Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The proposed methods incorporate prior information about the statistical dependency among observations, while at the same time processing data in real-time and in a fully decentralized manner. A detailed mean-square analysis is carried out in order to prove stability and evaluate the steady-state performance of the proposed strategies. Finally, we also illustrate how the proposed techniques can be easily extended in order to incorporate thresholding operators for sparsity recovery applications. Numerical results show the potential advantages of using such techniques for distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin note: text overlap with arXiv:1206.309

A unique theory of all forces

In discussing the construction of a consistent theory of quantum gravity unified with the gauge interactions we are naturally led to a string theory. We review its properties and the five consistent supersymmetric string theories in ten dimensions. We finally discuss the evidence that these theories are actually special limits of a unique 11-dimensional theory, called M-theory, and a recent conjecture for its explicit formulation as a supersymmetric Matrix theory.Comment: 11 pages, Latex. Talk given at the Conference `Beyond the standard model', V, Balholm, Norway, May 199

A new lattice Boltzmann model for interface reactions between immiscible fluids

In this paper, we describe a lattice Boltzmann model to simulate chemical reactions taking place at the interface between two immiscible fluids. The phase-field approach is used to identify the interface and its orientation, the concentration of reactant at the interface is then calculated iteratively to impose the correct reactive flux condition. The main advantages of the model is that interfaces are considered part of the bulk dynamics with the corrective reactive flux introduced as a source/sink term in the collision step, and, as a consequence, the model’s implementation and performance is independent of the interface geometry and orientation. Results obtained with the proposed model are compared to analytical solution for three different benchmark tests (stationary flat boundary, moving flat boundary and dissolving droplet). We find an excellent agreement between analytical and numerical solutions in all cases. Finally, we present a simulation coupling the Shan Chen multiphase model and the interface reactive model to simulate the dissolution of a collection of immiscible droplets with different sizes rising by buoyancy in a stagnant fluid

Analysis, Simulation and Control of a New Measles Epidemic Model

In this paper the problem of modeling and controlling the measles epidemic spread is faced. A new model is proposed and analysed; besides the categories usually considered in measles modeling, the susceptible, the exposed, the infected, the removed and, less frequently, the quarantine individuals, two new categories are herein introduced: the immunosuppressed subjects, that can not be vaccinated, and the patients with an additional complication, not risky by itself but dangerous if caught togeter with the measles. These two novelties are taken into account in designing and scheduling suitably control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. An analysis of the model is developed and the optimal control strategies are compared with other not optimized actions. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society when an epidemic spread occurs, such as the quarantine intervention

Distributed Estimation and Control of Algebraic Connectivity over Random Graphs

In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power iteration method that allows each node to estimate and track the algebraic connectivity of the underlying expected graph. Using results from stochastic approximation theory, we prove that the proposed method converges almost surely (a.s.) to the desired value of connectivity even in the presence of imperfect communication scenarios. The estimation strategy is then used as a basic tool to adapt the power transmitted by each node of a wireless network, in order to maximize the network connectivity in the presence of realistic Medium Access Control (MAC) protocols or simply to drive the connectivity toward a desired target value. Numerical results corroborate our theoretical findings, thus illustrating the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures.Comment: To appear in IEEE Transactions on Signal Processin

The Physics of the θ\theta-angle for Composite Extensions of the Standard Model

We analyse the $\theta$-angle physics associated to extensions of the standard model of particle interactions featuring new strongly coupled sectors. We start by providing a pedagogical review of the $\theta$-angle physics for Quantum Chromodynamics (QCD) including also the axion properties. We then move to analyse composite extensions of the standard model elucidating the interplay between the new $\theta$-angle with the QCD one. We consider first QCD-like dynamics and then generalise it to consider several kinds of new strongly coupled gauge theories with fermions transforming according to different matter representations. Our analysis is of immediate use for different models of composite Higgs dynamics, composite dark matter and inflation.Comment: ReVTeX, 30 page

State Feedback Optimal Control with Singular Solution for a Class of Nonlinear Dynamics

The paper studies the problem of determining the optimal control when singular arcs are present in the solution. In the general classical approach the expressions obtained depend on the state and the costate variables at the same time, so requiring a forward-backward integration for the computation of the control. In this paper, sufficient conditions on the dynamics structure are provided and discussed in order to have both the control and the switching function depending on the state only, so simplifying the computation avoiding the necessity of the backward integration. The approach has been validated on a classical SIR epidemic model