Abstract: Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is necessarily absolutely continuous with respect to the Lebesgue measure and (ii) the convergence automatically takes place in the total variation topology...

GP studied preferences over menus (sets) of alternatives. This implicitly means that the decision maker chooses a menu and then selects an alternative from the menu. Consider a compact metric space Z of prizes. Let ∆ be the set of all Borel probability measures over Z. An element in ∆ represents an alternative for (implicit) choice. Assume that ∆ is endowed with the topology of weak convergence...

The protein universe corresponds to the set of all proteins found in all organisms. A way to explore it is by taking into account the domain content of the proteins. However, some part of sequences and many entire sequences remain un-annotated despite a converging number of domain families. The un-annotated part of the protein universe is referred to as the dark proteome and remains poorly char...

One of the most exciting developments in the theory of distributed computing in recent years has been the application of powerful concepts from topology to prove results about computability in resilient distributed systems. Topology is a branch of mathematics that deals with connectivity and convergence of certain types of objects. As it turns out, the higher dimensional connectivity properties...

Let {Fn} be a sequence of random variables belonging to a nite sum of Wiener chaoses. Assume further that it converges in distribution towards F∞ satisfying Var(F∞) > 0. Our rst result is a sequential version of a theorem by Shigekawa [25]. More precisely, we prove, without additional assumptions, that the sequence {Fn} actually converges in total variation and that the law of F∞ is absolutely ...

The objective of this study was to obtain a quantitative assessment of the monophyly of morning glory taxa, specifically the genus Ipomoea and the tribe Argyreieae. Previous systematic studies of morning glories intimated the paraphyly of Ipomoea by suggesting that the genera within the tribe Argyreieae are derived from within Ipomoea; however, no quantitative estimates of statistical support w...

The space of dynamically marked rational maps can be identified with a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In this paper we describe a topology on the quotient of this space under the natural action of its group of isomorphisms. This topology is proved to be consistent with this notion of converge...

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

We prove that the additive group (E∗, τk(E)) of an L∞-Banach space E, with the topology τk(E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving that the topological group (E∗, τk(E)) is uniformly homeomorphic to a subset of ` κ 2 for some κ. As an immediat...

The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of submanifolds of configuration space is investigated, corroborating the hypothesis that, in general, a change of the topology within this family is a necessa...