The concavity of R\`enyi entropy power

We associate to the p-th R\'enyi entropy a definition of entropy power, which is the natural extension of Shannon's entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in $R^n$. We show that the R\'enyi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behaviour in correspondence to the Barenblatt source-type solutions. We then shown that the p-th R\'enyi entropy power of a probability density which solves the nonlinear diffusion of order p, is a concave function of time. This result extends Costa's concavity inequality for Shannon's entropy power to R\'enyi entropies

A parallel genetic algorithm for the Steiner Problem in Networks

This paper presents a parallel genetic algorithm to the Steiner Problem in Networks. Several previous papers have proposed the adoption of GAs and others metaheuristics to solve the SPN demonstrating the validity of their approaches. This work differs from them for two main reasons: the dimension and the characteristics of the networks adopted in the experiments and the aim from which it has been originated. The reason that aimed this work was namely to build a comparison term for validating deterministic and computationally inexpensive algorithms which can be used in practical engineering applications, such as the multicast transmission in the Internet. On the other hand, the large dimensions of our sample networks require the adoption of a parallel implementation of the Steiner GA, which is able to deal with such large problem instances

Active networks: an evolution of the internet

Active Networks can be seen as an evolution of the classical model of packet-switched networks. The traditional and ”passive” network model is based on a static definition of the network node behaviour. Active Networks propose an “active” model where the intermediate nodes (switches and routers) can load and execute user code contained in the data units (packets). Active Networks are a programmable network model, where bandwidth and computation are both considered shared network resources. This approach opens up new interesting research fields. This paper gives a short introduction of Active Networks, discusses the advantages they introduce and presents the research advances in this field

Complete off-shell effects for top-antitop + jet production with leptonic decays at the LHC

A brief summary of the calculation of the NLO QCD corrections to the process pp -> e+ ve mu- v_mu bb~ j + X is reported. This provides a complete description of the process of t-tbar + jet production with leptonic decays beyond the narrow-width approximation. Off-shell effects for top quarks and W boson decays are fully taken into account, namely all resonant and non-resonant contributions are included in the fixed-order calculation. Selected results for total and differential cross sections are shown for the case of the LHC Run I at the energy of 8 TeV.Comment: 8 pages, 4 figures. To appear in the Proceedings of the 24th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2016), 11-15 April 2016, DESY Hamburg, German

Virtual Element Methods for hyperbolic problems on polygonal meshes

In the present paper we develop the Virtual Element Method for hyperbolic problems on polygonal meshes, considering the linear wave equations as our model problem. After presenting the semi-discrete scheme, we derive the convergence estimates in H^1 semi-norm and L^2 norm. Moreover we develop a theoretical analysis on the stability for the fully discrete problem by comparing the Newmark method and the Bathe method. Finally we show the practical behaviour of the proposed method through a large array of numerical tests

Accurate prediction of electroweak observables and impact on the Higgs mass bound

I discuss the importance of the O(g^4 m_t^2/\mw^2) corrections to the effective electroweak angle and Mw in the indirect determination of the Higgs mass. I emphasize the r\^ole of a very precise Mw measurement on the Mh estimate.Comment: 9 pages, LaTex, uses appb.sty. Talk presented at the Zeuthen Workshop on Elementary Particle Theory "Loops and Legs in Gauge Theories" Rheinsberg, Germany, April 19-24, 199

The Poincare'-Nekhoroshev map

We study a generalization of the familiar Poincar\'e map, first implicitely introduced by N.N. Nekhoroshev in his study of persistence of invariant tori in hamiltonian systems, and discuss some of its properties and applications. In particular, we apply it to study persistence and bifurcation of invariant tori.Comment: arxiv version is already officia