Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: A computational discussion

We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs $\Gamma$-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam $\beta$-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (${\mathbf F}=m{\mathbf a}$). At higher energies we discuss partial agreement between time and ensemble averages.Comment: New title, revision of the text. EPJ latex, 4 figure

On Link Estimation in Dense RPL Deployments

The Internet of Things vision foresees billions of devices to connect the physical world to the digital world. Sensing applications such as structural health monitoring, surveillance or smart buildings employ multi-hop wireless networks with high density to attain sufficient area coverage. Such applications need networking stacks and routing protocols that can scale with network size and density while remaining energy-efficient and lightweight. To this end, the IETF RoLL working group has designed the IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL). This paper discusses the problems of link quality estimation and neighbor management policies when it comes to handling high densities. We implement and evaluate different neighbor management policies and link probing techniques in Contiki’s RPL implementation. We report on our experience with a 100-node testbed with average 40-degree density. We show the sensitivity of high density routing with respect to cache sizes and routing metric initialization. Finally, we devise guidelines for design and implementation of density-scalable routing protocols

Ultrafunctions and Applications

This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a field which contains infinite and infinitesimal numbers. Ultrafunctions have been introduced to provide generalized solutions to equations which do not have any solutions not even among the distributions. Some of these applications will be presented in the second part of this paper

Coupling and Applications

This paper presents a self-contained account for coupling arguments and applications in the context of Markov processes. We first use coupling to describe the transport problem, which leads to the concepts of optimal coupling and probability distance (or transportation-cost), then introduce applications of coupling to the study of ergodicity, Liouville theorem, convergence rate, gradient estimate, and Harnack inequality for Markov processes.Comment: 16 page

Neural Network Applications

Artificial neural networks, also called neural networks, have been used successfully in many fields including engineering, science and business. This paper presents the implementation of several neural network simulators and their applications in character recognition and other engineering area