outlier detection with the kernelized spatial depth function statistical depth functions provide from the deepest point a center outward ordering of multidimensional data in this sense depth functions can measure the extremeness or outlyingness of a data point with respect to a given data set hence they can detect outliers observations that appear extreme relative to the rest of the observations of the various statistical depths the spatial depth is especially appealing because of its computational efficiency and mathematical tractability in this article we propose a novel statistical depth the kernelized spatial depth ksd which generalizes the spatial depth via positive definite kernels by choosing a proper kernel the ksd can capture the local structure of a data set while the spatial depth fails we demonstrate this by the half moon data and the ring shaped data based on the ksd we propose a novel outlier detection algorithm by which an observation with a depth value less than a threshold is declared as an outlier the proposed algorithm is simple in structure the threshold is the only one parameter for a given kernel it applies to a one class learning setting in which normal observations are given as the training data as well as to a missing label scenario where the training set consists of a mixture of normal observations and outliers with unknown labels we give upper bounds on the false alarm probability of a depth based detector these upper bounds can be used to determine the threshold we perform extensive experiments on synthetic data and data sets from real applications the proposed outlier detector is compared with existing methods the ksd outlier detector demonstrates a competitive performance

necessary conditions of asymptotic stability for unilateral dynamical systems in this paper we develop a mathematical tool that can be used to state necessary conditions of asymptotic stability of isolated stationary solutions of a class of unilateral dynamical systems more precisely nonlinear evolution variational inequalities are considered instability criteria are also given applications can be found in mechanics or electrical circuits

an influence of unilateral sources and sinks in reaction diffusion systems exhibiting turing s instability on bifurcation and pattern formation abstract we consider a general reaction diffusion system exhibiting turing s diffusion driven instability in the first part of the paper we supplement the activator equation by unilateral integral sources and sinks of the type k u x k d k and k u x k d k these terms measure an average of the concentration over the set k and are active only when this average decreases below or increases above the value of the reference spatially homogeneous steady state which is shifted to the origin we show that the set of diffusion parameters in which spatially heterogeneous stationary solutions can bifurcate from the reference state is smaller than in the classical case without any unilateral integral terms this problem is studied for the case of mixed pure neumann and periodic boundary conditions in the second part of the paper we investigate the effect of both unilateral terms of the type u u and unilateral integral terms on the pattern formation using numerical experiments on the system with well known schnakenberg kinetics

new beams of global bifurcation points for a reaction diffusion system with inequalities or inclusions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that an obstacle e g a unilateral membrane modeled either in terms of inequalities or of inclusions introduces whole beams of new global bifurcation points of spatially non homogeneous stationary solutions which lie in parameter domains which are excluded as bifurcation points for the problem without the obstacle

direction and stability of bifurcating solutions for a signorini problem abstract the equation u u g u u 0 is considered in a bounded domain in r 2 with a signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary it is assumed that g 0 0 for r is a bifurcation parameter a given eigenvalue of the linearized equation with the same boundary conditions is considered a smooth local bifurcation branch of non trivial solutions emanating at 0 from trivial solutions is studied we show that to know a direction of the bifurcating branch it is sufficient to determine the sign of a simple expression involving the corresponding eigenfunction u 0 in the case when 0 is the first eigenvalue and the branch goes to the right we show that the bifurcating solutions are asymptotically stable in w 1 2 norm the stability of the trivial solution is also studied and an exchange of stability is obtained

unilateral sources and sinks of an activator in reaction diffusion systems exhibiting diffusion driven instability abstract a reaction diffusion system exhibiting turing s diffusion driven instability is considered the equation for an activator is supplemented by unilateral terms of the type s x u s x u describing sources and sinks active only if the concentration decreases below and increases above respectively the value of the basic spatially constant solution which is shifted to zero we show that the domain of diffusion parameters in which spatially non homogeneous stationary solutions can bifurcate from that constant solution is smaller than in the classical case without unilateral terms it is a dual information to previous results stating that analogous terms in the equation for an inhibitor imply the existence of bifurcation points even in diffusion parameters for which bifurcation is excluded without unilateral sources the case of mixed dirichlet neumann boundary conditions as well as that of pure neumann conditions is described

intrinsic analysis of statistical estimation the parametric statistical models with suitable regularity conditions have a natural riemannian manifold structure given by the information metric since the parameters are merely labels for the probability measures an inferential statement should be formulated through intrinsic objects invariant under reparametrizations in this context the estimators will be random objects valued on the manifold corresponding to the statistical model in spite of these considerations classical measures of an estimator s performance like the bias and the mean square error are clearly dependent on the statistical model parametrizations in this paper the authors work with extended notions of mean value and moments of random objects which take values on a hausdorff and connected manifold equipped with an affine connection in particular the riemannian manifold case is considered this extension is applied to the bias and the mean square error study in statistical point estimation theory under this approach an intrinsic version of the cramer rao lower bound is obtained a lower bound which depends on the intrinsic bias and the curvature of the statistical model for the mean square of the rao distance the invariant measure analogous to the mean square error further the behavior of the mean square of the rao distance of an estimator when conditioning with respect to a sufficient statistic is considered obtaining intrinsic versions of the rao blackwell and lehmann scheffe theorems asymptotic properties complete the study

the mahalanobis distance and elliptic distributions summary the mahalanobis distance is shown to be an appropriate measure of distance between two elliptic distributions having different locations but a common shape this extends a result long familiar in multivariate analysis to a class of nonnormal distributions it can also be used to show that the sample version of the mahalanobis distance is appropriate under both estimative and predictive approaches to estimation for the family of multivariate normal distributions differing only in location

bifurcation for a reaction diffusion system with unilateral and neumann boundary conditions abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability if supplemented by pure neumann boundary conditions we show by a degree theoretic approach that an obstacle e g a unilateral membrane modeled in terms of inequalities introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable moreover this parameter domain is rather different from the known case when also dirichlet conditions are assumed in particular bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know

continuity compactness and degree theory for operators in systems involving p laplacians and inclusions the study of weak solutions for systems of nonlinear partial differential equations of elliptic type with inclusions leads to a multivalued operator of superposition type in sobolev spaces we show that under natural assumptions this operator has the properties which allow to apply degree theory fixed point index for multivalued maps more precisely this operator is upper semicontinuous and compact with nonempty convex compact values for the particular case of systems involving p laplacians we show that there is a homeomorphism transforming the whole system to a situation for which a fixed point index is available

stability and instability matrices for linear evolution variational inequalities this paper deals with the characterization of the stability and instability matrices for a class of unilaterally constrained dynamical systems represented as linear evolution variational inequalities levi such systems can also be seen as a sort of differential inclusion or in special cases as linear complementarity systems which in turn are a class of hybrid dynamical systems examples show that the stability of the unconstrained system and that of the constrained system may drastically differ various criteria are proposed to characterize the stability or the instability of levi

bifurcation points for a reaction diffusion system with two inequalities abstract we consider a reaction diffusion system of activator inhibitor or substrate depletion type which is subject to diffusion driven instability we show that obstacles e g a unilateral membrane for both quantities modeled in terms of inequalities introduce a new bifurcation of spatially non homogeneous steady states in the domain of stability of the trivial solution of the corresponding classical problem without obstacles

time series analysis of non gaussian observations based on state space models from both classical and bayesian perspectives the analysis of non gaussian time series by using state space models is considered from both classical and bayesian perspectives the treatment in both cases is based on simulation using importance sampling and antithetic variables markov chain monte carlo methods are not employed non gaussian disturbances for the state equation as well as for the observation equation are considered methods for estimating conditional and posterior means of functions of the state vector given the observations and the mean square errors of their estimates are developed these methods are extended to cover the estimation of conditional and posterior densities and distribution functions the choice of importance sampling densities and antithetic variables is discussed the techniques work well in practice and are computationally efficient their use is illustrated by applying them to a univariate discrete time series a series with outliers and a volatility series

positive solutions of variational inequalities a degree theoretic approach if the mapping a is strictly monotone and coercive is equivalent to a fixed point equation u m u in k cf section 1 suppose that m is continuous and maps bounded subsets of k into compact ones then due to the fact that k is a retract of x it is possible to define a fixed point index of m with properties similar to those associated with the leray schauder degree 1 sect 111 in section 1 we introduce another index which is based on the previous one but has the advantage of being directly related to inequality rather than to the fixed point equation u m u in section 2 we apply this new index in order to show that if c is a closed convex subset of k then under suitable assumptions upon f the set of solutions of the inequality

rational approximations for values of derivatives of the gamma function the arithmetic nature of euler s constant is still unknown and even getting good rational approximations to it is difficult recently aptekarev managed to find a third order linear recurrence with polynomial coefficients which admits two rational solutions a n and b n such that a n b n converges sub exponentially to viewed as 1 where r is the usual gamma function although this is not yet enough to prove that it is a major step in this direction in this paper we present a different but related approach based on simultaneous pade approximants to euler s functions from which we construct and study a new third order recurrence that produces a sequence in z whose height grows like the factorial and that converges sub exponentially to log z for any complex number z 0 where log is defined by its principal branch we also show how our approach yields in theory rational approximations of numbers related to s 1 for any integer s 1 in particular we construct a sixth order recurrence which provides simultaneous rational approximations of factorial height converging sub exponentially to the numbers and 1 2 1 2 2 2

selberg s integral and linear forms in zeta values using selberg s integral we present some new euler type integral representations of certain nearly poised hypergeometric series these integrals are also shown to produce linear forms in odd and or even zeta values that generalize previous work of the author

smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem the implicit function theorem is applied in a nonstandard way to abstract variational inequalities depending on a possibly infinite dimensional parameter in this way results on smooth continuation of solutions as well as of eigenvalues and eigenvectors are established under certain particular assumptions the abstract results are applied to a linear second order elliptic eigenvalue problem with nonlocal unilateral boundary conditions schrodinger operator with the potential as the parameter

loss of stability at turning points in nonlinear elliptic variational inequalities a considerable amount of work has been devoted in recent years to stationary free boundary problems in particular obstacle problems have been the subject of extensive work concerning existence estimates and regularity of the solution or of the coincidence set and occurrence of multiple solutions in 6 8 161 the authors consider obstacle problems with nonlinear forcing terms leading to multiple solutions hence to turning points when a real parameter appears in the forcing term a local study of the branches of solutions is set up the results obtained are the extension in a weaker form of those well known for equations ll 12 however some important classical questions remain open for obstacle problems

some global bifurcation results for elastic plates this paper is concerned with global bifurcation results of some buckling problems for thin elastic plates under von karman s model we consider these problems as applications of a general topological degree analysis for bifurcation of variational inequalities

estimation of high density regions using one class neighbor machines in this paper we investigate the problem of estimating high density regions from univariate or multivariate data samples we estimate minimum volume sets whose probability is specified in advance known in the literature as density contour clusters this problem is strongly related to one class support vector machines ocsvm we propose a new method to solve this problem the one class neighbor machine ocnm and we show its properties in particular the ocnm solution asymptotically converges to the exact minimum volume set prespecified finally numerical results illustrating the advantage of the new method are shown

on the indices of fixed points of mappings in cones and applications abstract assume that k is a cone in a banach space and a k k is completely continuous we obtain a formula for the index in k of a fixed point of a under the assumption that a linearization exists and satisfies an invertibility condition we then use this formula to generalize some results of amann on the number of fixed points of a to the case where k has empty interior

global bifurcation for quasivariational inequalities of reaction diffusion type abstract we consider a reaction diffusion system with implicit unilateral boundary conditions introduced by u mosco we show that global continua of stationary spatially nonhomogeneous solutions bifurcate in the domain of parameters where bifurcation in the case of classical boundary conditions is excluded the problem is formulated as a quasivariational inequality and the proof is based on the leray schauder degree

on line inference for hidden markov models via particle filters we consider the on line bayesian analysis of data by using a hidden markov model where inference is tractable conditional on the history of the state of the hidden component a new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type the algorithm is similar to the mixture kalman filter but uses a different resampling algorithm we prove that this resampling algorithm is computationally efficient and optimal among unbiased resampling algorithms in terms of minimizing a squared error loss function in a practical example that of estimating break points from well log data our new particle filter outperforms two other particle filters one of which is the mixture kalman filter by between one and two orders of magnitude

a model for perturbed production or measurement processes involving compound normal distributions to solve an easy to understand real world problem we invite the reader to travel through many useful concepts related to the important models provided by the compound normal distributions this class of distributions is a subclass of the multivariate elliptical distributions that allows a clearcut interpretation of a data generating mechanism useful in certain situations a multivariate elliptical distribution is characterized by the existence of a particular function f in the special case of a compound normal distribution the function f appears to be simply the one sided laplace stieltjes transform lst of the mixing distribution this fact allows in particular to easily express the covariance matrix and the kurtosis parameter of the compound normal in terms of derivatives evaluated at the origin of the lst of the mixing distribution an example of application of the results is the asymptotic theory for canonical correlation analysis the asymptotic distributions of the sample canonical correlation coefficients and of statistics used for testing hypotheses about the population coefficients have very simple forms in the case of compound normal distributions they depend on the lst of the mixing distribution through the kurtosis parameter here we focus our attention on the inference on the simple correlation coefficient r of the components of bivariate compound normal distributions we illustrate with a simple example in industrial engineering how inference on r is affected by the choice of the associated mixing distribution

eigenvalues and bifurcation for problems with positively homogeneous operators and reaction diffusion systems with unilateral terms abstract reaction diffusion systems satisfying assumptions guaranteeing turing s instability and supplemented by unilateral terms of type v and v are studied existence of critical points and sometimes also bifurcation of stationary spatially non homogeneous solutions are proved for rates of diffusions for which it is excluded without any unilateral term the main tool is a general result giving a variational characterization of the largest eigenvalue for positively homogeneous operators in a hilbert space satisfying a condition related to potentiality and existence of bifurcation for equations with such operators the originally non variational non symmetric system is reduced to a single equation with a positively homogeneous potential operator and the abstract results mentioned are used

on the principle of linearized stability for variational inequalities on etudie la stabilite des solutions stationnaires d inegalites variationnelles paraboliques dans des espaces de hilbert

bifurcation points and eigenvalues of inequalities of reaction diffusion type on demontre certaines assertions concernant les points de bifurcation et les valeurs propres de systemes de reaction diffusion avec des conditions unilaterales

a particle filtering scheme for processing time series corrupted by outliers the literature in engineering and statistics is abounding in techniques for detecting and properly processing anomalous observations in the data most of these techniques have been developed in the framework of static models and it is only in recent years that we have seen attempts that address the presence of outliers in nonlinear time series for a target tracking problem described by a nonlinear state space model we propose the online detection of outliers by including an outlier detection step within the standard particle filtering algorithm the outlier detection step is implemented by a test involving a statistic of the predictive distribution of the observations such as a concentration measure or an extreme upper quantile we also provide asymptotic results about the convergence of the particle approximations of the predictive distribution and its statistics and assess the performance of the resulting algorithms by computer simulations of target tracking problems with signal power observations

some crandall rabinowitz type results and applications to reaction diffusion systems abstract for a small lipschitz perturbation of a smooth equation the existence of exactly two bifurcation points near a simple eigenvalue is shown the result is applied to reaction diffusion systems subject to turing s diffusion driven instability under small unilateral obstacles

degree instability and bifurcation of reaction diffusion systems with obstacles near certain hyperbolas abstract for a reaction diffusion system which is subject to turing s diffusion driven instability and which is equipped with unilateral obstacles of various types the nonexistence of bifurcation of stationary solutions near certain critical parameter values is proved the result implies assertions about a related mapping degree which in turn implies for small obstacles the existence of a new branch of bifurcation points spatial patterns induced by the obstacle

bifurcation direction and exchange of stability for variational inequalities on nonconvex sets abstract this paper concerns crandall rabinowitz type bifurcation for abstract variational inequalities on nonconvex sets and with multidimensional bifurcation parameter we derive formulae which determine the bifurcation direction and in the case of potential operators the stability of all solutions close to the bifurcation point in particular it follows that in some cases an exchange of stability appears similar to the case of equations but in some other cases stable nontrivial solutions bifurcate at points where there is no loss of stability of the trivial solution as an application we consider a system of two second order odes with nonconvex unilateral boundary conditions

diophantine properties for q analogues of dirichlet s beta function at positive integers in this paper we define q analogues of dirichlet s beta function at positive integers which can be written as q s k 1 s d k k d d s 1 q k for s where q is a complex number such that q 1 and is the nontrivial dirichlet character modulo 4 for odd s these expressions are connected with the automorphic world in particular with eisenstein series of level 4 from this we derive through nesterenko s work the transcendance of the numbers q 2s 1 for q algebraic such that 0 q 1 our main result concerns the nature of the numbers q 2s we give a lower bound for the dimension of the vector space over spanned by 1 q 2 q 4 q a where 1 q 1 1 and a is an even integer as consequences for 1 q 1 1 on the one hand there is an infinity of irrational numbers among q 2 q 4 and on the other hand at least one of the numbers q 2 q 4 q 20 is irrational

diophantine properties of numbers related to catalan s constant 1 as a linear form in 1 and even beta valuesonly the following lemma 2 is almost the same as the correspondingone in br and we only include a sketch of the proof we would like toemphasise the fact that it is essentially the well poisedness of the series thatenables us to produce this parity dependant behaviour when

reaction diffusion systems destabilizing effect of unilateral conditions on considere un systeme de reaction diffusion dans un domaine r n soit v une solution stationnaire et spatialement homogene avec les conditions aux limites de neumann on etudie la stabilite linearisee de v

attractivity theory for second order non smooth dynamical systems with application to dry friction in this paper we study the attractivity properties of the set of stationary solutions for a general class of second order non smooth dynamical system involving friction term sufficient conditions for the local attractivity of the set of stationary solutions are given in the case of dry friction and negative viscous damping an estimation of the attraction domain is also given in this case applications can be found in unilateral mechanics

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

direction and stability of bifurcation branches for variational inequalities we consider a class of variational inequalities with a multidimensional bifurcation parameter under assumptions guaranteeing the existence of smooth families of nontrivial solutions bifurcating from the set of trivial solutions the direction of bifurcation is shown in a neighborhood of bifurcation points of a certain type in the case of potential operators also the stability and instability of bifurcating solutions and of the trivial solution is described in the sense of minima of the potential in particular an exchange of stability is observed

unilateral regulation breaks regularity of turing patterns we consider a reaction diffusion system undergoing turing instability and augment it by an additional unilateral source term we investigate its influence on the turing instability and on the character of resulting patterns the nonsmooth positively homogeneous unilateral term v has favorable properties but the standard linear stability analysis cannot be performed we illustrate the importance of the nonsmoothness by a numerical case study which shows that the turing instability can considerably change if we replace this term by its arbitrarily precise smooth approximation however the nonsmooth unilateral term and all its approximations yield qualitatively similar patterns although not necessarily developing from small disturbances of the spatially homogeneous steady state further we show that the unilateral source breaks the approximate symmetry and regularity of the classical patterns and yields asymmetric and irregular patterns moreover a given system with a unilateral source produces spatial patterns even for diffusion parameters with ratios closer to 1 than the same system without any unilateral term

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed

on dirichlet s lambda function abstract let s n 0 1 2 n 1 s s n 0 1 n 2 n 1 s and s n 1 1 n 1 n s be the dirichlet lambda function its alternating form and the dirichlet eta function respectively according to a recent historical book by varadarajan 25 p 70 these three functions were investigated by euler under the notations n s l s and m s respectively in this paper we shall present some additional properties for them that is we obtain a number of infinite families of linear recurrence relations for s at positive even integer arguments 2 m convolution identities for special values of s at even arguments and special values of s at odd arguments and a power series expansion for the alternating hurwitz zeta function j s a which involves a known one for s

smooth bifurcation branches of solutions for a signorini problem abstract we study a bifurcation problem for the equation u u g u u 0 on a rectangle with signorini boundary conditions on a part of one edge and mixed zero dirichlet and neumann boundary conditions on the rest of the boundary here r is the bifurcation parameter and g is a small perturbation we prove under certain assumptions concerning an eigenfunction u 0 corresponding to an eigenvalue 0 of the linearized equation with the same nonlinear boundary conditions the existence of a local smooth branch of nontrivial solutions bifurcating from the trivial solutions at 0 in the direction of u 0 the contact sets of these nontrivial solutions are intervals which change smoothly along the branch the main tool of the proof is a local equivalence of the unilateral bvp to a system consisting of a corresponding classical bvp and of two scalar equations to this system classical crandall rabinowitz type local bifurcation techniques scaling and implicit function theorem are applied

degree and global bifurcation for elliptic equations with multivalued unilateral conditions abstract a bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is considered the existence of global bifurcation between two eigenvalues of a certain type of the laplacian is proved for a class of abstract inclusions with compact multivalued mappings in a hilbert space it is shown how the degree can be determined near the eigenvalues of a particular type of an associated linear single valued problem and the jump of the degree is proved as a consequence global bifurcation for such abstract inclusions is obtained the weak formulation of the boundary value problem mentioned is a particular case