recursive maximum likelihood identification of jump markov nonlinear systems we present an online method for joint state and parameter estimation in jump markov non linear systems jmnls state inference is enabled via the use of particle filters which makes the method applicable to a wide range of non linear models to exploit the inherent structure of jmnls we design a rao blackwellized particle filter rbpf where the discrete mode is marginalized out analytically this results in an efficient implementation of the algorithm and reduces the estimation error variance the proposed rbpf is then used to compute recursively in time smoothed estimates of complete data sufficient statistics together with the online expectation maximization algorithm this enables recursive identification of unknown model parameters including the transition probability matrix the method is also applicable to online identification of jump markov linear systems jmls the performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data

critical points of multidimensional random fourier series variance estimates we investigate the number of critical points of a gaussian random smooth function ue on the m torus tm m m approximating the gaussian white noise as e 0 let n ue denote the number of critical points of ue we prove the existence of constants c c such that as e goes to zero the expectation of the random variable emn ue converges to c while its variance is extremely small and behaves like c em

random k sat two moments suffice to cross a sharp threshold many np complete constraint satisfaction problems appear to undergo a phase transition from solubility to insolubility when the constraint density passes through a critical threshold in all such cases it is easy to derive upper bounds on the location of the threshold by showing that above a certain density the first moment expectation of the number of solutions tends to zero we show that in the case of certain symmetric constraints considering the second moment of the number of solutions yields nearly matching lower bounds for the location of the threshold specifically we prove that the threshold for both random hypergraph 2 colorability property b and random not all equal k sat is 2 k 1 ln 2 o 1 as a corollary we establish that the threshold for random k sat is of order theta 2 k resolving a long standing open problem

state estimation in stochastic hybrid systems with sparse observations in this note we study the problem of state estimation for a class of sampled measurement stochastic hybrid systems where the continuous state x satisfies a linear stochastic differential equation and noisy measurements y are taken at assigned discrete time instants the parameters of both the state and measurement equation depend on the discrete state q of a continuous time finite markov chain even in the fault detection setting we consider at most one transition for q is admissible the switch may occur between two observations whence it turns out that the optimal estimates cannot be expressed in parametric form and time integrations are unavoidable so that the known estimation techniques cannot be applied we derive and implement an algorithm for the estimation of the states x q and of the discrete state switching time that is convenient for both recursive update and the eventual numerical quadrature numerical simulations are illustrated

deinterleaving pulse trains using discrete time stochastic dynamic linear models pulse trains from a number of different sources are often received on the one communication channel it is then of interest to identify which pulses are from which source based on different source characteristics this sorting task is termed deinterleaving the authors propose time domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival toa and pulse energy if available of the pulses received on the one communication channel they formulate the pulse train deinterleaving problem as a stochastic discrete time dynamic linear model dlm the discrete time variable k being associated with the kth received pulse the time varying parameters of the dlm depend on the sequence of active sources the deinterleaving detection estimation task can then be done optimally via linear signal processing using the kalman filter or recursive least squares when the source periods are constant and tree searching the optimal solution however is computationally infeasible for other than small data lengths since the number of possible sequences grow exponentially with data length the authors propose and study two of a number of possible suboptimal solutions 1 forward dynamic programming with fixed look ahead rather than total look ahead as required for the optimal scheme 2 a probabilistic teacher kalman filtering for the detection estimation task

loss surface of xor artificial neural networks training an artificial neural network involves an optimization process over the landscape defined by the cost loss as a function of the network parameters we explore these landscapes using optimization tools developed for potential energy landscapes in molecular science the number of local minima and transition states saddle points of index one as well as the ratio of transition states to minima grow rapidly with the number of nodes in the network there is also a strong dependence on the regularization parameter with the landscape becoming more convex fewer minima as the regularization term increases we demonstrate that in our formulation stationary points for networks with n h hidden nodes including the minimal network required to fit the xor data are also stationary points for networks with n h 1 hidden nodes when all the weights involving the additional node are zero hence smaller networks trained on xor data are embedded in the landscapes of larger networks our results clarify certain aspects of the classification and sensitivity to perturbations in the input data of minima and saddle points for this system and may provide insight into dropout and network compression

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

approximate ultrametricity for random measures and applications to spin glasses in this paper we introduce a notion called approximate ultrametricity which encapsulates the phenomenology of a sequence of random probability measures having supports that behave like ultrametric spaces insofar as they decompose into nested balls we provide a sufficient condition for a sequence of random probability measures on the unit ball of an infinite dimensional separable hilbert space to admit such a decomposition whose elements we call clusters we also characterize the laws of the measures of the clusters by showing that they converge in law to the weights of a ruelle probability cascade these results apply to a large class of classical models in mean field spin glasses we illustrate the notion of approximate ultrametricity by proving a conjecture of talagrand regarding mixed p spin glasses that is known to imply a prediction of dotsenko franz mezard 2016 wiley periodicals inc

expectation maximization algorithms for map estimation of jump markov linear systems in a jump markov linear system the state matrix observation matrix and the noise covariance matrices evolve according to the realization of a finite state markov chain given a realization of the observation process the aim is to estimate the state of the markov chain assuming known model parameters computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations we present three expectation maximization em algorithms for state estimation to compute maximum a posteriori map state sequence estimates which are also known as bayesian maximum likelihood state sequence estimates mlses the first em algorithm yields the map estimate for the entire sequence of the finite state markov chain the second em algorithm yields the map estimate of the continuous state of the jump linear system the third em algorithm computes the joint map estimate of the finite and continuous states the three em algorithms optimally combine a hidden markov model hmm estimator and a kalman smoother ks in three different ways to compute the desired map state sequence estimates unlike the conditional mean state estimates which require computational cost exponential in the data length the proposed iterative schemes are linear in the data length

satisfiability threshold for random regular nae sat we consider the random regular k nae sat problem with n variables each appearing in exactly d clauses for all k exceeding an absolute constant it k 0 we establish explicitly the satisfiability threshold d star equiv d star k we prove that for d d star the problem is unsatisfiable with high probability if the threshold d star lands exactly on an integer we show that the problem is satisfiable with probability bounded away from both zero and one this is the first result to locate the exact satisfiability threshold in a random constraint satisfaction problem exhibiting the condensation phenomenon identified by krzakala et al proc natl acad sci 104 25 10318 10323 2007 our proof verifies the one step replica symmetry breaking formalism for this model we expect our methods to be applicable to a broad range of random constraint satisfaction problems and combinatorial problems on random graphs

blind equalization of iir channels using hidden markov models and extended least squares in this paper we present a blind equalization algorithm for noisy iir channels when the channel input is a finite state markov chain the algorithm yields estimates of the iir channel coefficients channel noise variance transition probabilities and state of the markov chain unlike the optimal maximum likelihood estimator which is computationally infeasible since the computing cost increases exponentially with data length our algorithm is computationally inexpensive our algorithm is based on combining a recursive hidden markov model hmm estimator with a relaxed spr strictly positive real extended least squares els scheme in simulation studies we show that the algorithm yields satisfactory estimates even in low snr we also compare the performance of our scheme with a truncated fir scheme and the constant modulus algorithm cma which is currently a popular algorithm in blind equalization

strong asymptotics of orthogonal polynomials with respect to exponential weights we consider asymptotics of orthogonal polynomials with respect to weights w x dx e q x dx on the real line where q x 2m k 0 qkx k q2m 0 denotes a polynomial of even order with positive leading coefficient the orthogonal polynomial problem is formulated as a riemann hilbert problem following 22 23 we employ the steepest descent type method introduced in 18 and further developed in 17 19 in order to obtain uniform plancherel rotach type asymptotics in the entire complex plane as well as asymptotic formulae for the zeros the leading coefficients and the recurrence coefficients of the orthogonal polynomials c 1999 john wiley sons inc

nonlinear techniques for interference suppression in spread spectrum systems the binary nature of direct sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose the case of a gaussian interferer with known autoregressive parameters is considered using simulations it is shown that an approximate conditional mean acm filter of the masreliez type performs significantly better than the optimum linear kalman bucy filter for the case of interferers with unknown parameters the nature of the nonlinearity in the acm filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction two versions of this filter are considered one in which the filter coefficients are updated using the widrow lms algorithm and another in which the coefficients are updated using an approximate gradient algorithm simulations indicate that the nonlinear filter with lms updates performs substantially better than the linear filter for both narrowband gaussian and single tone interferers whereas the gradient algorithm gives slightly better performance for gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer

dynamic spectral shape features as acoustic correlates for initial stop consonants a comprehensive investigation of two acoustic feature sets for english stop consonants spoken in syllable initial position was conducted to determine the relative invariance of the features that cue place and voicing the features evaluated were overall spectral shape encoded as the cosine transform coefficients of the nonlinearly scaled amplitude spectrum and formants in addition features were computed both for the static case i e from one 25 ms frame starting at the burst and for the dynamic case i e as parameter trajectories over several frames of speech data all features were evaluated with speaker independent automatic classification experiments using the data from 15 speakers to train the classifier and the data from 15 different speakers for testing the primary conclusions from these experiments as measured via automatic recognition rates are as follows 1 spectral shape features are superior to both formants and formants plus amplitudes 2 features extracted from the dynamic spectrum are superior to features extracted from the static spectrum and 3 features extracted from the speech signal beginning with the burst onset are superior to features extracted from the speech signal beginning with the vowel transition dynamic features extracted from the smoothed spectra over a 60 ms interval timed to begin with the burst onset appear to account for the primary vowel context effects automatic recognition results for the 6 stops 93 7 based on 20 features was better than the rates obtained with human listeners for a 50 ms segment 89 9 and only slightly worse than the rates obtained by human listeners for a 100 ms interval 96 6 thus the basic conclusion from our work is that dynamic spectral shape features are acoustically invariant cues for both place and voicing in initial stop consonants

modeling the judgment of vowel quality differences the hypothesis of this study is that the auditory cues relevant to listeners judgment of vowel quality are a spectral representation of loudness density versus pitch a model is described that generates such patterns for steady state vowels in addition to the nonlinear transformations underlying the loudness density and pitch scales it incorporates experimentally established characteristics associated with frequency resolution and masking such as the critical band concept this model is combined with a measure of auditory perceptual distance which operating on pairs of vowels treats each stimulus representation as a single spectral shape in order to test the distance metric and the model experimental data were gathered from listeners numerical estimates of quality differences between stimulus pairs which compared four formant and two formant vowels the correlation between experimental and theoretical results was 0 89 we interpret this value to indicate that the present definition of auditory cue and auditory distance can be said to account for the experimental behavior of our listeners only in a rather gross fashion on the other hand the theory was developed on the basis of rather conservative assumptions about the nature of auditory cues for instance the model ignores the possibility of temporal coding and certain nonlinear effects and it does not pay special attention to spectral peaks seen in that light the agreement between observed and predicted auditory distance is remarkably good

the complexity of spherical p spin models a second moment approach recently auffinger ben arous and cern initiated the study of critical points of the hamiltonian in the spherical pure pp spin spin glass model and established connections between those and several notions from the physics literature denoting the number of critical values less than nunu by crtn u crtn u they computed the asymptotics of 1nlog ecrtn u 1nlog ecrtn u as nn the dimension of the sphere goes to we compute the asymptotics of the corresponding second moment and show that for p 3p 3 and sufficiently negative uu it matches the first moment e crtn u 2 e crtn u 2 1 as an immediate consequence we obtain that crtn u e crtn u 1crtn u e crtn u 1 in l2l2 and thus in probability for any uu for which ecrtn u ecrtn u does not tend to 00 we prove that the moments match on an exponential scale

on the overlap in the multiple spherical sk models in order to study certain questions concerning the distribution of the overlap in sherrington kirkpatrick type models such as the chaos and ultrametricity problems it seems natural to study the free energy of multiple systems with constrained overlaps one can write analogues of guerra s replica symmetry breaking bound for such systems but it is not at all obvious how to choose informative functional order parameters in these bounds we were able to make some progress for spherical pure p spin sk models where many computations can be made explicitly for pure 2 spin model we prove ultrametricity and chaos in an external field for the pure p spin model for even p 4 without an external field we describe two possible values of the overlap of two systems at different temperatures we also prove a somewhat unexpected result which shows that in the 2 spin model the support of the joint overlap distribution is not always witnessed at the level of the free energy and for example ultrametricity holds only in a weak sense

first order methods almost always avoid strict saddle points we establish that first order methods avoid strict saddle points for almost all initializations our results apply to a wide variety of first order methods including manifold gradient descent block coordinate descent mirror descent and variants thereof the connecting thread is that such algorithms can be studied from a dynamical systems perspective in which appropriate instantiations of the stable manifold theorem allow for a global stability analysis thus neither access to second order derivative information nor randomness beyond initialization is necessary to provably avoid strict saddle points

sum rules via large deviations in this paper a sum rule means a relationship between a functional defined on a subset of all probability measures on r involving the reverse kullback leibler divergence with respect to a particular distribution and recursion coefficients related to the orthogonal polynomial construction the first sum rule is the szeg o verblunsky theorem see simon 2011 theorem 1 8 6 p 29 and concerns the case of trigonometrical polynomials on the torus more recently killip and simon killip and simon 2003 have given a revival interest to this subject by showing a quite surprising sum rule for measures dominating the semicircular distribution indeed this sum rule includes a contribution of the atomic part of the measure away from the support of the circular law in this paper we recover this sum rules by using only large deviations tools on random matrices furthermore we obtain new up to our knowledge magic sum rules for the reverse kullback leibler divergence with respect to the pastur marchenko or kesten mckay distributions as in the semicircular case these formulas generally include a contribution of the atomic part appearing away from the support of the reference measure from the point of view of large deviations we obtain these formulas by showing a large deviation principle for the point mass measure concentrated on random eigenvalues of classical ensembles and combine it with a large deviation principle due to gamboa and rouault 2011 for the recursion coefficients

iterative algorithms for state estimation of jump markov linear systems jump markov linear systems jmlss are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system in this paper we present original deterministic and stochastic iterative algorithms for optimal state estimation of jmlss the first stochastic algorithm yields minimum mean square error mmse estimates of the finite state space markov chain and of the continuous state of the jmls a deterministic and a stochastic algorithm are given to obtain the marginal maximum a posteriori mmap sequence estimate of the finite state markov chain finally a deterministic and a stochastic algorithm are derived to obtain the mmap sequence estimate of the continuous state of the jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problem of deconvolution of bernoulli gaussian bg processes and the problem of tracking a maneuvering target are addressed

adaptive nonlinear filters for narrow band interference suppression in spread spectrum cdma systems this paper presents a novel nonlinear filter and parameter estimator for narrow band interference suppression in code division multiple access spread spectrum systems as in the article by rusch and poor 1994 the received sampled signal is modeled as the sum of the spread spectrum signal modeled as a finite state independently identically distributed i i d process here we generalize to a finite state markov chain narrow band interference modeled as a gaussian autoregressive process and observation noise modeled as a zero mean white gaussian process the proposed algorithm combines a recursive hidden markov model hmm estimator kalman filter kf and the recursive expectation maximization algorithm the nonlinear filtering techniques for narrow band interference suppression presented in rusch and poor and our proposed hmm kf algorithm have the same computational cost detailed simulation studies show that the hmm kf algorithm outperforms the filtering techniques in rusch and poor in particular significant improvements in the bit error rate and signal to noise ratio snr enhancement are obtained in low to medium snr furthermore in simulation studies we investigate the effect on the performance of the hmm kf and the approximate conditional mean acm filter in the paper by rusch and poor when the observation noise variance is increased as expected the performance of the hmm kf and acm algorithms worsen with increasing observation noise and number of users however hmm kf significantly outperforms acm in medium to high observation noise

maximum likelihood estimation of transition probabilities of jump markov linear systems this paper describes an online maximum likelihood estimator for the transition probabilities associated with a jump markov linear system jmls the maximum likelihood estimator is derived using the reference probability method which exploits an hypothetical probability measure to find recursions for complex expectations expectation maximization em procedure is utilized for maximizing the likelihood function in order to avoid the exponential increase in the number of statistics of the optimal em algorithm we make interacting multiple model imm type approximations the resulting method needs the mode weights of an imm filter with n3 components where n is the number of models in the jmls the algorithm can also supply base state estimates and covariances as a by product the performance of the estimator is illustrated on two simulated examples and compared to a recently proposed alternative

on the energy landscape of the mixed even p spin model we investigate the energy landscape of the mixed even p spin model with ising spin configurations we show that for any given energy level between zero and the maximal energy with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level furthermore their magnetizations and overlaps are concentrated around some fixed constants in particular at the level of maximal energy we prove that the hamiltonian exhibits exponentially many orthogonal peaks this improves the results of chatterjee disorder chaos and multiple valleys in spin glasses 2009 and ding et al ann probab 43 6 3468 3493 2015 where the former established a logarithmic size of the number of the orthogonal peaks while the latter proved a polynomial size our second main result obtains disorder chaos at zero temperature and at any external field as a byproduct this implies that the fluctuation of the maximal energy is superconcentrated when the external field vanishes and obeys a gaussian limit law when the external field is present

maximum likelihood estimation of the dynamic shock error model abstract in this paper an efficient estimation technique in the time domain for the dynamic shock error model is developed this approach utilizes a state space representation of the model and the kalman filtering technique to obtain the maximum likelihood estimates the resulting estimates are shown to be consistent and asymptotically normal with the inverse of the information matrix as their precision measure a consistent estimate of the information matrix is suggested to obtain the standard errors of the estimates

on the satisfiability threshold and clustering of solutions of random 3 sat formulas we study the structure of satisfying assignments of a random 3 sat formula in particular we show that a random formula of density a 4 453 almost surely has no non trivial core assignments core assignments are certain partial assignments that can be extended to satisfying assignments and have been studied recently in connection with the survey propagation heuristic for random sat their existence implies the presence of clusters of solutions and they have been shown to exist with high probability below the satisfiability threshold for k sat with k 9 d achlioptas f ricci tersenghi on the solution space geometry of random constraint satisfaction problems in proc 38th acm symp theory of computing stoc 2006 pp 130 139 our result implies that either this does not hold for 3 sat or the threshold density for satisfiability in 3 sat lies below 4 453 the main technical tool that we use is a novel simple application of the first moment method

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

random 2 sat results and problems in the random 2 sat problem we are given a set c of m disjunctions of two literals chosen at random within the 2n2 pairs of distinct literals coming from n logical variables the basic problem is to nd out for which values of the ratio m n the disjunctions in c are almost surely simultaneously satisfiable or almost surely not simultaneously satisfiable as n tends to infinity the purpose of this paper is to review the main steps in the solution of this problem starting with the location of the asymptotic critical ratio around 8 years ago and ending with the recent almost complete solution due to bollob4as et al thus this paper is not a review in the usual sense of the word i e it does not include all the known results about random 2 sat we will also make a few comments concerning the behaviour of the number of satisfying assignments of random instances of 2 sat below the critical ratio a problem relevant to theoretical physics

random matrices and complexity of spin glasses cern y abstract we give an asymptotic evaluation of the complexity of spherical p spin spin glass models via random matrix theory this study enables us to obtain detailed infor mation about the bottom of the energy landscape including the absolute minimum the ground state the other local minima and describe an interesting layered structure of the low critical values for the hamiltonians of these models we also show that our ap proach allows us to compute the related tap complexity and extend the results known in the physics literature as an independent tool we prove a ldp for the k th largest eigenvalue of the goe extending the results of bdg01 how many critical values of given index and below a given level does a typical random morse function have on a high dimensional manifold our work addresses this question in a very special case we look at certain natural random gaussian functions on the n dimensional sphere known as p spin spherical spin glass models we cannot yet answer the question above about the typical number but we can study thoroughly the mean number which we show is exponentially large in n we introduce a new identity based on the classical kac rice formula relating random matrix theory and the problem of counting these critical values using this identity and tools from random matrix theory we give an asymptotic evaluation of the complexity of these spherical spin glass models the complexity mentioned here is defined as the mean number of critical points of given index whose value is below or above a given level this includes the important question of counting the mean number of local minima below a given level and in particular the question of finding the ground state energy the minimal value of the hamiltonian we show that this question is directly related to the study of the edge of the spectrum of the gaussian orthogonal ensemble goe the question of computing the complexity of mean field spin glass models has recently been thoroughly studied in the physics literature see for example clr03 and the refer ences therein mainly for a different measure of the complexity i e the mean number of solutions to the thouless anderson palmer equations or tap complexity our approach to the complexity enables us to recover known results in the physics literature about tap complexity to compute the ground state energy when p is even and to describe an interesting layered structure of the low energy levels of the hamiltonians of these models which might prove useful for the study of the metastability of langevin dynamics for these models in longer time scales than those studied in bdg01 the paper is organised as follows in section 2 we give our main results in section 3 we prove two main formulas theorem 2 1 and 2 2 relating random matrix theory specif ically the goe and spherical spin glasses these formulas are direct consequences of the kac rice formula we learned the version needed here in the book at07 for another modern account see aw09 the main new ingredient is the fact that for spherical spin glass models the hessian of the hamiltonian at a critical point conditioned on the value of the hamiltonian is a symmetric gaussian random matrix with independent entries up to symmetry plus a diagonal matrix this implies in particular that it is possible to

replica symmetry breaking condition exposed by random matrix calculation of landscape complexity we start with a rather detailed general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random n 1 dimensional gaussian landscape and confined by a spherically symmetric potential suitably growing at infinity then we employ random matrix methods to calculate the density of stationary points as well as minima of the associated energy surface this is used to show that for a generic smooth concave confining potentials the condition of the zero temperature replica symmetry breaking coincides with one signaling that both mean total number of stationary points in the energy landscape and the mean number of minima are exponential in n for such systems the annealed complexity of minima vanishes cubically when approaching the critical confinement whereas the cumulative annealed complexity vanishes quadratically different behaviour reported in our earlier short communication fyodorov et al in jetp lett 85 261 2007 was due to non analyticity of the hard wall confinement potential finally for the simplest case of parabolic confinement we investigate how the complexity depends on the index of stationary points in particular we show that in the vicinity of critical confinement the saddle points with a positive annealed complexity must be close to minima as they must have a vanishing fraction of negative eigenvalues in the hessian

broken replica symmetry bounds in the mean field spin glass model by using a simple interpolation argument in previous work we have proven the existence of the thermodynamic limit for mean field disordered models including the sherrington kirkpatrick model and the derrida p spin model here we extend this argument in order to compare the limiting free energy with the expression given by the parisi ansatz and including full spontaneous replica symmetry breaking our main result is that the quenched average of the free energy is bounded from below by the value given in the parisi ansatz uniformly in the size of the system moreover the difference between the two expressions is given in the form of a sum rule extending our previous work on the comparison between the true free energy and its replica symmetric sherrington kirkpatrick approximation we give also a variational bound for the infinite volume limit of the ground state energy per site

an online sequential algorithm for the estimation of transition probabilities for jump markov linear systems this paper describes a new method to estimate the transition probabilities associated with a jump markov linear system the new algorithm uses stochastic approximation type recursions to minimize the kullback leibler divergence between the likelihood function of the transition probabilities and the true likelihood function since the calculation of the likelihood function of the transition probabilities is impossible an incomplete data paradigm which has been previously applied to a similar problem for hidden markov models is used the algorithm differs from the existing algorithms in that it assumes that the transition probabilities are deterministic quantities whereas the existing approaches consider them to be random variables with prior distributions

free energy and complexity of spherical bipartite models we investigate both free energy and complexity of the spherical bipartite spin glass model we first prove a variational formula in high temperature for the limiting free energy based on the well known crisanti sommers representation of the mixed p spin spherical model next we show that the mean number of local minima at low levels of energy is exponentially large in the size of the system and we derive a bound on the location of the ground state energy

brief paper risk sensitive filtering for jump markov linear systems in this paper a risk sensitive multiple model filtering algorithm is derived using the reference probability methods first the approximation of the interacting multiple model imm algorithm is identified in the reference probability domain then the same type of approximation is used to derive the finite dimensional risk sensitive filtering algorithm the derived algorithm reduces to the imm filter when the risk sensitive parameter goes to zero and reduces to the risk sensitive filter for linear gauss markov systems when the number of models is unity the algorithm performs better in a simulated uncertain parameter scenario than the imm filter

two solutions to diluted p spin models and xorsat problems we derive analytical solutions for p spin models with finite connectivity at zero temperature these models are the statistical mechanics equivalent of p xorsat problems in theoretical computer science we give a full characterization of the phase diagram location of the phase transitions static and dynamic together with a description of the clustering phenomenon taking place in configurational space we use two alternative methods the cavity approach and a rigorous derivation

local minima in disordered mean field ferromagnets we consider the complexity of random ferromagnetic landscapes on the hypercube pm 1 n given by ising models on the complete graph with i i d non negative edge weights this includes in particular the case of bernoulli disorder corresponding to the ising model on a dense random graph mathcal g n p previous results had shown that with high probability as n rightarrow infty the gradient search energy lowering algorithm initialized uniformly at random converges to one of the homogeneous global minima all plus or all minus here we devise two modified algorithms tailored to explore the landscape at near zero magnetizations where the effect of the ferromagnetic drift is minimized with these we numerically verify the landscape complexity of random ferromagnets finding a diverging number of 1 spin flip stable local minima as n rightarrow infty we then investigate some of the properties of these local minima e g typical energy and magnetization and compare to the situation where the edge weights are drawn from a heavy tailed distribution

on the optimization landscape of tensor decompositions non convex optimization with local search heuristics has been widely used in machine learning achieving many state of art results it becomes increasingly important to understand why they can work for these np hard problems on typical data the landscape of many objective functions in learning has been conjectured to have the geometric property that all local optima are approximately global optima and thus they can be solved efficiently by local search algorithms however establishing such property can be very difficult in this paper we analyze the optimization landscape of the random over complete tensor decomposition problem which has many applications in unsupervised learning especially in learning latent variable models in practice it can be efficiently solved by gradient ascent on a non convex objective we show that for any small constant varepsilon 0 among the set of points with function values 1 varepsilon factor larger than the expectation of the function all the local maxima are approximate global maxima previously the best known result only characterizes the geometry in small neighborhoods around the true components our result implies that even with an initialization that is barely better than the random guess the gradient ascent algorithm is guaranteed to solve this problem however achieving such a initialization with random guess would still require super polynomial number of attempts our main technique uses kac rice formula and random matrix theory to our best knowledge this is the first time when kac rice formula is successfully applied to counting the number of local optima of a highly structured random polynomial with dependent coefficients

the expectation maximization algorithm for symbol unsynchronized sequence detection the expectation maximization em algorithm for maximizing likelihood functions combined with the viterbi algorithm is applied to the problem of sequence detection when symbol timing information is not present although the em algorithm is noncausal results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations making it both of theoretical and of practical interest a practical algorithm based on the em algorithm is introduced it reduces the computational burden and improves performance by making use of timing estimates in previous observation windows

the perceptual relevance of locus equations identification curves were estimated for the english consonants b d g using five formant cv synthetic stimuli comprehensively sampling the f2 onset f2 vowel acoustic space in the vicinity of b d g locus equations h sussman et al j acoust soc am 90 1309 1325 1991 the stimuli included 10 english monophthongal vowel contexts 11 levels of f2 onset per vowel and 3 levels of f3 onset orthogonally varied with the f2 variables 10 vowels 11 f2 onsets 3 f3 onsets 330 stimuli after brief training each of six subjects three male and three female was presented eight trials of each of the stimuli one or two trials per day over a period of several days systems of identification curves were visualized as identification surfaces situated in locus equation acoustic space and were overlaid with acoustic data from five male speakers in order to judge the degree of correspondence between perception and acoustic data a chi square analysis was also performed in order to quantify the correspondence be

stochastic sampling algorithms for state estimation of jump markov linear systems jump markov linear systems are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system the computational cost in computing conditional mean or maximum a posteriori map state estimates of the markov chain or the state of the jump markov linear system grows exponentially in the number of observations we present three globally convergent algorithms based on stochastic sampling methods for state estimation of jump markov linear systems the cost per iteration is linear in the data length the first proposed algorithm is a data augmentation da scheme that yields conditional mean state estimates the second proposed scheme is a stochastic annealing sa version of da that computes the joint map sequence estimate of the finite and continuous states finally a metropolis hastings da scheme based on sa is designed to yield the map estimate of the finite state markov chain convergence results of the three above mentioned stochastic algorithms are obtained computer simulations are carried out to evaluate the performances of the proposed algorithms the problem of estimating a sparse signal developing from a neutron sensor based on a set of noisy data from a neutron sensor and the problem of narrow band interference suppression in spread spectrum code division multiple access cdma systems are considered

matrix completion from a few entries let m be an n n matrix of rank r and assume that a uniformly random subset e of its entries is observed we describe an efficient algorithm which we call optspace that reconstructs m from e o rn observed entries with relative root mean square error 1 2 rmse c nr e 1 2 with probability larger than 1 1 n3 further if r o 1 and m is sufficiently unstructured then optspace reconstructs it exactly from e o n log n entries with probability larger than 1 1 n3 this settles in the case of bounded rank a question left open by candes and recht and improves over the guarantees for their reconstruction algorithm the complexity of our algorithm is o e r log n which opens the way to its use for massive data sets in the process of proving these statements we obtain a generalization of a celebrated result by friedman kahn szemeredi and feige ofek on the spectrum of sparse random matrices

an improvement to the interacting multiple model imm algorithm computing the optimal conditional mean state estimate for a jump markov linear system requires exponential complexity and hence practical filtering algorithms are necessarily suboptimal in the target tracking literature suboptimal multiple model filtering algorithms such as the interacting multiple model imm method and generalized pseudo bayesian gpb schemes are widely used for state estimation of such systems we derive a reweighted interacting multiple model algorithm although the imm algorithm is an approximation of the conditional mean state estimator our algorithm is a recursive implementation of a maximum a posteriori map state sequence estimator this map estimator is an instance of a previous version of the em algorithm known as the alternating expectation conditional maximization aecm algorithm computer simulations indicate that the proposed reweighted imm algorithm is a competitive alternative to the popular imm algorithm and gpb methods

gibbs states and the set of solutions of random constraint satisfaction problems abstract an instance of a random constraint satisfaction problem defines a random subset the set of solutions of a large product space x n the set of assignments we consider two prototypical problem ensembles random k satisfiability and q coloring of random regular graphs and study the uniform measure with support on s as the number of constraints per variable increases this measure first decomposes into an exponential number of pure states clusters and subsequently condensates over the largest such states above the condensation point the mass carried by the n largest states follows a poisson dirichlet process for typical large instances the two transitions are sharp we determine their precise location further we provide a formal definition of each phase transition in terms of different notions of correlation between distinct variables in the problem the degree of correlation naturally affects the performances of many search sampling algorithms empirical evidence suggests that local monte carlo markov chain strategies are effective up to the clustering phase transition and belief propagation up to the condensation point finally refined message passing techniques such as survey propagation may also beat this threshold message passing algorithms phase transitions random graphs

large deviations for wigner s law and voiculescu s non commutative entropy we study the spectral measure of gaussian wigner s matrices and prove that it satisfies a large deviation principle we show that the good rate function which governs this principle achieves its minimum value at wigner s semicircular law which entails the convergence of the spectral measure to the semicircular law as a conclusion we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about voiculescu s non commutative entropy

bicolouring random hypergraphs we study the problem of bicolouring random hypergraphs both numerically and analytically we apply the zero temperature cavity method to find analytical results for the phase transitions dynamic and static in the one step replica symmetry breaking 1rsb approximation these points appear to be in agreement with the results of the numerical algorithm in the second part we implement and test the survey propagation algorithm for specific bicolouring instances in the so called hard sat phase

phase transitions in the q coloring of random hypergraphs we study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied hypergraph coloring is a constraint satisfaction problem where each constraint includes k variables that must be assigned one out of q colors in such a way that there are no monochromatic constraints i e there are at least two distinct colors in the set of variables belonging to every constraint this problem generalizes naturally coloring of random graphs k 2 and bicoloring of random hypergraphs q 2 both of which were extensively studied in past works the study of random hypergraph coloring gives us access to a case where both the size q of the domain of the variables and the arity k of the constraints can be varied at will our work provides explicit values and predictions for a number of phase transitions that were discovered in other constraint satisfaction problems but never evaluated before in hypergraph coloring among other cases we revisit the hypergraph bicoloring problem q 2 where we find that for k 3 and k 4 the colorability threshold is not given by the one step replica symmetry breaking analysis as the latter is unstable towards more levels of replica symmetry breaking we also unveil and discuss the coexistence of two different 1rsb solutions in the case of q 2 k 4 finally we present asymptotic expansions for the density of constraints at which various phase transitions occur in the limit where q and or k diverge

locus equations derived from compensatory articulation locus equations are linear regressions of the onset of f2 transitions on their offsets these functions vowel normalize the f2 transitions such that they are able to characterize consonantal place categories the purpose of this research was to determine if compensatory articulation due to bite blocks would alter the normally linear relationship between f2 transition onset and offset frequencies or alter the differential slopes and y intercepts of locus equations as a function of stop place six speakers three male and three female each produced bvt dvt and gvt tokens for ten vowel contexts under normal and bite block conditions extremely linear and practically identical scatterplots were obtained in the two speaking conditions no adaptation to the bite blocks was found when comparing locus equations derived from the initial versus the final bite block trial results are discussed in relation to the orderly output constraint which postulates a perceptual function for linearly related f2 transition end points within consonantal place categories

on the limitation of spectral methods from the gaussian hidden clique problem to rank one perturbations of gaussian tensors we consider the following detection problem given a realization of a symmetric matrix x of dimension n distinguish between the hypothesis that all upper triangular variables are independent and identically distributed i i d gaussians variables with mean 0 and variance 1 and the hypothesis where x is the sum of such matrix and an independent rank one perturbation this setup applies to the situation where under the alternative there is a planted principal submatrix b of size l for which all upper triangular variables are i i d gaussians with mean 1 and variance 1 whereas all other upper triangular elements of x not in b are i i d gaussians variables with mean 0 and variance 1 we refer to this as the gaussian hidden clique problem when l 1 epsilon sqrt n epsilon 0 it is possible to solve this detection problem with probability 1 o n 1 by computing the spectrum of x and considering the largest eigenvalue of x we prove that this condition is tight in the following sense when l no algorithm that examines only the eigenvalues of x can detect the existence of a hidden gaussian clique with error probability vanishing as n to infty we prove this result as an immediate consequence of a more general result on rank one perturbations of k dimensional gaussian tensors in this context we establish a lower bound on the critical signal to noise ratio below which a rank one signal cannot be detected

phase space geometry and slow dynamics we describe a non arrhenius mechanism for the slowing down of dynamics that is inherent to the high dimensionality of the phase space we show that such a mechanism is at work both in a family of mean field spin glass models without any domain structure and in the case of ferromagnetic domain growth the marginality of spin glass dynamics as well as the existence of a quasi equilibrium regime can be understood within this scenario we discuss the question of ergodicity in an out of equilibrium situation

tensor completion based on nuclear norm minimization for 5d seismic data reconstruction abstractmany standard seismic data processing and imaging techniques require regularly sampled data prestack seismic data are multidimensional signals that can be represented via low rank fourth order tensors in the frequency space f x domain we propose to adopt tensor completion strategies to recover unrecorded observations and to improve the signal to noise ratio of prestack seismic volumes tensor completion can be posed as an inverse problem and solved by minimizing a convex objective function the objective function contains two terms a data misfit and a nuclear norm the data misfit measures the proximity of the reconstructed seismic data to the observations the nuclear norm constraints the reconstructed data to be a low rank tensor in essence we solve the prestack seismic reconstruction problem via low rank tensor completion the cost function of the problem is minimized using the alternating direction method of multipliers we present synthetic examples to illustrate the behavior of the al

the extremal process of critical points of the pure p spin spherical spin glass model recently sharp results concerning the critical points of the hamiltonian of the p spin spherical spin glass model have been obtained by means of moments computations in particular these moments computations allow for the evaluation of the leading term of the ground state i e of the global minimum in this paper we study the extremal point process of critical points that is the point process associated to all critical values in the vicinity of the ground state we show that the latter converges in distribution to a poisson point process of exponential intensity in particular we identify the correct centering of the ground state and prove the convergence in distribution of the centered minimum to a minus gumbel variable these results are identical to what one obtains for a sequence of i i d variables correctly normalized namely we show that the model is in the universality class of rem

complexity of random smooth functions on the high dimensional sphere we analyze the landscape of general smooth gaussian functions on the sphere in dimension n when n is large we give an explicit formula for the asymptotic complexity of the mean number of critical points of finite and diverging index at any level of energy and for the mean euler characteristic of level sets we then find two possible scenarios for the bottom landscape one that has a layered structure of critical values and a strong correlation between indexes and critical values and another where even at levels below the limiting ground state energy the mean number of local minima is exponentially large we end the paper by discussing how these results can be interpreted in the language of spin glasses models

an investigation of locus equations as a source of relational invariance for stop place categorization locus equations were investigated as a potential metric capable of illustrating relational invariance for place of articulation in voiced initial stop consonants independently of vowel context locus equations are straight line regression fits to data points formed by plotting onsets of f2 transitions along the y axis and their corresponding midvowel nuclei along the x axis twenty subjects 10 male and 10 female produced b v t d v t and g v t tokens for ten vowel contexts each cvc token was repeated in a carrier phrase five times yielding 50 tokens per stop place category formant measures were obtained using the macspeech lab ii speech analysis system extremely linear regression functions were found characterized by distinct slopes and y intercepts as a function of place of articulation a discriminant analysis using f2onset and vowel frequencies as predictors showed 82 78 and 67 classification rates for labial alveolar and velar place using derived slope and y intercept values as predictors led to 100 classification into stop place categories a neurobiologically oriented perspective on the invariance issue is developed and a brain based recognition algorithm for stop place integrating burst and f2 trajectory cues is offered

a new look at survey propagation and its generalizations this article provides a new conceptual perspective on survey propagation which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k sat problems even with densities close to the satisfiability threshold we first describe how any sat formula can be associated with a novel family of markov random fields mrfs parameterized by a real number 0 1 we then show that applying belief propagation a well known message passing technique for estimating marginal probabilities to this family of mrfs recovers a known family of algorithms ranging from pure survey propagation at one extreme e 1 to standard belief propagation on the uniform distribution over sat assignments at the other extreme e 0 configurations in these mrfs have a natural interpretation as partial satisfiability assignments on which a partial order can be defined we isolate cores as minimal elements in this partial ordering which are also fixed points of survey propagation and the only assignments with positive probability in the mrf for e 1 our experimental results for k e 3 suggest that solutions of random formulas typically do not possess non trivial cores this makes it necessary to study the structure of the space of partial assignments for 0 can be viewed as a smoothed version of the uniform distribution over satisfying assignments e 0 finally we isolate properties of gibbs sampling and message passing algorithms that are typical for an ensemble of k sat problems

finite dimensional smoothers for map state estimation of bilinear systems in this paper we present two finite dimensional iterative algorithms for maximum a posteriori map state sequence estimation of bilinear systems bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems our iterative algorithms for state estimation are based on the expectation maximization em algorithm and outperform the widely used extended kalman smoother eks unlike the eks these em algorithms are optimal in the map sense finite dimensional solutions to the state sequence estimation problem for bilinear models we also present recursive on line versions of the two algorithms and show that they outperform the extended kalman filter ekf our main conclusion is that the em based algorithms presented in this paper are novel nonlinear filtering methods that perform better than traditional methods such as the ekf

free energy of the spherical mean field model we compute at any temperature the free energy of the multi p spin spherical model when only terms for p even are considered

on line estimation of hidden markov model parameters based on the kullback leibler information measure sequential or online hidden markov model hmm signal processing schemes are derived and their performance is illustrated by simulation the online algorithms are sequential expectation maximization em schemes and are derived by using stochastic approximations to maximize the kullback leibler information measure the schemes can be implemented either as filters or fixed lag or sawtooth lag smoothers they yield estimates of the hmm parameters including transition probabilities markov state levels and noise variance in contrast to the offline em algorithm baum welch scheme which uses the fixed interval forward backward scheme the online schemes have significantly reduced memory requirements and improved convergence and they can estimate hmm parameters that vary slowly with time or undergo infrequent jump changes similar techniques are used to derive online schemes for extracting finite state markov chains imbedded in a mixture of white gaussian noise wgn and deterministic signals of known functional form with unknown parameters

a fourier view on the r transform and related asymptotics of spherical integrals abstract we estimate the asymptotics of spherical integrals of real symmetric or hermitian matrices when the rank of one matrix is much smaller than its dimension we show that it is given in terms of the r transform of the spectral measure of the full rank matrix and give a new proof of the fact that the r transform is additive under free convolution these asymptotics also extend to the case where one matrix has rank one but complex eigenvalue a result related with the analyticity of the corresponding spherical integrals

aging of spherical spin glasses sompolinski and zippelius 1981 propose the study of dynamical systems whose invariant measures are the gibbs measures for hard to analyze statistical physics models of interest in the course of doing so physicists often report of an aging phenomenon for example aging is expected to happen for the sherrington kirkpatrick model a disordered mean field model with a very complex phase transition in equilibrium at low temperature we shall study the langevin dynamics for a simplified spherical version of this model the induced rotational symmetry of the spherical model reduces the dynamics in question to an n dimensional coupled system of ornstein uhlenbeck processes whose random drift parameters are the eigenvalues of certain random matrices we obtain the limiting dynamics for n approaching infinity and by analyzing its long time behavior explain what is aging mathematically speaking what causes this phenomenon and what is its relationship with the phase transition of the corresponding equilibrium invariant measures

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

entropy landscape and non gibbs solutions in constraint satisfaction problems we study the entropy landscape of solutions for the bicoloring problem in random graphs a representative difficult constraint satisfaction problem our goal is to classify which types of clusters of solutions are addressed by different algorithms in the first part of the study we use the cavity method to obtain the number of clusters with a given internal entropy and determine the phase diagram of the problem e g dynamical rigidity and satisfiability unsatisfiability sat unsat transitions in the second part of the paper we analyze different algorithms and locate their behavior in the entropy landscape of the problem for instance we show that a smoothed version of a decimation strategy based on belief propagation is able to find solutions belonging to subdominant clusters even beyond the so called rigidity transition where the thermodynamically relevant clusters become frozen these nonequilibrium solutions belong to the most probable unfrozen clusters

optimal simultaneous detection and estimation of filtered discrete semi markov chains an optimal algorithm for the detection of noisy filtered discrete semi markov chains is presented estimation of the underlying model parameters is also considered for a given path of the discrete semi markov chain the optimum estimates of the model parameters obtained by the maximum likelihood method are expressed as functions of the path these functions are then used to derive a single maximum a posteriori criterion for the optimal detection of the unknown single path the final optimization is carried out numerically by a combination of gradient divide and conquer and search techniques this set of techniques is referred to as the integer most likely search detector experimental results using synthetic data demonstrate the potential of the algorithm

on the energy landscape of spherical spin glasses abstract we investigate the energy landscape of the spherical mixed even p spin model near its maximum energy we relate the distance between pairs of near maxima to the support of the parisi measure at zero temperature we then provide an algebraic relation that characterizes one step replica symmetric breaking parisi measures for these measures we show that any two nonparallel spin configurations around the maximum energy are asymptotically orthogonal to each other in sharp contrast we study models with full replica symmetry breaking and show that all possible values of the asymptotic distance are attained near the maximum energy

a note on mixed matrix moments for the complex ginibre ensemble we consider the mixed matrix moments for the complex ginibre ensemble these are well known we consider the relation to the expected overlap functions of chalker and mehlig this leads to new asymptotic problems for the overlap we obtain some results but we also state some remaining open problems

spectral tilt change in stop consonant perception there exists no clear understanding of the importance of spectral tilt for perception of stop consonants it is hypothesized that spectral tilt may be particularly salient when formant patterns are ambiguous or degraded here it is demonstrated that relative change in spectral tilt over time not absolute tilt significantly influences perception of b vs d experiments consisted of burstless synthesized stimuli that varied in spectral tilt and onset frequency of the second formant in experiment 1 tilt of the consonant at voice onset was varied in experiment 2 tilt of the vowel steady state was varied results of these experiments were complementary and revealed a significant contribution of relative spectral tilt change only when formant information was ambiguous experiments 3 and 4 replicated experiments 1 and 2 in an aba ada context the additional tilt contrast provided by the initial vowel modestly enhanced effects in experiment 5 there was no effect for absolute tilt when consonant an

topology trivialization and large deviations for the minimum in the simplest random optimization finding the global minimum of a cost function given by the sum of a quadratic and a linear form in n real variables over n 1 dimensional sphere is one of the simplest yet paradigmatic problems in optimization theory known as the trust region subproblem or constraint least square problem when both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field we first identify and study two distinct large n scaling regimes in which the linear term magnetic field leads to a gradual topology trivialization i e reduction in the total number mathcal n tot of critical stationary points in the cost function landscape in the first regime mathcal n tot remains of the order n and the cost function energy has generically two almost degenerate minima with the tracy widom tw statistics in the second regime the number of critical points is of the order of unity with a finite probability for a single minimum in that case the mean total number of extrema minima and maxima of the cost function is given by the laplace transform of the tw density and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the tw law though the full form of that distribution is not yet known to us one of its far tails can be inferred from the large deviation theory for the global minimum in the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large deviation approximation by finding both the rate function and the leading pre exponential factor

a cross linguistic investigation of locus equations as a phonetic descriptor for place of articulation a previous study h sussman h mccaffrey and s matthews j acoust soc am 90 1309 1325 1991 of american english cv coarticulation showed a remarkably linear relationship between onset frequencies of f2 transitions plotted on the y axis in relation to the f2 midvowel target frequencies plotted on the x axis for cvc tokens with initial b d g and ten medial vowel contexts slope and y intercept values of regression functions fit to these scatterplots locus equations were shown to serve as statistically powerful phonetic descriptors of place of articulation the present study extends the locus equation metric to three additional languages thai cairene arabic and urdu having both two and four place contrasts for syllable initial voiced stops a total of 14 speakers thai 6 arabic 3 urdu 5 produced 1740 cvc tokens that were acoustically analyzed using macspeech lab ii strong linear regression relationships were found for every stop category across all speakers slopes and y intercepts systematically varied as a function of place of articulation cross language comparisons of stop place categories were performed but variability of slope and y intercept means tempered conclusions concerning the existence of cv phonetic hot spots

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

online bayesian estimation of transition probabilities for markovian jump systems markovian jump systems mjss evolve in a jump wise manner by switching among simpler models according to a finite markov chain whose parameters are commonly assumed known this paper addresses the problem of state estimation of mjs with unknown transition probability matrix tpm of the embedded markov chain governing the jumps under the assumption of a time invariant but random tpm an approximate recursion for the tpms posterior probability density function pdf within the bayesian framework is obtained based on this recursion four algorithms for online minimum mean square error mmse estimation of the tpm are derived the first algorithm for the case of a two state markov chain computes the mmse estimate exactly if the likelihood of the tpm is linear in the transition probabilities its computational load is however increasing with the data length to limit the computational cost three alternative algorithms are further developed based on different approximation techniques truncation of high order moments quasi bayesian approximation and numerical integration respectively the proposed tpm estimation is naturally incorporable into a typical online bayesian estimation scheme for mjs e g generalized pseudo bayesian gpb or interacting multiple model imm thus adaptive versions of mjs state estimators with unknown tpm are provided simulation results of tpm adaptive imm algorithms for a system with failures and maneuvering target tracking are presented

information theoretic thresholds from the cavity method abstract vindicating a sophisticated but non rigorous physics approach called the cavity method we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models we work out several concrete applications of these general results for instance we pinpoint the exact condensation phase transition in the potts antiferromagnet on the random graph thereby improving prior approximate results contucci et al 2013 34 further we prove the conjecture from krzakala et al 2007 55 about the condensation phase transition in the random graph coloring problem for any number q 3 of colors moreover we prove the conjecture on the information theoretic threshold in the disassortative stochastic block model decelle et al 2011 35 additionally our general result implies the conjectured formula for the mutual information in low density generator matrix codes montanari 2005 73

local optima of the sherrington kirkpatrick hamiltonian we study local optima of the hamiltonian of the sherrington kirkpatrick model we compute the exponent of the expected number of local optima and determine the typical value of the hamiltonian we study local optima of the hamiltonian of the sherrington kirkpatrick model we compute the exponent of the expected number of local optima and determine the typical value of the hamiltonian

the geometry of the gibbs measure of pure spherical spin glasses we analyze the statics for pure p spin spherical spin glass models with p ge 3 at low enough temperature with f n beta denoting the free energy we compute the logarithmic second order term of nf n beta and prove that for an appropriate centering c n beta nf n beta c n beta is a tight sequence we further establish the absence of temperature chaos those results follow from the following geometric picture we prove for the gibbs measure of interest by itself asymptotically the measure splits into infinitesimal spherical bands centered at deep minima playing the role of pure states for the pure models the latter makes precise the picture of many valleys separated by high mountains and significant parts of the tap analysis from the physics literature

energy landscape of the finite size mean field 2 spin spherical model and topology trivialization motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes pels for several statistical mechanics models we perform a numerical study of the finite size 2 spin spherical model using both numerical polynomial homotopy continuation and a reformulation via non hermitian matrices the continuation approach computes all of the complex stationary points of this model while the matrix approach computes the real stationary points using these methods we compute the average number of stationary points while changing the topology of the pel as well as the variance histograms of these stationary points are presented along with an analysis regarding the complex stationary points this work connects topology trivialization to two different branches of mathematics algebraic geometry and catastrophe theory which is fertile ground for further interdisciplinary research