autour de la conjecture de l markus sur les varietes affines for any subgroupg of n we introduce some integer discg n called thediscompacity ofg this number measures to what extent the closure ofg is not compact the markus conjecture says that a compact affinely flat unimodular manifold is complete our main result called the discompact theorem is that this conjecture is true under the assumption that the linear holonomy i e the parallel transport has discompacity 1 because discso n 1 1 1 this ensures that a compact flat lorentz manifoldm is geodesically complete hence by a previous result of w goldman and y kamishima gk such am is up to finite covering a solvmanifold this achieves the proof of a bieberbach s theorem for compact lorentz flat manifolds

a combined wigner ville and maximum entropy method for high resolution time frequency analysis of seismic data abstractthe variation of frequency content of a seismic trace with time carries information about the properties of the subsurface reflectivity sequence as a result analysis of the data in terms of the local frequency content can provide a worthwhile addition to the standard procedures that are used in seismic processing and seismostratigraphic interpretation the theory of quadratic time frequency tf representations such as the wigner ville distribution wvd provides a solid foundation for local frequency analysis of seismic data and seismic attribute extraction however because of its quadratic nature the wvd processes cross terms which can limit the readability of the decomposition to overcome this problem we have used the key idea of the maximum entropy method of burg to compute a prediction error operator associated with the power spectrum of a given signal the operator was then used to extend the kernel of wigner ville of the signal given by the elements of its covariance matrix the

compact lorentz manifolds with local symmetry we prove a structure theorem for compact aspherical lorentz manifolds with abundant local symmetry if m is a compact aspherical real analytic complete lorentz manifold such that the isometry group of the universal cover has semisimple identity component then the local isometry orbits in m are roughly fibers of a fiber bundle a corollary is that if m has an open dense locally homogeneous subset then m is locally homogeneous acknowledgements i thank my dissertation advisor benson farb for his guidance and encouragement i also thank abdelghani zeghib with whom i had helpful conversations while working on this project in loving memory of laura sue jung kang

site bond percolation problems we study a percolation process in which both sites and bonds are randomly blocked independent of each other in the bethe lattice the exact solution for the percolation threshold is found to be a hyperbola in thex p plane wherex andp are the respective probabilities of each site and bond being unblocked percolation threshold for a square and a simple cubic lattice is obtained by computer simulation we also present a result obtained by a real space renormalization group technique for the square lattice

towards a genuinely polynomial algorithm for linear programming a linear programming algorithm is called genuinely polynomial if it requires no more than p m n arithmetic operations to solve problems of order m times n where p is a polynomial it is not known whether such an algorithm exists we present a genuinely polynomial algorithm for the simpler problem of solving linear inequalities with at most two variables per inequality the number of operations required is o mn 3 log text m the technique used was developed in a previous paper where a novel binary search idea was introduced

three dimensional metrics with a spherical homogeneous model one finds the moduli spaces of isocurved homogeneous metrics on s3 then one determines the germs of three dimensional analytic metrics with a spherical homogeneous model

an improved design of high resolution quadratic time frequency distributions for the analysis of nonstationary multicomponent signals using directional compact kernels this paper presents a new advanced methodology for designing high resolution time frequency distributions tfds of multicomponent nonstationary signals that can be approximated using piece wise linear frequency modulated pw lfm signals most previous kernel design methods assumed that signals auto terms are mostly centered around the origin of the nu tau ambiguity domain while signal cross terms are mostly away from the origin this study uses a multicomponent test signal for which each component is modeled as a pw lfm signal it finds that the above assumption is a very rough approximation of the location of the auto terms energy and cross terms energy in the ambiguity domain and it is only valid for signals that are well separated in the t f domain a refined investigation led to improved specifications for separating cross terms from auto terms in the nu tau ambiguity domain the resulting approach first represents the signal in the ambiguity domain and then applies a multidirectional signal dependent compact kernel that accounts for the direction of the auto terms energy the resulting multidirectional distribution mdd approach proves to be more effective than classical methods like extended modified b distribution s method or compact kernel distribution in terms of auto terms resolution and cross terms suppression results on simulated and real data validate the improved performance of the mdd showing up to 8 gain as compared to more standard state of the art tfds

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

seismic sequence analysis and attribute extraction using quadratic time frequency representations the variation of frequency content of a seismic trace with time carries information about the properties of the subsurface reflectivity sequence as a result analysis of the data in terms of the local frequency content can provide a worthwhile addition to the standard procedures that are used in seismo stratigraphic interpretation the theory of quadratic time frequency representations provides a solid foundation for local frequency analysis of seismic data and seismic attribute extraction two applications of the quadratic time frequency representations are demonstrated seismic sequence analysis and seismic attribute extraction the joint time frequency representation of a seismic reflection pattern is often much more easily interpreted in terms of subsurface stratification than the time or frequency domain description alone we show how the time frequency representation can be used to delineate seismic sequences on the basis of the time frequency characteristics of the signal there exists a close rel

use of cross time frequency estimators for structural identification in non stationary conditions and under unknown excitation abstract this paper introduces a new structural identification method for use in non stationary conditions which applies to structures and systems in normal serviceability conditions under unknown excitation the proposed method uses auto and cross time frequency transforms of accelerometer signals recorded from the structure to identify the vibration modes the transforms considered are those in cohen s class which in addition to possessing valuable properties for the analysis of mechanical signals lend themselves to a clear interpretation in energy terms this method enables modal parameters to be reliably estimated and an earlier technique proposed by the authors which was based on modal filters to be improved it is further shown that the cross correlation based estimators are more effective than techniques based on auto transformations due to their noise filtering properties finally a method to refine the estimate of modal shapes which avoids autocorrelation is proposed the accuracy of the procedure was assessed by means of numerical simulations

a signal dependent time frequency representation fast algorithm for optimal kernel design a time frequency representation based on an optimal signal dependent kernel has been previously been proposed in an attempt to overcome one of the primary limitations of bilinear time frequency distributions that the best kernel and distribution depend on the signal to be analyzed the optimization formulation for the signal dependent kernel results in a linear program with a unique feature a tree structure that summarizes a set of constraints on the kernel the authors present a fast algorithm based on sorting to solve a special class of linear programs that includes the problem of interest for a kernel with q variables the running time of the algorithm is o q log q which is several orders of magnitude less than any other known method for solving this class of linear program this efficiency enables the computation of the signal dependent optimal kernel time frequency representation at a cost that is on the same order as a fixed kernel distribution an important property of the optimal kernel is that it takes on essentially only the values of 1 and 0

isometry groups of lorentz manifolds soit v une variete de lorentz a n dimensions si v g est compacte analytique reelle simplement convexe alors le groupe d isometrie is v g est compact

periodic geodesics and geometry of compact lorentzian manifolds with a killing vector field we study the geometry and the periodic geodesics of a compact lorentzian manifold that has a killing vector field which is timelike somewhere using a compactness argument for subgroups of the isometry group we prove the existence of one timelike non self intersecting periodic geodesic if the killing vector field is nowhere vanishing then there are at least two distinct periodic geodesics as a special case compact stationary manifolds have at least two periodic timelike geodesics we also discuss some properties of the topology of such manifolds in particular we show that a compact manifold m admits a lorentzian metric with a nowhere vanishing killing vector field which is timelike somewhere if and only if m admits a smooth circle action without fixed points

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

fast computation of the ambiguity function and the wigner distribution on arbitrary line segments by using the fractional fourier transformation of the time domain signals closed form expressions for the projections of their auto or cross ambiguity functions are derived based on a similar formulation for the projections of the auto and cross wigner distributions and the well known two dimensional 2 d fourier transformation relationship between the ambiguity and wigner domains closed form expressions are obtained for the slices of both the wigner distribution and the ambiguity function by using discretization of the obtained analytical expressions efficient algorithms are proposed to compute uniformly spaced samples of the wigner distribution and the ambiguity function located on arbitrary line segments with repeated use of the proposed algorithms samples in the wigner or ambiguity domains can be computed on non cartesian sampling grids such as polar grids

an adaptive optimal kernel time frequency representation time frequency representations with fixed windows or kernels figure prominently in many applications but perform well only for limited classes of signals representations with signal dependent kernels can overcome this limitation however while they often perform well most existing schemes are block oriented techniques unsuitable for on line implementation or for tracking signal components with characteristics that change with time the time frequency representation developed in the present paper based on a signal dependent radially gaussian kernel that adapts over time surmounts these difficulties the method employs a short time ambiguity function both for kernel optimization and as an intermediate step in computing constant time slices of the representation careful algorithm design provides reasonably efficient computation and allows on line implementation certain enhancements such as cone kernel constraints and approximate retention of marginals are easily incorporated with little additional computation while somewhat more expensive than fixed kernel representations this new technique often provides much better performance several examples illustrate its behavior on synthetic and real world signals

a centrosymmetric kernel decomposition for time frequency distribution computation time frequency distributions tfds are bilinear transforms of the signal and as such suffer from a high computational complexity previous work has shown that one can decompose any tfd in cohen s class into a weighted sum of spectrograms this is accomplished by decomposing the kernel of the distribution in terms of an orthogonal set of windows in this paper we introduce a mathematical framework for kernel decomposition such that the windows in the decomposition algorithm are not arbitrary and that the resulting decomposition provides a fast algorithm to compute tfds using the centrosymmetric structure of the time frequency kernels we introduce a decomposition algorithm such that any tfd associated with a bounded kernel can be written as a weighted sum of cross spectrograms the decomposition for several different discrete time kernels are given and the performance of the approximation algorithm is illustrated for different types of signals

tomography time frequency transform the paper shows that the fractional fourier transform frft of a signal is the radon transform of the time frequency distribution of the same signal therefore a time frequency distribution known as the tomography time frequency transform ttft is defined as the inverse radon transform of the frft of the signal because the computation of the ttft does not explicitly require any window or kernel function high resolutions in both the frequency and time domains can be achieved when the signal contains multiple components the cross terms can be effectively removed by an adaptive filtering process that is applied on the frft rather than the final result therefore distortions made by the filtering process on the desired signal components can be minimized