Inverse problem beyond two-body interaction: The cubic mean-field Ising model.

In this paper, we solve the inverse problem for the cubic mean-field Ising model. Starting from configuration data generated according to the distribution of the model, we reconstruct the free parameters of the system. We test the robustness of this inversion procedure both in the region of uniqueness of the solutions and in the region where multiple thermodynamics phases are present.

Combined Effects of Age and Comorbidities on Electrocardiographic Parameters in a Large Non-Selected Population.

Background: Previous studies have evaluated average electrocardiographic (ECG) values in healthy subjects or specific subpopulations. However, none have evaluated ECG average values in not selected populations, so we examined ECG changes with respect to age and sex in a large primary population. Methods: From digitized ECG stored from 2008 to 2021 in the Modena province, 130,471 patients were enrolled. Heart rate, P, QRS and T wave axis, P, QRS and T wave duration, PR interval, QTc, and frontal QRS-T angle were evaluated. Results: All ECG parameters showed a dependence on age, but only some of them with a straight-line correlation: QRS axis (p < 0.001, R2 = 0.991, r = 0.996), PR interval (p < 0.001, R2 = 0.978, r = 0.989), QTc (p < 0.001, R2 = 0.935, r = 0.967), and, in over 51.5 years old, QRS-T angle (p < 0.001, R2 = 0.979, r = 0.956). Differences between females and males and in different clinical settings were observed. Conclusions: ECG changes with ageing are explainable by intrinsic modifications of the heart and thorax and with the appearance of cardiovascular diseases and comorbidities. Age-related reference values were computed and applicable in clinical practice. Significant deviations from mean values and from Z-scores should be investigated.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion.

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states.

In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.

Enhancing participation to health screening campaigns by group interactions.

Improving the prevention efficacy of health screening campaigns by increasing their attendance rate represents a challenge that calls for new strategies. This paper analyzes the response to a Pap test screening campaign of 155,000 women over the last decade. Using a mathematical model of statistical physics origins we derive a quantitative estimate of the mutual influence between participating groups. Different scenarios and possible actions are studied from the cost-benefit perspective. The performance of alternative strategies to improve participation are forecasted and compared. The results show that the standard strategies with incentives concentrated toward the low participating groups are outperformed by those toward pivotal groups with higher influence power. Our method provides a flexible tool useful to support policy maker decisions while complying with ethical regulations on privacy and confidentiality.

An analysis of a large dataset on immigrant integration in Spain. The statistical mechanics perspective on social action.

How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifiers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non-linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.

Structure of correlations in three dimensional spin glasses.

We investigate the low temperature phase of the three dimensional Edward-Anderson model with Bernoulli random couplings. We show that, at a fixed value Q of the overlap, the model fulfills the clustering property: The connected correlation functions between two local overlaps have power law decay. Our findings are in agreement with the replica symmetry breaking theory and show that the overlap is a good order parameter.

Ultrametricity in the Edwards-Anderson model.

We test the property of ultrametricity for the spin-glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to 20(3) spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution, our result contradicts the droplet theory.

Overlap equivalence in the Edwards-Anderson model.

We study the relative fluctuations of the link overlap and the square standard overlap in the three-dimensional Gaussian Edwards-Anderson model with zero external field. We first analyze the correlation coefficient and find that the two quantities are uncorrelated above the critical temperature. Below the critical temperature we find that the link overlap has vanishing fluctuations for fixed values of the square standard overlap and large volumes. Our data show that the conditional variance scales to zero in the thermodynamic limit. This implies that, if one of the two random variables tends to a trivial one (i.e., deltalike distributed), then the other does also, and as a consequence, the "trivial-nontrivial" picture should be dismissed. Our results show that the two overlaps are completely equivalent in the description of the low temperature phase of the Edwards-Anderson model.

Normally attracting manifolds and periodic behavior in one-dimensional and two-dimensional coupled map lattices.

We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable. (c) 1994 American Institute of Physics.