persistence exponents and scaling in two dimensional xy model and a nematic model the persistence exponents associated with the t 0 quenching dynamics of the two dimensional xy model and a two dimensional uniaxial spin nematic model have been evaluated using a numerical simulation the site persistence or the probability that the sign of a local spin component does not change starting from initial time t 0 up to a certain time t is found to decay as l t l t is the linear domain length scale with 0 305 0 020 for the two dimensional xy model and 0 199 0 009 for the two dimensional uniaxial spin nematic model we have also investigated the scaling at the late time of phase ordering associated with the correlated persistent sites in both models the persistence correlation length was found to grow in the same way as l t

on the approximate solutions of constrained inverse lipschitz function problems and inverse function theorems abstract we present a principle of approximate solutions of constrained inverse lipschitz function problems as corollaries and applications of the principle we obtain a result of convergence of an approximate solutions sequence for the constrained problems a conclusion relating direct and inverse images of upper and lower limits of a sequence of subsets and several versions of inverse lipschitz function theorems finally we give local uniqueness criteria for solutions to constrained nonlinear problems in finite dimension spaces

persistence exponents of non gaussian processes in statistical mechanics motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size if the evolution consists of linear decay the sample functions are of the random sawtooth type and the level dependent persistence exponent can be calculated exactly we then develop an expansion method valid for small curvature of the deterministic curve the curvature parameter g plays the role of the coupling constant of an interacting particle system the leading order curvature correction to is proportional to g 2 3 the expansion applies in particular to exponential decay in the limit of large level where the curvature correction considerably improves the linear approximation the langevin equation with gaussian white noise is recovered as a singular limiting case

self diffusion and visited surface in the droplet condensation problem breath figures abstract we study experimentally and theoretically new aspects of condensation growth and coalescence of droplets on a substrate we address in particular the dynamics of a marked droplet which undergoes coalescences with neighbouring droplets we find that the number of coalescences of the droplet grows as log t t is time and that the traveled distance increases as r t the average radius of the droplets at time t the fraction of the surface which was never covered by any droplet an important quantity for applications such as drug spreading or surface decontamination decays as t showing that completion occurs only slowly heuristic arguments accurate numerical simulations on simplified models which neglect polydispersity and an exact solution reported elsewhere a bray b derrida and c godreche europhys lett 27 1994 175 strongly support these findings and show that this power law decay is a generic feature common to many different situations finally the contour of the ensemble of dry sites appears fractal with dimension d 1 22 an experimental result not reproduced by the simplified models

pointwise tube formulas for fractal sprays and self similar tilings with arbitrary generators abstract in a previous paper by the first two authors a tube formula for fractal sprays was obtained which also applies to a certain class of self similar fractals the proof of this formula uses distributional techniques and requires fairly strong conditions on the geometry of the tiling specifically the inner tube formula for each generator of the fractal spray is required to be polynomial now we extend and strengthen the tube formula by removing the conditions on the geometry of the generators and also by giving a proof which holds pointwise rather than distributionally hence our results for fractal sprays extend to higher dimensions the pointwise tube formula for 1 dimensional fractal strings obtained earlier by lapidus and van frankenhuijsen our pointwise tube formulas are expressed as a sum of the residues of the tubular zeta function of the fractal spray in r d this sum ranges over the complex dimensions of the spray that is over the poles of the geometric zeta function of the underlying fractal string and the integers 0 1 d the resulting fractal tube formulas are applied to the important special case of self similar tilings but are also illustrated in other geometrically natural situations our tube formulas may also be seen as fractal analogues of the classical steiner formula

optimal mean square state and parameter estimation for stochastic linear systems with poisson noises this paper presents the mean square state and parameter estimation problem for stochastic linear systems with unknown multiplicative and additive parameters over linear observations where unknown parameters are considered poisson processes the original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states the obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters performance of the designed optimal state filter and parameter identifier is verified for both stable and unstable stochastic linear systems and compared against the mean square estimator designed for polynomial systems with white gaussian noises

phase ordering and persistence in a class of stochastic processes interpolating between the ising and voter models we study the dynamics of a class of two dimensional stochastic processes depending on two parameters which may be interpreted as two different temperatures respectively associated to interfacial and to bulk noise special lines in the plane of parameters correspond to the ising model voter model and majority vote model the dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing annihilating and branching random walkers we use the freedom allowed by the space of parameters to measure by numerical simulations the persistence probability of a generic model in the low temperature phase where the system coarsens this probability is found to decay at large times as a power law with a seemingly constant exponent we also discuss the connection between persistence and the nature of the interfaces between domains

large deviations and nontrivial exponents in coarsening systems we investigate the statistics of the mean magnetization of its large deviations and persistent large deviations in simple coarsening systems in particular we consider more specifically the case of the diffusion equation of the ising chain at zero temperature and of the two dimensional voter model for the diffusion equation at large times the mean magnetization has a limit law which is studied analytically using the independent interval approximation the probability of persistent large deviations defined as the probability that the mean magnetization was for all previous times greater than some level x decays algebraically at large times with an exponent continuously varying with x when x 1 is the usual persistence exponent similar behaviour is found for the glauber ising chain at zero temperature for the two dimensional voter model large deviations of the mean magnetization are algebraic while the probability of persistent large deviations seem to behave as the usual persistence probability

early time critical dynamics of lattices of coupled chaotic maps the early time critical dynamics of continuous ising like phase transitions is studied numerically for two dimensional lattices of coupled chaotic maps emphasis is placed on obtaining accurate estimates of the dynamic critical exponents ensuremath theta ensuremath and z the critical points of five different models are investigated varying the mode of update the coupling and the local map our results suggest that the nature of update is a relevant parameter for dynamic universality classes of extended dynamical systems generalizing results obtained previously for the static properties they also indicate that the universality observed for the static properties of ising like transitions of synchronously updated systems does not hold for their dynamic critical properties

the fermat rule for multifunctions on banach spaces using variational analysis we study vector optimization problems with objectives being closed multifunctions on banach spaces or in asplund spaces in particular in terms of the coderivatives we present fermat s rules as necessary conditions for an optimal solution of the above problems as applications we also provide some necessary conditions in terms of clarke s normal cones or the limiting normal cones for pareto efficient points

reproducing gaussian densities and linear gaussian detection abstract it is shown that the expected value of a gaussian density function of a gaussian random variable is another gaussian density function this is used to determine which of m partially observed gaussian linear systems is the most likely given the observations

recursive parameter estimation using incomplete data abstract stochastic approximation procedures are considered for the estimation of parameters using incomplete data one procedure is stated and illustrated which often leads to asymptotically efficient estimators others are developed which although possibly not optimal in the above sense will be very much easier to apply this will be particularly advantageous when quick recursive estimates are required examples are given and a link is made between one of the sub optimal methods and the em algorithm author

functional laws of the iterated logarithm for local empirical processes indexed by sets we introduce the notion of a multivariate local and tail empirical process indexed by sets and establish a number of functional laws of the iterated logarithm for such processes this leads to a unified methodology to study the almost sure behavior of various statistics which are local functionals of the empirical distribution such statistics include density estimators and the bahadur kiefer representation

exact finite dimensional filters for maximum likelihood parameter estimation of continuous time linear gaussian systems in this paper we derive a new class of finite dimensional filters for integrals and stochastic integrals of moments of the state for continuous time linear gaussian systems apart from being of significant mathematical interest these new filters can be used with the expectation maximization em algorithm to yield maximum likelihood estimates of the model parameters

characterization of minkowski measurability in terms of surface area abstract the r parallel set to a set a in euclidean space consists of all points with distance at most r from a recently the asymptotic behaviour of volume and surface area of the parallel sets as r tends to 0 has been studied and some general results regarding their relations have been established here we complete the picture regarding the resulting notions of minkowski content and s content in particular we show that a set is minkowski measurable if and only if it is s measurable i e if and only if its s content is positive and finite and that positivity and finiteness of the lower and upper minkowski contents imply the same for the s contents and vice versa the results are formulated in the more general setting of kneser functions furthermore the relations between minkowski and s contents are studied for more general gauge functions the results are applied to simplify the proof of the modified weyl berry conjecture in dimension one

asymptotically optimal discrete time nonlinear filters from stochastically convergent state process approximations we consider the problem of approximating optimal in the mmse sense nonlinear filters in a discrete time setting exploiting properties of stochastically convergent state process approximations more specifically we consider a class of nonlinear partially observable stochastic systems comprised by a possibly nonstationary hidden stochastic process the state observed through another conditionally gaussian stochastic process the observations under general assumptions we show that given an approximating process which for each time step is stochastically convergent to the state process in some appropriate sense an approximate filtering operator can be defined which converges to the true optimal nonlinear filter of the state in a strong and well defined sense i e compactly in time and uniformly in a completely characterized measurable set of probability measure almost unity also providing a purely quantitative justification of egoro s theorem for the problem at hand the results presented in this paper can form a common basis for the analysis and characterization of a number of heuristic approaches for approximating a large class of optimal nonlinear filters such as approximate grid based techniques known to perform well in a variety of applications

discontinuous versus smooth regression given measurements x i y i i 1 n we discuss methods to assess whether an underlying regression function is smooth continuous or differentiable or whether it has discontinuities the variance of the measurements is assumed to be unknown and is estimated simultaneously by regressing squared differences of the data formed with various span sizes on the span size itself we obtain an asymptotic linear model with dependent errors the parameters of this asymptotic linear model include the sum of the squared jump sizes as well as the variance of the measurements both parameters can be consistently estimated with mean squared error rates of convergence of n 2 3 for the sum of squared jump sizes and n 1 for the error variance we derive the asymptotic constants of the mean squared error mse and discuss the dependence of mse on the maximum span size l the test for the existence of jumps is formulated for the null hypothesis that the sum of squared jump sizes is 0 the asymptotic distribution of the test statistic is obtained essentially via a central limit theorem for u statistics we motivate and illustrate the methods with data surrounded by a scientific controversy concerning the question whether the growth of children occurs smoothly or rather in jumps

persistence exponents for fluctuating interfaces numerical and analytic results for the exponent ensuremath theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear langevin equations the models are parametrized by the dynamic roughness exponent ensuremath beta with 0l ensuremath beta l1 for ensuremath beta frac 1 2 the time evolution is markovian using simulations of solid on solid models of the discretized continuum equations as well as of the associated zero dimensional stationary gaussian process we address two problems the return of an initially flat interface and the return to an initial state with fully developed steady state roughness the two problems are shown to be governed by different exponents for the steady state case we point out the equivalence to fractional brownian motion which has a return exponent ensuremath theta s 1 ensuremath ensuremath beta the exponent ensuremath theta 0 for the flat initial condition appears to be nontrivial we prove that ensuremath theta 0 ensuremath rightarrow ensuremath infty for ensuremath beta ensuremath rightarrow 0 ensuremath theta 0 g ensuremath theta s for ensuremath beta l frac 1 2 and ensuremath theta 0 l ensuremath theta s for ensuremath beta g frac 1 2 and calculate ensuremath theta 0 s perturbatively to first order in an expansion around the markovian case ensuremath beta frac 1 2 using the exact result ensuremath theta s 1 ensuremath ensuremath beta accurate upper and lower bounds on ensuremath theta 0 can be derived which show in particular that ensuremath theta 0 g 1 ensuremath ensuremath beta 2 ensuremath beta for small ensuremath beta

does polynomial parallel volume imply convexity for a non empty compact set a d d 2 and r 0 let a r denote the set of points whose distance from a is r at the most it is well known that the volume v d a r of a r is a polynomial of degree d in the parameter r if a is convex we pursue the reverse question and ask whether a is necessarily convex if v d a r is a polynomial in r an affirmative answer is given in dimension d 2 counterexamples are provided for d 3 a positive resolution of the question in all dimensions is obtained if the assumption of a polynomial parallel volume is strengthened to the validity of a polynomial local steiner formula

analytical results for generalized persistence properties of smooth processes we present a general scheme to calculate within the independent interval approximation generalized level dependent persistence properties for processes having a finite density of zero crossings our results are especially relevant for the diffusion equation evolving from random initial conditions one of the simplest coarsening systems exact results are obtained in certain limits and rely on a new method to deal with constrained multiplicative processes an excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found

state and mode estimation for discrete time jump markov systems in this article we compute new state and mode estimation algorithms for discrete time gauss markov models whose parameter sets switch according to a known markov law an important feature of our algorithms is that they are based upon the exact filter dynamics computed in r j elliott f dufour and d sworder ieee trans automat control 41 1996 pp 1807 1810 the fundamental and well known obstacle in estimation of jump markov systems is managing the geometrically growing history of candidate hypotheses in our scheme we address this issue by proposing an extension of an idea due to viterbi our scheme maintains a fixed number of candidate paths in a history each identified by an optimal subset of estimated mode probabilities we compute finite dimensional suboptimal filters and smoothers which estimate the hidden state process and the mode probability our smoothers are based upon a duality between forward and backward dynamics further our smoothing algorithms are general and can be configured into the standard forms of fixed point fixed lag and fixed interval smoothers a computer simulation is included to demonstrate performance

persistence in nonequilibrium surface growth persistence probabilities of the interface height in 1 1 and 2 1 dimensional atomistic solid on solid stochastic models of surface growth are studied using kinetic monte carlo simulations with emphasis on models that belong to the molecular beam epitaxy mbe universality class both the initial transient and the long time steady state regimes are investigated we show that for growth models in the mbe universality class the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady state regimes for the mbe universality class the positive and negative persistence exponents in the steady state are found to be 0 66 0 02 and 0 78 0 02 respectively in 1 1 dimensions and 0 76 0 02 and 0 85 0 02 respectively in 2 1 dimensions the noise reduction technique is applied on some of the 1 1 dimensional models in order to obtain accurate values of the persistence exponents we show analytically that a relation between the steady state persistence exponent and the dynamic growth exponent found earlier to be valid for linear models should be satisfied by the smaller of the two steady state persistence exponents in the nonlinear models our numerical results for the persistence exponents are consistent with this prediction we also find that the steady state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state the dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form

a nondegenerate fuzzy optimality condition for constrained optimization problems without qualification conditions abstract fuzzy optimization conditions in terms of the frechet subdifferential for reflexive spaces were investigated by borwein treiman and zhu 1998 in 1 to achieve the nondegenerate form it is well known that some qualification conditions should be assumed in this paper we are going to prove that the nondegenerate fuzzy optimality condition even holds with no qualification conditions in asplund spaces in particular reflexive spaces for optimization problems with semi continuous and continuous data the results are even new in finite dimensional frameworks

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

probability distribution of persistent spins in an ising chain we study the probability distribution q n t of n t the fraction of spins unflipped up to time t in an ising chain with ferromagnetic interactions the distribution shows a peak at n nmax and in general is non gaussian and asymmetric in nature however for n nmax it shows a gaussian decay data collapse can be obtained when q n t l versus n nmax l is plotted with 0 45 and 0 6 interestingly nmax t shows different behaviour compared to n t p t the persistence probability which follows the well known behaviour p t t a quantitative estimate of the asymmetry and non gaussian nature of q n t is made by calculating its skewness and kurtosis

random sequential adsorption of lines and ellipses infinitely many lines of zero thickness may be adsorbed onto a plane without overlap and it is shown that the number of lines adsorbed should scale as 13 where is the number of adsorption trials per unit area of surface this is confirmed by numerical simulation the adsorption of ellipses with major and minor axes 2a 2b respectively is also studied the area coverage theta approaches its maximum value theta max as alpha as to infinity where alpha is typically 1 3 as b a decreases from unity theta max first increases to a maximum value 0 58 or 0 01 when b approximately 0 5 and then decreases a feature not noted in previous work

stationary definition of persistence for finite temperature phase ordering for the two dimensional kinetic ising model at finite temperature the local mean magnetization simply related to the fraction of time spent by a given spin in the positive direction has a limiting distribution singular at the onsager spontaneous magnetization the exponent of this singularity defines the persistence exponent we also study first passage exponents associated to persistent large deviations of and their temperature dependence

spin block persistence at finite temperature we explore a new definition of the persistence exponent measuring the probability that a spin never flips after a quench of an ising like model at a temperature while the usual definition only makes sense at t 0 this probability is now defined for spin blocks and a general scaling for it involving time and block linear size is introduced and illustrated by extensive simulations

phase ordering and persistence relative effects of space discretization chaos and anisotropy abstract the peculiar phase ordering properties of a lattice of coupled chaotic maps studied recently lemaitre chate phys rev lett 82 1999 1140 are revisited with the help of detailed investigations of interface motion it is shown that normal curvature driven like domain growth is recovered at larger scales than considered before and that the persistence exponent seems to be universal using generalized persistence spectra the properties of interface motion in this deterministic chaotic lattice system are found to interpolate between those of the two canonical reference systems the probabilistic ising model and the deterministic space continuous time dependent ginzburg landau equation

convexity and generalized second order derivatives for locally lipschitz functions abstract we define the generalized second order directional derivatives by means of the clarke generalized gradient for locally lipschitz functions then we give characterization of convexity and state a new sufficient optimality condition

differentiation of sets in measure abstract suppose f e for each e 0 1 is a bounded borel subset of r d and f e f 0 as e 0 let a e f e f 0 be symmetric difference and p be an absolutely continuous measure on r d we introduce the notion of derivative of f e with respect to e d f e d e d a e d e such that d d e p a e e 0 q d d e a e e 0 where q is another explicitly described measure although not in r d we discuss why this sort of derivative is needed to study local point processes in neighbourhood of a set in short if sequence of point processes n n n 1 2 is given on the class of set valued mappings f f such that all f e converge to the same f f 0 then the weak limit of the local processes n n a e f e f lives on the class of derivative sets d f e d e e 0 f f we compare this notion of the derivative set valued mapping with other existing notions

asymptotic results for the random sequential addition of unoriented objects asymptotic kinetics for random sequential addition of unoriented nonspherical objects is characterized by an algebraic time dependence by studying 1 d systems we show that the exponents describing the random sequential addition of objects with and without proper area are not simply related whereas the asymptotic behavior for rectangles follows the expected t 1 2 law the long time kinetics for infinitely thin line segments is governed by a nontrivial irrational exponent t 2 1 which results from a competition between creation and destruction of targets in the asymptotic regime

nature versus nurture predictability in low temperature ising dynamics consider a dynamical many body system with a random initial state subsequently evolving through stochastic dynamics what is the relative importance of the initial state nature versus the realization of the stochastic dynamics nurture in predicting the final state we examined this question for the two dimensional ising ferromagnet following an initial deep quench from t ensuremath infty to t 0 we performed monte carlo studies on the overlap between identical twins raised in independent dynamical environments up to size l 500 our results suggest an overlap decaying with time as t ensuremath ensuremath theta h with ensuremath theta h 0 22 ifmmode pm else textpm fi 0 02 the same exponent holds for a quench to low but nonzero temperature this heritability exponent may equal the persistence exponent for the two dimensional ising ferromagnet but the two differ more generally

maximum likelihood localization of narrow band autoregressive sources via the em algorithm the authors derive an expectation maximization algorithm for the maximum likelihood estimation of the directions of arrival of multiple narrowband autoregressive ar signals embedded in noise the proposed algorithm simultaneously estimates the location parameters the ar coefficients and the signals the additional structural information that the sources are of the ar type enables one to resolve the case in which the number of sources is equal to or possibly larger than the number of sensors the authors provide examples demonstrating that the proposed algorithm can resolve two spectrally and spatially closely spaced sources by using a two sensor array

a local steiner type formula for general closed sets and applications we introduce support curvature measures of an arbitrary closed set a in d and establish a local steiner type formula for the localized parallel volume of a we derive some of the basic properties of these support measures and explore how they are related to the curvature measures available in the literature then we use the support measures in analysing contact distributions of stationary random closed sets with a particular emphasis on the boolean model with general compact particles

a bound for the perimeter of inner parallel bodies abstract we provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body the bound depends only on the perimeter and inradius r of the original body and states that t 1 t r n 1 in particular the bound is independent of any regularity properties of as a by product of the proof we establish precise conditions for equality the proof which is straightforward is based on the construction of an extremal set for a certain optimization problem and the use of basic properties of mixed volumes

on line estimation of dynamic shock error models based on the kullback leibler information measure develops two sequential or on line estimation schemes in the time domain for dynamic shock error models which are special cases of errors in variables models the author s approach utilizes a state space representation of the model kalman filtering techniques and on line algorithms the first on line algorithm is based on the expectation maximization algorithm and uses a recursive gauss newton scheme to maximize the kullback leibler information measure the second on line algorithm the author proposes is a gradient based scheme and uses stochastic approximations to maximize the log likelihood in comparison to the off line maximum likelihood estimation scheme used in ghosh 1989 the author s on line algorithms have significantly reduced computational costs and negligible memory requirements simulations illustrate the satisfactory performance of the algorithms in estimating errors in variables systems with parameters that vary slowly with time or undergo infrequent jump changes

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

uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets given an elliptic integrand of class mathscr c 2 alpha we prove that finite unions of disjoint open wulff shapes with equal radii are the only volume constrained critical points of the anisotropic surface energy among all sets with finite perimeter and reduced boundary almost equal to its closure

constrained opinion dynamics freezing and slow evolution we study opinion formation in a population of leftists centrists and rightist in an interaction between neighbouring agents a centrist and a leftist can become both centrists or leftists and similarly for a centrist and a rightist while leftists and rightists do not affect each other the evolution is controlled by the initial density of centrists 0 for any spatial dimension the system reaches a centrist consensus with probability 0 while with probability 1 0 the final state is either an extremist consensus or a frozen population of leftists and rightists in one dimension we determine the opinion evolution by mapping the system onto a spin 1 ising model with zero temperature glauber kinetics the approach to the final state is governed by a t long time tail with 2 0 as 0 0 in the one dimensional frozen state the length distribution of single opinion domains has an algebraic small size tail x 2 1 and the average domain length is l2 where l is the length of the system

convergence analysis of stationary points in sample average approximation of stochastic programs with second order stochastic dominance constraints sample average approximation saa method has recently been applied to solve stochastic programs with second order stochastic dominance ssd constraints in particular hu et al math program 133 171 201 2012 presented a detailed convergence analysis of epsilon optimal values and epsilon optimal solutions of sample average approximated stochastic programs with polyhedral ssd constraints in this paper we complement the existing research by presenting convergence analysis of stationary points when saa is applied to a class of stochastic minimization problems with ssd constraints specifically under some moderate conditions we prove that optimal solutions and stationary points obtained from solving sample average approximated problems converge with probability one to their true counterparts moreover by exploiting some recent results on large deviation of random functions and sensitivity analysis of generalized equations we derive exponential rate of convergence of stationary points

infinite dimensional generalized jacobian properties and calculus rules the extension to infinite dimensional domains of clarke s generalized jacobian is the focus of this paper first a generalization of a fabian preiss theorem to the infinite dimensional setting is obtained as a consequence a new formula relating the clarke s generalized jacobians corresponding to finite dimensional spaces k l with k l is established furthermore in the infinite dimensional case basic properties pertaining the generalized jacobian are developed and then an identification of this set valued map is produced applications of these results in the form of chain rules including sum and product rules and a computational formula for continuous selections are derived

technical communique a zakai equation derivation of the extended kalman filter a discrete time filter is considered where both the observation and signal process have non linear dynamics with additive gaussian noise using the reference probability framework a convolution type zakai equation is obtained which updates the unnormalized conditional density using first order approximations this equation can be solved recursively and the extended kalman filter can be derived

on support measures in minkowski spaces and contact distributions in stochastic geometry this paper is concerned with contact distribution functions of a random closed set n 1 n in r d where the n are assumed to be random nonempty convex bodies these distribution functions are defined here in terms of a distance function which is associated with a strictly convex gauge body structuring element that contains the origin in its interior support measures with respect to such distances will be introduced and extended to sets in the local convex ring these measures will then be used in a systematic way to derive and describe some of the basic properties of contact distribution functions most of the results are obtained in a general nonstationary setting only the final section deals with the stationary case

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

outer minkowski content for some classes of closed sets we find conditions ensuring the existence of the outer minkowski content for d dimensional closed sets in mathbb r d in connection with regularity properties of their boundaries moreover we provide a class of sets including all sufficiently regular sets stable under finite unions for which the outer minkowski content exists it follows in particular that finite unions of sets with lipschitz boundary and a type of sets with positive reach belong to this class

asymptotic behavior of densities for two particle annihilating random walks consider the system of particles on d where particles are of two types a andb and execute simple random walks in continuous time particles do not interact with their own type but when ana particle meets ab particle both disappear i e are annihilated this system serves as a model for the chemical reactiona b inert we analyze the limiting behavior of the densities a t and b t when the initial state is given by homogeneous poisson random fields we prove that for equal initial densities a 0 b 0 there is a change in behavior fromd 4 where a t b t c t d 4 tod 4 where a t b t c tast for unequal initial densities a 0 b 0 a t e c l ind 1 a t e ct logt ind 2 and a t e ct ind 3 the termc depends on the initial densities and changes withd techniques are from interacting particle systems the behavior for this two particle annihilation process has similarities to those for coalescing random walks a a a and annihilating random walks a a inert the analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system

sequential normal compactness versus topological normal compactness in variational analysis abstract we study relationships between two normal compactness properties of sets in banach spaces that play an essential role in many aspects of variational analysis and its applications particularly in calculus rules for generalized differentiation necessary optimality and suboptimality conditions for optimization problems etc both properties automatically hold in finite dimensional spaces and reveal principal features of the infinite dimensional variational theory similar formulations of these properties involve the weak convergence of sequences and nets respectively containing generalized normal cones in duals to banach spaces we prove that these properties agree for a large class of banach spaces that include weakly compactly generated spaces we also show that they are always different in banach spaces whose unit dual ball is not weak sequentially compact moreover the sequential and topological normal compactness properties may not coincide even in non separable asplund spaces that admit an equivalent c smooth norm

differentiation of sets the general case abstract in recent work by khmaladze and weil 2008 and by einmahl and khmaladze 2011 limit theorems were established for local empirical processes near the boundary of compact convex sets k in r d the limit processes were shown to live on the normal cylinder of k respectively on a class of set valued derivatives in the latter result was based on the concept of differentiation of sets at the boundary k of k which was developed in khmaladze 2007 here we extend the theory of set valued derivatives to boundaries f of rather general closed sets f r d making use of a local steiner formula for closed sets established in hug last and weil 2004

iterative and sequential algorithms for multisensor signal enhancement in problems of enhancing a desired signal in the presence of noise multiple sensor measurements will typically have components from both the signal and the noise sources when the systems that couple the signal and the noise to the sensors are unknown the problem becomes one of joint signal estimation and system identification the authors specifically consider the two sensor signal enhancement problem in which the desired signal is modeled as a gaussian autoregressive ar process the noise is modeled as a white gaussian process and the coupling systems are modeled as linear time invariant finite impulse response fir filters the main approach consists of modeling the observed signals as outputs of a stochastic dynamic linear system and the authors apply the estimate maximize em algorithm for jointly estimating the desired signal the coupling systems and the unknown signal and noise spectral parameters the resulting algorithm can be viewed as the time domain version of the frequency domain approach of feder et al 1989 where instead of the noncausal frequency domain wiener filter the kalman smoother is used this approach leads naturally to a sequential adaptive algorithm by replacing the kalman smoother with the kalman filter and in place of successive iterations on each data block the algorithm proceeds sequentially through the data with exponential weighting applied to allow adaption to nonstationary changes in the structure of the data a computationally efficient implementation of the algorithm is developed an expression for the log likelihood gradient based on the kalman smoother filter output is also developed and used to incorporate efficient gradient based algorithms in the estimation process

new finite dimensional filters for parameter estimation of discrete time linear gaussian models the authors derive a new class of finite dimensional recursive filters for linear dynamical systems the kalman filter is a special case of their general filter apart from being of mathematical interest these new finite dimensional filters can be used with the expectation maximization em algorithm to yield maximum likelihood estimates of the parameters of a linear dynamical system important advantages of their filter based em algorithm compared with the standard smoother based em algorithm include 1 substantially reduced memory requirements and 2 ease of parallel implementation on a multiprocessor system the algorithm has applications in multisensor signal enhancement of speech signals and also econometric modeling

hidden gauss markov models for signal classification continuous state hidden markov models cs hmms are developed as a tool for signal classification analogs of the baum 1972 viterbi 1962 and baum welch algorithms are formulated for this class of models the cs hmm algorithms are then specialized to hidden gauss markov models hgmms with linear gaussian state transition and output densities a new gaussian refactorization lemma is used to show that the baum and viterbi algorithms for hgmms are implemented by two different formulations of the fixed interval kalman smoother the measurement likelihoods obtained from the forward pass of the hgmm baum algorithm and from the kalman filter innovation sequence are shown to be equal a direct link between the baum welch training algorithm and an existing expectation maximization em algorithm for gaussian models is demonstrated a new expression for the cross covariance between time adjacent states in hgmms is derived from the off diagonal block of the conditional joint covariance matrix a parameter invariance structure is noted for the hgmm likelihood function cs hmms and hgmms are extended to incorporate mixture densities for the a priori density of the initial state application of hgmms to signal classification is demonstrated with a three class test simulation

the steiner formula for minkowski valuations a steiner type formula for continuous translation invariant minkowski valuations is established in combination with a recent result on the symmetry of rigid motion invariant homogeneous bivaluations this new steiner type formula is used to obtain a family of brunn minkowski type inequalities for rigid motion intertwining minkowski valuations

stochastic integrals of set valued processes and fuzzy processes we define the stochastic integrals of a set valued process and a fuzzy process with respect to a cylindrical brownian motion on a hilbert space we also give their properties which are useful for the study of fuzzy stochastic differential equations and stochastic differential inclusions with a set valued diffusion term

nearest neighbor distances in diffusion controlled reactions modelled by a single mobile trap we consider a system consisting of an infinite number of identical particles on a latttce initially uniformly distributed which diffuse in the presence of a single mobile trap and ask for the time dependent behavior of the distance of the trap from the nearest particle this quantity is a measure of the tendency of the system to self segregate we show by a simulation incorporating the exact enumeration method that in one dtmension the expected distance l t scales as l t t as t 0 where the exponent a depends only on the ratio of the diffusion constants a heuristic expression for a ts suggested analogous to a rigorous exponent found by ben avraham for a similar but not identical problem the flux into the trap is found to vary as t t independent of the dtffusion constants

universal scaling function for domain growth in the glauber ising chain the equal time correlation function is calculated at t 0 for the one dimensional ising model with glauber dynamics random initial conditions appropriate to a sudden quench from non zero temperature are imposed averaging over initial conditions yields the scaling form c r t f r2 t the scaling function is given by f x integral 01 dy pi y 1 y 1 2 exp x 4y and is universal i e independent of the probability distribution for the initial conditions

the lagrange multiplier rule for super efficiency in vector optimization in this paper we study constrained multiobjective optimization problems with objectives being closed graph multifunctions in banach spaces in terms of the coderivatives and clarke s normal cones we establish lagrange multiplier rules for super efficiency as necessary or sufficient optimality conditions of the above problems

persistence in an antiferromagnetic ising system with conserved magnetisation abstract we obtain the persistence exponents for an antiferromagnetic ising system in which the magnetisation is kept constant this system belongs to model c system with non conserved order parameter with a conserved density and is expected to have persistence exponents different from that of model a system with no conservation but independent of the conserved density our numerical results for both local persistence at zero temperature and global persistence at the critical temperature however indicate that the exponents are dependent on the conserved magnetisation in both two and three dimensions this non universal feature is attributed to the presence of the conserved field and is special to the persistence phenomena

crossing intervals of non markovian gaussian processes we review the properties of time intervals between the crossings at a level m of a smooth stationary gaussian temporal signal the distribution of these intervals and the persistence are derived within the independent interval approximation iia these results grant access to the distribution of extrema of a general gaussian process exact results are obtained for the persistence exponents and the crossing interval distributions in the limit of large m in addition the small time behavior of the interval distributions and the persistence is calculated analytically for any m the iia is found to reproduce most of these exact results and its accuracy is also illustrated by extensive numerical simulations applied to non markovian gaussian processes appearing in various physical contexts

expressions for subdifferential and optimization problems defined by nonsmooth homogeneous functions abstract in this paper we prove a theoretical expression for subdifferentials of lower semicontinuous and homogeneous functions the theoretical expression is a generalization of the euler formula for differentiable homogeneous functions as applications of the generalized euler formula we consider constrained optimization problems defined by nonsmooth positively homogeneous functions in smooth banach spaces some results concerning karush kuhn tucker points and necessary optimality conditions for the optimization problems are obtained

exact adaptive filters for markov chains observed in gaussian noise abstract a discrete time finite state markov chain is observed through a real or vector valued function whose values are corrupted by gaussian noise by introducing a new measure exact unnormalized recursive estimates and smoothers are obtained for the state of the markov chain for the number of jumps from one state to another for the occupation time in any state and for processes related to the observation parameters using the em algorithm these allow estimates of all the parameters of the model to be revised including the variance of the gaussian noise in the observations the filters are therefore adaptive or self tuning

nonsmooth analysis on smooth manifolds we study infinitesimal properties of nonsmooth nondifferentiable functions on smooth manifolds the eigenvalue function of a matrix on the manifold of symmetric matrices gives a natural example of such a nonsmooth function a subdifferential calculus for lower semicontinuous functions is developed here for studying constrained optimization problems nonclassical problems of calculus of variations and generalized solutions of first order partial differential equations on manifolds we also establish criteria for monotonicity and invariance of functions and sets with respect to solutions of differential inclusions

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty