formulae for order one invariants of immersions of surfaces the universal order 1 invariant fu of immersions of a closed orientable surface into r3 whose existence has been established in t nowik order one invariants of immersions of surfaces into 3 space math ann 328 2004 261 283 is the direct sum fu n zfnh n zfnt m q where each fnh fnt is a z valued invariant and m q are z 2 valued invariants an explicit formula for the value of q on any embedding has been given in t nowik automorphisms and embeddings of surfaces and quadruple points of regular homotopies j differential geom 58 2001 421 455 in the present work we give explicit formulae for the value of each fnh fnt on all immersions and for the value of m on any embedding

a hybrid lower bound for parameter estimation of signals with multiple change points change point estimation has received much attention in the literature as it plays a significant role in several signal processing applications however the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters namely the parameters associated with the noise distribution and the change point locations in this paper we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters specifically we propose a hybrid cramer rao weiss weinstein bound and derive its associated closed form expressions numerical simulations assess the tightness of the proposed bound in the case of gaussian and poisson observations

order one invariants of planar curves we give a complete description of all order 1 invariants of planar curves 2008 elsevier inc all rights reserved

a general class of lower bounds in parameter estimation a general class of bayesian lower bounds on moments of the error in parameter estimation is formulated and it is shown that the cramer rao the bhattacharyya the bobrovsky zakai and the weiss weinstein lower bounds are special cases in the class the bounds can be applied to the estimation of vector parameters and any given function of the parameters the extension of these bounds to multiple parameter is discussed

vacuum isolating blow up threshold and asymptotic behavior of solutions for a nonlocal parabolic equation in this paper we consider a nonlocal parabolic equation associated with initial and dirichlet boundary conditions first we discuss the vacuum isolating behavior of solutions with the help of a family of potential wells then we obtain a threshold of global existence and blow up for solutions with critical initial energy furthermore for those solutions that satisfy j u0 d and i u0 0 we show that global solutions decay to zero exponentially as time tends to infinity and the norm of blow up solutions increases exponentially

weiss weinstein bound on multiple change points estimation in the context of multiple change points estimation performance analysis of estimators such as the maximum likelihood is often difficult to assess since the regularity assumptions are not met focusing on the estimators variance one can however use lower bounds on the mean square error in this paper we derive the so called weiss weinstein bound wwb that is known to be an efficient tool in signal processing to obtain a fair overview of the estimation behavior contrary to several works about performance analysis in the change point literature our study is adapted to multiple changes first useful formulas are given for a general estimation problem whatever the considered distribution of the data second closed form expressions are given in the cases of gaussian observations with changes in the mean and or the variance and changes in the mean rate of a poisson distribution furthermore a semidefinite programming formulation of the minimization procedure is given in order to compute the tightest wwb specifically it consists of finding the unique minimum volume covering the set constituted by hyperellipsoid elements that are generated using the derived candidate wwb matrices w r t the so called loewner partial ordering finally simulation results are provided to show the good behavior of the proposed bound

global existence nonexistence and asymptotic behavior of solutions for the cauchy problem of semilinear heat equations abstract in this paper we study the cauchy problem of semilinear heat equations by introducing a family of potential wells we first prove the invariance of some sets and isolating solutions then we obtain a threshold result for the global existence and nonexistence of solutions finally we discuss the asymptotic behavior of the solution

a fresh look at the bayesian bounds of the weiss weinstein family minimal bounds on the mean square error mse are generally used in order to predict the best achievable performance of an estimator for a given observation model in this paper we are interested in the bayesian bound of the weiss weinstein family among this family we have bayesian cramer rao bound the bobrovsky mayerwolf zakai bound the bayesian bhattacharyya bound the bobrovsky zakai bound the reuven messer bound and the weiss weinstein bound we present a unification of all these minimal bounds based on a rewriting of the minimum mean square error estimator mmsee and on a constrained optimization problem with this approach we obtain a useful theoretical framework to derive new bayesian bounds for that purpose we propose two bounds first we propose a generalization of the bayesian bhattacharyya bound extending the works of bobrovsky mayer wolf and zakai second we propose a bound based on the bayesian bhattacharyya bound and on the reuven messer bound representing a generalization of these bounds the proposed bound is the bayesian extension of the deterministic abel bound and is found to be tighter than the bayesian bhattacharyya bound the reuven messer bound the bobrovsky zakai bound and the bayesian cramer rao bound we propose some closed form expressions of these bounds for a general gaussian observation model with parameterized mean in order to illustrate our results we present simulation results in the context of a spectral analysis problem

confidence regions and tests for a change point in a sequence of exponential family random variables summary maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables with particular emphasis on the exponential distribution the exact null and alternative distributions of the test statistics are found and the power is compared with a test based on a linear trend statistic exact and approximate confidence regions for the change point are based on the values accepted by a level x likelihood ratio test and a modification of the method proposed by cox spj0tvoll 1982 the methods are applied to a classical data set on the time intervals between coal mine explosions and the change in variation of stock market returns in both cases the confidence regions for the change point cover historical events that may have caused the changes

on the high snr conditional maximum likelihood estimator full statistical characterization in the field of asymptotic performance characterization of the conditional maximum likelihood cml estimator asymptotic generally refers to either the number of samples or the signal to noise ratio snr value the first case has been already fully characterized although the second case has been only partially investigated therefore this correspondence aims to provide a sound proof of a result i e asymptotic in snr gaussianity and efficiency of the cml estimator in the multiple parameters case generally regarded as trivial but not so far demonstrated

barankin type lower bound on multiple change point estimation we compute lower bounds on the mean square error of multiple change point estimation in this context the parameters are discrete and the cramer rao bound is not applicable consequently we focus on computing the barankin bound bb the greatest lower bound on the covariance of any unbiased estimator which is still valid for discrete parameters in particular we compute the multi parameter version of the hammersley chapman robbins which is a barankin type lower bound we first give the structure of the so called barankin information matrix bim and derive a simplified form of the bb we show that the particular case of two change points is fundamental to finding the inverse of this matrix several closed form expressions of the elements of bim are given for changes in the parameters of gaussian and poisson distributions the computation of the bb requires finding the supremum of a finite set of positive definite matrices with respect to the loewner partial ordering although each matrix in this set of candidates is a lower bound on the covariance matrix of the estimator the existence of a unique supremum w r t to this set i e the tightest bound might not be guaranteed to overcome this problem we compute a suitable minimal upper bound to this set given by the matrix associated with the loewner john ellipsoid of the set of hyper ellipsoids associated to the set of candidate lower bound matrices finally we present some numerical examples to compare the proposed approximated bb with the performance achieved by the maximum likelihood estimator

bayesian bounds for matched field parameter estimation matched field methods concern estimation of source locations and or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation because of the nonlinear parameter dependence of the signal field the estimate is subject to ambiguities and the sidelobe contribution often dominates the estimation error below a threshold signal to noise ratio snr to study the matched field performance three bayesian lower bounds on mean square error are developed the bayesian crame spl acute r rao bound bcrb the weiss weinstein bound wwb and the ziv zakai bound zzb particularly for a multiple frequency multiple snapshot random signal model a closed form minimum probability of error associated with the likelihood ratio test is derived which facilitates error analysis in a wide scope of applications analysis and example simulations demonstrate that 1 unlike the local crb the bcrb is not achieved by the maximum likelihood estimate mle even at high snr if the local performance is not uniform across the prior parameter space 2 the zzb gives the closest mle performance prediction at most snr levels of practical interest 3 the zzb can also be used to determine the necessary number of independent snapshots achieving the asymptotic performance of the mle at a given snr 4 incoherent frequency averaging which is a popular multitone processing approach reduces the peak sidelobe error but may not improve the overall performance due to the increased ambiguity baseline and finally 5 effects of adding additional parameters e g environmental uncertainty can be well predicted from the parameter coupling

critical exponents for the blowup of solutions with sign changes in a semilinear parabolic equation ii abstract the blowup of solutions of the cauchy problem formula is studied let k be the set of functions on r which change sign k times it is shown that for p k 1 2 k 1 k 0 1 2 any solution with u 0 k blows up in finite time if 1 p p k whereas a global solution with u 0 k exists if p p k this is an extension of our previous result 17 in which a fast decay condition was imposed on initial data it is also shown in this paper that if u0 decays more slowly than x 2 p 1 as x then the solution blows up in finite time regardless of the number of sign changes

a bound for global solutions of semilinear heat equations we show that global positive solutions of the initial boundary value problem foru t u u p are bounded provided thatp 1 is subcritical our bound depends only on sup norm of the initial data and is useful to classify initial data by the asymptotic behavior of the solutions as time tend to infinity

immersions of surfaces into aspherical 3 manifolds we study finite order invariants of null homotopic immersions of a closed orientable surface into an aspherical orientable 3 manifold we give the foundational constructions and classify all order 1 invariants

finite time blow up and global existence for the nonlocal complex ginzburg landau equation abstract in this paper we consider the cauchy problem for a family of nonlocal complex ginzburg landau equation e i u t u 1 x n u p u p 2 u u on r n where 2 2 and r first the local well posedness in lebesgue spaces is established by a fixed point argument then we set up the h 2 regularity and derive the energy identities by constructing some invariant sets we further find some sufficient conditions on finite time blow up and global existence for solutions which in particular determines a sharp threshold of initial date when 0 in addition we estimate the lifespan of solutions as a function of and obtain the lower bound of the maximal existence time for r

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

persistence of wavefronts in delayed nonlocal reaction diffusion equations we develop a perturbation argument based on existing results on asymptotic autonomous systems and the fredholm alternative theory that yields the persistence of traveling wavefronts for reaction diffusion equations with nonlocal and delayed nonlinearities when the time lag is relatively small this persistence result holds when the nonlinearity of the corresponding ordinary reaction diffusion system is either monostable or bistable we then illustrate this general result using five different models from population biology epidemiology and bio reactors

on potential wells and applications to semilinear hyperbolic equations and parabolic equations abstract in this paper we generalize the family of potential wells to the initial boundary value problem of semilinear hyperbolic equations and parabolic equations u tt u f u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 and u t u f u x t 0 u x 0 u 0 x x u x t 0 x t 0 not only give a threshold result of global existence and nonexistence of solutions but also obtain the vacuum isolating of solutions finally we prove the global existence of solutions for above problem with critical initial conditions i u 0 0 e 0 d or i u 0 0 j u 0 d so payne and sattinger s results are generalized and improved in essential

a bound on mean square estimation error with background parameter mismatch in typical parameter estimation problems the signal observation is a function of the parameter set to be estimated as well as some background environmental system parameters assumed known the assumed background could differ from the true one leading to biased estimates even at high signal to noise ratio snr to analyze this background mismatch problem a ziv zakai type lower bound on the mean square error mse is developed based on the mismatched likelihood ratio test mlrt at high snr the bound incorporates the increase in mse due to estimation bias at low snr it includes the threshold effect due to estimation ambiguity the kernel of the bound s evaluation is the error probability associated with the mlrt a closed form expression for this error probability is derived under a random signal model typical of the bearing estimation passive source localization problem the mismatch is then analyzed in terms of the related ambiguity functions examples of bearing estimation with system array shape mismatch demonstrate that the developed bound describes the simulations of the maximum likelihood estimate well including the sidelobe introduced threshold behavior and the bias at high snr

nonlinear balance for reaction diffusion equations under nonlinear boundary conditions dissipativity and blow up the authors consider a reaction diffusion equation in a bounded smooth domain r n with nonlinear flux terms on the boundary of they derive suitable conditions on the nonlinear terms of the problem which imply its dissipativity the authors explore different situations in which there exist solutions of the problem that blow up in finite time the main tools in the proof of the results are either energy estimates or sub and super solution techniques

critical exponents of fujita type for inhomogeneous parabolic equations and systems abstract we consider the large time behavior of sign changing solutions of inhomogeneous parabolic equations and systems for example for u t u u p w x in r n 0 t we show the following if n 3 and r n w x dx 0 and 1 p n n 2 then all solutions blow up in finite time while if p n n 2 there are both global and nonglobal solutions we show by example that global solutions exist for all p 1 and w satisfying r n w x dx n 1 2 and r n w x dx 0 no solution can exist for all time extensions of the above result to various geometries and some other problems are indicated

joint segmentation of multivariate astronomical time series bayesian sampling with a hierarchical model astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series this paper approaches such problems using bayesian priors to represent relationships between signals with various degrees of certainty and not just rigid constraints the segmentation is conducted by using a hierarchical bayesian approach to a piecewise constant poisson rate model a gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm

finite time blow up for a class of parabolic or pseudo parabolic equations abstract in this paper we study the initial boundary value problem for a class of parabolic or pseudo parabolic equations u t a u t u b u k t u p 2 u x t 0 t where a 0 b l 1 with l 1 being the principal eigenvalue for on h 0 1 and k t 0 by using the potential well method levine s concavity method and some differential inequality techniques we obtain the finite time blow up results provided that the initial energy satisfies three conditions i j u 0 0 0 ii j u 0 0 d where d is a nonnegative constant iii 0 j u 0 0 c 0 where 0 involves the l 2 norm or h 0 1 norm of the initial data we also establish the lower and upper bounds for the blow up time in particular we obtain the existence of certain solutions blowing up in finite time with initial data at the nehari manifold or at arbitrary energy level

invariant sets and the blow up threshold for a nonlocal equation of parabolic type abstract in this paper we consider a nonlocal equation of parabolic type on a bounded smooth domain with dirichlet boundary condition first the well posedness in lebesgue spaces is established by using the banach fixed point theorem then we set up the regularity of the solution more interestingly we find the invariant sets for the initial boundary value problem and derive a threshold of blow up and global existence for its solution

finite time blowup and global solutions of euler type equations in matrix geometry in an interesting recent work professor sullivan has proposed a matrix version of the euler equation to approach this problem from a new angle motivated by his work we consider the finite time blowup and global solutions of euler type equations in the matrix geometry we set up some invariant sets of the flow equations and the invariant sets are defined via the use of the free energy functional and the nehari functional in the matrix geometry model the blowup result is obtained by the convexity method in an interesting recent work professor sullivan has proposed a matrix version of the euler equation to approach this problem from a new angle motivated by his work we consider the finite time blowup and global solutions of euler type equations in the matrix geometry we set up some invariant sets of the flow equations and the invariant sets are defined via the use of the free energy functional and the nehari functional in the matrix geometry model the blowup result is obtained by the convexity method

order one invariants of immersions of surfaces into 3 space we classify all order one invariants of immersions of a closed orientable surface f into 3 with values in an arbitrary abelian group we show that for any f and and any regular homotopy class of immersions of f into 3 the group of all order one invariants on is isomorphic to is the group of all functions from a set of cardinality our work includes foundations for the study of finite order invariants of immersions of a closed orientable surface into 3 analogous to chord diagrams and the 1 term and 4 term relations of knot theory