on varieties of almost minimal degree in small codimension abstract the present research grew out of the authors joint work m brodmann p schenzel arithmetic properties of projective varieties of almost minimal degree j algebraic geom in press it continues the study of the structure of projective varieties of almost minimal degree focusing to the case of small codimension in particular we give a complete list of all occurring betti diagrams in the cases where codim x 4

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

ideals with stable betti numbers componentwise linear ideals were introduced earlier to generalize the result that the stanley reisner ideal i of a simplicial complex has a linear resolution if and only if its alexander dual is cohen macaulay it turns out that i is componentwise linear if and only if is sequentially cohen macaulay in this paper we discuss betti number properties of componentwise linear ideals let i be a graded ideal of a polynomial ring s and gin i the generic initial ideal of i with respect to the reverse lexicographic term order on s our main result is that i and gin i admit the same graded betti numbers if and only if i is componentwise linear for the proof of this fact we describe some properties of the betti diagram of a generic initial ideal combinatorial implications for shifted complexes will also be discussed

surfaces in p4 with extremal general hyperplane section abstract optimal upper bounds for the cohomology groups of space curves have been derived recently curves attaining all these bounds are called extremal curves this note is a step to analyze the corresponding problems for surfaces we state optimal upper bounds for the second and third cohomology groups of surfaces in p 4 and show that surfaces attaining all these bounds exist and must have an extremal curve as general hyperplane section surprisingly all the first cohomology groups of such surfaces vanish it follows that an extremal curve does not lift to a locally cohen macaulay surface unless the curve is arithmetically cohen macaulay

wyner ziv coding over broadcast channels hybrid digital analog schemes a new hybrid digital analog scheme is proposed for lossy transmission of a gaussian source over a bandwidth matched gaussian broadcast channel with source side information available at each receiver the proposed scheme combines two schemes that were previously shown to achieve optimal point to point distortion power tradeoff simultaneously at all receivers under two distinct conditions stated in terms of channel and side information quality parameters for the two receiver case the combined scheme is shown to achieve the same kind of optimality for the entire region in the parameter space sandwiched between those two conditions crucial to this result is a new degree of freedom discovered in designing point to point hybrid digital analog schemes with side information when superimposed with analog transmission the proposed scheme outperforms all previously known schemes even outside the optimality region in the parameter space

on the joint source channel coding error exponent for discrete memoryless systems we investigate the computation of csisza spl acute r s bounds for the joint source channel coding jscc error exponent e sub j of a communication system consisting of a discrete memoryless source and a discrete memoryless channel we provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained these equivalent representations can be readily computed for arbitrary source channel pairs via arimoto s algorithm when the channel s distribution satisfies a symmetry property the bounds admit closed form parametric expressions we then use our results to provide a systematic comparison between the jscc error exponent e sub j and the tandem coding error exponent e sub t which applies if the source and channel are separately coded it is shown that e sub t spl les e sub j spl les 2e sub t we establish conditions for which e sub j e sub t and for which e sub j 2e sub t numerical examples indicate that e sub j is close to 2e sub t for many source channel pairs this gain translates into a power saving larger than 2 db for a binary source transmitted over additive white gaussian noise awgn channels and rayleigh fading channels with finite output quantization finally we study the computation of the lossy jscc error exponent under the hamming distortion measure

buchsbaum rim sheaves and their multiple sections abstract this paper begins by introducing and characterizing buchsbaum rim sheaves on z proj r where r is a graded gorenstein k algebra they are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free r modules then we study multiple sections of a buchsbaum rim sheaf b i e we consider morphisms p b of sheaves on z dropping rank in the expected codimension where h0 z p is a free r module the main purpose of this paper is to study properties of schemes associated to the degeneracy locus s of it turns out that s is often not equidimensional let x denote the top dimensional part of s in this paper we measure the difference between x and s compute their cohomology modules and describe ring theoretic properties of their coordinate rings moreover we produce graded free resolutions of x and s which are in general minimal among the applications we show how one can embed a subscheme into an arithmetically gorenstein subscheme of the same dimension and prove that zero loci of sections of the dual of a null correlation bundle are arithmetically buchsbaum

distributed source coding using syndromes discus design and construction we address the problem of compressing correlated distributed sources i e correlated sources which are not co located or which cannot cooperate to directly exploit their correlation we consider the related problem of compressing a source which is correlated with another source that is available only at the decoder this problem has been studied in the information theory literature under the name of the slepian wolf 1973 source coding problem for the lossless coding case and as rate distortion with side information for the lossy coding case we provide a constructive practical framework based on algebraic trellis codes dubbed as distributed source coding using syndromes discus that can be applicable in a variety of settings simulation results are presented for source coding of independent and identically distributed i i d gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded our results reveal the promise of this approach using trellis based quantization and coset construction the performance of the proposed approach is 2 5 db from the wyner ziv 1976 bound

an algorithm for the n lyapunov exponents of an n dimensional unknown dynamical system abstract an algorithm for estimating lyapunov exponents of an unknown dynamical system is designed the algorithm estimates not only the largest but all lyapunov exponents of the unknown system the estimation is carried out by a multivariate feedforward network estimation technique we focus our attention on deterministic as well as noisy system estimation the performance of the algorithm is very satisfactory in the presence of noise as well as with limited number of observations

projective subvarieties having large green lazarsfeld index abstract let x p n c be a nondegenerate projective irreducible subvariety of degree d and codimension c 1 the green lazarsfeld index of x denoted by index x is defined as the largest p such that the homogeneous ideal of x is generated by quadrics and the syzygies among them are generated by linear syzygies until the p 1 th stage thus index x is an important invariant in order to describe the minimal free resolution of x recently it is shown that d c 1 if and only if index x c and x is a del pezzo variety if and only if index x c 1 in this paper we prove that index x c 2 c 3 if and only if x is either a complete intersection of three quadrics or else an arithmetically cohen macaulay variety with d c 3 theorem 1 1 also we classify x with index x c 3 c 4 for the cases when d c 2 theorem 4 1 and when x is a smooth surface theorem 4 3

side information scalable source coding we consider the problem of side information scalable si scalable source coding where the encoder constructs a two layer description such that the receiver with high quality side information will be able to use only the first layer to reconstruct the source in a lossy manner while the receiver with low quality side information will have to receive both layers in order to decode we provide inner and outer bounds to the rate distortion r d region for general discrete memoryless sources the achievable region is tight when either one of the decoders requires a lossless reconstruction and when the distortion measures are degraded and deterministic furthermore the gap between the inner and the outer bounds can be bounded by certain constants when the squared error distortion measure is used the notion of perfect scalability is introduced for which necessary and sufficient conditions are given for sources satisfying a mild support condition using si scalable coding and successive refinement wyner ziv coding as basic building blocks we provide a complete characterization of the rate distortion region for the important quadratic gaussian source with multiple jointly gaussian side informations where the side information quality is not necessarily monotonic along the scalable coding order a partial result is provided for the doubly symmetric binary source under the hamming distortion measure when the worse side information is a constant for which one of the outer bounds is strictly tighter than the other

projective curves of degree codimension 2 in this article we study nondegenerate projective curves x subset mathbb p d 1 of degree d which are not arithmetically cohen macaulay note that x pi p widetilde x for a rational normal curve widetilde x subset mathbb p d and a point p in mathbb p d setminus widetilde x 2 our main result is about the relation between the geometric properties of x and the position of p with respect to widetilde x we show that the graded betti numbers of x are uniquely determined by the rank hbox rk widetilde x p of p with respect to widetilde x in particular x satisfies property n 2 p if and only if p leq quad rk widetilde x p 3 therefore property n 2 p of x is controlled by quad rk widetilde x p and conversely quad rk widetilde x p can be read off from the minimal free resolution of x this result provides a non linearly normal example for which the converse to theorem 1 1 in eisenbud et al compositio math 141 1460 1478 2005 holds also our result implies that for nondegenerate projective curves x subset mathbb p d 1 of degree d which are not arithmetically cohen macaulay there are exactly lfloor frac d 2 2 rfloor distinct betti tables

on the rate loss of multiple description source codes the rate loss of a multiresolution source code mrsc describes the difference between the rate needed to achieve distortion d sub i in resolution i and the rate distortion function r d sub i this paper generalizes the rate loss definition to multiple description source codes mdscs and bounds the mdsc rate loss for arbitrary memoryless sources for a two description mdsc 2dsc the rate loss of description i with distortion d sub i is defined as l sub i r sub i r d sub i i 1 2 where r sub i is the rate of the ith description the joint rate loss associated with decoding the two descriptions together to achieve central distortion d sub 0 is measured either as l sub 0 r sub 1 r sub 2 r d sub 0 or as l sub 12 l sub 1 l sub 2 we show that for any memoryless source with variance spl sigma sup 2 there exists a 2dsc for that source with l sub 1 spl les 1 2 or l sub 2 spl les 1 2 and a l sub 0 spl les 1 if d sub 0 spl les d sub 1 d sub 2 spl sigma sup 2 b l sub 12 spl les 1 if 1 d sub 0 spl les 1 d sub 1 1 d sub 2 1 spl sigma sup 2 c l sub 0 spl les l sub g0 1 5 and l sub 12 spl les l sub g12 1 otherwise where l sub g0 and l sub g12 are the joint rate losses of a gaussian source with variance spl sigma sup 2

model misspecification tests model building and predictability in complex systems abstract in this paper we show that significant advantages can be realized by using functions of simple variables such as time lags as directions in reconstruction spaces for complicated time series first we show that more sensitive model misspecification tests can be constructed when the candidate model is used as one of the directions in the reconstruction space this naturally results in misspecification tests based on the construction of conditional probabilities which can reveal misspecified models even when other powerful methods such as the bds test applied to a sequence of residuals fails second we show that model building and predictability of the time series can be substantially improved by using an informational criterion to determine the functions with which to associate the directions of the reconstruction space this criterion is of the form of a conditional probability and is related to a measure of the short term predictability of the time series we consider specifically an example in which the search space of functions is linear combinations of time lags and we compare the resulting model with a linear least squares fit to the data we also show that this optimized reconstruction space can improve longer term predictability we demonstrate this by comparing longer term predictions made using the optimized space with predictions made using a simple time lagged reconstruction space

generic projections the equations defining projective varieties and castelnuovo regularity for a reduced irreducible projective variety x of degree d and codimension e in mathbb p n the castelnuovo mumford regularity rm reg x is defined as the least k such that x is k regular i e h i mathbb p n mathcal i x k i 0 for i ge1 where mathcal i x subset cal o mathbb p n is the sheaf of ideals of x there is a long standing conjecture about k regularity see 5 rm reg x le d e 1 here we show that rm reg x le d e 1 10 for any smooth fivefold and rm reg x le d e 1 20 for any smooth sixfold by extending methods used in 10 furthermore we give a bound for the regularity of a reduced connected and equidimensional locally cohen macaulay curve or surface in terms of degree d codimension e and an arithmetic genus rho a see theorem 4 1

rank two acm bundles on the del pezzo threefold with picard number 3 abstract a del pezzo threefold f with maximal picard number is isomorphic to p 1 p 1 p 1 in the present paper we completely classify locally free sheaves e of rank 2 such that h i f e t 0 for i 1 2 and t z such a classification extends similar results proved by e arrondo and l costa regarding del pezzo threefolds with picard number 1

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

on u statistics and v mise statistics for weakly dependent processes some probabilistic limit theorems for hoeffding s u statistic 13 and v mises functional are established when the underlying processes are not necessarily independent we consider absolutely regular processes 24 and processes x n n 1 which are uniformly mixing 14 as well as their time reversal x n n 1 called uniformly mixing in both directions of time many authors have weakened the hypothesis of independence in statistical limit theorems and considered m dependent markov or weakly dependent processes in particular for u statistics under weak dependence sen 22 has considered mixing processes and derived a central limit theorem and a law of the iterated logarithm while yoshihara 26 proved central limit theorems and a s results in the absolutely regular and uniformly mixing case here we extend these results considerably and prove central limit theorems and their rate of convergence in the prohorov metric and a berry esseen type theorem functional central limit theorems and a s approximation by a brownian motion extensions to multisample versions and other extensions are briefly discussed

universal quantization for separate encodings and joint decoding of correlated sources we consider the multi user lossy source coding problem for continuous alphabet sources in a previous work ziv proposed a single user universal coding scheme which uses uniform quantization with dither followed by a lossless source encoder entropy coder in this paper we generalize ziv s scheme to the multi user setting for this generalized universal scheme upper bounds are derived on the redundancies defined as the differences between the actual rates and the closest corresponding rates on the boundary of the rate region for the mean square error distortion measure it is shown that this scheme can achieve redundancies of no more than 0 754 b per sample for each user these bounds are obtained without the knowledge of the multi user rate region which is an open problem in general as a direct consequence of these results the inner and outer bounds on the rate distortion achievable region are obtained

families of space curves with large cohomology abstract we investigate space curves with large cohomology to this end we introduce curves of subextremal type this class includes all subextremal curves based on geometric and numerical characterizations of curves of subextremal type we show that if the cohomology is not too small then they can be parameterized by the union of two generically smooth irreducible families one of them corresponds to the subextremal curves for curves of negative genus the general curve of each of these families is also a smooth point of the support of an irreducible component of the hilbert scheme the two components have the same large dimension and meet in a subscheme of codimension one

time series and dependent variables we present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series the method is particularly suited to series with broad band spectra such as chaotic series with or without noise we derive quantities j e based on conditional probabilities whose magnitude roughly speaking is an indicator of the extent to which the kth element in the series is a deterministic function of the k j th element to within a measurement uncertainty e we apply our method to a number of deterministic time series generated by chaotic processes such as the tent logistic and h non maps as well as to sequences of quasi random numbers in all cases the 6j correctly indicate the expected dependencies we also show that the j are robust to the addition of substantial noise in a deterministic process in addition we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance e finally we discuss the behavior of the 6i as e approaches zero

curves of degree r 2 in pr cohomological geometric and homological aspects abstract let c p rk be a non degenerate projective curve of degree r 2 where r 3 by means of the hartshorne rao module of c we distinguish 4 different possible cases and an exceptional case which only appears if r 3 in any case c is obtained either by means of an embedding of an arbitrary smooth curve c 0 of genus 2 or by projecting an elliptic normal curve from a point or by projecting a rational normal curve from a line finally the possible minimal free resolutions of the homogeneous coordinate ring of c are studied

extended degree functions and monomial modules the arithmetic degree the smallest extended degree and the homological degree are invariants that have been proposed as alternatives of the degree of a module if this module is not cohen macaulay we compare these degree functions and study their behavior when passing to the generic initial or the lexicographic submodule this leads to various bounds and to counterexamples to a conjecture of gunston and vasconcelos respectively particular attention is given to the class of sequentially cohen macaulay modules the results in this case lead to an algorithm that computes the smallest extended degree

dependent variables in broad band continuous time series in this paper we continue our development of new methods for the analysis of broad band time series by deriving quantities which are able to indicate deterministic dependence of an element in one time series on elements in other time series these methods are very broadly applicable and are particularly well suited to the study of continuous time series in which the value of the function may depend on derivatives of the function itself or on other quantities we apply our methods to a number of mathematical examples including the lorentz equation the h6non heiles equations the forced brusselator and the mackey glass equation we show that our methods are very successful at indicating deterministic dependencies in these systems even if the time series are highly chaotic statistical aspects of our procedure are discussed as are a number of interesting and surprising epistomological implications

non degenerate curves with maximal hartshorne rao module extending results for space curves we establish bounds for the cohomology of a non degenerate curve in projective n space as a consequence for any given n we determine all possible pairs d g where d is the degree and g is the arithmetic genus of the curve furthermore we show that curves attaining our bounds always exist and describe properties of these extremal curves in particular we determine the hartshorne rao module the generic initial ideal and the graded betti numbers of an extremal curve

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

on successive refinement for the wyner ziv problem achievable rates are characterized for successive refinement sr in the wyner ziv scenario namely in the presence of correlated side information si at the receivers in this setting the encoder is assumed to operate in two stages where the first corresponds to relatively low rate and high distortion and the second comprising a refinement code on top of the first code is aimed at reproduction at reduced distortion both decoders for low rate high distortion and for high rate low distortion are equipped with si streams correlated to the source but unavailable to the encoder furthermore it is assumed that the decoder that receives the higher rate bitstream i e the additional refinement bits accesses also si of better quality than that of the lower resolution decoder by better quality we mean that the source and the si are modeled together as a stochastically degraded joint source where the encoded symbols the si at the refinement stage and the si at the initial coarse stage form a markov chain in this order for a memoryless joint process that includes the source to be encoded and its instantaneously correlated si streams necessary and sufficient conditions are furnished in terms of single letter formulas for the achievability of a pair of rates corresponding to two given distortion levels special attention is devoted to the degenerate but important case where the two si streams at the two decoders are identical for this case conditions are provided for successive refinability in the sense of the existence of codes that asymptotically achieve the wyner ziv rate distortion function simultaneously at both distortion levels in this context the doubly symmetric binary source with the hamming distortion measure and the jointly gaussian source with the squared error distortion measure are successively refinable in the wyner ziv setting it is demonstrated that a source that is not successively refinable in the ordinary sense i e without si may become successively refinable in the presence of si at the decoders

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

analog matching of colored sources to colored channels analog uncoded transmission provides a simple and robust scheme for communicating a gaussian source over a gaussian channel under the mean squared error mse distortion measure unfortunately its performance is usually inferior to the all digital separation based source channel coding solution which requires exact knowledge of the channel at the encoder the loss comes from the fact that except for very special cases e g white source and channel of matching bandwidth bw it is impossible to achieve perfect matching of source to channel and channel to source by linear means we show that by combining prediction and modulo lattice operations it is possible to match any colored gaussian source to any colored gaussian noise channel of possibly different bw hence achieve shannon s optimum attainable performance r d c furthermore when the source and channel bws are equal but otherwise their spectra are arbitrary this scheme is asymptotically robust in the sense that for high signal to noise ratio snr a single encoder independent of the noise variance achieves the optimum performance the derivation is based upon a recent modulo lattice modulation scheme for transmitting a wyner ziv source over a dirty paper channel

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

rate distortion function when side information may be present at the decoder a discrete memoryless source x sub k is to be coded into a binary stream of rate r bits symbol such that x sub k can be recovered with minimum possible distortion the system is to be optimized for best performance with two decoders one of which has access to side information about the source for given levels of average distortion for these two decoders the minimum achievable rate r in the usual shannon theory sense is given as a per letter minimization of information theoretic quantities the problem is solved for two cases where the encoder is and is not informed of the side information

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

on the genus and hartshorne rao module of projective curves in this paper optimal upper bounds for the genus and the dimension of the graded components of the hartshorne rao module of curves in projective n space are established this generalizes earlier work by hartshorne h and martin deschamps and perrin mdp special emphasis is put on curves in bf p 4 the first main result is a so called restriction theorem it says that a non degenerate curve of degree d geq 4 in bf p 4 over a field of characteristic zero has a non degenerate general hyperplane section if and only if it does not contain a planar curve of degree d 1 see th 1 3 then using methods of brodmann and nagel bounds for the genus and hartshorne rao module of curves in bf p n with non degenerate general hyperplane section are derived it is shown that these bounds are best possible in a very strict sense coupling these bounds with the restriction theorem gives the second main result for curves in bf p 4 then curves of maximal genus are investigated the betti numbers of their minimal free resolutions are computed and a description of all reduced curves of maximal genus in bf p n of degree geq n 2 is given finally all pairs d g of integers which really occur as the degree d and genus g of a non degenerate curve in bf p 4 are described

lattices for distributed source coding jointly gaussian sources and reconstruction of a linear function consider a pair of correlated gaussian sources x 1 x 2 two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder the decoder is interested in reconstructing a linear combination of x 1 and x 2 to within a mean square distortion of d we obtain an inner bound to the optimal rate distortion region for this problem a portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components x 1 and x 2 first this results in a better rate region for certain parameter values our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory we then consider the case of linear reconstruction of k sources and provide an inner bound to the optimal rate distortion region some parts of the inner bound are achieved using the following coding structure lattice vector quantization followed by ldquocorrelatedrdquo lattice structured binning

systematic lossy source channel coding the fundamental limits of systematic communication are analyzed in systematic transmission the decoder has access to a noisy version of the uncoded raw data analog or digital the coded version of the data is used to reduce the average reproduced distortion d below that provided by the uncoded systematic link and or increase the rate of information transmission unlike the case of arbitrarily reliable error correction d spl rarr 0 for symmetric sources channels where systematic codes are known to do as well as nonsystematic codes we demonstrate that the systematic structure may degrade the performance for nonvanishing d we characterize the achievable average distortion and we find necessary and sufficient conditions under which systematic communication does not incur loss of optimality the wyner ziv 1976 rate distortion theorem plays a fundamental role in our setting the general result is applied to several scenarios for a gaussian bandlimited source and a gaussian channel the invariance of the bandwidth signal to noise ratio snr in decibels product is established and the optimality of systematic transmission is demonstrated bernoulli sources transmitted over binary symmetric channels and over certain gaussian channels are also analyzed it is shown that if nonnegligible bit error rate is tolerated systematic encoding is strictly suboptimal

on robustness of hybrid digital analog source channel coding with bandwidth mismatch for transmission of memoryless gaussian sources over channels with additive white gaussian noise the tradeoff between the distortion when the channel quality is good versus bad is investigated under the constraint that the distortion is optimal when the channel has the targeted median quality the problem was proposed by tian and shamai who subsequently proved remarkable achievability results for bandwidth expansion ratios kappa which are integers or unit fractions i e kappa 2 3 4 ldots or kappa 1 2 1 3 1 4 ldots their result is extended here to all kappa geq 2 and kappa leq 1 2 by generalizing the hybrid digital analog hda scheme of wilson et al to the case of bandwidth mismatch finally novel schemes are proposed for 1 2 leq kappa and 1 achieving nontrivial tradeoffs outperforming all known schemes these latter schemes rely on another extension of the hda scheme by wilson et al namely the relaxation of the independence of source and channel input sequences

single sample robust joint source channel coding achieving asymptotically optimum scaling of sdr versus snr in this paper we consider the problem of zero delay encoding a single source sample robust joint source channel coding over an additive white gaussian noise channel we propose a new scheme that unlike previously known coding schemes achieves the optimal scaling of the source signal to distortion ratio sdr versus channel signal to noise ratio snr also we propose a family of robust codes which together maintain a bounded gap with the optimum sdr curve in terms of decibel to show the importance of this result we derive some theoretical bounds on the asymptotic performance of a widely used class of delay limited hybrid digital analog hda coding schemes based on superposition of analog and digital components we show that unlike the delay unlimited case for this class of delay limited hda codes the asymptotic performance loss is unbounded in terms of decibels although the main focus of this paper is on uniform sources it is also shown that the results are also valid for a more general class of well behaved distributions

correlation integral as a tool for distinguishing between dynamics and statistics in time series data abstract we propose a new test for time series data for proper choice of processing technique dynamical or statistical it is based upon the normalized slope of the correlation integral m m 1 d ln c d ln where m is the embedding dimension it is shown that when does not tend to 0 on the resolved range of scales as m grows then there will be serious limitations for dynamical methods even if the data are dynamical by nature in the latter case it means that the length of time series does not allow to resolve small scales and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques such as estimating lyapunov exponents or predicting time series

rigorous statistical procedures for data from dynamical systems various questions about the invariant measures of a dynamical system can be answered by computations of regular functionals or by ranking methods based on a set of observations this includes symmetry tests and the determination of dimension coefficients the paper contains the theoretical results and several simulations explain the methods

the hilbert function of generic plane sections of curves of ℙ3 a characteristic condition is given on a zero dimensional differentiable 0 sequenceh hi i 0 h1 3 in order to be the hilbert function of a generic plane section of a reduced irreducible curve of 3 hence of points of 2 with the uniform position property in this way an answer is given to some question stated by harris in ha2

on the rate loss of multiresolution source codes in the wyner ziv setting in this paper we present upper bounds on the rate loss of the multiresolution source code in the wyner ziv setting wz mrsc we define two types of rate loss the side information rate loss and the multiresolution rate loss to measure the nonsuccessive refinability the former compares the rates achievable by a given wz mrsc to the corresponding minimal rates achievable by single resolution wyner ziv codes and the latter refers to the difference between the rates achievable by a given wz mrsc and the minimal achievable rates by any wz mrsc at the same resolution we bound these two types of rate loss from above and show that the side information rate loss and corresponding successive refinability largely depend on the side information while there exist small universal constant upper bounds on the multiresolution rate loss that are generally independent of the side information

finding the embedding dimension and variable dependencies in time series we present a general method the test which establishes functional dependencies given a sequence of measurements the approach is based on calculating conditional probabilities from vector component distances imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the embedding dimension and variable dependencies the power of the method is illustrated on synthetic time series with different time lag dependencies and noise levels and on the sunspot data the virtue of the method for preprocessing data in the context of feedforward neural networks is demonstrated also its applicability for tracking residual errors in output units is stressed

the rate loss in the wyner ziv problem the rate distortion function for source coding with side information at the decoder the wyner ziv problem is given in terms of an auxiliary random variable which forms a markov chain with the source and the side information this markov chain structure typical to the solution of multiterminal source coding problems corresponds to a loss in coding rate with respect to the conditional rate distortion function i e to the case where the encoder is fully informed we show that for difference or balanced distortion measures this loss is bounded by a universal constant which is the minimax capacity of a suitable additive noise channel furthermore in the worst case this loss is equal to the maximin redundancy over the rate distortion function of the additive noise test channel for example the loss in the wyner ziv problem is less than 0 5 bit sample in the squared error distortion case and it is less than 0 22 bit for a binary source with hamming distance these results have implications also in universal quantization with side information and in more general multiterminal source coding problems

curves of degree two and ropes on a line their ideals and even liaison classes abstract in this paper we investigate degree two curves of arbitrary codimension this requires to study also ropes supported on a line after establishing several characterizations of ropes supported on a line we describe their homogeneous ideals and hartshorne rao modules in particular we characterize the arithmetically buchsbaum ropes then we describe the even gorenstein liaison classes of the non arithmetically buchsbaum non degenerate ropes generalizing a well know result of migliore on double lines of codimension two the result relies on the explicit description of certain arithmetically gorenstein curves with maximal tangent spaces at each point as a consequence we can decide if two curves of degree two belong to the same gorenstein liaison class finally we show as an application how ropes can be used in order to construct quasi extremal curves

rate distortion when side information may be absent the problem is considered of encoding a discrete memoryless source when correlated side information may or may not be available to the decoder it is assumed that the side information is not available to the encoder the rate distortion function r d l d 2 is determined where d 1 is the distortion achieved with side information and d 2 is the distortion achieved without it a generalization is made to the case of m decoders each of which is privy to its own side information an appropriately defined d admissible rate for this general case is shown to equal r d when the side information sources satisfy a specified degradedness condition explicit results are obtained in the quadratic gaussian case and in the binary hamming case

canonical curves with low apolarity abstract let k be an algebraically closed field and let c be a non hyperelliptic smooth projective curve of genus g defined over k since the canonical model of c is arithmetically gorenstein macaulay s theory of inverse systems allows us to associate to c a cubic form f in the divided power k algebra r g 3 in g 2 variables the apolarity ap c of c is the minimal number t of linear form l 1 l t r g 3 needed to write f as the sum of their divided power cubes it is easy to see that ap c g 2 and p de poi and f zucconi classified curves with ap c g 2 when k c in this paper we give a complete characteristic free classification of curves c with apolarity g 1 and g 2

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

distortion bounds for broadcasting with bandwidth expansion we consider the problem of broadcasting a single gaussian source to two listeners over a gaussian broadcast channel with rho channel uses per source sample where rho 1 a distortion pair d1 d2 is said to be achievable if one can simultaneously achieve a mean squared error mse d1 at receiver 1 and d2 at receiver 2 the main result of this correspondence is an outer bound for the set of all achievable distortion pairs that is we find necessary conditions under which d1 d2 is achievable we then apply this result to the problem of point to point transmission over a gaussian channel with unknown signal to noise ratio snr and rho 1 we show that if a system must be optimal at a certain snrmin then asymptotically the system distortion cannot decay faster than o 1 snr as for achievability we show that a previously reported scheme due to mittal and phamdo 2002 is optimal at high snr we introduce two new schemes for broadcasting with bandwidth expansion combining digital and analog transmissions we finally show how a system with a partial feedback returning from the bad receiver to the transmitter and to the good receiver achieves a distortion pair that lies on the outer bound derived here

some linear syzygy conjectures in this paper we introduce four conjectures refining a very useful result of mark green s on the linear part of the free resolution of a graded module over a polynomial ring we prove a number of special cases of the conjectures including all cases pertaining to modules over a polynomial ring in at most four variables in a later paper we will give a complete classification of the nets of skew symmetric transformations on a sdimensional vector space over an algebraically closed field from which we deduce that our conjectures are true in five variables as well

a bound on the geometric genus of projective varieties verifying certain flag conditions fix integers n r s1 sl and let s n r s1 sl be the set of all integral projective and nondegenerate varieties v of degree s1 and dimension n in the projective space pr such that for all i 2 l v does not lie on any variety of dimension n i 1 and degree sl we determine an upper bound gh n r s1 sl depending only on n r s1 sl for the number g n r s1 sl max pg v v s n r s1 sl where pg v denotes the geometric genus of v in case n 1 and l 2 the study of an upper bound for the geometric genus has a quite long history and for n 1 l 2 and s2 r n it has been introduced by harris we exhibit sharp results for particular ranges of our numerical data n r s1 sl for instance we extend halphen s theorem for space curves to the case of codimension two and characterize the smooth complete intersections of dimension n in pn 3 as the smooth varieties of maximal geometric genus with respect to appropriate flag condition this result applies to smooth surfaces in p5 next we discuss how far gh n r s1 sl is from g n r s1 sl and show a sort of lifting theorem which states that at least in certain cases the varieties v s n r s1 sl of maximal geometric genus g n r s1 sl must in fact lie on a flag such as v v n s1 v n 1 s2 v n l 1 sl p r where v j s denotes a subvariety of pr of degree s and dimension j we also discuss further generalizations of flag conditions and finally we deduce some bounds for castelnuovo s regularity of varieties verifying flag conditions 0 introduction fix integers n r s1 sl such that 1 n r 2 2 l r n and let s n r s1 sl be the set of all integral projective and nondegenerate varieties v of degree s1 and dimension n in the projective space p such that for all i 2 l v does not lie on any variety of dimension n i 1 and degree sl we determine an upper bound g n r s1 sl depending only on n r s1 sl for the number g n r s1 sl max pg v v s n r s1 sl 0 1 received by the editors october 23 1995 1991 mathematics subject classification primary 14j99 14m07 14m10 secondary 14f17

joint source channel coding of a gaussian mixture source over the gaussian broadcast channel suppose that we want to send a description of a single source to two listeners through a gaussian broadcast channel where the channel is used once per source sample the problem of joint source channel coding is to design a communication system to minimize the distortion d sub 1 at receiver 1 and at the same time minimize the distortion d sub 2 at receiver 2 if the source is gaussian the optimal solution is well known and it is achieved by an uncoded analog scheme we consider a gaussian mixture source we derive inner and outer bounds for the distortion region of all d sub 1 d sub 2 pairs that are simultaneously achievable the outer bound is based on the entropy power inequality while the inner bound is attained by a digital over analog encoding scheme which we present we also show that if the modes of the gaussian mixture are highly separated our bounds are tight and hence our scheme attains the entire distortion region this optimal region exceeds the region attained by separating source and channel coding although it does not contain the ideal point d sub 1 d sub 2 r sup 1 c sub 1 r sup 1 c sub 2

statistical tests for deterministic effects in broad band time series we derive a normalized version of the indicators of savit and green and prove that these normalized statistics have asymptotically a normal distribution with a mean of zero and standard deviation of one if the time series is random in the sense of being lid independent and identically distributed we verify this result numerically and study the magnitude of the finite size effects we also show that these statistics are very sensitive to the existence of deterministic effects in the series even if the underlying deterministic structure is complex such as those generated by a chaotic system we show that with moderate amounts of data the statistics can easily indicate the presence of an underlying attractor even in the presence of iid noise which is as large as or greater than the signal finally we discuss the generalization of our approach to include 1 other null hypotheses besides lid which express assumptions of specific dependencies and 2 the study of deterministic effects between more than one time series

non degenerate projective curves with very degenerate hyperplane section in this paper we study the hilbert scheme of non degenerate locally cohen macaulay projective curves with general hyperplane section spanning a linear space of dimension 2 and minimal hilbert function the main result is that those curves are almost always the general element of a generically smooth component hn d g of the corresponding hilbert scheme moreover we show that the curves with maximal cohomology almost always correspond to smooth points of hn d g

projective embeddings of projective schemes blown up at subschemes suppose x is a nonsingular projective scheme z a nonsingular closed subscheme of x let x be the blowup of x centered at z e0 the pull back of a general hyperplane in x and e the exceptional divisor in this paper we study projective embeddings of x given by divisors when x satisfies a necessary condition we give explicit values of d and such that for all e 0 and embeds x as a projectively normal and arithmetically cohen macaulay scheme we also give a uniform bound for the regularities of the ideal sheaves of these embeddings and study their asymptotic behaviour as t gets large compared to e when x is a surface and z is a 0 dimensional subscheme we further show that these embeddings possess property np for all t e 0

geometric consequences of extremal behavior in a theorem of macaulay f s macaulay gave necessary and sufficient conditions on the growth of a nonnegative integer valued function which determine when such a function can be the hilbert function of a standard graded k algebra we investigate some algebraic and geometric consequences which arise from the extremal cases of macaulay s theorem our work also builds on the fundamental work of g gotzmann our principal applications are to the study of hilbert functions of zeroschemes with uniformity conditions as a consequence we have new strong limitations on the possible hilbert functions of the points which arise as a general hyperplane section of an irreducible curve