Evaluation of advanced optimisation methods for estimating Mixed Logit models

The performances of different simulation-based estimation techniques for mixed logit modeling are evaluated. A quasi-Monte Carlo method (modified Latin hypercube sampling) is compared with a Monte Carlo algorithm with dynamic accuracy. The classic Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization algorithm line-search approach and trust region methods, which have proved to be extremely powerful in nonlinear programming, are also compared. Numerical tests are performed on two real data sets: stated preference data for parking type collected in the United Kingdom, and revealed preference data for mode choice collected as part of a German travel diary survey. Several criteria are used to evaluate the approximation quality of the log likelihood function and the accuracy of the results and the associated estimation runtime. Results suggest that the trust region approach outperforms the BFGS approach and that Monte Carlo methods remain competitive with quasi-Monte Carlo methods in high-dimensional problems, especially when an adaptive optimization algorithm is used

Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the notion of relaxation height in a general energy landscape and we prove sufficient conditions which are valid even in presence of multiple metastable states. We show how these results can be used to approach the problem of multiple metastable states via the use of the modern theories of metastability. We finally apply these general results to the Blume--Capel model for a particular choice of the parameters ensuring the existence of two multiple, and not degenerate in energy, metastable states

Metastability for reversible probabilistic cellular automata with self--interaction

The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the existence of many fixed points and cyclic pairs of the zero temperature dynamics, in which the system can be trapped in its way to the stable phase. %The characterization of the metastable behavior %of a system in the context of parallel dynamics is a very difficult task, %since all the jumps in the configuration space are allowed. Our strategy is based on recent powerful approaches, not needing a complete description of the fixed points of the dynamics, but relying on few model dependent results. We compute the exit time, in the sense of logarithmic equivalence, and characterize the critical droplet that is necessarily visited by the system during its excursion from the metastable to the stable state. We need to supply two model dependent inputs: (1) the communication energy, that is the minimal energy barrier that the system must overcome to reach the stable state starting from the metastable one; (2) a recurrence property stating that for any configuration different from the metastable state there exists a path, starting from such a configuration and reaching a lower energy state, such that its maximal energy is lower than the communication energy

Sum of exit times in series of metastable states in probabilistic cellular automata

Reversible Probabilistic Cellular Automata are a special class of automata whose stationary behavior is described by Gibbs--like measures. For those models the dynamics can be trapped for a very long time in states which are very different from the ones typical of stationarity. This phenomenon can be recasted in the framework of metastability theory which is typical of Statistical Mechanics. In this paper we consider a model presenting two not degenerate in energy metastable states which form a series, in the sense that, when the dynamics is started at one of them, before reaching stationarity, the system must necessarily visit the second one. We discuss a rule for combining the exit times from each of the metastable states

Diagnostic accuracy of short-time inversion recovery sequence in Graves' ophthalmopathy before and after prednisone treatment

Introduction: In Graves' Ophthalmopathy, it is important to distinguish active inflammatory phase, responsive to immunosuppressive treatment, from fibrotic unresponsive inactive one. The purpose of this study is, first, to identify the relevant orbital magnetic resonance imaging signal intensities before treatment, so to classify patients according to their clinical activity score (CAS), discriminating inactive (CAS3) subjects and, second, to follow post-steroid treatment disease. Methods: An observational study was executed on 32 GO consecutive patients in different phases of disease, based on clinical and orbital Magnetic Resonance Imaging parameters, compared to 32 healthy volunteers. Orbital Magnetic Resonance Imaging was performed on a 1.5 tesla Magnetic Resonance Unit by an experienced neuroradiologist blinded to the clinical examinations. Results: In pre-therapy patients, compared to controls, a medial rectus muscle statistically significant signal intensity ratio (SIR) in short-time inversion recovery (STIR) (long TR/TE) sequence was found, as well as when comparing patients before and after treatment, both medial and inferior rectus muscle SIR resulted significantly statistically different in STIR. These increased outcomes explain the inflammation oedematous phase of disease, moreover after steroid administration, compared to controls; patients presented lack of that statistically significant difference, thus suggesting treatment effectiveness. Conclusion: In our study, we proved STIR signal intensities increase in inflammation oedematous phase, confirming STIR sequence to define active phase of disease with more sensibility and reproducibility than CAS alone and to evaluate post-therapy involvement. © 2014 Springer-Verlag

Microwave-induced thermal escape in Josephson junctions

We investigate, by experiments and numerical simulations, thermal activation processes of Josephson tunnel junctions in the presence of microwave radiation. When the applied signal resonates with the Josephson plasma frequency oscillations, the switching current may become multi-valued in a temperature range far exceeding the classical to quantum crossover temperature. Plots of the switching currents traced as a function of the applied signal frequency show very good agreement with the functional forms expected from Josephson plasma frequency dependencies on the bias current. Throughout, numerical simulations of the corresponding thermally driven classical Josephson junction model show very good agreement with the experimental data.Comment: 10 pages and 4 figure