Asymptotic Consensus Without Self-Confidence

This paper studies asymptotic consensus in systems in which agents do not necessarily have self-confidence, i.e., may disregard their own value during execution of the update rule. We show that the prevalent hypothesis of self-confidence in many convergence results can be replaced by the existence of aperiodic cores. These are stable aperiodic subgraphs, which allow to virtually store information about an agent's value distributedly in the network. Our results are applicable to systems with message delays and memory loss.Comment: 13 page

Statistical Inference using the Morse-Smale Complex

The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare multivariate functions. In this paper, we present some statistical results on estimating Morse-Smale complexes. This allows us to derive new results for two existing methods: mode clustering and Morse-Smale regression. We also develop two new methods based on the Morse-Smale complex: a visualization technique for multivariate functions and a two-sample, multivariate hypothesis test.Comment: 45 pages, 13 figures. Accepted to Electronic Journal of Statistic

Feature Selection For High-Dimensional Clustering

We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to the selected features. The output of the method consists of a list of relevant features, and cluster assignments. We provide explicit bounds on the error rate of the resulting clustering. In addition, we provide the first error bounds on mode based clustering.Comment: 11 pages, 2 figure

L^{2}-restriction bounds for eigenfunctions along curves in the quantum completely integrable case

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $\int_{\gamma} |\phi_{j}^{\hbar}|^2 ds = {\mathcal O}(|\log \hbar|)$ for generic curves $\gamma$ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov are always attained for certain exceptional subsequences of eigenfunctions.Comment: Correct some typos and added some more detail in section

Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms

We describe a global optimization technique using `basin-hopping' in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features which recent work suggests must be present in an energy landscape for efficient relaxation to the global minimum. The transformation associates any point in configuration space with the local minimum obtained by a geometry optimization started from that point, effectively removing transition state regions from the problem. However, unlike other methods based upon hypersurface deformation, this transformation does not change the global minimum. The lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.Comment: 8 pages, 3 figures, revte

On Lennard-Jones type potentials and hard-core potentials with an attractive tail

We revisit an old tree graph formula, namely the Brydges-Federbush tree identity, and use it to get new bounds for the convergence radius of the Mayer series for gases of continuous particles interacting via non absolutely summable pair potentials with an attractive tail including Lennard-Jones type pair potentials