Connectivity of inhomogeneous random graphs

We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a separable metric space, and let their indices form the vertex set of a graph. An edge (i,j) is added with probability min(1, \K(X_i,X_j) log n/n), where \K \ge 0 is a fixed kernel. We show that, under reasonably weak assumptions, the connectivity threshold of the model can be determined.Comment: 13 pages. To appear in Random Structures and Algorithm

Upstream open loop control of the recirculation area downstream of a backward-facing step

The flow downstream a backward-facing step is controlled using a pulsed jet placed upstream of the step edge. Experimental velocity fields are computed and used to the recirculation area quantify. The effects of jet amplitude, frequency and duty cycle on this recirculation area are investigated for two Reynolds numbers (Re=2070 and Re=2900). The results of this experimental study demonstrate that upstream actuation can be as efficient as actuation at the step edge when exciting the shear layer at its natural frequency. Moreover it is shown that it is possible to minimize both jet amplitude and duty cycle and still achieve optimal efficiency. With minimal amplitude and a duty-cycle as low as 10\% the recirculation area is nearly canceled

Temperley-Lieb, Brauer and Racah algebras and other centralizers of su(2)

In the spirit of the Schur-Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible representations of su(2). As a first step we show that the Racah algebra always surjects onto the centralizer. We then offer a conjecture regarding the description of the kernel of the map, which depends on the irreducible representations. If true, this conjecture would provide a presentation of the centralizer as a quotient of the Racah algebra. We prove this conjecture in several cases. In particular, while doing so, we explicitly obtain the Temperley-Lieb algebra, the Brauer algebra and the one-boundary Temperley-Lieb algebra as quotients of the Racah algebra

Regularized Optimal Transport and the Rot Mover's Distance

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed regularization based on the Boltzmann-Shannon entropy related to the Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We call the regularized optimal transport distance the rot mover's distance in reference to the classical earth mover's distance. We develop two generic schemes that we respectively call the alternate scaling algorithm and the non-negative alternate scaling algorithm, to compute efficiently the regularized optimal plans depending on whether the domain of the regularizer lies within the non-negative orthant or not. These schemes are based on Dykstra's algorithm with alternate Bregman projections, and further exploit the Newton-Raphson method when applied to separable divergences. We enhance the separable case with a sparse extension to deal with high data dimensions. We also instantiate our proposed framework and discuss the inherent specificities for well-known regularizers and statistical divergences in the machine learning and information geometry communities. Finally, we demonstrate the merits of our methods with experiments using synthetic data to illustrate the effect of different regularizers and penalties on the solutions, as well as real-world data for a pattern recognition application to audio scene classification