bounds for green s functions on noncompact hyperbolic riemann orbisurfaces of finite volume in jorgenson and kramer compos math 142 679 700 2006 derived bounds for the canonical green s function and the hyperbolic green s function defined on a compact hyperbolic riemann surface in this article we extend these bounds to noncompact hyperbolic riemann orbisurfaces of finite volume and of genus greater than zero which can be realized as a quotient space of the action of a fuchsian subgroup of first kind on the hyperbolic upper half plane

functional compression through graph coloring motivated by applications to sensor networks and privacy preserving databases we consider the problem of functional compression the objective is to separately compress possibly correlated discrete sources such that an arbitrary but fixed deterministic function of those sources can be computed given the compressed data from each source we consider both the lossless and lossy computation of a function specifically we present results of the rate regions for three instances of the problem where there are two sources 1 lossless computation where one source is available at the decoder 2 under a special condition lossless computation where both sources are separately encoded and 3 lossy computation where one source is available at the decoder for all of these instances we present a layered architecture for distributed coding first preprocess data at each source using colorings of certain characteristic graphs and then use standard distributed source coding a la slepian and wolfs scheme to compress them for the first instance our results extend the approach developed by orlitsky and roche 2001 in the sense that our scheme requires simpler structure of coloring rather than independent sets as in the previous case as an intermediate step to obtain these results we obtain an asymptotic characterization of conditional graph coloring for an or product of graphs generalizing a result of korner 1973 which should be of interest in its own right

tuning to resonances with iterative time reversal this paper considers a distributed wave based sensing system that probes a scene consisting of multiple interacting idealized targets each sensor is a collocated transmit receive pair that is capable of transmitting arbitrary wideband waveforms we address the problem of finding the space time transmit waveform that provides the best target detection performance in the sense of maximizing the energy scattered back into the receivers our approach is based on earlier theoretical work that showed for an idealized infinite half space geometry that the solution could be constructed by an iterative time reversal tr process in this paper we give a more realistic example involving a two sensor time domain system we show that for this system the iterative tr process can be used to tune automatically to all the target resonances that are within the bandwidth of the interrogating radar system we show that although obtaining eigenvalues and hence resonances of the scattering operator is in general unstable using the iterative tr process to obtain the resonances is a stable process moreover we show that these resonance frequencies are connected to the poles of the singularity expansion method

a survey of the theory of source coding with a fidelity criterion the purpose of this paper is threefold 1 to acquaint the reader with the types of problems that have been considered in the area of source coding with a fidelity criterion 2 to survey results that have been obtained on these problems and 3 to outline future research trends in the area

indirect and direct gaussian distributed source coding problems we consider the distributed source coding system of l correlated gaussian sources y l l 1 2 ldots l which are noisy observations of correlated gaussian remote sources x k k 1 2 ldots k we assume that y l t y 1 y 2 ldots y l is an observation of the source vector x k t x 1 x 2 ldots x k having the form y l ax k n l where a is a l times k matrix and n l t n 1 n 2 ldots n l is a vector of l independent gaussian random variables also independent of x k in this system l correlated gaussian observations are separately compressed by l encoders and sent to the information processing center we study the remote source coding problem where the decoder at the center attempts to reconstruct the remote source x k we consider three distortion criteria based on the covariance matrix of the estimation error on x k for each of those three criteria we derive explicit inner and outer bounds of the rate distortion region next in the case of k l and a i l we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation y l x l n l to investigate this problem we shall establish a result that provides a strong connection between the remote source coding problem and multiterminal source coding problem using this result we derive several new partial solutions to the multiterminal source coding problem

the gaussian ceo problem for scalar sources with arbitrary memory in this paper we consider the achievable sum rate distortion tradeoff for the gaussian central estimation officer ceo problem with a scalar source having arbitrary memory we describe how the arbitrary memory problem can be fully characterized by using known results for the vector ceo problem and then we formulate the variational problem of minimizing the sum rate subject to a distortion constraint to solve the problem we extend the conventional lagrange method and show that if the solution exists it should consist of a zero part and a non zero part where the non zero part is determined by solving a set of euler equations by calculating the second variation of the min sum rate problem a sufficient condition is also found that can be used to determine if the necessary solution results in the minimal sum rate the special case of two terminals is examined in detail and it is shown that an analytical solution is possible in this case analysis and discussion with examples are provided to illustrate the theoretical results the general solution obtained in this paper is shown to be compatible with the previous results for cases such as the problem of rate evaluation for sources without memory

multiterminal source coding with high resolution we consider separate encoding and joint decoding of correlated continuous information sources subject to a difference distortion measure we first derive a multiterminal extension of the shannon lower bound for the rate region then we show that this shannon outer bound is asymptotically tight for small distortions these results imply that the loss in the sum of the coding rates due to the separation of the encoders vanishes in the limit of high resolution furthermore lattice quantizers followed by slepian wolf lossless encoding are asymptotically optimal we also investigate the high resolution rate region in the remote coding case where the encoders observe only noisy versions of the sources for the quadratic gaussian case we establish a separation result to the effect that multiterminal coding aimed at reconstructing the noisy sources subject to the rate constraints followed by estimation of the remote sources from these reconstructions is optimal under certain regularity conditions on the structure of the coding scheme

distributed source coding using abelian group codes a new achievable rate distortion region a distributed source coding problem with a joint distortion criterion that depends on the sources and the reconstruction is considered in this work while the prevalent trend in information theory has been to prove achievability results using shannon s random coding arguments using structured random codes offer rate gains over unstructured random codes for many problems motivated by this a new achievable rate distortion region an inner bound to the performance limit is presented for this problem for discrete memoryless sources based on good structured random nested codes built over abelian groups for certain sources and distortion functions the new rate region is shown to be strictly bigger than the berger tung rate region which has been the best known achievable rate region for this problem till now this is done using numerical plots achievable rates for single user source coding using abelian group codes are also obtained as a corollary of the main coding theorem it is shown that nested linear codes achieve the shannon rate distortion function in the arbitrary discrete memoryless case

the singular function expansion in time dependent scattering a class of linear initial boundary value problems relevant to time dependent scattering is solved exactly in terms of the complete orthogonal set of singular functions of the appropriate integral operator the method is primarily presented as a mathematically defensible alternative to the eigenmode expansion method the results extend the singularity expansion method to include the steady state response at source frequencies and provide a connection between resonance behavior in the steady state and low loss natural modes the method furthermore leads to an efficient automatic algorithm for the determination of natural modes and natural frequencies by observation of the singular values the conclusions are supported by numerical calculations

distributed rate distortion with common components we describe a scheme for rate distortion with distributed encoding in which the sources to be compressed contain a common component we show that this scheme is optimal in some situations and that it strictly improves upon existing schemes which do not make full use of common components this establishes that independent quantization followed by independent binning is not optimal for the two encoder problem with a distortion constraint on one source we also show that independent quantization and binning is suboptimal for the three encoder problem in which the goal is to reproduce one of the sources losslessly this provides a counterexample that is fundamentally different from one provided earlier by korner and marton the proofs rely on the binary analogue of the entropy power inequality and the existence of a rate loss for the binary symmetric wyner ziv problem

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 the optimality of binning for distributed hypothesis testing we study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data the aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value for related problems in distributed source coding schemes based on random binning perform well and are often optimal for distributed hypothesis testing however the use of binning is hindered by the fact that the overall error probability may be dominated by errors in the binning process we show that despite this complication binning is optimal for a class of problems in which the goal is to test against conditional independence we then use this optimality result to give an outer bound for a more general class of instances of the problem

rate region of the quadratic gaussian two encoder source coding problem we determine the rate region of the quadratic gaussian two encoder source coding problem this rate region is achieved by a simple architecture that separates the analog and digital aspects of the compression furthermore this architecture requires higher rates to send a gaussian source than it does to send any other source with the same covariance our techniques can also be used to determine the sum rate of some generalizations of this classical problem our approach involves coupling the problem to a quadratic gaussian ldquoceo problem rdquo

arakelov self intersection numbers of minimal regular models of modular curves x_0 p 2 x0 p2 we compute an asymptotic expression for the arakelov self intersection number of the relative dualizing sheaf of edixhoven s minimal regular model for the modular curve x 0 p 2 over mathbb q the computation of the self intersection numbers are used to prove an effective version of the bogolomov conjecture for the semi stable models of modular curves x 0 p 2 and obtain a bound on the stable faltings height for those curves in a companion article banerjee and chaudhuri in isr j math 2020

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

the asymptotic behavior of green s functions for degenerating hyperbolic surfaces given a degenerating family of riemann surfaces of genus g 2 it is a natural and important question to study their spectral behaviors in particular green s functions during degeneration see 9 10 17 11 13 and 5 by the uniformization theorem any riemann surface of genus g 2 has a canonical metric of constant curvature 1 from now on we call a riemann surface with this canonical metric a hyperbolic surface and a degenerating family of hyperbolic surfaces is denoted by st l 0 the degeneration of st is caused by the pinching of several simple closed geodesics 71 l 7 1 on st that is the lengths of these geodesics go to zero as l 0 let at be the laplacian of st then the kernel of at consists of functions which are constant on each connected component of st and at is invertible on the orthogonal complement of the kernel the schwartz kernel of this inverse is called the green function of st and denoted by g z w t for z w sl we would like to study the asymptotic behavior of g z w i as l o in order to compare functions on s o and st we use the harmonic map of infinite energy so s 71 l 7 l constructed by wolf el4 intuitively speaking this map z opens up each node a pair of cusps of so into a simple closed pinching geodesic of sf at first we assume that there is only one pinching geodesic l 7 of length l on s if 7 separates st then so has two components se and so z of genus g gz respectively

perturbation of resonances abstract resonances are often treated under the assumption that they are simple poles of the resolvent kernel green s function there are no physical or mathematical reasons which exclude the existence of multiple poles of green s functions even in the case when the potential is real valued in this case the poles in the physical sheet are simple since the schrodinger operator is selfadjoint but the poles on the unphysical sheet are not necessarily simple we prove that sufficiently small perturbations of the potential or boundary in diffraction problems do not increase the multiplicity of the resonances on any fixed compact domain of the complex plane we also observe that a knowledge of the set of the green s function poles does not determine the potential uniquely

the likelihood encoder for lossy compression a likelihood encoder is studied in the context of lossy source compression the analysis of the likelihood encoder is based on the soft covering lemma it is demonstrated that the use of a likelihood encoder together with the soft covering lemma yields simple achievability proofs for classical source coding problems the cases of the point to point rate distortion function the rate distortion function with side information at the decoder i e the wyner ziv problem and the multi terminal source coding inner bound i e the berger tung problem are examined in this paper furthermore a non asymptotic analysis is used for the point to point case to examine the upper bound on the excess distortion provided by this method the likelihood encoder is also related to a recent alternative technique using the properties of random binning

points de petite hauteur sur les courbes modulaires x0 n let n be a square free integer prime to 6 let the imbeding of x 0 n in its jacobian relative to the point we show that the set is finite and that is infinite this explicit form of the bogomolov conjecture is obtained by an estimation of the self intersection of the dualizing sheaf in the sense of arakelov theory of modular curves this result is obtained by estimating several quantities attached to the arakelov metric on x 0 n starting with petersson s trace formula

lattice based robust distributed source coding for three correlated sources the problem of robust distributed source coding for three correlated sources is studied in this work a lattice based scheme is proposed and the analysis of its performance is provided in the high resolution regime special attention is paid to the degenerate case where the three sources are gaussian and identical in this case our scheme is shown to achieve within an asymptotic gap of 0 069 bits in terms of rate per description from the information theoretic limit of quadratic symmetric gaussian multiple description coding with central and individual decoders when the side distortion and the ratio between the central and side distortions both approach 0

source coding theory for a triangular communication system a rate distortion problem is considered for a triangular communication system tcs which has one encoder f and two decoders g sub x and g sub y the encoder f maps correlated source outputs x sup k y sup k to two codewords w sub x and w sub y which are sent to g sub x and g sub y respectively the decoders g sub x and g sub y can communicate with each other via rate constrained channels as many times as they need and g sub x reproduces x spl circ sup k while g sub y reproduces y spl circ sup k the admissible rate distortion region is determined for this tcs furthermore the relations between the tcs and the gray wyner 1974 system wyner s 1974 common information yamamoto s cascade communication system 1981 and the successive refinement system are discussed

multiple access channels with states causally known at transmitters it has been recently shown by lapidoth and steinberg that strictly causal state information can be beneficial in multiple access channels macs specifically it was proved that the capacity region of a two user mac with independent states each known strictly causally to one encoder can be enlarged by letting the encoders send compressed past state information to the decoder in this study a generalization of the said strategy is proposed whereby the encoders compress also the past transmitted codewords along with the past state sequences the proposed scheme uses a combination of long message encoding compression of the past state sequences and codewords without binning and joint decoding over all transmission blocks the proposed strategy has been recently shown by lapidoth and steinberg to strictly improve upon the original one capacity results are then derived for a class of channels that include two user modulo additive state dependent macs moreover the proposed scheme is extended to state dependent macs with an arbitrary number of users finally output feedback is introduced and an example is provided to illustrate the interplay between feedback and availability of strictly causal state information in enlarging the capacity region

the multiple access channel with causal side information common state we show that if a memoryless multiple access channel mac is governed by an independent and identically distributed state sequence then unlike the single user case the capacity region is typically increased if the state is revealed to the encoders in a strictly causal way for this scenario we derive inner and outer bounds on the capacity region for the gaussian mac whose state sequence comprises the channel noise we compute the capacity region and propose a variation on the schalkwijk kailath scheme that achieves capacity with a double exponential decay of the maximal probability of error we also study the causal case for which we derive an achievable region which is typically strictly larger than the region achievable with naive shannon strategies

harmonic differentials and infinite geodesic joining two punctures on a riemann surface let m be a hyperbolic riemann surface of finite volume the harmonic dual form to an infinite geodesic joining two punctures on m is obtained in two different ways first of all using the degeneration of hyperbolic eisenstein series it is made explicit in terms of these secondly generalizing the construction of kudla and millson to the case of an infinite geodesic joining two punctures we give an automorphic realization of this harmonic form

on the asymptotic behavior of counting functions associated to degenerating hyperbolic riemann surfaces abstract in this article we will study what we call weighted counting functions on hyperbolic riemann surfaces of finite volume ifmis compact then we define the weighted counting function forw 0 to be n m w t n t t n w where n is the set of eigenvalues of the laplacian which acts on the space of smooth functions onm ifmis non compact then we define the weighted counting functionnm w t via the inverse laplace transform from which one can express the weighted counting function in terms of spectral data associated tom see proposition 5 1 and remark 5 2 using the convergence results from jl2 concerning the regularized heat trace on finite volume hyperbolic riemann surfaces we shall prove the following results t heorem let mldenote a degenerating family of compact or non compact hyperbolic riemann surfaces of finite volume which converges to the non compact hyperbolic surface m0 let s ldenote the set of lengths of pinching geodesics on the family of surfaces ml for w 0and t 1 4 let g l w t 2 w 1 16 1 2 n 1 l k s 1 l k sinfh nl k 2 t 1 4 nl k 2 2 w 1 2 2 j w 1 2 nl k t 1 4 where js x is the j bessel function and x is the standard gamma function for0 t 3 2andt 0 we have n m l w t g l w t n m 0 w t o 1 as l 0 b for w 0andt 0 we have n m l w t g l w t o l k s l log 1 l k as l 0 c for w 0andt 1 4 we have g l w t 2 w 1 t 1 4 w 1 2 4 1 2 w 3 2 l k s l log 1 l k o 1 as l 0 observe that by takingt

multiterminal source coding achievable rates and reliability some open problems concerning classical multiterminal configuration in which two correlated sources x and y are encoded separately and decoded by common decoder with respect to a fidelity criterion for messages of both sources are resolved the results of berger and yeung 1989 are expanded in two directions first we determine the rate distortion region r spl delta of achievable rates r sub x r sub y for a given spl delta spl delta sub x spl delta sub y with spl delta sub x the permissible distortion level for reproduction of x and spl delta sub y for y thus we give a full solution of the problem noted by kaspi and berger 1982 they constructed the inner bound for r spl delta and solved by berger and yeung for the case of one distortion second we introduce the notion of rate reliability distortion region for the multiterminal source encoding problem more precisely the region of admissible rates of codes ensuring exponential decrease with a given exponent e 0 of the probability of exceeding the distortion levels spl delta sub x or spl delta sub y the inner and outer bounds for this region r e spl delta are constructed the analytical representation obtained for r spl delta proved to be somewhat simpler than that considered by kaspi and berger and by berger and yeung ours uses only variables pertaining to the problem statement with no auxiliary ones

two way source coding with a helper consider the two way rate distortion problem in which a helper sends a common limited rate message to both users based on side information at its disposal we characterize the region of achievable rates and distortions when the markov relation helper user 1 user 2 holds the main insight of the result is that in order to achieve the optimal rate the helper may use a binning scheme as in wyner ziv where the side information at the decoder is the further user namely user 2 we derive these regions explicitly for the gaussian sources with square error distortion analyze a tradeoff between the rate from the helper and the rate from the source and examine a special case where the helper has the freedom to send different messages at different rates to the encoder and the decoder the converse proofs use a technique for verifying markov relations via undirected graphs

on the geometry and laplacian of a graph abstract let g be a simple graph on n vertices and let l be the laplacian matrix of g we point out some connections between the geometric properties of g and the spectrum of l the multiplicities and eigenspaces as well as the eigenvalues of l are of geometric interest some historical information and relations of l to other matrices associated with g are also described

application of the singular function expansion to an integral equation for scattering the dirichlet scattering problem is solved exactly for a surface of arbitrary smooth shape the solution is given in terms of the complete orthonormal set of functions defined on the surface and arising as singular functions of the integral operator since the singular values do not have a point of accumulation at zero the method is of much greater practical value than the eigenmode expansion method eem since the terms in the infinite series are naturally ordered by size of singular value the dominance of one or several terms in the series may be established without explicit evaluation of the coupling coefficients extentions of the method to other boundary value problems and applications to the singularity expansion method sem are described

distributed source coding of correlated gaussian remote sources we consider the distributed source coding system for l correlated memoryless gaussian remote sources specified with l correlated gaussian random variables xi i 1 2 l we deal with the case where each of l distributed encoders cannot directly observe the source xi but its noisy version yi xi ni here ni i 1 2 l are independent additive l gaussian noises also independent of xi i 1 2 l on this coding system the determination problem of the rate distortion region remains open in general in this paper we derive explicit outer and inner bounds of the rate distortion region we further find an explicit sufficient condition for those two bounds to match we also study the sum rate part of the rate distortion region when the correlation has some symmetrical property we derive an explicit upper bound of the sum rate part from the inner bounds of the rate distortion region on a lower bound we derive a new explicit bound by making full use of the symmetrical property of the correlation we further derive an explicit necessary and sufficient condition for the lower bound to coincide with the upper bound

degenerescence de series d eisenstein hyperboliques in this work we deal with hyperbolic eisenstein series and more particularly given a degenerating family sl l 0 of riemann surfaces with their canonical hyperbolic metrics we work out the degeneration of hyperbolic eisenstein series associated to the pinching geodesics in sl our principal results are theorems 2 2 4 1 et 4 2

calculating resonances natural frequencies and extracting them from transient fields mathematical formulation and analysis of numerical methods for calculating the natural frequencies resonances are given stability of these methods towards roundoff errors and small perturbations of the obstacles is established some formulas for the variations of the natural frequencies due to small perturbations of the surface of the obstacle are given a simple new method for extraction of resonances from transient fields is given

on network functional compression in this thesis we consider different aspects of the functional compression problem in functional compression the computation of a function or some functions of sources is desired at the receiver s the rate region of this problem has been considered in the literature under certain restrictive assumptions in chapter 2 of this thesis we consider this problem for an arbitrary tree network and asymptotically lossless computations in particular for one stage tree networks we compute a rate region and for an arbitrary tree network we derive a rate lower bound based on the graph entropy we introduce a new condition on colorings of source random variables characteristic graphs called the coloring connectivity condition c c c we show that unlike the condition mentioned in doshi et al this condition is necessary and sufficient for any achievable coding scheme based on colorings we also show that unlike entropy graph entropy does not satisfy the chain rule for one stage trees with correlated sources and general trees with independent sources we propose a modularized coding scheme based on graph colorings to perform arbitrarily closely to the derived rate lower bound we show that in a general tree network case with independent sources to achieve the rate lower bound intermediate nodes should perform some computations however for a family of functions and random variables called chain rule proper sets it is sufficient to have intermediate nodes act like relays to perform arbitrarily closely to the rate lower bound in chapter 3 of this thesis we consider a multi functional version of this problem with side information where the receiver wants to compute several functions with different side information random variables and zero distortion our results are applicable to the case with several receivers computing different desired functions we define a new concept named multi functional graph entropy which is an extension of graph entropy defined by k6rner we show that the minimum achievable rate for this problem is equal to conditional multi functional graph entropy of the source random variable given the side information we also propose a coding scheme based on graph colorings to achieve this rate in these proposed coding schemes one needs to compute the minimum entropy coloring a coloring random variable which minimizes the entropy of a characteristic graph in general finding this coloring is an np hard problem however in chapter 4 we show that depending on the characteristic graph s structure there are some interesting cases where finding the minimum entropy coloring is not np hard but tractable and practical in one of these cases we show that by having a non zero joint probability condition on random variables distributions for any desired function finding the minimum entropy coloring can be solved in polynomial time in another case we show that if the desired function is a quantization function this problem is also tractable we also consider this problem in a general

ends of hyperbolic 3 manifolds let n h3 f be a hyperbolic 3 manifold which is homeomorphic to the interior of a compact 3 manifold we prove that n is geometrically tame as a consequence we prove that f s limit set l is either the entire sphere at infinity or has measure zero we also prove that n s geodesic flow is ergodic if and only if lf is the entire sphere at infinity department of mathematics stanford university stanford california 94305 current address department of mathematics university of michigan ann arbor michigan 48109 e mail address dick canary math lsa umich edu this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 06 utc all use subject to http about jstor org terms

multiterminal source encoding with one distortion criterion the authors unify earlier investigations concerning the encoding of two correlated sources x sub k y sub k by means of separate encoders decoding is done by a single decoder which receives the outputs from both encoders the reconstruction of x sub k is required to be perfect in the usual shannon sense the authors determine the admissible rate region r d where d is the distortion of the reconstruction of y sub k the binary hamming case is investigated explicitly

geometrical finiteness for hyperbolic groups abstract in this paper we give an account of the notion of geometrical finiteness as applied to discrete groups acting on hyperbolic space of any dimension we prove the equivalence of various definitions of geometrical finiteness and describe the geometry of fundamental domains we give a complete account of when dirichiet domains are finite sided

an improved outer bound for multiterminal source coding we prove a new outer bound on the rate distortion region for the multiterminal source coding problem this bound subsumes the best outer bound in the literature and improves upon it strictly in some cases the improved bound enables us to obtain a new conclusive result for the binary erasure version of the ceo problem the bound recovers many of the converse results that have been established for special cases of the problem including the recent one for the gaussian two encoder problem

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

the asymptotics of the arakelov geen s function and faltings delta invariant we study the behavior of the arakelov green s function and faltings delta invariant on degenerating riemann surfaces

on the resolvent of the laplacian on functions for degenerating surfaces of finite geometry we consider families y n of degenerating hyperbolic surfaces the surfaces are geometrically finite of fixed topological type let z n be the selberg zeta function of y n and let z d n be the contribution of the pinched geodesics to z n extending a result of wolpert s we prove that z n s z d n s converges to the zeta function of the limit surface for all s with mathrm re s 1 2 the technique is an examination of resolvent of the laplacian which is composed from that for elementary surfaces via meromorphic fredholm theory the resolvent delta n t 1 is shown to converge for all totin 1 4 infty we also use this property to define approximate eisenstein functions and scattering matrices

on the rate loss of multiple sources codes in the wyner ziv setting in this paper we consider the rate loss and achievable region of multiple sources codes also named multiterminal source codes in the wyner ziv setting wz msc in which two stationary memoryless sources x y are compressed separately from each other at respective rates r1 and r2 and the joint decoder having access to the side information s which is correlated with sources x y reconstructs x and y with distortion d1 and d2 respectively we define the rate loss l1 r1 rx y s d1 l2 r2 ry x s d2 and l0 r1 r2 rx y s d1 d2 for general real valued stationary memoryless sources and mean squared error distortion measure we show that the rate loss can be bounded by li ki 1 i 1 2 and l0 1 where k1 rx y s d1 d2 ry s d2 rx y s d1 and k2 rx y s d1 d2 rx s d1 ry x s d2 when the sources and side information have a jointly gaussian distribution we give upper bounds of k1 and k2 by a function of conditional correlation coefficient xy s for a special case when there is no side information our result tightens feng s rate loss bounds using our upper bounds of the rate loss we give good approximations of the achievable region

on almost fuchsian manifolds almost fuchsian manifold is a class of complete hyperbolic threemanifolds a such three manifold is a quasi fuchsian manifold that contains a closed incompressible minimal surface with principal curvatures everywhere in the range of 1 1 in such a manifold the minimal surface is unique and embedded hence one can parametrize these hyperbolic three manifolds by their minimal surfaces in this paper we obtain estimates on several geometric and analytical quantities of an almost fuchsian manifold m in terms of the data on the minimal surface in particular we obtain an upper bound for the hyperbolic volume of the convex core of m and an upper bound on the hausdorff dimension of the limit set associated to m we also constructed a quasi fuchsian manifold which admits more than one minimal surface and it does not admit a foliation of closed surfaces of constant mean curvature

asymptotics of small eigenvalues of riemann surfaces on determine le comportement asymptotique precis des petites valeurs propres du laplacien sur une surface de riemann

the wyner ziv problem with multiple sources this paper provides bounds on the rate distortion region for the distributed compression scenario where two or more sources are compressed separately for a decoder that has access to side information conclusive rate distortion results are found for the case where the sources are conditionally independent given the side information

the rate distortion function for the quadratic gaussian ceo problem a new multiterminal source coding problem called the ceo problem was presented and investigated by berger zhang and viswanathan recently viswanathan and berger have investigated an extension of the ceo problem to gaussian sources and call it the quadratic gaussian ceo problem they considered this problem from a statistical viewpoint deriving some interesting results in this paper we consider the quadratic gaussian ceo problem from a standpoint of multiterminal rate distortion theory we regard the ceo problem as a certain multiterminal remote source coding problem with infinitely many separate encoders whose observations are conditionally independent if the remote source is given this viewpoint leads us to a complete solution to the problem we determine the tradeoff between the total amount of rate and squared distortion deriving an explicit formula of the rate distortion function the derived function has the form of a sum of two nonnegative functions one is a classical rate distortion function for single gaussian source and the other is a new rate distortion function which dominates the performance of the system for a relatively small distortion it follows immediately from our result that the conjecture of viswanathan and berger on the asymptotic behavior of minimum squared distortion for large rates is true

duality of a source coding problem and the semi deterministic broadcast channel with rate limited cooperation the wyner ahlswede korner wak empirical coordination problem where the encoders cooperate via a finite capacity one sided link is considered the coordination capacity region is derived by combining several source coding techniques such as wyner ziv coding binning and superposition coding furthermore a semi deterministic sd broadcast channel bc with one sided decoder cooperation is considered duality principles relating the two problems are presented and the capacity region for the sd bc setting is derived the direct part follows from an achievable region for a general bc that is tight for the sd scenario a converse is established by using telescoping identities the sd bc is shown to be operationally equivalent to a class of relay bcs and the correspondence between their capacity regions is established the capacity region of the sd bc is transformed into an equivalent region that is shown to be dual to the admissible region of the wak problem in the sense that the information measures defining the corner points of both regions coincide achievability and converse proofs for the equivalent region are provided for the converse we use a probabilistic construction of auxiliary random variables that depends on the distribution induced by the codebook several examples illustrate the results

reliability in source coding with side information we study error exponents for source coding with side information both achievable exponents and converse bounds are obtained for the following two cases lossless source coding with coded information and lossy source coding with full side information wyner ziv these results recover and extend several existing results on source coding error exponents and are tight in some circumstances our bounds have a natural interpretation as a two player game between nature and the code designer with nature seeking to minimize the exponent and the code designer seeking to maximize it in the wyner ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events the gaussian and binary erasure cases are examined in detail

the distributed karhunen loeve transform the karhunen loeve transform klt is a key element of many signal processing and communication tasks many recent applications involve distributed signal processing where it is not generally possible to apply the klt to the entire signal rather the klt must be approximated in a distributed fashion this paper investigates such distributed approaches to the klt where several distributed terminals observe disjoint subsets of a random vector we introduce several versions of the distributed klt first a local klt is introduced which is the optimal solution for a given terminal assuming all else is fixed this local klt is different and in general improves upon the marginal klt which simply ignores other terminals both optimal approximation and compression using this local klt are derived two important special cases are studied in detail namely the partial observation klt which has access to a subset of variables but aims at reconstructing them all and the conditional klt which has access to side information at the decoder we focus on the jointly gaussian case with known correlation structure and on approximation and compression problems then the distributed klt is addressed by considering local klts in turn at the various terminals leading to an iterative algorithm which is locally convergent sometimes reaching a global optimum depending on the overall correlation structure for compression it is shown that the classical distributed source coding techniques admit a natural transform coding interpretation the transform being the distributed klt examples throughout illustrate the performance of the proposed distributed klt this distributed transform has potential applications in sensor networks distributed image databases hyper spectral imagery and data fusion

bounds on faltings s delta function through covers let x be a compact riemann surface of genus gx 1 in 1984 g faltings introduced a new invariant fal x associated to x in this paper we give explicit bounds for fal x in terms of fundamental dierential geometric invariants arising from x when gx 1 as an application we are able to give bounds for faltings s delta function for the family of modular curves x0 n in terms of the genus only in combination with work of a abbes p michel and e ullmo this leads to an asymptotic formula for the faltings height of the jacobian j0 n associated to x0 n

rate distortion for correlated sources with partially separated encoders we resolve some open problems concerning the encoding of a pair of correlated sources with respect to a fidelity criterion two encoders are used one encoder observes only the output of the first source while the other is supplied both with the second source output and with partial information about the first source at some predetermined rate a general coding theorem is proved which established that cal s ast a certain region defined in terms of single letter information theoretic quantities is an inner bound to the region of all attainable vectors of rates and distortions for certain cases of interest the converse is proved too thereby establishing the rate distortion region for these cases

a semi continuous version of the berger yeung problem we present a continuous dual of multiterminal source encoding with one distortion criterion the berger yeung 1989 problem a continuous source x is encoded with high resolution d sub x spl rarr 0 with the aid of a helper i e a correlated discrete or continuous source y that is encoded separately subject to some arbitrary distortion criterion d sub y we find the asymptotic form of the set of achievable coding rates r d sub x d sub y of the x and y encoders as d sub x spl rarr 0 two extreme cases of our result provide high resolution interpretations to the classical work of wyner 1975 1978 ahlswede 1975 korner 1975 and ziv 1976 on source coding with side information

lower bounds for lambda sb 1 on a finite volume hyperbolic manifold soit m une variete hyperbolique a n dimensions de volume fini v et soit 1 le premier element positif dans le spectre discret pour le probleme f f 0 sur m on considere des bornes inferieures pour 1 dans le cas de volume fini

multiterminal source coding under logarithmic loss we consider the classical two encoder multiterminal source coding problem where distortion is measured under logarithmic loss we provide a single letter description of the achievable rate distortion region for all discrete memoryless sources with finite alphabets by doing so we also give the rate distortion region for the m encoder ceo problem also under logarithmic loss several applications and examples are given

an effective bound for the huber constant for cofinite fuchsian groups let be a cofinite fuchsian group acting on hyperbolic two space let m be the corresponding quotient space for a closed geodesic of m let l denote its length the prime geodesic counting function m u is defined as the number of inconjugate primitive closed geodesics such that e l 1 m u 0 m j 1 4 we call the absolute constant c m the huber constant the objective of this paper is to give an effectively computable upper bound of c m for an arbitrary cofinite fuchsian group as a corollary we bound the huber constant for psl 2 z showing that c m 16 607 349 020 658 exp 30 44086643

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity