seismic denoising using the redundant lifting scheme abstractseparating linear coherent noise such as ground roll from reflections remains a key challenge in seismic processing by adapting the redundant lifting scheme rls a wavelet transform method to seismic data we have determined how the wavelet domain can be used to suppress coherent and random noise the rls operates on a trace by trace basis decomposing each time series into wavelet coefficient wc time series and consequently a single gather in a shot receiver or common depth point domain into a series of wc subgathers sgs the decomposition changes the relative magnitude of wcs of various events reflection head wave ground roll etc from one sg to another without affecting their moveout in sg s in which the wcs of undesired events were significantly stronger than the desired events the wcs can be surgically muted selective muting in carefully chosen sgs attenuates undesired events while having minimal effects on frequency spectra of the desired events in addition random noi

image identification and restoration in the subband domain when faced with a large support point spread function psf the iterative expectation maximization em algorithm which is often used for psf identification is very sensitive to the initial psf estimate to deal with this problem the authors propose to do em image identification and restoration in the subband domain after the image is first divided into subbands the em algorithm is applied to each subband separately since the psf can be taken to have smaller support in each subband these subbands should be less of a problem with the em model identification they also introduce an adaptive subband em method for use in the upper frequency subbands

statistical mechanics of a single particle in a multiscale random potential parisi landscapes in finite dimensional euclidean spaces we construct an n dimensional gaussian landscape with multiscale translation invariant logarithmic correlations and investigate the statistical mechanics of a single particle in this environment in the limit of high dimension n the free energy of the system and overlap function are calculated exactly using the replica trick and parisi s hierarchical ansatz in the thermodynamic limit we recover the most general version of the derrida s generalized random energy model grem the low temperature behaviour depends essentially on the spectrum of length scales involved in the construction of the landscape if the latter consists of k discrete values the system is characterized by a k step replica symmetry breaking solution we argue that our construction is in fact valid in any finite spatial dimensions n 1 we discuss the implications of our results for the singularity spectrum describing multifractality of the associated boltzmann gibbs measure finally we discuss several generalizations and open problems such as the dynamics in such a landscape and the construction of a generalized multifractal random walk

inhomogeneous gaussian image models for estimation and restoration two inhomogeneous gaussian image models are presented for estimation and restoration by incorporating the local statistics of an image a homogeneous autoregressive ar random field can be extended to an inhomogeneous ar field this inhomogeneous random field can provide a better description of the image than the homogeneous one as a consequence of this improved modeling a minimum mean square error estimator mmse based on the inhomogeneous gaussian model can produce good results in both subjective and objective criteria two image models are proposed for use in image estimation and restoration a residual image model original image minus the space variant mean and a normalized image model residual image divided by space variant standard variation the novel aspect of these models is the use of an autoregressive dynamical model for residual and normalized images some aspects of parameter estimation are discussed and simulation results are presented

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

the parisi formula has a unique minimizer in 1979 parisi phys rev lett 43 1754 1756 1979 predicted a variational formula for the thermodynamic limit of the free energy in the sherrington kirkpatrick model and described the role played by its minimizer this formula was verified in the seminal work of talagrand ann math 163 1 221 263 2006 and later generalized to the mixed p spin models by panchenko ann probab 42 3 946 958 2014 in this paper we prove that the minimizer in parisi s formula is unique at any temperature and external field by establishing the strict convexity of the parisi functional

large system analysis of joint channel and data estimation for mimo ds cdma systems this paper presents a large system analysis of the performance of joint channel estimation multiuser detection and per user decoding ce mudd for randomly spread multiple input multiple output mimo direct sequence code division multiple access ds cdma systems a suboptimal receiver based on successive decoding in conjunction with linear minimum mean squared error lmmse channel estimation is investigated the replica method developed in statistical mechanics is used to evaluate the performance in the large system limit where the number of users and the spreading factor tend to infinity while their ratio and the number of transmit and receive antennas are kept constant joint ce mudd based on lmmse channel estimation is compared to several methods of one shot channel estimation i e methods that do not utilize decoded data symbols to refine the initial channel estimates in terms of spectral efficiency joint ce mudd is found to significantly reduce the rate loss caused by transmission of pilot signals when compared to the receivers based on one shot channel estimation this holds particularly for multiple antenna systems as a result joint ce mudd can provide significant performance gains compared to the receivers based on one shot channel estimation

on properties of parisi measures we investigate the structure of parisi measures the functional order parameters of mixed p spin models in mean field spin glasses in the absence of external field we prove that a parisi measure satisfies the following properties first at all temperatures the support of any parisi measure contains the origin if it contains an open interval then the measure has a smooth density on this interval next we give a criterion on temperature parameters for which a parisi measure is neither replica symmetric nor one replica symmetry breaking finally we show that in the sherrington kirkpatrick model slightly above the critical temperature the largest number in the support of a parisi measure is a jump discontinuity an analogue of these results is discussed in the spherical mixed p spin models as a tool to establish these facts and of independent interest we study functionals of the associated parisi pdes and derive regularity properties of their solutions

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

the parisi formula in this chapter we prove the parisi formula which gives the limiting value of the free energy per site for the sherrington kirkpatrick model at each temperature starting with the famous result of guerra that the parisi formula provided a bound for this free energy we make full use of poisson dirichlet cascades we then use the same techniques to prove in a strong sense that in presence of an external field the overlaps are positive

large deviations guerra s and a s s schemes and the parisi hypothesis we investigate the problem of computing lim n to infty frac 1 an log ez n a for any value of a where z n is the partition function of the celebrated sherrington kirkpatrick sk model or of some of its natural generalizations this is a natural large deviation problem its study helps to get a fresh look at some of the recent ideas introduced in the area and raises a number of natural questions we provide a complete solution for a 0

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

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

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

some properties of the phase diagram for mixed p spin glasses in this paper we study the parisi variational problem for mixed p spin glasses with ising spins our starting point is a characterization of parisi measures whose origin lies in the first order optimality conditions for the parisi functional which is known to be strictly convex using this characterization we study the phase diagram in the temperature external field plane we begin by deriving self consistency conditions for parisi measures that generalize those of de almeida and thouless to all levels of replica symmetry breaking rsb and all models as a consequence we conjecture that for all models the replica symmetric phase is the region determined by the natural analogue of the de almeida thouless condition we show that for all models the complement of this region is in the rsb phase furthermore we show that the conjectured phase boundary is exactly the phase boundary in the plane less a bounded set in the case of the sherrington kirkpatrick model we extend this last result to show that this bounded set does not contain the critical point at zero external field

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

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

exact solution of the gauge symmetric p spin glass model on a complete graph we consider a gauge symmetric version of the p spin glass model on a complete graph the gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of guerra fields inst commun 30 161 2001 to rigorously compute the free energy in the case of pairwise interactions p 2 where we have a gauge symmetric version of the sherrington kirkpatrick model we get the free energy and magnetization for all values of external parameters our analysis also works for even p 4 except in a range of parameters surrounding the phase transition line and for odd p 3 in a more restricted region we also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd p and justify the absence of replica symmetry breaking our initial motivation for considering this model came from problems related to communication over a noisy channel and is briefly explained

low temperature asymptotics of spherical mean field spin glasses in this paper we study the low temperature limit of the spherical crisanti sommers variational problem we identify the gamma limit of the crisanti sommers functionals thereby establishing a rigorous variational problem for the ground state energy of spherical mixed p spin glasses as an application we compute moderate deviations of the corresponding minimizers in the low temperature limit in particular for a large class of models this yields moderate deviations for the overlap distribution as well as providing sharp interpolation estimates between models we then analyze the ground state energy problem we show that this variational problem is dual to an obstacle type problem this duality is at the heart of our analysis we present the regularity theory of the optimizers of the primal and dual problems this culminates in a simple method for constructing a finite dimensional space in which these optimizers live for any model as a consequence of these results we unify independent predictions of crisanti leuzzi and auffinger ben arous regarding the one step replica symmetry breaking 1rsb phase in this limit we find that the positive replicon eigenvalue and pure like conditions are together necessary for optimality but that neither are themselves sufficient answering a question of auffinger and ben arous in the negative we end by proving that these conditions completely characterize the 1rsb phase in 2 p spin models

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

the analysis of longitudinal ordinal response data in continuous time abstract a simple markov model is developed for assessing the predictive effect of time dependent covariates on an intermittently observed ordinal response in continuous time this is accomplished by reparameterizing an ergodic intensity matrix in terms of its equilibrium distribution and a parametrically independent component that assesses the rate of movement between ordinal categories the effect of covariates on the equilibrium distribution can then be modeled using any link appropriate for ordinal data a robust maximum likelihood estimator based on this model that is consistent and asymptotically normal is constructed practical data analysis issues are discussed and a simple diagnostic tool for assessing model adequacy is developed the utility of these methods is demonstrated with several analyses of visual acuity data including a comparison analysis based on generalized estimating equation gee methods

about a solvable mean field model of a gaussian spin glass in a series of papers we have studied a modified hopfield model of a neural network with learned words characterized by a gaussian distribution the model can be represented as a bipartite spin glass with one party described by dichotomic ising spins and the other party by continuous spin variables with an a priori gaussian distribution by application of standard interpolation methods we have found it useful to compare the neural network model bipartite from one side with two spin glass models each monopartite from the other side of these the first is the usual sherrington kirkpatrick model the second is a spin glass model with continuous spins and inbuilt highly nonlinear smooth cut off interactions this model is an invaluable laboratory for testing all techniques which have been useful in the study of spin glasses the purpose of this paper is to give a synthetic description of the most peculiar aspects by stressing the necessary novelties in the treatment in particular it will be shown that the control of the infinite volume limit according to the well known guerra toninelli strategy requires in addition one to consider the involvement of the cut off interaction in the interpolation procedure moreover the control of the ergodic region the annealed case cannot be directly achieved through the standard application of the borel cantelli lemma but requires previous modification of the interaction this remark could find useful application in other cases the replica symmetric expression for the free energy can be easily reached through a suitable version of the doubly stochastic interpolation technique however this model shares the unique property that the fully broken replica symmetry ansatz can be explicitly calculated a very simple sum rule connects the general expression of the fully broken free energy trial function with the replica symmetric one the definite sign of the error term shows that the replica solution is optimal then we follow a deep strategy developed by talagrand to conclude that the replica symmetric ansatz not only gives a bound for the free energy which cannot be improved by symmetry breaking but gives also the true value for the free energy for the sake of completeness we study also the fluctuations of the centered and rescaled overlaps by following a method similar to that exploited for the sherrington kirkpatrick model in the replica symmetric region

construction of pure states in mean field models for spin glasses if a mean field model for spin glasses is generic in the sense that it satisfies the extended ghirlanda guerra identities and if the law of the overlaps has a point mass at the largest point q of its support we prove that one can decompose the configuration space into a sequence of sets ak such that generically the overlap of two configurations is equal to q if and only if they belong to the same set ak for the study of the overlaps each set ak can be replaced by a single point combining this with a recent result of panchenko a connection between ghirlanda guerra identities and ultrametricity ann probab 2008 to appear this proves that if the overlaps take only finitely many values ultrametricity occurs we give an elementary self contained proof of this result based on simple inequalities and an averaging argument

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

identification and restoration of noisy blurred images using the expectation maximization algorithm a maximum likelihood approach to the blur identification problem is presented the expectation maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way in order to improve the performance of the identification algorithm low order parametric image and blur models are incorporated into the identification method the resulting iterative technique simultaneously identifies and restores noisy blurred images

an application of isotonic longitudinal marginal regression to monitoring the healing process this paper discusses marginal regression for repeated ordinal measurements that are isotonic over time such data are often observed in longitudinal studies on healing processes where due to recovery the status of patients only improves or stays the same we show how this prior information can be used to construct appropriate and parsimoniously parametrized marginal models as a second aspect we also incorporate nonparametric fitting of covariate effects via a penalized quasi likelihood or gee approach we illustrate our methods by an application to injuries from sporting activities

fluctuations of the free energy in the mixed p spin models with external field we show that the free energy in the mixed p spin models of spin glasses does not superconcentrate in the presence of external field which means that its variance is of the order suggested by the poincare inequality this complements the result of chatterjee who showed that the free energy superconcentrates when there is no external field for models without odd p spin interactions for p geqslant 3 we prove the central limit theorem for the free energy at any temperature and give an explicit formula for the limiting variance although we only deal with the case of ising spins all our results can be extended to the spherical models as well

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

proportional hazards model for repeated measures with monotonic ordinal response in this paper we present a proportional hazards model to determine the effect of predictors on repeated measures data with ordinal response that is monotonic over time the model can handle both categorical and continuous predictors it naturally models the time spent in the response states the assumption of proportional hazards can be partially assessed if replicates individuals with identical covariate vectors are available censoring can be incorporated into the model although it does require additional modelling if the censoring is informative

hierarchical exchangeability of pure states in mean field spin glass models the main result in this paper is motivated by the mezard parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models such as the random k sat model at positive temperature using the fact that one can safely assume the validity of the ghirlanda guerra identities in these models we prove hierarchical exchangeability of pure states for the asymptotic gibbs measures which allows us to apply a representation result for hierarchically exchangeable arrays recently proved in austin and panchenko in probab theory relat fields 2013 comparing this representation with the predictions of the mezard parisi ansatz one can see that the key property still missing is that the multi overlaps between pure states depend only on their overlaps

extremal cuts of sparse random graphs for erd s renyi random graphs with average degree and uniformly random regular graph on nn vertices we prove that with high probability the size of both the max cut and maximum bisection are n 4 p 4 o o n n 4 p 4 o o n while the size of the minimum bisection is n 4 p 4 o o n n 4 p 4 o o n our derivation relates the free energy of the anti ferromagnetic ising model on such graphs to that of the sherrington kirkpatrick model with p 0 7632p 0 7632 standing for the ground state energy of the latter expressed analytically via parisi s formula

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

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

remarks on the interpolation method we discuss a generalization of the classic condition of validity of the interpolation method for the density of quenched free energy of mean field spin glasses the condition is written just in terms of the l 2 metric structure of the gaussian random variables as an example of application we deduce the existence of the thermodynamic limit for a grem model with infinite branches for which the classic conditions of validity fail we underline the dependence of the density of quenched free energy just on the metric structure and discuss the models from a metric viewpoint

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

the parisi ultrametricity conjecture in this paper we prove that the support of a random measure on the unit ball of a separable hilbert space that satises the ghirlanda guerra identities must be ultrametric with probability one this implies the parisi ultrametricity conjecture in mean eld spin glass models such as the sherrington kirkpatrick and mixed p spin models for which gibbs measures are known to satisfy the ghirlanda guerra identities in the thermodynamic limit

multiple levels of symmetry breaking in the previous paper in this volume we have studied the p spin interaction model just below the critical temperature and we have rigorously proved several aspects of the physicists prediction that this model exhibits one level of symmetry breaking in the present paper we show how to construct systems that exhibit an arbitrarily large but finite number of levels of symmetry breaking as the temperature decreases such systems exhibit many phase transitions as the structure of the overlaps gains complexity this phenomenon does not seem to have been described previously even in the physics literature

expected estimating equations for missing data measurement error and misclassification with application to longitudinal nonignorable missing data missing data measurement error and misclassification are three important problems in many research fields such as epidemiological studies it is well known that missing data and measurement error in covariates may lead to biased estimation misclassification may be considered as a special type of measurement error for categorical data nevertheless we treat misclassification as a different problem from measurement error because statistical models for them are different indeed in the literature methods for these three problems were generally proposed separately given that statistical modeling for them are very different the problem is more challenging in a longitudinal study with nonignorable missing data in this article we consider estimation in generalized linear models under these three incomplete data models we propose a general approach based on expected estimating equations eees to solve these three incomplete data problems in a unified fashion this eee approach can be easily implemented and its asymptotic covariance can be obtained by sandwich estimation intensive simulation studies are performed under various incomplete data settings the proposed method is applied to a longitudinal study of oral bone density in relation to body bone density

the sherrington kirkpatrick model a challenge for mathematicians the sherrington kirkpatrick sk model for spin glasses is deceptively simple to state yet its rigorous study represents a considerable challenge we report here some modest progresses obtained through elementary methods even in the supposedly simple high temperature region a number of basic questions remain unsolved

correcting for misclassification for a monotone disease process with an application in dental research motivated by a longitudinal oral health study we evaluate the performance of binary markov models in which the response variable is subject to an unconstrained misclassification process and follows a monotone or progressive behavior theoretical and empirical arguments show that the simple version of the model can be used to estimate the prevalence incidences and misclassification parameters without the need of external information and that the incidence estimators associated with the model outperformed approaches previously proposed in the literature we propose an extension of the simple version of the binary markov model to describe the relationship between the covariates and the prevalence and incidence allowing for different classifiers we implemented a bayesian version of the extended model and show that under the settings of our motivating example the parameters can be estimated without any external information finally the analyses of the motivating problem are presented

rigorous low temperature results for the mean field p spins interaction model we prove that just below the critical temperature the mean field p spins interaction model for p suitably large spontaneously decomposes into different states the asymptotic overlaps between any two different states are zero under a mild unproven hypothesis on the weight distribution of these states we prove that they are pure states this situation is called in physics one level of symmetry breaking

a recursive algorithm for maximum likelihood based identification of blur from multiple observations a maximum likelihood based method is proposed for blur identification from multiple observations of a scene when the relations among the blurring functions are known the estimate of blur obtained using the proposed method is very good since direct computation of the likelihood function becomes difficult as the number of images increases we propose an algorithm to compute the likelihood function recursively

an approach to chaos in some mixed p spin models we consider the problems of chaos in disorder and temperature for coupled copies of the mixed p spin models under certain assumptions on the parameters of the models first we prove a weak form of chaos by showing that the overlap is concentrated around its gibbs average depending on the disorder and then obtain several results toward strong chaos by providing control of the overlap between two systems in terms of their parisi measures

modeling repeated measures with monotonic ordinal responses and misclassification with applications to studying maturation abstract many longitudinal studies of children are concerned with the modeling of monotonic responses such as growth and sexual maturation the national heart lung and blood institute growth and health study nghs is a longitudinal study designed to examine the effect of growth and maturation on the development of obesity and related cardiovascular risk factors among black and white adolescent girls sexual maturation is measured with an ordinal outcome and is known to be measured with sizable diagnostic error of interest is examining the effects of race and age on the sexual maturation process here we propose a class of models for analyzing repeated monotonic ordinal responses with diagnostic misclassification in which we separately model the underlying monotonic response and misclassification processes we develop an em algorithm for maximum likelihood estimation that incorporates covariates and randomly missing data we use the method to analyze the nghs sexual maturation data

spatio temporal adaptive 3 d kalman filter for video this paper presents three dimensional spatio temporal kalman filters for video as the extension of the two dimensional 2 d reduced update kalman filter rukf approach for images we start out with three dimensional 3 d rukf a shift invariant recursive estimator with efficiency advantages over the 3 d wiener filter then we turn to the motion compensated extension mc rukf which gives improved performance when coupled with a motion estimator since motion compensation sometimes fails causing severe fluctuations in temporal correlation we then present multimodel mc rukf to adapt to variation in temporal and spatial correlation by detecting the local image model out of a class and using it in mc rukf finally we introduce a novel multiscale model detection algorithm for use in high noise environments

the legendre structure of the parisi formula we show that the parisi formula of the mixed p spin model is a concave function of the squared inverse temperature this allows us to derive a new expression for the parisi formula that involves the inverse temperature and the parisi measure as legendre conjugate variables

modeling of multivariate monotone disease processes in the presence of misclassification motivated by a longitudinal oral health study the signal tandmobiel study we propose a multivariate binary inhomogeneous markov model in which unobserved correlated response variables are subject to an unconstrained misclassification process and have a monotone behavior the multivariate baseline distributions and markov transition matrices of the unobserved processes are defined as a function of covariates through the specification of compatible full conditional distributions distinct misclassification models are discussed in all cases the possibility that different examiners were involved in the scoring of the responses of a given subject across time is taken into account a full bayesian implementation of the model is described and its performance is evaluated using simulated data we provide theoretical and empirical evidence that the parameters can be estimated without any external information about the misclassification parameters finally the analyses of the motivating study are presented a

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

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