This paper presents a new method for classifying surface data via spectral representations of shapes. Our approach benefits classification problems that involve data living on surfaces, such as in cortical parcellation. For instance, current methods for labeling cortical points into surface parcels often involve a slow mesh deformation toward pre-labeled atlases, requiring as much as 4 hours wi...

Least squares spectral combination is a well-known technique in physical geodesy. The established technique either suffers from the assumption of no correlations of errors between degrees or from a global optimisation of the variance or mean square error of the estimator. Today Earth gravitational models are available together with their full covariance matrices to rather high degrees, extra in...

The efficiency of simulation algorithms for max-stable processes relies on the choice of the spectral representation: different choices result in different sequences of finite approximations to the process. We propose a constructive approach yielding a normalized spectral representation that solves an optimization problem related to the efficiency of simulating max-stable processes. The simulat...

In this lecture, we discuss some spectral techniques and their applications. The goal of spectral techniques is to study and deduce the characteristics of a matrix by looking at its spectrum (i.e. eigenvalues of matrix). Although spectral methods can be applied to any problem instance with matrix representation, we will be focussing on graph theoretic problems in this lecture. Over the past two...

We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semiclassical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an oscillatory integral representation of the spe...

We present an approach to de Branges’s theory of Hilbert spaces of entire functions that emphasizes the connections to the spectral theory of differential operators. The theory is used to discuss the spectral representation of one-dimensional Schrödinger operators and to solve the inverse spectral problem.

0 0 t t t t t = + ()cos () + () sin () 1. Spectral analysis Y , Y Y Y t. Y Y Y Y ω ωt dω ω ωt dω Y. Our focus thus far has been on considering how the timeseries reacts to a sequence of innovations and the implications of the relationship between and for the covariance (or correlation) between and at distinct dates and We speak of this as analysing the properties of in the time domain. We might...

Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs). We employ spectral representations to introduce a number of innovations to C...

A spectral parameter power series (SPPS) representation for regular solutions of singular Bessel type Sturm-Liouville equations with complex coefficients is obtained as well as an SPPS representation for the (entire) characteristic function of the corresponding spectral problem on a finite interval. It is proved that the set of zeros of the characteristic function coincides with the set of all ...