Statics and dynamics of selfish interactions in distributed service systems

We study a class of games which model the competition among agents to access some service provided by distributed service units and which exhibit congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones.Comment: 30 pages, 10 figure

Probing the Majorana nature of the neutrino with neutrinoless double beta decay

Neutrinoless double beta decay (NDBD) is the only experiment that could probe the Majorana nature of the neutrino. Here we study the theoretical implications of NDBD for models yielding tri-bimaximal lepton mixing like A4 and S4.Comment: Talk given at TAUP09, July 1-5, 2009 (Roma).The proceeding will be published in Journal of Physics, Conference Series (Editors: E. Coccia, L. Pandola, N. Fornengo, R. Aloisio

Light Higgs bosons from a strongly interacting Higgs sector

The mass and the decay width of a Higgs boson in the minimal standard model are evaluated by a variational method in the limit of strong self-coupling interaction. The non-perturbative technique provides an interpolation scheme between strong-coupling regime and weak-coupling limit where the standard perturbative results are recovered. In the strong-coupling limit the physical mass and the decay width of the Higgs boson are found to be very small as a consequence of mass renormalization. Thus it is argued that the eventual detection of a light Higgs boson would not rule out the existence of a strongly interacting Higgs sector.Comment: 2 figure

The Pion Structure Function in a Constituent Model

Using the recent relatively precise experimental results on the pion structure function, obtained from Drell--Yan processes, we quantitatively test an old model where the structure function of any hadron is determined by that of its constituent quarks. In this model the pion structure function can be predicted from the known nucleon structure function. We find that the data support the model, at least as a good first approximation.Comment: 9 pages, 3 figure

Optimizing spread dynamics on graphs by message passing

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the last decades, many efforts have been devoted to understand the typical behaviour of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception of models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem

Electroweak Precision Tests: A Concise Review

1. Introduction 2. Status of the Data 3. Precision Electroweak Data and the Standard Model 4. A More General Analysis of Electroweak Data 4.1 Basic Definitions and Results 4.2 Experimental Determination of the Epsilon Variables 4.3 Comparing the Data with the Minimal Supersymmetric Standard Model 5. Theoretical Limits on the Higgs Mass 6. ConclusionComment: Submitted to Int. Journal of Modern Physics

Containing epidemic outbreaks by message-passing techniques

The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected infection under a given epidemic model. Although computing the expected infection is a hard computational problem, simple and efficient mean-field approximations have been put forward in the literature in recent years. The optimization problem can be recast into a constrained one in which the constraints enforce local mean-field equations describing the average stationary state of the epidemic process. For a wide class of epidemic models, including the susceptible-infected-removed and the susceptible-infected-susceptible models, we define a message-passing approach to network immunization that allows us to study the statistical properties of epidemic outbreaks in the presence of immunized nodes as well as to find (nearly) optimal immunization sets for a given choice of parameters and costs. The algorithm scales linearly with the size of the graph and it can be made efficient even on large networks. We compare its performance with topologically based heuristics, greedy methods, and simulated annealing

Relationship between clustering and algorithmic phase transitions in the random k-XORSAT model and its NP-complete extensions

We study the performances of stochastic heuristic search algorithms on Uniquely Extendible Constraint Satisfaction Problems with random inputs. We show that, for any heuristic preserving the Poissonian nature of the underlying instance, the (heuristic-dependent) largest ratio $\alpha_a$ of constraints per variables for which a search algorithm is likely to find solutions is smaller than the critical ratio $\alpha_d$ above which solutions are clustered and highly correlated. In addition we show that the clustering ratio can be reached when the number k of variables per constraints goes to infinity by the so-called Generalized Unit Clause heuristic.Comment: 15 pages, 4 figures, Proceedings of the International Workshop on Statistical-Mechanical Informatics, September 16-19, 2007, Kyoto, Japan; some imprecisions in the previous version have been correcte

Ultraviolet Completion of Flavour Models

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. We discuss the phenomenological implications of the explicit completions, such as lepton flavour violating contributions that arise through the exchange of messenger fields.Comment: 18 pages, 8 figure

Indication for Light Sneutrinos and Gauginos from Precision Electroweak Data

The present Standard Model fit of precision data has a low confidence level, and is characterized by a few inconsistencies. We look for supersymmetric effects that could improve the agreement among the electroweak precision measurements and with the direct lower bound on the Higgs mass. We find that this is the case particularly if the 3.6 sigma discrepancy between sin^2 theta_eff from leptonic and hadronic asymmetries is finally settled more on the side of the leptonic ones. After the inclusion of all experimental constraints, our analysis selects light sneutrinos, with masses in the range 55-80 GeV, and charged sleptons with masses just above their experimental limit, possibly with additional effects from light gauginos. The phenomenological implications of this scenario are discussed.Comment: 17 pages LaTex, 9 figures, uses epsfi