The intent of this article is to study some special n-dimensional continua lying in products of n curves. (The paper may be viewed as a sequel to [K-KS 1]; majority of its content is an improved version of a portion of [K-K-S].) We show that if X is a locally connected, so-called, quasi n-manifold lying in a product of n curves then rankH(X) ≥ n. Moreover, if rankH(X) < 2n then X can be represe...

Felix Klein emphasized the intrinsic connection between symmetry groups and geometries in his Erlangen Program. Perhaps motivated by Klein, Gleason ([5]) posed a very general conjecture on topologizing symmetry groups that he regarded as fundamental for a general study of geometries. Gleason in fact proved his conjecture in a very special case. The purpose of this paper is to show that Gleason’...

We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than ε, agrees up to generation K with a regular μ-ary tree, where μ is the essential minimum of the offspring distribution and the random variable K is strongly concentrated near an explicit deterministic function growing like a multiple of log(1/ε). More precisely, we show that if μ ≥ 2 then with hi...

In 1977, Baillon and Haddad proved that if the gradient of a convex and continuously differentiable function is nonexpansive, then it is actually firmly nonexpansive. This result, which has become known as the Baillon-Haddad theorem, has found many applications in optimization and numerical functional analysis. In this note, we propose short alternative proofs of this result and strengthen its ...

This paper studies sparse density estimation via l1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a g...

This paper seeks to understand the factors that cause disputes at the World Trade Organization to move from the negotiation stage to the panel stage. We hypothesize that transfer payments between states are costly to arrange and that the lowest-cost transfers are those that relate directly to the issue in dispute. This implies that when the subject matter of the dispute has an all-or-nothing ch...

Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally homogeneous spaces later formed the context of Thurston’s 3-dimensional geometrization program. The basic problem is for a given topology Σ an...