We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular Λ Cold Dark Matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of −0.8 or less – roughly the equivalent of using a Spherical Overdensity group finder for haloes. Each of the simulations contains thousands of voids. The distribut...

The 2-Opt heuristic is a very simple, easy-to-implement local search heuristic for the traveling salesman problem. While it usually provides good approximations to the optimal tour in experiments, its worst-case performance is poor. In an attempt to explain the approximation performance of 2-Opt, we analyze the smoothed approximation ratio of 2-Opt. We obtain a bound of O(log(1/σ)) for the smoo...

3 Signal Processing 4 3.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Spectrogram Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Multitaper Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 Visualizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Looking myopically at the larger features of the likelihood function, absent some fine detail, can theoretically improve maximum likelihood estimation. Such estimators are, in fact, used routinely, since numerical techniques for maximizing a computationally expensive likelihood function or for maximizing a Monte Carlo approximation to a likelihood function may be unable to investigate small sca...

In Continuous Speech Recognition (CSR) systems a Language Model (LM) is required to represent the syntactic constraints of the language. Then a smoothing technique needs to be applied to avoid null LM probabilities. Each smoothing technique leads to a different LM probability distribution. Test set perplexity is usually used to evaluate smoothing techniques but the relationship with acoustic mo...

We study the method of smoothed analysis for understanding the complexity of algorithms. We first discuss the need for defining an alternative to worst case complexity and discuss some alternatives considered in analysis of algorithms. We then discuss smoothed analysis, introduced by Spielman and Teng [22] and describe how one could do a smoothed analysis of an algorithm. There are a few design...

We propose a new complexity measure for movement of objects, the smoothed motion complexity. Many applications are based on algorithms dealing with moving objects, but usually data of moving objects is inherently noisy due to measurement errors. Smoothed motion complexity considers this imprecise information and uses smoothed analysis [13] to model noisy data. The input is object to slight rand...

We state a maximum principle for the gradient of the minima of integral functionals I (u)G Ω [ f (∇u)Cg(u)] dx, on ūCW 1,1 0 (Ω ), just assuming that I is strictly convex. We do not require that f, g be smooth, nor that they satisfy growth conditions. As an application, we prove a Lipschitz regularity result for constrained minima.

In arithmetic geometry, cohomology groups are not vector spaces as in classical algebraic geometry but rather euclidean lattices. As a consequence, to understand these groups we need to evaluate not only their rank, but also their successive minima, which are fundamental invariants in the geometry of numbers. The goal of this article is to perform this task for line bundles on projective curves...