We present a method for bounding, and in some cases computing, the spectral gap for systems of many particles evolving under the influence a random collision mechanism. In particular, the method yields the exact spectral gap in a model due to Mark Kac of energy conserving collisions with one dimensional velocities. It is also sufficiently robust to provide qualitatively sharp bounds also in the...

We report a novel hyperspectral optical sensor capable of providing image information with four degrees of freedom (4D), i.e. volumetric spatial information and spectral information simultaneously, in real time. The imaging principle is based on the diffraction properties of volume holographic optical elements designed as spatial-spectral filters. The 4D imager can be configured to image object...

A volume hologram has two degenerate Bragg-phase-matching dimensions and provides the capability of volume holographic imaging. We demonstrate two volume holographic imaging architectures and investigate their imaging resolution, aberration, and sensitivity. The first architecture uses the hologram directly as an objective imaging element where strong aberration is observed and confirmed by sim...

In this paper we study the relationship between a very classical algebraic object associated to a filtration of topological spaces, namely a spectral sequence introduced by Leray in the 1940’s, and a more recently invented object that has found many applications – namely, its persistent homology groups. We show the existence of a long exact sequence of groups linking these two objects and using...

We consider an alignment algorithm for reconstructing global coordinates of a given data set from coordinates constructed for data points in small local neighborhoods through computing a spectral subspace of an alignment matrix. We show that, under certain conditions, the null space of the alignment matrix recovers global coordinates even when local point sets have different dimensions. This re...

We discuss how compactified extra dimensions may have potentially observable effects which grow as the compactification scale decreases. This arises because of lightcone fluctuations in the uncompactified dimensions which can result in the broadening of the spectral lines from distant sources. We analyze this effect in a five dimensional model, and argue that data from gamma ray burst sources r...

At high temperature the infrared modes of a weakly coupled quantum field theory can be treated nonperturbatively in real time using the classical field approximation. We use this to introduce a nonperturbative approach to the calculation of finite-temperature spectral functions, employing the classical KMS condition in real time. The method is illustrated for the one-particle spectral function ...

The aim of sound morphing is to obtain a sound that falls perceptually between two (or more) sounds. Ideally, we want to morph perceptually relevant features of sounds and be able to independently manipulate them. In this work we present a method to obtain perceptually intermediate spectral envelopes guided by highlevel spectral shape descriptors and a technique that employs evolutionary comput...

We study the direct and inverse spectral problems for semiclassical operators of the form S = S0 + ~V , where S0 = 12 ( −~∆Rn + |x| ) is the harmonic oscillator and V : R → R is a tempered smooth function. We show that the spectrum of S forms eigenvalue clusters as ~ tends to zero, and compute the first two associated “band invariants”. We derive several inverse spectral results for V , under v...

The shallow water equations in Cartesian coordinates and two dimensions are solved on the Connection Machine 2 (CM-2) using both the spectral and finite difference methods. A description of these implementations is presented together with a brief discussion of the CM-2 as it relates to these specific computations. The finite difference code was written both in C* and *LISP and the spectral code...