k da in this paper we are concerned with categorical relations between non splittable extensions and the trivial extensions and we shall establish some relation between them for some class of algebras to which hereditary algebras belong we prove the following where mod a denotes the category of finitely generated left a modules without projective summands

line search filter inexact secant methods for nonlinear equality constrained optimization we present inexact secant methods in association with line search filter technique for solving nonlinear equality constrained optimization for large scale applications it is expensive to get an exact search direction and hence we use an inexact method that finds an approximate solution satisfying some appropriate conditions the global convergence of the proposed algorithm is established by using line search filter technique the second order correction step is used to overcome the maratos effect while the line search filter inexact secant methods have superlinear local convergence rate finally the results of numerical experiments indicate that the proposed methods are efficient for the given test problems

projected affine scaling interior point newton s method with line search filter for box constrained optimization abstract we present a new projected affine scaling interior point newton s method with a line search filter algorithm for nonlinear optimization problems with box constraints the global convergence of the proposed algorithm is established under some reasonable conditions furthermore the method is shown to be locally quadratically convergent under the strong second order sufficiency condition without assuming strict complementarity of the solution numerical experiments are presented that confirm the robustness and efficiency of the approach

positive galois coverings of self injective algebras abstract in the article we study the structure of galois coverings of self injective artin algebras with infinite cyclic galois groups in particular we characterize all basic connected self injective artin algebras having galois coverings by the repetitive algebras of basic connected artin algebras and with the galois groups generated by positive automorphisms of the repetitive algebras

global convergence of slanting filter methods for nonlinear programming in this paper we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates independently of how these iterates are computed we prove that all accumulation points of the sequence generated by the algorithm are feasible computing the new iterates by the inexact restoration method we prove stationarity of all accumulation points of the sequence

an active set newton algorithm for large scale nonlinear programs with box constraints a new algorithm for large scale nonlinear programs with box constraints is introduced the algorithm is based on an efficient identification technique of the active set at the solution and on a nonmonotone stabilization technique it possesses global and superlinear convergence properties under standard assumptions a new technique for generating test problems with known characteristics is also introduced the implementation of the method is described along with computational results for large scale problems

automorphisms of repetitive algebras abstract let b be the repetitive algebra of a finite dimensional algebra b over a field k by the b bimodule db hom b k and let be the nakayama automorphism of b we determine the positive automorphisms of b such that the orbit algebra b is isomorphic to a splittable extension algebra of b by the b bimodule db for an automorphism of b and we characterize weakly symmetric algebras and symmetric algebras of the form b with a positive automorphism of b as an application we characterize some class of weakly symmetric algebras with non periodic generalized standard auslander reiten components

polar codes are optimal for lossy source coding we consider lossy source compression of a binary symmetric source using polar codes and a low complexity successive encoding algorithm it was recently shown by arikan that polar codes achieve the capacity of arbitrary symmetric binary input discrete memoryless channels under a successive decoding strategy we show the equivalent result for lossy source compression i e we show that this combination achieves the rate distortion bound for a binary symmetric source we further show the optimality of polar codes for various multiterminal problems including the binary wyner ziv and the binary gelfand pinsker problems our results extend to general versions of these problems

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

an algorithm for source coding subject to a fidelity criterion based on string matching a practical suboptimal universal block source coding scheme subject to a fidelity criterion is proposed the algorithm is an extension of the lempel ziv algorithm and is based on string matching with distortion it is shown that given average distortion d 0 the algorithm achieves a rate of exceeding r d 2 for a large class of sources and distortion measures tighter bounds on the rate are derived for discrete memoryless sources and for memoryless gaussian sources

fixed slope universal lossy data compression corresponding to any lossless codeword length function l three universal lossy data compression schemes are presented one is with a fixed rate another is with a fixed distortion and a third is with a fixed slope the former two universal lossy data compression schemes are the generalization of yang kieffer s see ibid vol 42 no 1 p 239 45 1995 results to the general case of any lossless codeword length function l whereas the third is new in the case of fixed slope spl lambda 0 our universal lossy data compression scheme works as follows for any source sequence x sup n of length n the encoder first searches for a reproduction sequence y sup n of length n which minimizes a cost function n sup 1 l y sup n spl lambda spl rho sub n x sup n y sup n over all reproduction sequences of length n and then encodes x sup n into the binary codeword of length l y sup n associated with y sup n via the lossless codeword length function l where spl rho sub n x sup n y sup n is the distortion per sample between x sup n and y sup n under some mild assumptions on the lossless codeword length function l it is shown that when this fixed slope data compression scheme is applied to encode a stationary ergodic source the resulting encoding rate per sample and the distortion per sample converge with probability one to r sub spl lambda and d sub spl lambda respectively where d sub spl lambda r sub spl lambda is the point on the rate distortion curve at which the slope of the rate distortion function is spl lambda this result holds particularly for the arithmetic codeword length function and lempel ziv codeword length function the main advantage of this fixed slope universal lossy data compression scheme over the fixed rate fixed distortion universal lossy data compression scheme lies in the fact that it converts the encoding problem to a search problem through a trellis and then permits one to use some sequential search algorithms to implement it simulation results show that this fixed slope universal lossy data compression scheme combined with a suitable search algorithm is promising

nonlinear sparse graph codes for lossy compression we propose a scheme for lossy compression of discrete memoryless sources the compressor is the decoder of a nonlinear channel code constructed from a sparse graph we prove asymptotic optimality of the scheme for any separable letter by letter bounded distortion criterion we also present a suboptimal compression algorithm which exhibits near optimal performance for moderate block lengths

a derivative free method for solving box constrained underdetermined nonlinear systems of equations abstract a derivative free iterative method for solving bound constrained underdetermined nonlinear systems is presented the procedure consists of a quasi newton method that uses the broyden update formula and a globalized line search that combines the strategy of grippo lampariello and lucidi with the li and fukushima one global convergence results are proved and numerical experiments are presented

universal trellis coded quantization a new form of trellis coded quantization based on uniform quantization thresholds and on the fly quantizer training is presented the universal trellis coded quantization utcq technique requires neither stored codebooks nor a computationally intense codebook design algorithm its performance is comparable with that of fully optimized entropy constrained trellis coded quantization ectcq for most encoding rates the codebook and trellis geometry of utcq are symmetric with respect to the trellis superset this allows sources with a symmetric probability density to be encoded with a single variable rate code rate allocation and quantizer modeling procedures are given for utcq which allow access to continuous quantization rates an image coding application based on adaptive wavelet coefficient subblock classification arithmetic coding and utcq is presented the excellent performance of this coder demonstrates the efficacy of utcq we also present a simple scheme to improve the perceptual performance of utcq for certain imagery at low bit rates this scheme has the added advantage of being applied during image decoding without the need to reencode the original image

a new subspace limited memory bfgs algorithm for large scale bound constrained optimization an active set limited memory bfgs algorithm for large scale bound constrained optimization is introduced the active sets are based on guessing technique to be identified at each iteration the search direction in free subspace is determined by limited memory bfgs l bfgs algorithm which provides an efficient means for attacking large scale optimization problems the implementations of the method on cute test problems are described

projected newton methods for optimization problems with simple constraints we consider the problem min f x x geqq 0 and propose algorithms of the form x k 1 x k alpha k d k nabla f x k where cdot denotes projection on the positive orthant alpha k is a stepsize chosen by an armijo like rule and d k is a positive definite symmetric matrix which is partly diagonal we show that d k can be calculated simply on the basis of second derivatives of f so that the resulting newton like algorithm has a typically superlinear rate of convergence with other choices of d k convergence at a typically linear rate is obtained the algorithms are almost as simple as their unconstrained counterparts they are well suited for problems of large dimension such as those arising in optimal control while being competitive with existing methods for low dimensional problems the effectiveness of the newton like algorithm is demonstrated via computational examples involving as many as 10 000 variables extensions to general linearly constrained pr

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

lossy compression of discrete sources via the viterbi algorithm we present a new lossy compressor for finite alphabet sources for coding a sequence xn the encoder starts by assigning a certain cost to each possible reconstruction sequence it then finds the one that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor the cost of each sequence is a linear combination of its distance from the sequence xn and a linear function of its kth order empirical distribution the structure of the cost function allows the encoder to employ the viterbi algorithm to find the sequence with minimum cost we identify a choice of the coefficients used in the cost function which ensures that the algorithm universally achieves the optimum rate distortion performance for any stationary ergodic source in the limit of large provided that increases as o log n iterative techniques for approximating the coefficients which alleviate the computational burden of finding the optimal coefficients are proposed and studied

a suboptimal lossy data compression based on approximate pattern matching a practical suboptimal variable source coding algorithm for lossy data compression is presented this scheme is based on approximate string matching and it naturally extends the lossless lempel ziv 1977 data compression scheme among others we consider the typical length of an approximately repeated pattern within the first n positions of a stationary mixing sequence where d percent of mismatches is allowed we prove that there exists a constant r sub 0 d such that the length of such an approximately repeated pattern converges in probability to 1 r sub 0 d log n pr but it almost surely oscillates between 1 r sub spl infin d log n and 2 r sub 1 d log n where r sub spl infin d r sub 0 d r sub 1 d 2 are some constants these constants are natural generalizations of renyi entropies to the lossy environment more importantly we show that the compression ratio of a lossy data compression scheme based on such an approximate pattern matching is asymptotically equal to r sub 0 d we also establish the asymptotic behavior of the so called approximate waiting time n sub l which is defined as the time until a pattern of length c repeats approximately for the first time we prove that log n sub l l spl rarr r sub 0 d pr as l spl rarr spl infin in general r sub 0 d r d where r d is the rate distortion function thus for stationary mixing sequences we settle in the negative the problem investigated by steinberg and gutman by showing that a lossy extension of the wyner ziv 1989 scheme cannot be optimal

rate constrained simulation and source coding i i d sources necessary conditions for asymptotically optimal sliding block or stationary codes for source coding and rate constrained simulation of memoryless sources are presented and used to motivate a design technique for trellis encoded source coding and rate constrained simulation the code structure has intuitive similarities to classic random coding arguments as well as to fake process methods and alphabet constrained methods experimental evidence shows that the approach provides comparable or superior performance in comparison with previously published methods on common examples sometimes by significant margins

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

on stochastic scheduling with in tree precedence constraints we consider the problem of optimal scheduling of a set of jobs obeying in tree precedence constraints when a number m of processors is available it is assumed that the service times of different jobs are independent identically distributed random variables subject to a minor assumption on the service time distribution we show that policies of the highest level first type are optimal asymptotically as the number of jobs tends to infinity

superlinear and quadratic convergence of affine scaling interior point newton methods for problems with simple bounds without strict complementarity assumption a class of affine scaling interior point methods for bound constrained optimization problems is introduced which are locally q superlinear or q quadratic convergent it is assumed that the strong second order sufficient optimality conditions at the solution are satisfied but strict complementarity is not required the methods are modifications of the affine scaling interior point newton methods introduced by t f coleman and y li math programming 67 189 224 1994 there are two modifications one is a modification of the scaling matrix the other one is the use of a projection of the step to maintain strict feasibility rather than a simple scaling of the step a comprehensive local convergence analysis is given a simple example is presented to illustrate the pitfalls of the original approach by coleman and li in the degenerate case and to demonstrate the performance of the fast converging modifications developed in this paper

channel polarization a method for constructing capacity achieving codes for symmetric binary input memoryless channels a method is proposed called channel polarization to construct code sequences that achieve the symmetric capacity i w of any given binary input discrete memoryless channel b dmc w the symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability channel polarization refers to the fact that it is possible to synthesize out of n independent copies of a given b dmc w a second set of n binary input channels wn i 1 les i les n such that as n becomes large the fraction of indices i for which i wn i is near 1 approaches i w and the fraction for which i wn i is near 0 approaches 1 i w the polarized channels wn i are well conditioned for channel coding one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining codes constructed on the basis of this idea are called polar codes the paper proves that given any b dmc w with i w 0 and any target rate r i w there exists a sequence of polar codes cfrn nges1 such that cfrn has block length n 2n rate ges r and probability of block error under successive cancellation decoding bounded as pe n r les o n 1 4 independently of the code rate this performance is achievable by encoders and decoders with complexity o n logn for each

gauss newton based bfgs method with filter for unconstrained minimization one class of the lately developed methods for solving optimization problems are filter methods in this paper we attached a multidimensional filter to the gauss newton based bfgs method given by li and fukushima d li m fukushima a globally and superlinearly convergent gauss newton based bfgs method for symmetric nonlinear equations siam journal of numerical analysis 37 1 1999 152 172 in order to reduce the number of backtracking steps the proposed filter method for unconstrained minimization problems converges globally under the standard assumptions it can also be successfully used in solving systems of symmetric nonlinear equations numerical results show reasonably good performance of the proposed algorithm

extensions over hereditary artinian rings with self dualities i in this paper we study the finitely generated indecomposable modules over an arbitrary extension over an artinian ring with self morita duality let a be an artinian ring with self duality and t an extension over a with kernel q see 11 chap xiv sect 21 such that qa and a q are isomorphic to injective hulls of top a and topla respectively such an a module q will be called quasi frobenius then it will be proved that