on the limiting distribution of lempel ziv 78 redundancy for memoryless sources we study the lempel ziv 78 algorithm and show that its normalized redundancy rate tends to a gaussian distribution for memoryless sources we accomplish it by extending findings from our 1995 paper in particular by presenting a new simplified proof of the central limit theorem clt for the number of phrases in the lz 78 algorithm we first analyze the asymptotic behavior of the total path length in the associated digital search tree built from independent sequences then a renewal theory type argument yields clt for lz 78 scheme here we extend our analysis of lz 78 algorithm to present new results on the convergence of moments moderate and large deviations and clt for the normalized redundancy in particular we confirm that the average redundancy rate decays as 1 log n and we find that the variance is of order 1 n where n is the length of the text

approximation of a laminated microstructure for a rotationally invariant double well energy density we give error estimates for the approximation of a laminated microstructure which minimizes the energy int omega phi nabla v x dx for a rotationally invariant double well energy density phi a we present error estimates for the convergence of the deformation in l 2 the convergence of directional derivatives of the deformation in the twin planes the weak convergence of the deformation gradient the convergence of the microstructure or young measure of the deformation gradients and the convergence of nonlinear integrals of the deformation gradient

the reliability functions of the general source with fixed length coding the reliability function problems with fixed length source coding for the general source are studied for all rates r our fundamental philosophy in doing so is to convert all of the reliability function problems to the pertinent computation problems in the large derivation probability theory it turns out that this kind of new methodology which was previously developed by han see ibid vol 43 p 1145 64 1997 enables us to establish quite compact general formulas of the reliability function for general sources including all nonstationary and or nonergodic sources with countably infinite alphabet such general formulas are presented from the information spectrum point of view

periodic orbits and non integrability of henon heiles systems we apply the averaging theory of second order to study the periodic orbits for a generalized henon heiles system with two parameters which contains the classical henon heiles system two main results are shown the first result provides sufficient conditions on the two parameters of these generalized systems which guarantee that at any positive energy level the hamiltonian system has periodic orbits these periodic orbits form in the whole phase space a continuous family of periodic orbits parameterized by the energy the second result shows that for the non integrable henon heiles systems in the sense of liouville arnol d which have the periodic orbits analytically found with averaging theory cannot exist any second first integral of class in particular for any second first integral of class we prove that the classical henon heiles system and many generalizations of it are not integrable in the sense of liouville arnol d moreover the tools we use for studying the periodic orbits and the non liouville arnol d integrability can be applied to hamiltonian systems with an arbitrary number of degrees of freedom

constructing a completely integrable system via algebro geometric data we use the algebro geometric data given by a genus 2 jacobian a curve and a line bundle on the jacobian and the action of a group of translates on the theta sections of this line bundle to reconstruct an integrable system the geodesic motion on so 4 metric ii so termed after adler and van moerbeke

the simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation we study simply laminated microstructures of a martensitic crystal capable of undergoing a cubic to orthorhombic transformation of type mathcal p 432 to mathcal p 222 the free energy density modeling such a crystal is minimized on six energy wells that are pairwise rank one connected we consider the energy minimization problem with dirichlet boundary data compatible with an arbitrary but fixed simple laminate we first show that for all but a few isolated values of transformation strains this problem has a unique young measure solution solely characterized by the boundary data that represents the simply laminated microstructure we then present a theory of stability for such a microstructure and apply it to the conforming finite element approximation to obtain the corresponding error estimates for the finite element energy minimizers

asymptotically optimal classification for multiple tests with empirically observed statistics the decision problem of testing m hypotheses when the source is kth order markov and there are m or fewer training sequences of length n and a single test sequence of length n is considered k m n n are all given it is shown what the requirements are on m n n to achieve vanishing exponential error probabilities and how to determine or bound the exponent a likelihood ratio test that is allowed to produce a no match decision is shown to provide asymptotically optimal error probabilities and minimum no match decisions as an important serial case the binary hypotheses problem without rejection is discussed it is shown that for this configuration only one training sequence is needed to achieve an asymptotically optimal test

twofold universal prediction schemes for achieving the finite state predictability of a noisy individual binary sequence the problem of predicting the next outcome of an individual binary sequence corrupted by noise using finite memory is considered the conditional finite state fs predictability of an infinite individual sequence given its noisy version is defined as the minimum fraction of errors that can be made by any fs predictor fed by the noisy version it is proved that the conditional fs predictability can be attained almost surely by universal sequential prediction schemes in the case where the noisy version is the output of a binary symmetric channel bsc whose input is the clean individual sequence in particular universal predictors of the original noise free setting which operate on the noisy sequence have this property moreover these universal predictors do not depend on the crossover probability characterizing the bsc it is seen that the noisy setting gives rise to additional criteria by which the performance of prediction schemes can be assessed finally a closer look is taken at the conditional fs predictability and this quantity is proposed as an additional measure of the complexity of a sequence perhaps finer and more informative than the predictive complexity of the noise free setting

generalized tops and moment maps to loop algebras using a combination of hamiltonian reduction under continuous and discrete symmetry groups the lax equations for the motion of generalized tops are derived as part of a general approach to moment map embeddings of integrable hamiltonian systems in loop algebras

motion of four dimensional rigid body around a fixed point an elementary approach i the goal of this letter is to give an elementary approach to the solution of euler frahm equations for the manakov four dimensional case for this we use the kotter approach and some results from the original papers by schottky weber and caspary we hope that such an approach will be useful for the solution of the problem of an n dimensional top

a new class of integrable systems we present a family of dynamical systems associated with the motion of a particle in two space dimensions these systems possess a second integral of motion quadratic in velocities apart from the hamiltonian and are thus completely integrable they were found through the derivation and subsequent resolution of the integrability condition in the form of a partial differential equation pde for the potential a most important point is that the same pde was derived through considerations on the analytic structure of the singularities of the solutions weak painleve property

the full geometry of kowalewski s top and 1 2 abelian surfaces revue sur les varietes abeliennes les automorphismes d une courbe elliptique surfaces abeliennes t 2 de polarisation 1 2 jacobiens hyperelliptiques comme recouvrements doubles de t 2 les tores t 2 comme doubles recouvrements des jacobiens hyperelli courbe de kowalewski et surfaces abeliennes de polarisation 2 4

on the connection between hyperelliptic separability and painleve integrability we consider systems of odes which are associated with some physically significant examples shallow water equilibrium solutions travelling waves of the harry dym equation a lotka volterra system of competing species and the geodesic flow on the triaxial ellipsoid the first three are shown to share the following properties i they are hyperelliptically separable systems hss and after a suitable nonlinear time transformation become algebraically completely integrable aci and ii they are of the weak painleve type and become full painleve after the application of this transformation the geodesic flow on the other hand although it passes the usual painleve test does not possess a full set of free constants and thus one may not conclude whether it has the painleve property or not this system is also hss and becomes aci after the application of a suitable nonlinear time transformation we also combine our geometric analytical investigation with a numerical analysis of the system in the complex plane and show that there is perfect correspondence between the results of the two approaches this correspondence strengthens the reliability of such numerical studies and helps us better understand their implication in cases where such nonlinear transformations to complete integrability are not available

the kowalewski and henon heiles motions as manakov geodesic flows on so 4 a two dimensional family of lax pairs the invariant surfaces for the kowalewski top the henon heiles system and the manakov geodesic flow onso 4 complete into abelian surfacesa by adjoining in each case a divisord of arithmetic genus 9 these divisors belong to the same linear system ona and they each define a polarization 2 4 therefore there are rational maps transforming the kowalewski top and the henon heiles system into manakov s geodesic flow onso 4 this paper deals with the precise geometric relationship between these three problems it is based on the splitting of the 8 dimensional space of sections ofd theta functions into an even and an odd part and also on a normal form for the six quadrics describinga as embedded in 7 as a byproduct we get a 2 dimensional family of lax pairs for both the kowalewski top and the henon heiles system

painleve property and geometry abstract the painleve property for discrete hamiltonian systems implies the existence of a symplectic manifold which augments the original phase space and on which the flows exist and are analytic for all times the augmented manifold is constructed by expanding the hamilton jacobi equation a complete classification of the types of poles allowed in complex time is given for hamiltonians which separate into the direct product of hyperelliptic curves for such systems bounds on the degrees of the polynomial separating variable change and the other integrals in involution can be found from the pole series and the hamilton jacobi equation it is shown how branching can arise naturally in a painleve system

variable to fixed length codes provide better large deviations performance than fixed to variable length codes it is proved that for finite alphabet finite state unifilar sources variable to fixed length codes provide better large deviations performance of the empirical compression ratio than fixed to variable length codes it is shown how to construct a universal variable to fixed length code that achieves the optimal performance

the kowalevski top its r matrix interpretation and bihamiltonian formulation the lax pair representation for the kowalevski top and for the kowalevski gyrostat are obtained directly via the r matrix method the construction of reyman and semenov tian shansky is then used to give a bihamiltonian description of the kowalevski gyrostat

constitutive theory for some constrained elastic crystals abstract some of the observations of a 15 superconductors near cubic tetragonal phase transformations suggest treating them as thermoelastic bodies subject to certain material constraints here we begin to develop a theory of this kind

estimating the number of states of a finite state source the problem of estimating the number of states of a finite alphabet finite state source is investigated an estimator is developed that asymptotically attains the minimum probability of understanding the number of states among all estimators with a prescribed exponential decay rate of overestimation probability the proposed estimator relies on the lempel ziv data compression algorithm in an intuitively appealing manner

quantum and semiclassical representations over lagrangian submanifolds in su 2 so 4 and su 1 1 irreducible representations of three simplest lie algebras are realized over lagrangian submanifolds over closed curves tori and spheres in coadjoint orbits the intertwining operator is constructed which enables to pass from an abstract representation to a representation the integral kernel of the intertwining operator involves special coherent states the simple integral formulas are obtained for exact and semiclassical eigenvectors and for solutions of the cauchy problem over lie algebras mentioned in the title the hamiltonians considered are nonanalytic in general

remarks on kowalevski s top we present a review of some results on kowalevski s top kt in classical and quantum mechanics the following items are considered i the generalized kt gkt on the lie algebras so 4 e 3 and so 3 1 ii kowalevski s gyrostat on these algebras iii action of the gkt iv quantum counterparts of the kt v semiclassical quantization of the gkt vi generalization of the kt by chaplygin and goryachev at l 0 and its lax representation unsolved questions are also discussed

numerical analysis of oscillations in multiple well problems variational problems which fail to be convex occur often in the study of ordered materials such as crystals in these problems the energy density for the material has multiple potential wells in this paper we study multiple well problems by first determining the analytic properties of energy minimizing sequences and then by estimating the continuous problem by an approximation using piecewise linear finite elements we show that even when there is no minimizer of the energy the approximations still take on a predictable structure

lax representation and poisson geometry of the kowalevski top we discuss the poisson structure underlying the two field kowalevski gyrostat and the kowalevski top we start from their lax structure and construct a suitable pencil of poisson brackets which endows these systems with the structure of bi hamiltonian completely integrable systems we study the casimir functions of such pencils and show how it is possible to frame the kowalevski systems within the so called gel fand zakharevich bi hamiltonian setting for integrable systems

on the competitive optimality of huffman codes let x be a discrete random variable drawn according to a probability mass function p x and suppose p x is dyadic i e log 1 p x is an integer for each x it is shown that the binary code length assignment l x log 1 p x dominates any other uniquely decodable assignment l x in expected length in the sense that el x pr l x l x which indicates l is also optimal in the short run in general if p is not dyadic then l log 1 p dominates l 1 in expected length and competitivity dominates l 1 where l is any other uniquely decodable code

universal coding information prediction and estimation a connection between universal codes and the problems of prediction and statistical estimation is established a known lower bound for the mean length of universal codes is sharpened and generalized and optimum universal codes constructed the bound is defined to give the information in strings relative to the considered class of processes the earlier derived minimum description length criterion for estimation of parameters including their number is given a fundamental information theoretic justification by showing that its estimators achieve the information in the strings it is also shown that one cannot do prediction in gaussian autoregressive moving average arma processes below a bound which is determined by the information in the data

kowalewski s asymptotic method kac moody lie algebras and regularization we use an effective criterion based on the asymptotic analysis of a class of hamiltonian equations to determine whether they are linearizable on an abelian variety i e solvable by quadrature the criterion is applied to a system with hamiltonian h 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 sum limits i 1 l p i 2 sum limits i 1 l 1 exp left sum limits j 1 l n ij x j right parametrized by a real matrixn n ij of full rank it will be solvable by quadrature if and only if for alli j 2 n nt ij n n t jj 1 is a nonpositive integer i e the interactions correspond to the toda systems for the kac moody lie algebras the criterion is also applied to a system of gross neveu

on empirical cumulant generating functions of code lengths for individual sequences we consider the problem of lossless compression of individual sequences using finite state fs machines from the perspective of the best achievable empirical cumulant generating function cgf of the code length i e the normalized logarithm of the empirical average of the exponentiated code length since the probabilistic cgf is minimized in terms of the renyi entropy of the source one of the motivations of this paper is to derive an individual sequence analogue of the renyi entropy in the same way that the fs compressibility is the individual sequence counterpart of the shannon entropy we consider the cgf of the code length both from the perspective of fixed to variable length coding and the perspective of variable to variable v v length coding where the latter turns out to yield a better result that coincides with the fs compressibility we also extend our results to compression with side information available at both the encoder and decoder in this case the v v version no longer coincides with the fs compressibility but results in a different complexity measure

approximation of martensitic microstructure with general homogeneous boundary data we consider the approximation of martensitic microstructure for a class of martensitic transformations we model such microstructures by multi well energy minimization problems with general homogeneous boundary data under our assumptions on such boundary data the underlying microstructure can be nonunique we first show that any energy minimizing sequence converges strongly to a unique macroscopic deformation that is precisely the homogeneous deformation in the boundary condition we then prove a series of estimates for the approximation of admissible deformations to the unique macroscopic deformation of the microstructure and for the closeness of the gradients of admissible deformations to the energy wells

universal prediction of individual binary sequences in the presence of noise the problem of predicting the next outcome of an individual binary sequence based on noisy observations of the past is considered the goal of the predictor is to perform for each individual sequence almost as well as the best in a set of experts where performance is evaluated using a general loss function a comprehensive approach to prediction in this noisy setting is presented and proven generally efficient under appropriate conditions as an illustration of the applicability of the approach suggested for concrete situations two important special cases are explicitly treated the first is the case where the data corrupting noise process is binary valued where the observed bit is the bitwise xor of the clean bit and the noise bit the second case is that of real valued additive noise it is shown that even in this more challenging situation where the information available to the predictor regarding the past sequence is incomplete a predictor can be guaranteed to successfully compete with a whole set of experts in considerably strong senses

lie point symmetries and first integrals the kowalevski top we show how the lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations the method of reduction increase of order developed by nucci j math phys 37 1772 1775 1996 is essential noether s theorem is neither necessary nor considered the most striking example we present is the relationship between lie group analysis and the famous first integral of the kowalevski top

guessing subject to distortion we investigate the problem of guessing a random vector x within distortion level d our aim is to characterize the best attainable performance in the sense of minimizing in some probabilistic sense the number of required guesses g x until the error falls below d the underlying motivation is that g x is the number of candidate codewords to be examined by a rate distortion block encoder until a satisfactory codeword is found in particular for memoryless sources we provide a single letter characterization of the least achievable exponential growth rate of the spl rho th moment of g x as the dimension of the random vector x grows without bound in this context we propose an asymptotically optimal guessing scheme that is universal both with respect to the information source and the value of spl rho we then study some properties of the exponent function e d spl rho along with its relation to the source coding exponents finally we provide extensions of our main results to the gaussian case guessing with side information and sources with memory

optimum overflow thresholds in variable length source coding allowing non vanishing error probability the variable length source coding problem allowing the error probability up to some constant is considered for general sources in this problem the optimum mean codeword length of variable length codes has already been determined on the other hand in this paper we focus on the overflow or excess codeword length probability instead of the mean codeword length the infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold in this paper we first derive finite length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds then by using these bounds we determine the general formula of the optimum overflow thresholds in both of the first order and second order forms next we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed length source coding problem finally we apply the general formula derived in this paper to the case of stationary memoryless sources

elliptic solutions and blow up in an integrable henon heiles system we consider an integrable case of the henon heiles system and use an isomorphism with the two gap kdv flow to construct families of real elliptic trajectories which are associated with two gap elliptic solitons of the kdv equation some of these solutions exhibit blow up in finite time

guessing individual sequences generating randomized guesses using finite state machines motivated by earlier results on universal randomized guessing we consider an individual sequence approach to the guessing problem in this setting the goal is to guess a secret individual deterministic vector x n x 1 ldots x n by using a finite state machine that sequentially generates randomized guesses from a stream of purely random bits we define the finite state guessing exponent as the asymptotic normalized logarithm of the minimum achievable moment of the number of randomized guesses generated by any finite state machine until x n is guessed successfully we show that the finite state guessing exponent of any sequence is intimately related to its finite state compressibility due to lempel and ziv and it is asymptotically achieved by the decoder of a certain modified version of the 1978 lempel ziv data compression algorithm a k a the lz78 algorithm fed by purely random bits the results are also extended to the case where the guessing machine has access to a side information sequence y n y 1 ldots y n which is also an individual sequence

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

finite element analysis of a class of stress free martensitic microstructures this work is concerned with the finite element approximation of a class of stress free martensitic microstructures modeled by multi well energy minimization finite element energy minimizing sequences are first constructed to obtain bounds on the minimum energy over all admissible finite element deformations a series of error estimates are then derived for finite element energy minimizers

on universal types the universal type class of a sequence xn is defined in analogy to the notion underlying the classical method of types two sequences of the same length are said to be of the same universal lz type if and only if they yield the same dictionary or equivalently parsing tree in the incremental parsing of ziv and lempel 1978 it is shown that for any finite order k the variational distance between the kth order empirical probability distributions of two sequences of the same universal type vanishes as the sequence length tends to infinity consequently for any k and any kth order probability assignment the difference between the normalized logarithms of the probabilities assigned to two sequences of the same universal type also vanishes asymptotically the size of a universal type class is studied and it is shown that its asymptotic behavior parallels that of the conventional counterpart with the lz78 code length playing the role of the empirical entropy the number of universal types for sequences of length n is estimated and shown to be of the form exp 1 o 1 gamman logn for a well characterized constant gamma algorithms for enumerating the sequences in a universal type class and for drawing a sequence from the class with uniform probability are described as an application the problem of universal simulation of individual sequences is considered a sequence drawn with uniform probability from the universal type class of xn is an optimal simulation of xn in a well defined mathematical sense

nonconforming finite element approximation of crystalline microstructure we consider a class of nonconforming nite element approxima tions of a simply laminated microstructure which minimizes the nonconvex variational problem for the deformation of martensitic crystals which can un dergo either an orthorhombic to monoclinic double well or a cubic to tetrag onal triple well transformation we rst establish a series of error bounds in terms of elastic energies for the l 2 approximation of derivatives of the de formation in the direction tangential to parallel layers of the laminate for the l 2 approximation of the deformation for the weak approximation of the de formation gradient for the approximation of volume fractions of deformation gradients and for the approximation of nonlinear integrals of the deformation gradient we then use these bounds to give corresponding convergence rates for quasi optimal nite element approximations

lax representation for the systems of s kowalevskaya type we describe a number of dynamical systems that are generalizations of the s kowalevskaya system and admit the lax representation

a unified approach to painleve expansions abstract the painleve test for partial differential equations developed by weiss tabor and carnevale wtc is examined in detail and shown to provide a unified approach to the integrable properties of both ordinary and partial differential equations a simple modification of the wtc procedure used for partial differential equations enables us to determine the lax pairs hirota equations and auto backlund transformations for ordinary differential equations including a new lax pair for an integrable case of the henon heiles system a detailed study of the kdv hierarchy is made and a complete picture of the pattern of resonances for all solution branches is obtained the role of the singular branches is examined in detail and important new insights obtained in particular we find that each singular branch is simply a re expansion of the principal branch about a point on the pole manifold at which several isolated poles coalesce a parallel analysis is carried out for the akns hierarchy

simultaneous separation for the kowalevski and goryachev chaplygin gyrostats in the special case of zero square integral the kowalevski gyrostat and goryachev chaplygin gyrostat share a simple separation of variables originated from the 4 4 lax matrix

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

analysis of the finite element approximation of microstructure in micromagnetics the solution to nonconvex variational problems is often characterized by microstructure the variational problem for the magnetization field in micromagnetics has a nonconvex constraint and energy minimizing sequences of magnetization fields can have oscillations whose scale converges to zero but whose amplitude remains finite it is shown that the finite element approximation of the magnetization field for this variational problem does not converge pointwise as the mesh is refined but that nonlinear functions of the approximate magnetization fields converge weakly or equivalently all local spatial averages of nonlinear functions of the approximate magnetization field converge as the mesh is refined which implies the convergence as the mesh is refined of the probability distribution of the approximate magnetization fields in local spatial domains a norm is given to measure the convergence of this microstructure and we prove a rate of convergence in this norm

isospectral hamiltonian flows in finite and infinite dimensions i generalized moser systems and moment maps into loop algebras a moment map jr jia gl r is constructed from the poisson manifold j a of rank r perturbations of a fixed n xn matrix a to the dual r f e positive part of the formal loop algebra i r g r c 1 the adler kostant symes theorem is used to give hamiltonians which generate commutative isospectral flows on g r the pull back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in j a the latter may be identified with flows on finite dimensional coadjoint orbits in g and linearized on the jacobi variety of an invariant spectral curve xr which generically is an r sheeted riemann surface reductions of j a are derived corresponding to subalgebras of gl r c and sl r c determined as the fixed point set of automorphism groupes generated by involutions i e jdl the classical algebras as well as reductions to twisted subalgebras of s r c the theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of pde s

a new integrable case of the motion of the 4 dimensional rigid body a lax pair for a new family of integrable systems on so 4 is presented the construction makes use of a twisted loop algebra of theg 2 lie algebra we also describe a general scheme producing integrable cases of the generalized rigid body motion in an external field which have a lax representation with spectral parameter several other examples of multi dimensional tops are discussed

universal coding with minimum probability of codeword length overflow lossless block to variable length source coding is studied for finite state finite alphabet sources the aim is to minimize the probability that the normalized length of the codeword will exceed a given threshold b subject to the kraft inequality it is shown that the lempel ziv algorithm 1978 asymptotically attains the optimal performance in the sense just defined independently of the source and the value of b for the subclass of unifilar markov sources faster convergence to the asymptotic optimum performance can be accomplished by using the minimum description length universal code for this subclass it is demonstrated that these universal codes are also nearly optimal in the sense of minimizing buffer overflow probability and asymptotically optimal in a competitive sense

geodesic flow on so 4 and the intersection of quadrics this note studies the relationship between the complete integrability of geodesic flow on so 4 with a left invariant metric and the geometry of the intersection of four quadrics in p 6

guessing revisited a large deviations approach the problem of guessing a random string is revisited a close relation between guessing and compression is first established then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation property with a certain rate function then the limiting guessing exponent exists and is a scalar multiple of the legendre fenchel dual of the rate function other sufficient conditions related to certain continuity properties of the information spectrum are briefly discussed this approach highlights the importance of the information spectrum in determining the limiting guessing exponent all known prior results are then re derived as example applications of our unifying approach

tradeoffs between the excess code length exponent and the excess distortion exponent in lossy source coding lossy compression of a discrete memoryless source dms with respect to a single letter distortion measure is considered we study the best attainable tradeoff between the exponential rates of the probabilities that the codeword length and that the cumulative distortion exceed respective thresholds for two main cases the first scenario examined is that where the source is corrupted by a discrete memoryless channel dmc prior to reaching the coder in the second part of this work we examine the universal setting where the noise free source is an unknown member p sub spl theta of a given family p sub spl theta spl theta spl isin spl theta here inspired by an approach which was proven fruitful previously in the context of composite hypothesis testing we allow the constraint on the excess code length exponent to be spl theta dependent corollaries are derived for some special cases of interest including marton s 1974 classical source coding exponent and its generalization to the case where the constraint on the rate of the code is relaxed from an almost sure constraint to a constraint on the excess code length exponent

finite element analysis of microstructure for the cubic to tetragonal transformation martensitic crystals which can undergo a cubic to tetragonal phase transformation have a nonconvex energy density with three symmetry related rotationally invariant energy wells we give estimates for the numerical approximation of a first order laminate for such martensitic crystals we give bounds for the l2 convergence of directional derivatives in the twin plane for the l2 convergence of the deformation for the weak convergence of the deformation gradient for the convergence of the microstructure and for the convergence of nonlinear integrals of the deformation gradient

optimal lossless data compression non asymptotics and asymptotics this paper provides an extensive study of the behavior of the best achievable rate and other related fundamental limits in variable length strictly lossless compression in the non asymptotic regime the fundamental limits of fixed to variable lossless compression with and without prefix constraints are shown to be tightly coupled several precise quantitative bounds are derived connecting the distribution of the optimal code lengths to the source information spectrum and an exact analysis of the best achievable rate for arbitrary sources is given fine asymptotic results are proved for arbitrary not necessarily prefix compressors on general mixing sources nonasymptotic explicit gaussian approximation bounds are established for the best achievable rate on markov sources the source dispersion and the source varentropy rate are defined and characterized together with the entropy rate the varentropy rate serves to tightly approximate the fundamental nonasymptotic limits of fixed to variable compression for all but very small block lengths

the kowalewski top 99 years later a lax pair generalizations and explicit solutions a natural lax pair for the kowalewski top is derived by using a general group theoretic approach this gives a new insight into the algebraic geometry of the top and leads to its complete solution via finite band integration theory

kowalewski s top on the lie algebras o 4 e 3 and o 3 1 the authors extend the lax pair for kowalewski s top kt obtained by haine and horozov 1987 to the lie algebras o 4 and o 3 1 the results are expressed in terms of a solution of the neumann system they derive formulae for the action variables by analogy with the e 3 kt case and obtain a useful representation for the equations of motion that demonstrate explicitly the separation of variables

bifurcations of invariant manifolds in the generalized henon heiles system abstract the generalized henon heiles hamiltonian h 1 2 q dot 1 2 q dot 2 2 aq 1 2 bq 2 2 q 1 2 q 2 e 3 q 2 3 in the integrable case e 6 is studied from topological point of view the topology of the real level sets for all generic values of the constants of the motion and all generic bifurcations of the liouville tori and cylinders are described by making use of the reach algebraic structure of the problem

csiszar s cutoff rates for arbitrary discrete sources csiszar s 1995 forward spl beta cutoff rate given a fixed spl beta 0 for a discrete source is defined as the smallest number r sub 0 such that for every r r sub 0 there exists a sequence of fixed length codes of rate r with probability of error asymptotically vanishing as e sup n spl beta r r0 for a discrete memoryless source dms the forward spl beta cutoff rate is shown by csiszar to be equal to the source renyi 1961 entropy an analogous concept of reverse spl beta cutoff rate regarding the probability of correct decoding is also characterized by csiszar in terms of the renyi entropy in this work csiszar s results are generalized by investigating the spl beta cutoff rates for the class of arbitrary discrete sources with memory it is demonstrated that the limsup and liminf renyi entropy rates provide the formulas for the forward and reverse spl beta cutoff rates respectively consequently new fixed length source coding operational characterizations for the renyi entropy rates are established