curvature decay estimates of graphical mean curvature flow in higher codimensions we derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions to the best of our knowledge this is the first such estimates without assuming smallness of first derivatives of the defining map an immediate application is a convergence theorem of the mean curvature flow of the graph of an area decreasing map between flat riemann surfaces

estimation of close sinusoids in colored noise and model discrimination this paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown earlier attempts have assumed the additive noise to be independent next we develop decision rules for checking whether the observed signal has only one sinusoid or two close sinusoids all of the earlier studies assumed that there are two close sinusoids in the signal another model discrimination problem considered is the determination of the causal structure of the observed periodicity a rule is given to test whether the observation comes from a sinusoid plus additive noise possible colored or the observation comes from a stationary autoregressive model we also present a numerical study showing the efficacy of the robust estimation procedure for estimating the two frequencies and the decision rules for checking the number of dominant frequencies and the causal mechanism finally we compare the proposed method to well known methods used for two close sinusoids in white noise

direction finding using noise covariance modeling we consider the problem of direction finding in the presence of colored noise whose covariance matrix is unknown we show that the ambient noise covariance matrix can be modeled by a sum of hermitian matrices known up to a multiplicative scalar using this model we estimate jointly the directions of arrival of the signals and the noise model parameters we show that under certain conditions it is possible to obtain unbiased and efficient estimates of the signal direction the cramer rao bound is used as the principal analysis tool computer simulations using the maximum likelihood estimator provide a validation of the analytical results

cores of tangent cones and clarke s tangent cone it is known that clarke s tangent cone at any point of any subset of rn is always both unique and convex by contrast nearly all other notions of convex tangent cone in the literature are monotone in the sense that if a convex cone k is a tangent cone at a point x0 of a set c rn then k k c c automatically implies that k is a tangent cone of the same type for c at x0 this carries the rider that such tangent cones are not unique and in general even maximal convex tangent cones are not unique in this paper it is shown that for most monotone types one can identify preferred tangent cones for c at x0 called core tangent cones of that type such that maximal core tangent cones are unique and convex

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

mean curvature flows and isotopy of maps between spheres let f be a smooth map between unit spheres of possibly different dimensions we prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions a corollary is that any area decreasing map between unit spheres of possibly different dimensions is isotopic to a constant map c 2004 wiley periodicals inc

nonsmooth milyutin dubovitskii theory and clarke s tangent cone in optimization theory the idea of approximating nonconvex sets by convex cones which satisfy an abstract condition the intersection principle is due to milyutin and dubovitskii this approach has been successfully applied to optimization problems with differentiable data the validity of the intersection principle for the clarke tangent cone which is the apposite approximant for nonsmooth constraints is established via an intersection theorem which relates the clarke tangent cone of an intersection of sets to the intersection of the individual clarke tangent cones provided the latter are inseparable this allows an extension of the milyutin dubovitskii approach to nonsmooth optimization theory a multiplier rule of the type obtained by clarke and hiriart urruty for a nonsmooth inequality constrained problem is thereby encompassed within milyutin dubovitskii theory

convex subcones of the contingent cone in nonsmooth calculus and optimization the tangential approximants most useful in nonsmooth analysis and optimization are those which lie between the clarke tangent cone and the bouligand contigent cone a study of this class of tangent cones is undertaken here it is shown that although no convex subcone of the contingent cone has the isotonicity property of the contingent cone there are such convex subcones which are more accurate approximants than the clarke tangent cone and possess an associated subdifferential calculus that is equally strong in addition a large class of convex subcones of the contingent cone can replace the clarke tangent cone in necessary optimality conditions for a nonsmooth mathematical program however the clarke tangent cone plays an essential role in the hypotheses under which these calculus rules and optimality conditions are proven overall the results obtained here suggest that the most complete theory of nonsmooth analysis combines a number of different tangent cones

epi lipschitz like sets in banach space theorems and examples on considere un espace de banach x et on etudie quelles proprietes un ensemble c dans x doit avoir pour que le cone tangent de clarke t c x et le cone normal n c x mesurent adequatement le comportement a la frontiere de x dans c

robust estimation of sinusoidal signals with colored noise using decentralized processing a technique is developed for the estimation of the number of signals and their central frequencies using decentralized processing when it is known a priori that the observations consist of a finite number of sinusoidal signals corrupted by an additive colored random noise process with unknown correlations such a noise sequence may be caused by jamming from a hostile agent the authors decentralized processing scheme is one in which each sensor estimates the frequencies and their covariance matrix and sends the results to the fusion center at the fusion center since the estimates from the sensors have a mixture density that is possibly not gaussian a robust technique is utilized to combine the estimates even when the numbers of frequencies transmitted by the various sensors are identical determining corresponding frequencies from each sensor is not a straightforward task also outliers caused by line splitting or by spurious frequencies are hard to detect these problems can be resolved by two methods the so called refitting method and the ranking method algorithms for both are presented in detail

direction finding in the presence of colored noise by candidate identification a method is developed for identifying correct angles of arrivals from a set of candidate angles that contains spurious angles and the true ones under the assumption that the colored noise is an autoregressive process and that a uniform linear array of sensors is used the procedure is based on a relation derived for the higher order reflection coefficients corresponding to the autocorrelation sequence of the signal plus noise it is shown that the higher order reflection coefficients of a set of plane waves impinging on a uniform linear array of sensors in the presence of an unknown spatially autoregressive colored noise process are equal to an order independent linear combination of the values of the fourier transform of the corresponding optimal linear least squares normalized prediction error filter at the electric phase angles of the plane waves the magnitudes of the coefficients are then used to decide whether a given candidate direction of arrival corresponds to an actual plane wave or not the estimation of candidate angles is also briefly discussed

tangent sets calculus and necessary conditions for extremality in this paper we deduce some relations concerning the tangent sets to the inverse image of a set under a function and we use these relations to derive necessary conditions for extremality in the form of a multiplier rule

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

long time existence and convergence of graphic mean curvature flow in arbitrary codimension let f 1 2 be a map between compact riemannian manifolds of constant curvature this article considers the evolution of the graph of f in 1 2 by the mean curvature flow under suitable conditions on the curvature of 1 and 2 and the differential of the initial map we show that the flow exists smoothly for all time at each instant t the flow remains the graph of a map ft and ft converges to a constant map as t approaches infinity this also provides a regularity estimate for lipschitz initial data

homotopy of area decreasing maps by mean curvature flow abstract let f m n be a smooth area decreasing map between two riemannian manifolds m g m and n g n under weak and natural assumptions on the curvatures of m g m and n g n we prove that the mean curvature flow provides a smooth homotopy of f to a constant map

adaptive notch filtering for the retrieval of sinusoids in noise in this paper an adaptive notch filter is developed employing a frequency domain and time domain analysis for the enhancement and tracking of sinusoids in additive noise colored or white the notch filter is implemented as a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter the resulting notch filter requires few parameters facilitates the formation of the desired band rejection filter response and also leads to various useful implementations cascade parallel for the adaptation of the filter coefficients the stochastic gauss newton algorithm is used the convergence of this updating procedure is established by studying the associated differential equation also it is shown that the structure present in the problem enables truncation of the gradient thereby reducing the complexity of adapting the filter coefficients simulation results are presented to substantiate the analysis and to demonstrate the potential of the notch filtering technique

ioffe s normal cone and the foundations of welfare economics the infinite dimensional theory abstract we establish the relevance of ioffe s normal cone for basic theorems of welfare economics in the context of a commodity space formalized as a vactor lattice and endowed with a locally convex linear topology in which the positive cone is closed

a local regularity theorem for mean curvature flow this paper proves curvature bounds for mean curvature flows and other related flows in regions of spacetime where the gaussian densities are close to 1

detection and localization in colored noise via generalized least squares a method for detection and localization of multiple signals in spatially colored noise by an arbitrary passive sensor array is presented the method also enables exploitation of prior knowledge that the signals are uncorrelated so as to improve the performance and to allow detection and localization even if the number of signals exceeds the number of sensors the estimation based on the generalized least squares criterion is both consistent and asymptotically efficient the detection is performed via the minimum description length mdl principle and is proved to be consistent simulation results confirming the theoretical results are included

which subgradients have sum formulas on donne une formule de somme generale valable pour un cone tangent avec une courte liste de proprietes

volumetric array prewhitening direction finders such as music experience loss of resolution and increased bias in the presence of nonwhite noise this paper presents two versions of a steepest descent gradient algorithm that prewhiten the signal received by an arbitrarily oriented volumetric sensor array minimizing these undesirable effects the algorithms optimize a whiteness functional over a surface with desirable properties including low dimensionality unimodality and concavity two ambient noise models facilitate algorithm development through succinct parameterization the first which is a novel linear matricial ambient noise model based on a spherical harmonic expansion places no constraints on array geometry the second model requires a spatially uniformly sampled sensor array and reduces problem dimensionality associated with exact multidimensional autoregressive modeling the algorithms estimate a stacked vector arrangement of the model parameters application with music demonstrates enhanced performance in terms of angular resolution and detection of low signal to noise ratio snr sources

nonsmooth calculus in finite dimensions the notion of subgradient originally defined for convex functions has in recent years been extended via the upper subderivative to cover functions that are not necessarily convex or even continuous a number of calculus rules have been proven for these generalized subgradients this paper develops the finite dimensional generalized subdifferential calculus for strictly lower semicontinuous functions under considerably weaker hypotheses than those previously used the most general finite dimensional convex subdifferential calculus results are recovered as corollaries other corollaries given include new necessary conditions for optimality in a nonsmooth mathematical program various chain rule formulations are considered equality in the subdifferential calculus formulae is proven under hypotheses weaker than the usual subdifferential regularity assumptions

mean curvature flow of compact spacelike submanifolds in higher codimension we prove the longtime existence for mean curvature flow of a smooth n dimensional spacelike submanifold of an n m dimensional manifold whose metric satisfies the timelike curvature condition

direction estimation in partially unknown noise fields the problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered the unknown noise covariance is assumed to obey a linear parametric model using this model the maximum likelihood directions parameter estimate is derived and a large sample approximation is formed it is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ml aml estimator furthermore a closed form expression of the cramer rao bound on the direction parameter is provided a perturbation analysis with respect to a small error in the assumed noise model is carried out and an expression of the asymptotic bias due to the model mismatch is given computer simulations and an application of the proposed technique to a full scale passive sonar experiment is provided to illustrate the results

evolution of contractions by mean curvature flow in this article we investigate length decreasing maps f m rightarrow n between riemannian manifolds m n of dimensions m ge 2 and n respectively assuming that m is compact and n is complete such that begin aligned sec m sigma quad text and quad mathrm ric m ge m 1 sigma ge m 1 sec n ge mu end aligned where sigma mu are positive constants we show that the mean curvature flow provides a smooth homotopy of f into a constant map