On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses

We start from recently published numerical data by Hatano and Gubernatis cond-mat/0008115 to discuss properties of convergence to equilibrium of optimized Monte Carlo methods (bivariate multi canonical and parallel tempering). We show that these data are not thermalized, and they lead to an erroneous physical picture. We shed some light on why the bivariate multi canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include

Comment on "Ising Spin Glasses in a Magnetic Field"

In ref. cond-mat/9811419 Houdayer and Martin analyze the T=0 3d EA spin glass with a magnetic field $B$. By using a new, powerful method, they determine an effective critical field $B_c$ as a function of the lattice size $L$. They use their results to deduce that the model is behaving like in the droplet approach and not like the mean-field theory. We show here, by using some unpublished data, that this very interesting method and numerical results are completely compatible with the behavior implied by the Replica Symmetry Breaking theory.Comment: One page comment about ref. cond-mat/9811419, including two eps figure

Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).Comment: 48 pages, 21 figures. v2: the published versio

Comment on "Evidence for the Droplet/Scaling Picture of Spin Glasses"

In a recent letter Moore et al. claim to exhibit evidence for a non-mean-field behavior of the $3d$ Ising spin glass. We show that their claim is insubstantial, and by analyzing in detail the behavior of the Migdal-Kadanoff approximation (MKA) as compared to the behavior of the Edwards-Anderson (EA) spin glass we find further evidence of a mean-field like behavior of the $3d$ spin glass.Comment: 1 page comment including one postscript figur

4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.Comment: Physrev format, 5 ps figures include

Optimal two-stage spatial sampling design for estimating critical parameters of SARS-CoV-2 epidemic: Efficiency versus feasibility

The COVID-19 pandemic presents an unprecedented clinical and healthcare challenge for the many medical researchers who are attempting to prevent its worldwide spread. It also presents a challenge for statisticians involved in designing appropriate sampling plans to estimate the crucial parameters of the pandemic. These plans are necessary for monitoring and surveillance of the phenomenon and evaluating health policies. In this respect, we can use spatial information and aggregate data regarding the number of verifed infections (either hospitalized or in compulsory quarantine) to improve the standard two-stage sampling design broadly adopted for studying human populations. We present an optimal spatial sampling design based on spatially balanced sampling techniques. We prove its relative performance analytically in comparison to other competing sampling plans, and we also study its properties through a series of Monte Carlo experiments. Considering the optimal theoretical properties of the proposed sampling plan and its feasibility, we discuss suboptimal designs that approximate well optimality and are more readily applicable

On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses

We start from recently published numerical data by Hatano and Gubernatis cond-mat/0008115 to discuss properties of convergence to equilibrium of optimized Monte Carlo methods (bivariate multi canonical and parallel tempering). We show that these data are not thermalized, and they lead to an erroneous physical picture. We shed some light on why the bivariate multi canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include

HySIA: Tool for Simulating and Monitoring Hybrid Automata Based on Interval Analysis

We present HySIA: a reliable runtime verification tool for nonlinear hybrid automata (HA) and signal temporal logic (STL) properties. HySIA simulates an HA with interval analysis techniques so that a trajectory is enclosed sharply within a set of intervals. Then, HySIA computes whether the simulated trajectory satisfies a given STL property; the computation is performed again with interval analysis to achieve reliability. Simulation and verification using HySIA are demonstrated through several example HA and STL formulas.Comment: Appeared in RV'17; the final publication is available at Springe

Equilibrium valleys in spin glasses at low temperature

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional reference

Present-Day Surface Deformation in North-East Italy Using InSAR and GNSS Data

Geodetic data can detect and estimate deformation signals and rates due to natural and anthropogenic phenomena. In the present study, we focus on northeastern Italy, an area characterized by similar to 1.5-3 mm/yr of convergence rates due to the collision of Adria-Eurasia plates and active subsidence along the coasts. To define the rates and trends of tectonic and subsidence signals, we use a Multi-Temporal InSAR (MT-InSAR) approach called the Stanford Method for Persistent Scatterers (StaMPS), which is based on the detection of coherent and temporally stable pixels in a stack of single-master differential interferograms. We use Sentinel-1 SAR images along ascending and descending orbits spanning the 2015-2019 temporal interval as inputs for Persistent Scatterers InSAR (PSI) processing. We apply spatial-temporal filters and post-processing steps to reduce unrealistic results. Finally, we calibrate InSAR measurements using GNSS velocities derived from permanent stations available in the study area. Our results consist of mean ground velocity maps showing the displacement rates along the radar Line-Of-Sight for each satellite track, from which we estimate the east-west and vertical velocity components. Our results provide a detailed and original view of active vertical and horizontal displacement rates over the whole region, allowing the detection of spatial velocity gradients, which are particularly relevant to a better understanding of the seismogenic potential of the area. As regards the subsidence along the coasts, our measurements confirm the correlation between subsidence and the geological setting of the study area, with rates of similar to 2-4 mm/yr between the Venezia and Marano lagoons, and lower than 1 mm/yr near Grado