braided vector fields on a quantum hyperboloid via the quantum group uq sl 2 we introduce a new method of defining a space of braided vector fields on a quantum hyperboloid our method is based on the lyubashenko sudbery construction see lyubashenko and sudbery 1998 j math phys 39 3487 and references therein and it consists in realizing its generators braided analogs of hyperbolic infinitesimal rotations via those of the quantum group uq sl 2 our main result consists in showing that the space of braided vector fields is a projective module over the coordinate algebra of the quantum hyperboloid

multicommodity max flow min cut theorems and their use in designing approximation algorithms in this paper we establish max flow min cut theorems for several important classes of multicommodity flow problems in particular we show that for any n node multicommodity flow problem with uniform demands the max flow for the problem is within an o log n factor of the upper bound implied by the min cut the result which is existentially optimal establishes an important analogue of the famous 1 commodity max flow min cut theorem for problems with multiple commodities the result also has substantial applications to the field of approximation algorithms for example we use the flow result to design the first polynomial time polylog n times optimal approximation algorithms for well known np hard optimization problems such as graph partitioning min cut linear arrangement crossing number vlsi layout and minimum feedback arc set applications of the flow results to path routing problems network reconfiguration communication in distributed networks scientific computing and rapidly mixing markov chains are also described in the paper categories and subject descriptors f 2 2 analysis of algorithms and problem complexity

wave equations on q minkowski space we give a systematic account of a component approach to the algebra of forms onq minkowski space introducing the corresponding exterior derivative hodge star operator coderivative laplace beltrami operator and lie derivative using this braided differential geometry we then give a detailed exposition of theq d alembert andq maxwell equation and discuss some of their non trivial properties such as for instance plane wave solutions for theq maxwell field we also give aq spinor analysis of theq field strength tensor

apparatus for linear predictive coding and decoding of speech using residual wave form time access compression a speech coding and decoding apparatus for use in linear predictive coding of a speech signal includes coding apparatus having a pitch analyzing element for separating an analysis frame into one or more blocks and calculating the strength of correlativity between pitch periods of a residual waveform in each block a residual partially compresing element compresses the time axis of the residual waveform in a block having a high correlativity strength a residual quantizing element quantizes the compressed residual waveform while preferentially allotting quantization allotment bits to the compressed portion of the residual waveform decoding apparatus includes a residual inverse quantizing element for inversely quantizing the residual waveform by the same bit allotment a residual partially expanding element expands the compressed portion of the residual waveform to its original length and supplies it to a linear predictive synthesis filter

piecemeal graph exploration by a mobile robot we study how a mobile robot can learn an unknown environment in a piecemeal manner the robot s goal is to learn a complete map of its environment while satisfying the constraint that it must return every so often to its starting position for refueling say the environment is modeled as an arbitrary undirected graph which is initially unknown to the robot we assume that the robot can distinguish vertices and edges that it has already explored we present a surprisingly efficient algorithm for piecemeal learning an unknown undirected graph g v e in which the robot explores every vertex and edge in the graph by traversing at most o e v1 o 1 edges this nearly linear algorithm improves on the best previous algorithm in which the robot traverses at most o e v2 edges we also give an application of piecemeal learning to the problem of searching a graph for a treasure

speech coding decoding method having an excitation signal a speech coding method in which spectrum parameter representing a spectrum envelope and a pitch parameter representing a pitch are obtained from an input discrete speech signal a frame interval is divided into subintervals in accordance with the pitch parameter a sound source signal in one of the subintervals is obtained by obtaining a multipulse with respect to a difference signal obtained by performing prediction on the basis of a past sound source signal correction information for correcting at least one of the amplitude and the phase of the sound source signal are obtained and output in other pitch intervals in the frame

multi pulse excitation linear predictive speech coder a multi pulse excitation linear predictive speech coder operates in accordance with an analysis by synthesis method for determining the excitation the coder 10 comprises an lpc analyzer 11 a multi phase excitation generator 13 means 12 14 for forming an error signal representative of the difference between an original speech signal s n and a synthetic speech signal s n a filter 15 for perceptually weighting the error signal and means 16 responsive to the weighted error signal e n for generating pulse parameters controlling the excitation generator 13 so as to minimize a predetermined measure of the weighted error signal the lpc parameters and the pulse parameters of the excitation signal x n are encoded for efficient storage or transmission the bit capacity required for pulse position encoding of the excitation signal x n is considerably reduced by arranging the excitation generator 16 for an excitation signal x n which in each excitation interval l consists of a pulse pattern having a grid of a predetermined number q of equidstant pulses and by arranging the control means 16 for generating pulse parameters characterizing the grid position k relative to the beginning of the excitation interval l and the variable amplitudes bk j 1 j q of the pulses of the grid

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

method of transmitting at low throughput a speech signal by celp coding and corresponding system a method is provided for transmitting a digital speech signal at low throughput coding is performed by code excited linear prediction in order to generate a code signal a waveform being represented by an initial vector o of dimension l from a filter for synthesizing by a reference waveform selected from a dictionary of reference vectors v relating to a criterion of minimum deviation min h v 2 representing a target vector through perceptual weighting of the initial vector o a dictionary y factorized as a product of basis vectors yi of n ary form which are corrected by a scale factor i of distribution of the excitation energy and a dictionary g y of gains gk are established to represent the dictionary of the reference vectors v vk i gk yi the criterion is established by calculating c gk i yi 2gk gk 2 formed of the scalar products and perceptual energies to the initial vector o is assigned the optimal reference vector vk i gk i yi represented by just the index values k i

double mode long term prediction in speech coding a method of coding a sampled speech signal vector in an analysis by synthesis coding procedure includes the step of forming an optimum excitation vector comprising a linear combination of a code vector from a fixed code book and a long term predictor vector a first estimate of the long term predictor vector is formed in an open loop analysis a second estimate of the long term predictor vector is formed in a closed loop analysis finally each of the first and second estimates are combined in an exhaustive search with each code vector of the fixed code book to form that excitation vector that gives the best coding of the speech signal vector

all pairs nearly 2 approximate shortest paths in o n2polylogn time let g v e be an unweighted undirected graph on v n vertices and e m edges let d u v denote the distance between vertices u v v an algorithm is said to compute all pairs t approximate shortest paths distances for some t 1 if for each pair of vertices u v v the path distance reported by the algorithm is not longer greater than t d u v this paper presents two extremely simple randomized algorithms for computing all pairs nearly 2 approximate distances the first algorithm requires an expected o m 2 3nlogn n 2 time and for any u v v reports a distance no greater than 2 d u v 1 our second algorithm requires an expected o n 2log 3 2n time and for any u v v reports a distance bounded by 2 d u v 3

multi pulse speech coder speech is coded such that it can be generated by a pulse excitation sequence filtered by an lpc linear preductive coding filter the sequence contains in each of successive frame periods pulses whose positions and amplitudes may be varied these variables are selected at the coding end to reduce the error between the input and regenerated speech signals the selection process involves derivation of an initial estimate followed by an iterative adjustment process in which pulses having a low energy contribution are tested in alternative positions and transferred to them if a reduced error results

lattice filter parameterization and modeling of nonstationary processes a general theory of constant parameter modular lattice models for discrete time nonstationary second order processes is presented a complete parametrization of such processes in terms of schur and congruence coefficients is derived by developing a natural connection between the displacement structure of a covariance matrix and schur s test for positive definiteness of matrices schur coeffieients provide a simple solution to problems of covariance extension and rational spectral approximation for nonstationary covariances and they coincide with the well known reflection or parcor coefficients when the covariance is stationary the congruence coefficients provide the time varying gains of a tapped delay line realization of the whitening filter for the process a constant parameter realization of the same filter is derived by combining a lattice filter structure with a tapped delay line both with time invariant gains this configuration also provides a recursive relation for the congruence coefficients namely a generalized levinson szego recursion the tapped delay line part of the realization can be eliminated by introducing the concept of admissibility admissibility also reduces the parametrization of a nonstationary process to schur coefficients alone in analogy to stationary processes which are completely characterized by their parcor coefficients

speech analysis synthesis method and apparatus therefor an impulse sequence of a pitch frequency is detected from a phase equalized prediction residual of an input speech signal s t and a quasi periodic impulse sequence is obtained by processing the impulse sequence so that a fluctuation in its pitch frequency is within an allowed limit range the magnitudes of the quasi periodic impulse sequence are so determined as to minimize an error between the waveform of a synthesized speech obtainable by exciting an all pole filter 18 with the quasi periodic impulse sequence and the waveform of a phase equalized speech obtainable by applying the input speech signal to a phase equalizing filter 5 preferably the quasi periodic impulse sequence is supplied to the all pole filter after being applied to a zero filter 10 in which it is given features of the prediction residual of the speech coefficients of the zero filter are also determined so that the error of the waveforms of the synthesized speech and the phase equalized speech is minimum

representations of the generalized lie algebra we construct finite dimensional irreducible representations of two quantum algebras related to the generalized lie algebra introduced by lyubashenko and sudbery we consider separately the cases of q generic and q at roots of unity some of the representations have no classical analogue even for generic q some of the representations have no analogue to the finite dimensional representations of the quantized enveloping while in those that do there are different matrix elements

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

a method to determine the excitation pulse positions within a speech frame a method of determining the positions within a speech frame for a given number n j n1 n2 of excitation pulses in a linear predictive speech encoder the method is a combination of two known methods in accordance with the invention the positions of the excitation pulses are calculated in a number of calculation stages j in accordance with the first method and the positions of the excitation pulses are calculated in a number of calculation stages n1 n2 nl in accordance with the second method each with a starting point from one of a number of positions mi mk mr calculated in accordance with the first method therewith to obtain one of a number l of pulse placements and the proportion between the number of calculation stages j and max n1 n2 respectively according to the first and the second method respectively is chosen so as to obtain the least calculation complexity for a certain given speech quality two different embodiments of the second method are described

near linear time construction of sparse neighborhood covers this paper introduces a near linear time sequential algorithm for constructing a sparse neighborhood cover this implies analogous improvements from quadratic to near linear time for any problem whose solution relies on network decompositions including small edge cuts in planar graphs approximate shortest paths and weight and distance preserving graph spanners in particular an o log n approximation to the k shortest paths problem on an n vertex e edge graph is obtained that runs in soh n e k time

high probability parallel transitive closure algorithms there is a straightforward algorithm for computing the transitive closure of an n node graph in o log 2 n time on an erew pram using n 3 log n processors or indeed with m n log n processors if serial matrix multiplication in m n time can be done this algorithm is within a log factor of optimal in work processor time product for solving the all pairs transitive closure problem for dense graphs however this algorithm is far from optimal when either a the graph is sparse or b we want to solve the single source transitive closure problem it would be ideal to have an mathcal nc algorithm for transitive closure that took about e processors for the single source problem on a graph with n nodes and e geqq n arcs or about en processors for the all pairs problem on the same graph while an algorithm that good cannot be offered algorithms with the following performance can be offered 1 for single source tilde o n varepsilon time with tilde o en 1 2 varepsil

generalized lie algebras of type an it is shown that the quantized enveloping algebra of sl n contains a generalized lie algebra defined by means of axioms similar to woronowicz s this gives rise to lie algebra like generators and relations for the locally finite part of the quantized enveloping algebra and suggests a canonical poincare birkhoff witt basis

the maxwell operator on q minkowski space and q hyperboloid algebras we introduce an analog of the maxwell operator on a q minkowski space algebra treated as a particular case of the so called reflection equation algebra and on certain of its quotients we treat the space of quantum differential forms as a projective module in the spirit of the serre swan approach also we use braided tangent vector fields which are q analogs of poisson vector fields associated with the lie bracket sl 2

graph distances in the data stream model we explore problems related to computing graph distances in the data stream model the goal is to design algorithms that can process the edges of a graph in an arbitrary order given only a limited amount of working memory we are motivated by both the practical challenge of processing massive graphs such as the web graph and the desire for a better theoretical understanding of the data stream model in particular we are interested in the trade offs between model parameters such as per data item processing time total space and the number of passes that may be taken over the stream these trade offs are more apparent when considering graph problems than they were in previous streaming work that solved problems of a statistical nature our results include the following 1 spanner construction there exists a single pass tilde o tn 1 1 t space tilde o t 2n 1 t time per edge algorithm that constructs a 2t 1 spanner for t omega log n log log n the algorithm satisfies the semistreaming space restriction of o n operatorname polylog n and has per edge processing time o operatorname polylog n this resolves an open question from j feigenbaum et al theoret comput sci 348 2005 pp 207 216 2 breadth first search bfs trees for any even constant k we show that any algorithm that computes the first k layers of a bfs tree from a prescribed node with probability at least 2 3 requires either greater than k 2 passes or tilde omega n 1 1 k space since constructing bfs trees is an important subroutine in many traditional graph algorithms this demonstrates the need for new algorithmic techniques when processing graphs in the data stream model 3 graph distance lower bounds any t approximation of the distance between two nodes requires omega n 1 1 t space we also prove lower bounds for determining the length of the shortest cycle and other graph properties 4 techniques for decreasing per edge processing we discuss two general techniques for speeding up the per edge computation time of streaming algorithms while increasing the space by only a small factor

q deformed poincare algebra theq differential calculus for theq minkowski space is developed the algebra of theq derivatives with theq lorentz generators is found giving theq deformation of the poincare algebra the reality structure of theq poincare algebra is given the reality structure of theq differentials is also found the real laplacian is constructed finally the comultiplication counit and antipode for theq poincare algebra are obtained making it a hopf algebra

speech signal coding using correlation valves between subframes a speech signal coding system for coding a speech signal at a bit rate of 8 to 4 kb s wherein the amount of calculation for fractional search of delays of an adaptive codebook is reduced significantly before a fractional delay of the adaptive codebook is found candidates of integer delay are found by an open loop using correlation values a search for a fractional delay by a closed loop is performed for a search range for fractional delays which is provided by several samples of each integer delay candidate thus found using the correlation values the fractional delay search is realized by polyphase filtering of an excitation signal in the past in the search a plurality of candidates of fractional delay may be found for each integer delay candidate from the adaptive codebook in this instance a fractional delay is determined decisively from the decimal delay candidates after a search of an excitation codebook

approximate distance oracles let g v e be an undirected weighted graph with vvv n and vev m let k 1 be an integer we show that g v e can be preprocessed in o kmn1 k expected time constructing a data structure of size o kn1p1 k such that any subsequent distance query can be answered approximately in o k time the approximate distance returned is of stretch at most 2k 1 that is the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k 1 a 1963 girth conjecture of erdos implies that n1p1 k space is needed in the worst case for any real stretch strictly smaller than 2kp1 the space requirement of our algorithm is therefore essentially optimal the most impressive feature of our data structure is its constant query time hence the name oracle previously data structures that used only o n1p1 k space had a query time of n1 k our algorithms are extremely simple and easy to implement efficiently they also provide faster constructions of sparse spanners of weighted graphs and improved tree covers and distance labelings of weighted or unweighted graphs