probability estimation in the rare events regime we address the problem of estimating the probability of an observed string that is drawn i i d from an unknown distribution motivated by models of natural language we consider the regime in which the length of the observed string and the size of the underlying alphabet are comparably large in this regime the maximum likelihood distribution tends to overestimate the probability of the observed letters so the good turing probability estimator is typically used instead we show that when used to estimate the sequence probability the good turing estimator is not consistent in this regime we then introduce a novel sequence probability estimator that is consistent this estimator also yields consistent estimators for other quantities of interest and a consistent universal classifier

on tests for normality the problem of deciding whether a sample of a random field was generated by a gaussian distribution is considered based on extensions of large deviation estimates due to m d donsker and s r s varadhan 1985 a test that is optimal in a generalized neyman pearson sense is proposed this test turns out to depend on properties of the entropy of gaussian processes and does not depend on cumulant computations

large deviations hypotheses testing and source coding for finite markov chains let x n n geq 1 be a finite markov chain with transition probability matrix of strictly positive entries a large deviation theorem is proved for the empirical transition count matrix and is used to get asymptotically optimal critical regions for testing simple hypotheses about the transition matrix as a corollary the error exponent in the source coding theorem for x n is obtained these results generalize the corresponding results for the independent and identically distributed case

asymptotically optimal quantizers for detection of i i d the asymptotic probability of error for quantization in maximum likelihood tests is analyzed the authors assume quantizers with large numbers of levels generated from a companding function a theorem that relates the companding function to the asymptotic probability of error is proved the companding function is then optimized

worst and average case privacy breaches in randomization mechanisms in a variety of contexts randomization is regarded as an effective technique to conceal sensitive information viewing randomization mechanisms as information theoretic channels we start from a semantic notion of security which expresses absence of any privacy breach above a given level of seriousness irrespective of any background information represented as a prior probability on the secret inputs we first examine this notion according to two dimensions worst vs average case single vs repeated observations in each case we characterize the security level achievable by a mechanism in a simple fashion that only depends on the channel matrix and specifically on certain measures of distance between its rows like norm 1 distance and chernoff information we next clarify the relation between our worst case security notion and differential privacy dp we show that while the former is in general stronger the two coincide if one confines to background information that can be factorized into the product of independent priors over individuals we finally turn our attention to expected utility in the sense of ghosh et al in the case of repeated independent observations we characterize the exponential growth rate of any reasonable utility function in the particular case the mechanism provides dp we study the relation of the utility rate with we offer either exact expressions or upper bounds for utility rate that apply to practically interesting cases such as the truncated geometric mechanism

universal and composite hypothesis testing via mismatched divergence for the universal hypothesis testing problem where the goal is to decide between the known null hypothesis distribution and some other unknown distribution hoeffding proposed a universal test in the nineteen sixties hoeffding s universal test statistic can be written in terms of kullback leibler k l divergence between the empirical distribution of the observations and the null hypothesis distribution in this paper a modification of hoeffding s test is considered based on a relaxation of the k l divergence referred to as the mismatched divergence the resulting mismatched test is shown to be a generalized likelihood ratio test glrt for the case where the alternate distribution lies in a parametric family of distributions characterized by a finite dimensional parameter i e it is a solution to the corresponding composite hypothesis testing problem for certain choices of the alternate distribution it is shown that both the hoeffding test and the mismatched test have the same asymptotic performance in terms of error exponents a consequence of this result is that the glrt is optimal in differentiating a particular distribution from others in an exponential family it is also shown that the mismatched test has a significant advantage over the hoeffding test in terms of finite sample size performance for applications involving large alphabet distributions this advantage is due to the difference in the asymptotic variances of the two test statistics under the null hypothesis

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

arimoto renyi conditional entropy and bayesian m ary hypothesis testing this paper gives upper and lower bounds on the minimum error probability of bayesian m ary hypothesis testing in terms of the arimoto renyi conditional entropy of an arbitrary order alpha the improved tightness of these bounds over their specialized versions with the shannon conditional entropy alpha 1 is demonstrated in particular in the case where m is finite we show how to generalize fano s inequality under both the conventional and list decision settings as a counterpart to the generalized fano s inequality allowing m to be infinite a lower bound on the arimoto renyi conditional entropy is derived as a function of the minimum error probability explicit upper and lower bounds on the minimum error probability are obtained as a function of the arimoto renyi conditional entropy for both positive and negative alpha furthermore we give upper bounds on the minimum error probability as functions of the renyi divergence in the setup of discrete memoryless channels we analyze the exponentially vanishing decay of the arimoto renyi conditional entropy of the transmitted codeword given the channel output when averaged over a random coding ensemble

asymptotic optimality of empirical likelihood for testing moment restrictions we show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the exponential rate at which the probability of a type i error tends to zero unless the possible distributions for the observed data are restricted appropriately from this it follows that for the optimality claim for empirical likelihood in kitamura 2001 to hold additional assumptions and qualifications are required under stronger assumptions than those in kitamura 2001 we establish the following optimality result i empirical likelihood controls the rate at which the probability of a type i error tends to zero and ii among all procedures for which the probability of a type i error tends to zero at least as fast empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for most alternatives this result further implies that empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their type i error probabilities

stability analysis of solitary wave solutions for the fourth order nonlinear boussinesq water wave equation abstract in the present study the nonlinear boussinesq type equation describe the bi directional propagation of small amplitude long capillary gravity waves on the surface of shallow water by using the extended auxiliary equation method we obtained some new soliton like solutions for the two dimensional fourth order nonlinear boussinesq equation with constant coefficient these solutions include symmetrical non symmetrical kink solutions solitary pattern solutions jacobi and weierstrass elliptic function solutions and triangular function solutions the stability analysis for these solutions are discussed

generalized two mode harmonic oscillator dynamical group and squeezed states in this paper we generalize our previous results of the generalized one mode harmonic oscillator to the generalized two mode case systematic use is made of the so 3 2 dynamical group and we are able to write a general form for the exact time evolution operator in terms of squeezing operators of one and two modes a complete classification of the exact solutions is made and we derive them explicitly whenever possible the relevant results on algebraic decomposition coherent state generators and classification of the solutions are shown in tables a plethora of soluble hamiltonians already treated in the literature which appear to be particular cases of the general formalism presented herein are analysed as well as new cases which to the authors knowledge have not yet been considered

distributed detection with empirically observed statistics consider a distributed detection problem in which the underlying distributions of the observations are unknown instead of these distributions noisy versions of empirically observed statistics are available to the fusion center these empirically observed statistics together with source test sequences are transmitted through different channels to the fusion center the fusion center decides which distribution the source sequence is sampled from based on these data for the binary case we derive the optimal type ii error exponent given that the type i error decays exponentially fast the type ii error exponent is maximized over the proportions of channels for both source and training sequences we conclude that as the ratio of the lengths of training to test sequences alpha tends to infinity using only one channel is optimal by calculating the derived exponents numerically we conjecture that the same is true when alpha is finite under certain conditions we relate our results to the classical distributed detection problem studied by tsitsiklis in which the underlying distributions are known finally our results are extended to the case of m ary distributed detection with a rejection option

asymptotic geometry of multiple hypothesis testing we present a simple geometrical interpretation for the solution to the multiple hypothesis testing problem in the asymptotic limit under this interpretation the optimal decision rule is a nearest neighbor classifier on the probability simplex

constrained epsilon minimax test for simultaneous detection and classification a constrained epsilon minimax test is proposed to detect and classify nonorthogonal vectors in gaussian noise with a general covariance matrix and in presence of linear interferences this test is epsilon minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability this loss is even more negligible as the signal to noise ratio is large furthermore it is also an epsilon equalizer test since its classification error probabilities are equalized up to a negligible difference when the signal to noise ratio is sufficiently large an asymptotically equivalent test with a very simple form is proposed this equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of euclidean distance numerical experiments on active user identification in a multiuser system confirm the theoretical findings

on the numerical solution of nonlinear burgers type equations using meshless method of lines abstract in this paper a meshless method of lines mmol is proposed for the numerical solution of nonlinear burgers type equations this technique does not require a mesh in the problem domain and only a set of scattered nodes provided by initial data is required for the solution of the problem using some radial basis functions rbfs the scheme is tested for various examples the results obtained by this method are compared with the exact solutions and some earlier work

on classification with empirically observed statistics and universal data compression classification with empirically observed statistics is studied for finite alphabet sources efficient universal discriminant functions are described and shown to be related to universal data compression it is demonstrated that if one of the probability measure of the two classes is not known it is still possible to define a universal discrimination function which performs as the optimal likelihood ratio discriminant function which can be evaluated only if the probability measures of the two classes are available if both of the probability measures are not available but training vectors from at least one of the two classes are available it is demonstrated that no discriminant function can perform efficiency of the length of the training vectors does not grow at least linearly with the length of the classified vector a universal discriminant function is introduced and shown to perform efficiently when the length of the training vectors grows linearly with the length of the classified sequence in the sense that it yields an error exponent that is arbitrarily close to that of the optimal discriminant function

discriminating quantum states the multiple chernoff distance we consider the problem of testing multiple quantum hypotheses rho 1 otimes n ldots rho r otimes n where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state it is known that the minimal average error probability p e decays exponentially to zero that is p e exp xi n o n however this error exponent xi is generally unknown except for the case that r 2 in this paper we solve the long standing open problem of identifying the above error exponent by proving nussbaum and szkola s conjecture that xi min i neq j c rho i rho j the right hand side of this equality is called the multiple quantum chernoff distance and c rho i rho j max 0 leq s leq1 log operatorname tr rho i s rho j 1 s has been previously identified as the optimal error exponent for testing two hypotheses rho i otimes n versus rho j otimes n the main ingredient of our proof is a new upper bound for the average error probability for testing an ensemble of finite dimensional but otherwise general quantum states this upper bound up to a states dependent factor matches the multiple state generalization of nussbaum and szkola s lower bound specialized to the case r 2 we give an alternative proof to the achievability of the binary hypothesis chernoff distance which was originally proved by audenaert et al

a boussinesq system for two way propagation of nonlinear dispersive waves abstract in this report we study the system n t w x nw x 1 6 n xxt 0 w t n x ww x 1 6 w xxt 0 which describes approximately the two dimensional propagation of surface waves in a uniform horizontal channel of length l0 filled with an irrotational incompressible inviscid fluid which in its undisturbed state has depth h the non dimensional variables n x t and w x t represent the deviation of the water surface from its undisturbed position and the horizontal velocity at water level 2 3h respectively the natural initial boundary value problem corresponding to the situation wherein the channel is fitted with a wavemaker at both ends is formulated and analyzed theoretically we then present a numerical algorithm for the approximation of solutions of the system and prove the algorithm is fourth order accurate both in time and in space is unconditionally stable and has optimal computational complexity which is to say the operation cost per time step is of order m where m is the number of grid points in the spatial discretization further we implement the algorithm as a computer code and use it to study head on collisions of solitary waves our numerical simulations are compared with existing theoretical numerical and experimental results we have tentatively concluded that the system is a good candidate for modeling two dimensional surface water waves

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

a two layer approach to wave modelling a set of model equations for water wave propagation is derived by piecewise integration of the primitive equations of motion through two arbitrary layers within each layer an independent velocity profile is derived with two separate velocity profiles matched at the interface of the two layers the resulting set of equations has three free parameters allowing for an optimization with known analytical properties of water waves the optimized model equations show good linear wave characteristics up to kh 6 while the second order nonlinear behaviour is captured to kh 6 as well a numerical algorithm for solving the model equations is developed and tested against one and two horizontal dimension cases agreement with laboratory data is excellent

classroom note calculation of weights in finite difference formulas the classical techniques for determining weights in finite difference formulas were either computationally slow or very limited in their scope e g specialized recursions for centered and staggered approximations for adams bashforth adams moulton and bdf formulas for odes etc two recent algorithms overcome these problems for equispaced grids such weights can be found very conveniently with a two line algorithm when using a symbolic language such as mathematica reducing to one line in the case of explicit approximations for arbitrarily spaced grids we describe a computationally very inexpensive numerical algorithm

multivariate information bottleneck the information bottleneck ib method is an unsupervised model independent data organization technique given a joint distribution p x y this method constructs a new variable t that extracts partitions or clusters over the values of x that are informative about y algorithms that are motivated by the ib method have already been applied to text classification gene expression neural code and spectral analysis here we introduce a general principled framework for multivariate extensions of the ib method this allows us to consider multiple systems of data partitions that are interrelated our approach utilizes bayesian networks for specifying the systems of clusters and which information terms should be maintained we show that this construction provides insights about bottleneck variations and enables us to characterize the solutions of these variations we also present four different algorithmic approaches that allow us to construct solutions in practice and apply them to several real world problems

on the asymptotics of m hypothesis bayesian detection in two hypothesis detection problems with i i d observations the minimum error probability decays exponentially with the amount of data with the constant in the exponent equal to the chernoff distance between the probability distributions characterizing the hypotheses we extend this result to the general m hypothesis bayesian detection problem where zero cost is assigned to correct decisions and find that the bayesian cost function s exponential decay constant equals the minimum chernoff distance among all distinct pairs of hypothesized probability distributions

a sequential algorithm for the universal coding of finite memory sources the estimation and universal compression of discrete sources are considered and a sequential algorithm for the universal coding of finite memory sources attaining asymptotically minimum redundancy is presented the algorithm performs an online estimation of the source states and uses an arithmetic code

method of lines solutions of the extended boussinesq equations a numerical solution procedure based on the method of lines for solving the nwogu one dimensional extended boussinesq equations is presented the numerical scheme is accurate up to fifth order in time and fourth order accurate in space thus reducing all truncation errors to a level smaller than the dispersive terms retained by most extended boussinesq models exact solitary wave solutions and invariants of motions recently derived by the authors are used to specify initial data for the incident solitary waves in the numerical model of nwogu and for the verification of the associated computed solutions the invariants of motions and several error measures are monitored in order to assess the conservative properties and the accuracy of the numerical scheme the proposed method of lines solution procedure is general and can be easily modified to solve a wide range of boussinesq like equations in coastal engineering

weak convergence analysis of asymptotically optimal hypothesis tests in recent years solutions to various hypothesis testing problems in the asymptotic setting have been proposed using the results from large deviation theory such tests are optimal in terms of appropriately defined error exponents for the practitioner however error probabilities in the finite sample size setting are more important in this paper we show how results on weak convergence of the test statistic can be used to obtain better approximations for the error probabilities in the finite sample size setting while this technique is popular among statisticians for common tests we demonstrate its applicability for several recently proposed asymptotically optimal tests including tests for robust goodness of fit homogeneity tests outlier hypothesis testing and graphical model estimation

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

on optimum and nearly optimum data quantization for signal detection the application of companding approximation theory to the quantization of data for detection of coherent signals in a noisy environment is considered this application is twofold allowing for greater simplicity in both analysis and design of quantizers for detection systems most computational methods for designing optimum most efficient quantizers for signal detection systems are iterative and are extremely sensitive to initial conditions companding approximation theory is used here to obtain suitable initial conditions for this problem furthermore the companding approximation idea is applied to design suboptimum quantizers which are nearly as efficient as optimum quantizers when the number of levels is large in this design iteration is not needed to derive the parameters of the quantizer and the design procedure is very simple in this paper we explore this approach numerically and demonstrate its effectiveness for designing and analyzing quantizers in detection systems

asymptotically optimal matching of multiple sequences to source distributions and training sequences consider a finite set of sources each producing independent identically distributed observations that follow a unique probability distribution on a finite alphabet we study the problem of matching a finite set of observed sequences to the set of sources under the constraint that the observed sequences are produced by distinct sources in general the number of sequences n may be different from the number of sources m and only some k min m n of the observed sequences may be produced by a source from the set of sources of interest we consider two versions of the problem one in which the probability laws of the sources are known and another in which the probability laws of the sources are unspecified but one training sequence from each of the sources is available we show that both these problems can be solved using a sequence of tests that are allowed to produce no match decisions the tests ensure exponential decay of the probabilities of incorrect matching as the sequence lengths increase and minimize the no match decisions both the tests can be implemented using variants of the minimum weight matching algorithm applied to a weighted bipartite graph we also compare the performances obtained using these tests with those obtained using tests that do not consider the constraint that the sequences are produced by distinct sources for the version of the problem in which the probability laws of the sources are known we compute the rejection exponents and error exponents of the tests and show that the tests that make use of the constraint have better exponents than the tests that do not make use of this information

consistent algorithms for clustering time series the problem of clustering is considered for the case where every point is a time series the time series are either given in one batch offline setting or they are allowed to grow with time and new time series can be added along the way online setting we propose a natural notion of consistency for this problem and show that there are simple computationally efficient algorithms that are asymptotically consistent under extremely weak assumptions on the distributions that generate the data the notion of consistency is as follows a clustering algorithm is called consistent if it places two time series into the same cluster if and only if the distribution that generates them is the same in the considered framework the time series are allowed to be highly dependent and the dependence can have arbitrary form if the number of clusters is known the only assumption we make is that the marginal distribution of each time series is stationary ergodic no parametric memory or mixing assumptions are made when the number of clusters is unknown stronger assumptions are provably necessary but it is still possible to devise nonparametric algorithms that are consistent under very general conditions the theoretical findings of this work are illustrated with experiments on both synthetic and real data

su 1 1 intelligent states we construct all the intelligent states of the non compact generators of su 1 1 for every positive discrete representation of this lie algebra and discuss some of the properties of these states

universal entropy estimation via block sorting in this correspondence we present a new universal entropy estimator for stationary ergodic sources prove almost sure convergence and establish an upper bound on the convergence rate for finite alphabet finite memory sources the algorithm is motivated by data compression using the burrows wheeler block sorting transform bwt by exploiting the property that the bwt output sequence is close to a piecewise stationary memoryless source we can segment the output sequence and estimate probabilities in each segment experimental results show that our algorithm outperforms lempel ziv lz string matching based algorithms

the method of lines for solution of the one dimensional wave equation subject to an integral conservation condition hyperbolic partial differential equations with an integral condition serve as models in many branches of physics and technology recently much attention has been expended in studying these equations and there has been a considerable mathematical interest in them in this work the solution of the one dimensional nonlocal hyperbolic equation is presented by the method of lines the method of lines mol is a general way of viewing a partial differential equation as a system of ordinary differential equations the partial derivatives with respect to the space variables are discretized to obtain a system of odes in the time variable and then a proper initial value software can be used to solve this ode system we propose two forms of mol for solving the described problem several numerical examples and also some comparisons with finite difference methods will be investigated to confirm the efficiency of this procedure

universal composite hypothesis testing a competitive minimax approach a novel approach is presented for the long standing problem of composite hypothesis testing in composite hypothesis testing unlike in simple hypothesis testing the probability function of the observed data given the hypothesis is uncertain as it depends on the unknown value of some parameter the proposed approach is to minimize the worst case ratio between the probability of error of a decision rule that is independent of the unknown parameters and the minimum probability of error attainable given the parameters the principal solution to this minimax problem is presented and the resulting decision rule is discussed since the exact solution is in general hard to find and a fortiori hard to implement an approximation method that yields an asymptotically minimax decision rule is proposed finally a variety of potential application areas are provided in signal processing and communications with special emphasis on universal decoding

the error exponent for the noiseless encoding of finite ergodic markov sources a new approach to the classical fixed length noiseless source coding problem is proposed for the case of finite ergodic markov sources this approach is based on simple counting arguments the central notion of markov type a set containing all the source sequences having the same transition counts from letter to letter is introduced and the cardinality of such a set is evaluated via graph theoretical tools the error exponent is shown to be a weighted average of informational divergences and the universal character of the result is stressed as a corollary the classical source coding theorem determining the achievable rates is rederived

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

su 1 1 symmetry of multimode squeezed states we show that a class of multimode optical transformations that employ linear optics plus two mode squeezing can be expressed as su 1 1 operators these operations are relevant to state of the art continuous variable quantum information experiments including quantum state sharing quantum teleportation and multipartite entangled states using this su 1 1 description of these transformations we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often used restriction to gaussian states we analyze this basis show its application to a class of transformations and discuss its extension to more general quantum optical networks

hypothesis testing with the general source the asymptotically optimal hypothesis testing problem with general sources as the null and alternative hypotheses is studied under exponential type error constraints on the first kind of error probability our fundamental philosophy is to convert all of the hypothesis testing problems to the pertinent computation problems in the large deviation probability theory this methodologically new approach enables us to establish compact general formulas of the optimal exponents of the second kind of error and correct testing probabilities for the general sources including all nonstationary and or nonergodic sources with arbitrary abstract alphabet countable or uncountable these general formulas are presented from the information spectrum point of view

coherent state triplets and their inner products it is shown that if h is a hilbert space for a representation of a group g then there are triplets of spaces fh h fh in which fh is a space of coherent state or vector coherent state wave functions and fh is its dual relative to a conveniently defined measure it is shown also that there is a sequence of maps fh h fh which facilitates the construction of the corresponding inner products after completion if necessary the spaces fh h fh become isomorphic hilbert spaces it is shown that the inner product for h is often easier to evaluate in fh than in fh thus we obtain integral expressions for the inner products of coherent state and vector coherent state representations these expressions are equivalent to the algebraic expressions of k matrix theory but they are frequently more efficient to apply the construction is illustrated by many examples

a 2 sprt based approach to multiple model hypothesis testing for multi distribution detection this paper presents an approach to multiple model hypothesis testing mmht based on 2 sprt 2 mmsrpt for detecting unknown events that may have multiple possible distributions the sequential probability ratio test sprt based mmht method mmsprt is promising because of its efficiency and theoretical validity however it may suffer from sprt s lack of an upper bound on its stopping time especially in the mis specified case the proposed 2 mmsprt algorithm not only copes with this problem but also is in a setting that can provide efficient detection in the sense of minimizing the maximum expected sample size subject to error probability constraints specifically we prove the theoretical validity of 2 sprt for the problem of testing hypotheses with multivariate normal densities moreover we present a technique of forced independence and identical distribution i i d to map the non i i d likelihood ratio sequence to an i i d one which enables us to apply the sprt and 2 sprt effectively to the dynamic case under the linear gaussian assumption with a non identical distribution also 2 mmsprt s detection efficiency under some assumptions approximations is verified performance of 2 mmsprt is evaluated for signal detection and model set selection problems in several scenarios simulation results demonstrate the detection efficiency of the proposed 2 mmsprt compared with the mmsprt and some traditional tests

efficient sharing of a continuous variable quantum secret we propose an efficient scheme for sharing a continuous variable quantum secret using passive optical interferometry and squeezers this efficiency is achieved by showing that a maximum of two squeezers is required to extract the secret state and we obtain the cheapest configuration in terms of total squeezing cost squeezing is a cost for the dealer of the secret as well as for the receivers and we quantify limitations to the fidelity of the extracted secret state in terms of the squeezing employed by the dealer

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

an efficient high order explicit scheme for solving hamiltonian nonlinear wave equations in this work we propose and analyze a novel high order explicit scheme for efficiently solving hamiltonian nonlinear wave equations the new explicit scheme is based on the blend of a fourth order finite difference scheme for spatial discretization and a multidimensional extended runge kutta nystrom erkn method for time integration respectively the conservation law of the semi discrete energy is established the stability and convergence of the semidiscretization are examined the results of numerical experiments show that the blend of the finite difference approximation and multidimensional erkn method gives an efficient high order explicit scheme for hamiltonian nonlinear wave equations in comparison with some existing methods

quantum integrability in the multistate landau zener problem we analyze hamiltonians linear in the time variable for which the multistate landau zener lz problem is known to have an exact solution we show that they either belong to families of mutually commuting hamiltonians polynomial in time or reduce to the lz problem which is considered trivially integrable the former category includes the equal slope bow tie and generalized bow tie models for each of these models we explicitly construct the corresponding families of commuting matrices the equal slope model is a member of an integrable family that consists of the maximum possible number for a given matrix size of commuting matrices linear in time the bow tie model belongs to a previously unknown similarly maximal family of quadratic commuting matrices we thus conjecture that quantum integrability understood as the existence of nontrivial parameter dependent commuting partners is a necessary condition for the lz solvability descendants of the lz hamiltonian are e g general su 2 and hamiltonians time dependent linear chain linear nonlinear and double oscillators we explicitly obtain solutions to all these lz problems from the case