We study fine properties of Lévy trees that are random compact metric spaces introduced by Le Gall and Le Jan in 1998 as the genealogy of continuous state branching processes. Lévy trees are the scaling limits of Galton-Watson trees and they generalize Aldous’s continuum random tree which corresponds to the Brownian case. In this paper we prove that Lévy trees have always an exact packing measu...

We prove that if a metric probability space with a usual concentration property embeds into a Banach space X, then X has a proportional Euclidean subspace. In particular, this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings spaces with concentration properties (i.e. uniformly convex spaces) into l ∞, thus providing an ”isomorphic” extension to ...

The accuracy of the recently developed correlation energy functional of Wilson and Levy is investigated. The correlation contributions to first ionization potentials of first-row atoms, hydrides and dimers, as well as the contributions to the dissociation energies of neutral and ionic hydrides and dimers are calculated and compared with experimental values. It is found that the functional devel...

In Baumann (2005) I argued that reflections on a variation of the Monty Hall problem throws a very general sceptical light on the idea of single-case probabilities. Levy (2007) puts forward some interesting objections which I answer here. The notion of probability is so important that we cannot do without it, neither in science nor in everyday life nor in philosophy. At the same time there is m...

– Let X be a real Lévy process and let X↑ be the process conditioned to stay positive. We assume that 0 is regular for (−∞,0) and (0,+∞) with respect to X. Using elementary excursion theory arguments, we provide a simple probabilistic description of the reversed paths of X and X↑ at their first hitting time of (x,+∞) and last passage time of (−∞, x], on a fixed time interval [0, t], for a posit...

We study the diameter of Lévy trees that are random compact metric spaces obtained as the scaling limits of Galton-Watson trees. Lévy trees have been introduced by Le Gall and Le Jan (1998) and they generalise Aldous’ Continuum Random Tree (1991) that corresponds to the Brownian case. We first characterize the law of the diameter of Lévy trees and we prove that it is realized by a unique pair o...

Compared to the well-studied topic of human mobility in real geographic space, very few studies focus on human mobility in virtual space, such as interests, knowledge, ideas, and so forth. However, it relates to the issues of management of public opinions, knowledge diffusion, and innovation. In this paper, we assume that the interests of a group of online users can span a Euclidean space which...

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of i...

David Levy and Sandra Peart mean to revise the history of nineteenth-century British political economy. And more. In their latest, fascinating installment, The Vanity of the Philosopher, Peart and Levy argue that the transition from classical to post-classical economics is best understood as a sea change in the way political economists regarded human nature. What happened? Well, in the beginnin...

Abstract This research proposes a hybrid improved marine predator algorithm (IMPA) and deep gated recurrent unit (DGRU) model for profit prediction in financial accounting information systems (FAIS). The study addresses the challenge of real-time processing performance caused by increasing complexity networks due to growing size datasets. To enable effective comparison, new dataset is created u...