Distributed estimation from relative measurements of heterogeneous and uncertain quality

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes connected by an edge. In order to model heterogeneity and uncertainty of the measurements, we assume them to be affected by additive noise distributed according to a Gaussian mixture. In this original setup, we formulate the problem of computing the Maximum-Likelihood (ML) estimates and we design two novel algorithms, based on Least Squares regression and Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and performs the estimation from relative measurements, the soft classification of the measurements, and the estimation of the noise parameters. The second algorithm (Distributed LS-EM) is distributed and performs estimation and soft classification of the measurements, but requires the knowledge of the noise parameters. We provide rigorous proofs of convergence of both algorithms and we present numerical experiments to evaluate and compare their performance with classical solutions. The experiments show the robustness of the proposed methods against different kinds of noise and, for the Distributed LS-EM, against errors in the knowledge of noise parameters.Comment: Submitted to IEEE transaction

Background Estimation in a Gravitational Wave Experiment

The problem to estimate the background due to accidental coincidences in the search for coincidences in gravitational wave experiments is discussed. The use of delayed coincidences obtained by orderly shifting the event times of one of the two detectors is shown to be the most correctComment: Latex file. 6 pages, 3 figures. Submitted to the proceeding of the 3 GWDAW workshop (Rome, dic 1999) (International journal of Modern physics D

Theory of dressed states in quantum optics

The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both Dyson series and its dual, through renormalization group methods to remove secular terms from the perturbation series, give the opportunity of a full study of the solution of the Schr\"{o}dinger equation in different ranges of the parameters of the given hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to exploit the method at the best, a study is accomplished of the well-known Jaynes-Cummings model in the rotating wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is needed to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.Comment: Revtex, 17 page

Contemporaneous broad-band photometry and Hα\alpha observations of T Tauri stars

The study of contemporaneous variations of the continuum flux and emission lines is of great importance to understand the different astrophysical processes at work in T Tauri stars. In this paper we present the results of a simultaneous $BVRI$ and H$\alpha$ photometric monitoring, contemporaneous to medium-resolution spectroscopy of six T Tauri stars in the Taurus-Auriga star forming region. We have characterized the H$\alpha$ photometric system using synthetic templates and the contemporaneous spectra of the targets. We show that we can achieve a precision corresponding to 2$-$3 \AA\ in the H$\alpha$ equivalent width, in typical observing conditions. The spectral analysis has allowed us to determine the basic stellar parameters and the values of quantities related to the accretion. In particular, we have measured a significant veiling only for the three targets with the strongest H$\alpha$ emission (T Tau, FM Tau, and DG Tau). The broad-band photometric variations are found to be in the range 0.05$-$0.70 mag and are often paired to variations in the H$\alpha$ intensity, which becomes stronger when the stellar continuum is weaker. In addition, we have mostly observed a redder $V-I$ and a bluer $B-V$ color as the stars become fainter. For most of the targets, the timescales of these variations seem to be longer than the rotation period. One exception is T Tau, for which the broad-band photometry varies with the rotation period. The most plausible interpretation of these photometric and H$\alpha$ variations is that they are due to non-stationary mass accretion onto the stars, but rotational modulation can play a major role in some cases.Comment: 21 pages, 11 figures, accepted for publication in Acta Astronomic

A Quantum Many-Body Instability in the Thermodynamic Limit

Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends on the inability of the system to recover the phases. Gaussian decaying in time of the fidelity is proved for spin systems and radiation-matter interaction.Comment: 11 pages, 1 figure. Final version accepted for publication in Modern Physics Letters

New triple systems in the RasTyc sample of stellar X-ray sources

During the study of a large set of late-type stellar X-ray sources, we discovered a large fraction of multiple systems. In this paper we investigate the orbital elements and kinematic properties of three new spectroscopic triple systems as well as spectral types and astrophysical parameters (T_eff, log g, vsin i, log N(Li)) of their components. We conducted follow-up optical observations, both photometric and spectroscopic at high resolution, of these systems. We used a synthetic approach and the cross-correlation method to derive most of the stellar parameters. We estimated reliable radial velocities and deduced the orbital elements of the inner binaries. The comparison of the observed spectra with synthetic composite ones, obtained as the weighted sum of three spectra of non-active reference stars, allowed us to determine the stellar parameters for each component of these systems. We found all are only composed of main sequence stars. These three systems are certainly stable hierarchical triples composed of short-period inner binaries plus a tertiary component in a long-period orbit. From their kinematics and/or Lithium content, these systems result to be fairly young.Comment: Accepted for publication in A&A (on July 22, 2008

Dynamical decoherence in a cavity with a large number of two-level atoms

We consider a large number of two-level atoms interacting with the mode of a cavity in the rotating-wave approximation (Tavis-Cummings model). We apply the Holstein-Primakoff transformation to study the model in the limit of the number of two-level atoms, all in their ground state, becoming very large. The unitary evolution that we obtain in this approximation is applied to a macroscopic superposition state showing that, when the coherent states forming the superposition are enough distant, then the state collapses on a single coherent state describing a classical radiation mode. This appear as a true dynamical effect that could be observed in experiments with cavities.Comment: 9 pages, no figures. This submission substitutes paper quant-ph/0212148 that was withdrawn. Version accepted for publication in Journal of Physics B: Atomic, Molecular & Optical Physic

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The key technical difficulty in the study of these dynamics is that the right-hand sides of the equations are discontinuous and thus their solutions must be intended in some generalized sense: in our analysis, we consider both Carath'eodory and Krasovskii solutions. We first prove existence and completeness of Carath'e-o-dory solutions from every initial condition and we highlight a pathological behavior of Carath'eo-do-ry solutions, which can converge to points that are not (Carath'eodory) equilibria. Notably, such points can be arbitrarily far from consensus and indeed simulations show that convergence to non-consensus configurations is very common. In order to cope with these pathological attractors, we then study Krasovskii solutions. We give an estimate of the asymptotic distance of all Krasovskii solutions from consensus and we prove its tightness by an example of equilibrium such that this distance is quadratic in the number of agents. This fact implies that quantization can drastically destroy consensus. However, consensus is guaranteed in some special cases, namely when the communication among the individuals is described by either a complete or a complete bipartite graph

Thermodynamic Limit and Decoherence: Rigorous Results

Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. In a many-body system has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well definite boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.Comment: 5 pages, no figures. Contribution to proceedings of DICE 2006 (Piombino, Italy, September 11-15, 2006