the hilbert spectrum via wavelet projections non stationary signals are increasingly analysed in the time frequency domain to determine the variation of frequency components with time it was recently proposed in this journal that such signals could be analysed by projections onto the time frequency plane giving a set of monocomponent signals these could then be converted to analytic signals using the hilbert transform and their instantaneous frequency calculated which when weighted by the energy yields the hilbert energy spectrum for that projection agglomeration over projections yields the complete hilbert spectrum we show that superior results can be obtained using waveletbased projections the maximal overlap undecimated stationary translation invariant discrete wavelet transform and wavelet packet transforms are used with

bivariate instantaneous frequency and bandwidth the generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived these are uniquely defined whether the signal is represented as a pair of real valued signals or as one analytic and one anti analytic signal a nonstationary but oscillatory bivariate signal has a natural representation as an ellipse whose properties evolve in time and this representation provides a simple geometric interpretation for the bivariate instantaneous moments the bivariate bandwidth is shown to consist of three terms measuring the degree of instability of the time varying ellipse amplitude modulation with fixed eccentricity eccentricity modulation and orientation modulation or precession an application to the analysis of data from a free drifting oceanographic float is presented and discussed

transmutation techniques and observability for time discrete approximation schemes of conservative systems in this article we consider abstract linear conservative systems and their time discrete counterparts our main result is a representation formula expressing solutions of the continuous model through the solution of the corresponding time discrete one as an application we show how observability properties for the time continuous model yield uniform with respect to the time step observability results for its time discrete approximation counterparts provided the initial data are suitably filtered the main output of this approach is the estimate on the time under which we can guarantee uniform observability for the time discrete models besides using a reverse representation formula we also prove that this estimate on the time of uniform observability for the time discrete models is sharp we then conclude with some general comments and open problems

embedding formulations and complexity for unions of polyhedra it is well known that selecting a good mixed integer programming mip formulation is crucial for effectively obtaining a solution with state of the art solvers although best practices and guidelines for constructing good formulations abound there is rarely a single systematic construction approach that leads to the best possible formulation here we introduce embedding formulations and complexity as a new mip formulation paradigm for systematically constructing formulations for disjunctive constraints that are optimal with respect to size more specifically they yield the smallest possible ideal formulation i e one whose lp relaxation has integral extreme points among all formulations that only use 0 1 auxiliary variables we use the paradigm to characterize optimal formulations for special ordered sets of type 2 and certain piecewise linear functions of two variables we also show that the resultant formulations can provide a significant computational advantage over all known formulations for pi

2d grushin type equations minimal time and null controllable data abstract we study internal null controllability for degenerate parabolic equations of grushin type g x x 2 x 2 y y 2 0 in the rectangle x y 1 1 0 1 previous works proved that null controllability holds for weak degeneracies small and fails for strong degeneracies large moreover in the transition regime and with strip shaped control domains a positive minimal time is required in this paper we work with controls acting on two strips symmetric with respect to the degeneracy we give the explicit value of the minimal time and we characterize some initial data that can be steered to zero in time t when the system is not null controllable their regularity depends on the control domain and the time t we also prove that with a control that acts on one strip touching the degeneracy line x 0 then grushin type equations are null controllable in any time t 0 and for any degeneracy 0 our approach is based on a precise study of the observability property for the one dimensional heat equations satisfied by the fourier coefficients in variable y this precise study is done through a transmutation process on the resulting one dimensional wave equations by lateral propagation of energy method

analytic wavelet thresholding summary we introduce so called analytic stationary wavelet transform thresholding where using the discrete hilbert transform we create a complex valued analytic vector from which an amplitude vector is defined thresholding of a real valued wavelet coefficient at some transform level is carried out according to the corresponding value in this amplitude vector relevant statistical results follow from properties of the discrete hilbert transform analytic stationary wavelet transform thresholding is found to produce consistently a reduced mean squared error compared to using standard stationary wavelet transform or cycle spinning thresholding for signals with extensive oscillations at some transform levels this improvement is very marked furthermore we show that our thresholding test is invariant to phase shifts in the data whereas if complex wavelet filters are being used the filters must be analytic or anti analytic at each level of the wavelet transform

minimax threshold for denoising complex signals with waveshrink for the problem of signal extraction from noisy data waveshrink has proven to be a powerful tool both from an empirical and an asymptotic point of view waveshrink is especially efficient at estimating spatially inhomogeneous signals a key step of the procedure is the selection of the threshold parameter donoho and johnstone 1994 propose a selection of the threshold based on a minimax principle their derivation is specifically for real signals and real wavelet transforms in this paper we propose to extend the use of waveshrink to denoising complex signals with complex wavelet transforms we illustrate the problem of denoising complex signals with an electronic surveillance application

note on the cost of the approximate controllability for the heat equation with potential abstract we prove the approximate controllability for the heat equation with potential with a cost of order ec e when the target is in h 0 1 with a precision in l 2 norm also a quantification estimate of the unique continuation for initial data in l 2 of the heat equation with potential is established

on the observability of time discrete conservative linear systems abstract we consider various time discretization schemes of abstract conservative evolution equations of the form z a z where a is a skew adjoint operator we analyze the problem of observability through an operator b more precisely we assume that the pair a b is exactly observable for the continuous model and we derive uniform observability inequalities for suitable time discretization schemes within the class of conveniently filtered initial data the method we use is mainly based on the resolvent estimate given by burq and zworski in n burq m zworski geometric control in the presence of a black box j amer math soc 17 2 2004 443 471 electronic we present some applications of our results to time discrete schemes for wave schrodinger and kdv equations and fully discrete approximation schemes for wave equations

improving discrete model representations via symmetry considerations in this paper we focus on a useful modeling concept that is frequently ignored while formu lating discrete optimization problems very often there exists a natural symmetry inherent in the problem itself that if propagated to the model can hopelessly mire a branch and bound solver by burdening it to explore and eliminate such alternative symmetric solutions we discuss three applications where such a symmetry arises a telecommunications network design problem a noise pollution problem and a machine procurement and operation problem for each case we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability while using a popular modern day commercial branch and cut software cplex 6 5

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

multiple multidimensional morse wavelets this paper defines a set of operators that localize a radial image in space and radial frequency simultaneously the eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found the eigenfunctions are optimally concentrated over a given region of radial space and scale space defined via a triplet of parameters analytic forms for the energy concentration of the functions over the region are given the radial function localization operator can be generalised to an operator localizing any l2 ropf2 function it is demonstrated that the latter operator given an appropriate choice of localization region approximately has the same radial eigenfunctions as the radial operator based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude orientation and phase structure of locally oscillatory signals the full set of quaternionic wavelet functions are component by component orthogonal their statistical properties are tractable and forms for the variability of the estimators of the local phase and orientation are given as well as the local energy of the image by averaging estimators across wavelets a substantial reduction in the variance is achieved

the phase corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events this paper is concerned with the development and application of the phase corrected maximal overlap discrete wavelet packet transform modwpt the discrete cyclic filtering steps of the modwpt are fully explained energy preservation is proven with filter coefficients chosen from daubechie s least asymmetric class the optimum time shifts to apply to ensure approximate zero phase filtering at every level of the modwpt are studied and applied to the wavelet packet coefficients to give phase corrections which ensure alignment with the original time series also the time series values at each time are decomposed into details associated with each frequency band and these line up perfectly with features in the original time series since the details are shown to arise through exact zero phase filtering the phase corrected modwpt is applied to a non stationary time series of hourly averaged southern hemisphere solar magnetic field magnitude data acquired by the ulysses spacecraft the occurrence times of the shock waves previously determined via manual pattern matching on the raw data match those times in the time frequency plot where a broadband spectrum is obtained in other words the phase corrected modwpt provides an approach to picking the location of complicated events we demonstrate the superiority of the modwpt in interpreting timing information over two competing methods namely the cosine packet transform or local cosine transform and the short time fourier transform

the discrete wavelet transform wedding the a trous and mallat algorithms two separately motivated implementations of the wavelet transform are brought together it is observed that these algorithms are both special cases of a single filter bank structure the discrete wavelet transform the behavior of which is governed by the choice of filters in fact the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact moreover it is shown that the commonly used lagrange a trous filters are in one to one correspondence with the convolutional squares of the daubechies filters for orthonormal wavelets of compact support a systematic framework for the discrete wavelet transform is provided and conditions are derived under which it computes the continuous wavelet transform exactly suitable filter constraints for finite energy and boundedness of the discrete transform are also derived relevant signal processing parameters are examined and it is observed that orthonormality is balanced by restrictions on resolution

empirical mode decomposition using rational splines an application to rainfall time series empirical mode decomposition emd a relatively new form of time series decomposition has the feature of not assuming that a time series is linear or stationary as is implicitly done in fourier analysis in natural time series such as records of rainfall streamflow temperature etc where most variables exhibit nonlinear and non stationary behaviour this feature is particularly useful allowing more meaningful quantification of the proportion of variance in a time series due to fluctuations at different time scales than previous spectral analysis techniques however in its original form the emd algorithm relies on cubic spline interpolation of the extrema which often inflate the variance of the resultant components intrinsic mode functions and residual in this paper a suggested improvement to the emd algorithm using rational splines and flexible treatment of the end conditions is outlined and the consequent effect on three exemplary annual rainfall time series is assessed as a proof of concept it is recognized that many more examples are needed for the fine tuning of the ideas before it can be widely recommended and this work is currently underway

the monogenic wavelet transform this paper extends the 1 d analytic wavelet transform to the 2 d monogenic wavelet transform the transformation requires care in its specification to ensure suitable transform coefficients are calculated and it is constructed so that the wavelet transform may be considered as both local and monogenic this is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform classes of monogenic wavelets are proposed with suitable local properties it is shown that the monogenic wavelet annihilates anti monogenic signals that the monogenic wavelet transform is phase shift covariant and that the transform magnitude is phase shift invariant a simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived the monogenic wavelet ridges of local plane waves are given

a generalized demodulation approach to time frequency projections for multicomponent signals in this paper we introduce a flexible approach for the time frequency analysis of multicomponent signals involving the use of analytic vectors and demodulation the demodulated analytic signal is projected onto the time frequency plane so that as closely as possible each component contributes exclusively to a different tile in a wavelet packet tiling of the time frequency plane and at each time instant the contribution to each tile definitely comes from no more than one component a single reverse demodulation is then applied to all projected components the resulting instantaneous frequency of each component in each tile is not constrained to a set polynomial form in time and is readily calculated as is the corresponding hilbert energy spectrum two examples illustrate the method in order better to understand the effect of additive noise the approximate variance of the estimated instantaneous frequency in any tile has been formulated by starting with pure noise and studying its evolving covariance structure through each step of the algorithm the validity and practical utility of the resulting expression for the variance of the estimated instantaneous frequency is demonstrated via a simulation experiment

enhanced model formulations for optimal facility layout this paper presents an improved mixed integer programming mip model and effective solution strategies for the facility layout problem and is motivated by the work of meller et al 1999 this class of problems seeks to determine a least cost layout of departments having various size and area requirements within a rectangular building and it is challenging even for small instances the difficulty arises from the disjunctive constraints that prevent departmental overlaps and the nonlinear area constraints for each department which existing models have failed to approximate with adequate accuracy we develop several modeling and algorithmic enhancements that are demonstrated to produce more accurate solutions while also decreasing the solution effort required we begin by deriving a novel polyhedral outer approximation scheme that can provide as accurate a representation of the area requirements as desired we also design alternative methods for reducing problem symmetry evaluate the performance of several classes of valid inequalities explore the construction of partial convex hull representations for the disjunctive constraints and investigate judicious branching variable selection priority schemes the results indicate asubstantial increase in the accuracy of the layout produced while at the same time providing adramatic reduction in computational effort in particular three previously unsolved test problems from the literature for which meller et al s algorithm terminated prematurely after 24 cpu hours of computation on a sun ultra 2 workstation with 390 mb ram with respective optimality gaps of 10 14 26 45 and 40 have been solved to exact optimality with reasonable effort using our proposed approach

efficient models for the facility layout problem abstract in this paper two new models of the facility layout problem are presented linear continuous with absolute values in the objective function and constraints and linear mixed integer the linear mixed integer models have lesser number of integer variables than any other existing formulation for the facility layout problem while most other linear mixed integer models available in the literature have been obtained through a linearization of the quadratic assignment problem the ones presented in this paper are not the continuous models have an even more compact form an advantage of the formulations presented in this paper is that the location of sites need not be known a priori more importantly two of the formulations model the layout problem with facilities of unequal area solving the models presented with an unconstrained optimization algorithm yields good quality suboptimal solutions in a relatively low computation time the continuous models appear to be more useful for solving the facility layout problem than other models published in the literature

long time behavior of a coupled heat wave system arising in fluid structure interaction this paper is devoted to the analysis of the long time behavior of a coupled wave heat system in which a wave and a heat equation evolve in two bounded domains with natural transmission conditions at a common interface these conditions couple in particular the heat unknown with the velocity of the wave solution this model may be viewed as a simplified version of linearized models which arise in fluid structure interaction first we show the strong asymptotic stability of solutions to this system then based on the construction of ray like solutions by means of geometric optics expansions and a careful analysis of the transfer of energy at the interface we show the lack of uniform decay in general domains further we obtain a polynomial decay result for smooth solutions of the system under a suitable geometric assumption which guarantees that the heat domain envelopes the wave domain finally in the absence of geometric conditions we show a logarithmic decay result for the same system but with simplified transmission conditions at the interface we also analyze the difficulty there is to extend this result to the more natural transmission conditions

a translation invariant wavelet representation algorithm with applications we address the time varying problem of wavelet transforms and a new translation invariant wavelet representation algorithm is proposed using the algorithm introduced by beylkin see siam j numer anal vol 29 p 1716 1740 1992 we compute the wavelet transform for all the circular time shifts of a length n signal in o n log n operations the wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function we apply the translation invariant representation algorithm to a geoacoustic data compression application the results show that the new algorithm can reduce the distortion the squared error in our case substantially if the input signals are transients that are sensitive to time shifts

attainable subspaces and the bang bang property of time optimal controls for heat equations in this paper we study two subjects on internally controlled heat equations with time varying potentials the attainable subspaces and the bang bang property for some time optimal control problems we present some equivalent characterizations on the attainable subspaces and provide a sufficient condition to ensure the bang bang property both the above mentioned characterizations and the sufficient condition are closely related to some function spaces consisting of some solutions to the adjoint equations it seems for us that the existing ways to derive the bang bang property for heat equations with time invariant potentials see for instance h o fattorini infinite dimensional linear control systems the time optimal and norm optimal problems elsevier amsterdam 2005 f gozzi and p loreti siam j control optim 37 1999 pp 1195 1221 v mizel and t seidman siam j control optim 35 1997 pp 1204 1216 and g wang siam j control optim 47 2008 pp 1701 1720 do not work

a new algorithm for multicomponent signals analysis based on synchrosqueezing with an application to signal sampling and denoising in this paper we address the problem of the retrieval of the components from a multicomponent signal using ideas from the synchrosqueezing framework the emphasis is on the wavelet choice and we propose a novel algorithm based first on the detection of components followed by their reconstruction simulations illustrate how the proposed procedure compares with the empirical mode decomposition and other related methods in terms of mode mixing we conclude the paper by studying the sensitivity of the proposed technique to sampling and an application to signal denoising

exploiting special structures in constructing a hierarchy of relaxations for 0 1 mixed integer problems a new hierarchy of relaxations is presented that provides a unifying framework for constructing a spectrum of continuous relaxations spanning from the linear programming relaxation to the convex hull representation for linear mixed integer 0 1 problems this hierarchy is an extension of the reformulation linearization technique rlt of sherali and adams 1990 1994a and is particularly designed to exploit special structures specifically inherent special structures are exploited by identifying particular classes of multiplicative factors that are applied to the original problem to reformulate it as an equivalent polynomial programming problem and subsequently this resulting problem is linearized to produce a tighter relaxation in a higher dimensional space this general framework permits us to generate an explicit hierarchical sequence of tighter relaxations leading up to the convex hull representation a similar hierarchy can be constructed for polynomial mixed integer 0 1 problems additional ideas for further strengthening rlt based constraints by using conditional logical implications as well as relationships with sequential lifting are also explored several examples are presented to demonstrate how underlying special structures including generalized and variable upper bounding covering partitioning and packing constraints as well as sparsity can be exploited within this framework for some types of structures low level relaxations are exhibited to recover the convex hull of integer feasible solutions

a class of multivariate denoising algorithms based on synchrosqueezing univariate thresholding techniques based on high resolution time frequency algorithms such as the synchrosqueezing transform have emerged as important tools in removing noise from real world data low cost multichannel sensor technology has highlighted the need for direct multivariate denoising and to this end we introduce a class of multivariate denoising techniques based on the synchrosqueezing transform this is achieved by partitioning the time frequency domain so as to identify a set of modulated oscillations common to the constituent data channels within multivariate data and by employing a modified universal threshold in order to remove noise components while retaining signal components of interest this principle is used to introduce both the wavelet and fourier based multivariate synchrosqueezing denoising algorithms the performance of the proposed multivariate denoising algorithm is illustrated on both synthetic and real world data

sharp observability estimates for heat equations the goal of this article is to derive new estimates for the cost of observability of heat equations we have developed a new method allowing one to show that when the corresponding wave equation is observable the heat equation is also observable this method allows one to describe the explicit dependence of the observability constant on the geometry of the problem the domain in which the heat process evolves and the observation subdomain we show that our estimate is sharp in some cases particularly in one space dimension and in the multi dimensional radially symmetric case our result extends those in fattorini and russell arch rational mech anal 43 272 292 1971 to the multi dimensional setting and improves those available in the literature namely those by miller j differ equ 204 1 202 226 2004 siam j control optim 45 2 762 772 2006 atti accad naz lincei cl sci fis mat natur rend lincei 9 mat appl 17 4 351 366 2006 and tenenbaum and tucsnak j differ equ 243 1 70 100 2007 our approach is based on an explicit representation formula of some solutions of the wave equation in terms of those of the heat equation in contrast to the standard application of transmutation methods which uses a reverse representation of the heat solution in terms of the wave one we shall also explain how our approach applies and yields some new estimates on the cost of observability in the particular case of the unit square observed from one side we will also comment on the applications of our techniques to controllability properties of heat type equations