Topological origin of the phase transition in a mean-field model

We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological transition occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, also in topology the way the thermodynamic limit is taken is crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the text. To appear in Physical Review Letter

Response of Ventricular Repolarization to Simulated Microgravity Measured by Periodic Repolarization Dynamics Using Phase-Rectified Signal Averaging

Head-Down Bed Rest (HDBR) microgravity simulation induces cardiovascular deconditioning, including effects on ventricular repolarization. The index of Periodic Repolarization Dynamics (PRD) was developed to quantify low-frequency oscillations of cardiac repolarization. In this study, PRD was quantified by Phase Rectified Signal Averaging (PRDPRSA) and Continuous Wavelet Transform (PRDCWT) methods. PRD was analyzed in ECGs from 22 volunteers at rest and during orthostatic Tilt-Table Test (TTT) performed before and after -6° 60-days HDBR. Significant correlation was found between PRD measured by PRSA and CWT (Pearson''s ¿ = 0.93, p < 10-54 and Kendall''s t = 0.79 p < 10-38). A highly significant increase was found when PRDPRSA values were measured at POST-HDBR with respect to PRE-HDBR in the tilt phase: 1.40 [1.10] deg and 0.97 [0.90] deg (median [IQR]), p = 0.008, respectively. PRDPRSA also increased significantly in the tilt phase with respect to baseline, both at POST-HDBR (0.90 [0.57] deg, p = 0.003) and at PRE-HDBR (0.75 [0.45] deg, p = 0.011). PRD, either measured with PRSA or with CWT, is able to measure changes in ventricular repolarization induced by microgravity simulation as well as following sympathetic provocation

Land use influence on ambient PM2.5 and ammonia concentrations: Correlation analyses in the Lombardy region, Italy

Air pollution is identified as the primary environmental risk to health worldwide. Although most of the anthropic emissions are due to combustion processes, intensive farming activities may also contribute significantly, especially as a source of particulate matter 2.5 and ammonia. Investigations on particulate matter and precursors dynamics, identifying the most relevant environmental factors influencing their emissions, are critical to improving local and regional air quality policies. This work presents an analysis of the correlation between particulate matter 2.5 and ammonia concentrations, obtained from the Copernicus Atmosphere Monitoring Service, and local land use characteristics, to investigate the influence of agricultural activities on the space-time pollutant concentration patterns. The selected study area is the Lombardy region, northern Italy. Correlation is evaluated through Spearman’s coefficient. Agricultural areas resulted in a significant factor for high ammonia concentrations, while particulate matter 2.5 was strongly correlated with built-up areas. Natural areas resulted instead a protective factor for both pollutants. Results provide data-driven evidence of the land use effect on air quality, also quantifying such effects in terms of correlation coefficients magnitude

Phase transitions as topology changes in configuration space: an exact result

The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the Euler characteristic--of suitable submanifolds of configuration space--which shows a sharp discontinuity at the phase transition point, also at finite N. The present analytic result provides, with previous work, a new key to a possible connection of topological changes in configuration space as the origin of phase transitions in a variety of systems.Comment: REVTeX file, 5 pages, 1 PostScript figur

Hamiltonian dynamics of the two-dimensional lattice phi^4 model

The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure

Hamiltonian dynamics and geometry of phase transitions in classical XY models

The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of thermodynamical observables in place of ensemble averages, qualitatively new information is derived from the temperature dependence of Lyapunov exponents. A Riemannian geometrization of newtonian dynamics suggests to consider other observables of geometric meaning tightly related with the largest Lyapunov exponent. The numerical computation of these observables - unusual in the study of phase transitions - sheds a new light on the microscopic dynamical counterpart of thermodynamics also pointing to the existence of some major change in the geometry of the mechanical manifolds at the thermodynamical transition. Through the microcanonical definition of the entropy, a relationship between thermodynamics and the extrinsic geometry of the constant energy surfaces $\Sigma_E$ of phase space can be naturally established. In this framework, an approximate formula is worked out, determining a highly non-trivial relationship between temperature and topology of the $\Sigma_E$. Whence it can be understood that the appearance of a phase transition must be tightly related to a suitable major topology change of the $\Sigma_E$. This contributes to the understanding of the origin of phase transitions in the microcanonical ensemble.Comment: in press on Physical Review E, 43 pages, LaTeX (uses revtex), 22 PostScript figure

Automated Scar Segmentation from CMR-LGE Images Using a Deep Learning Approach

Aim. The presence of myocardial scar is a strong predictor of ventricular remodeling, cardiac dysfunction and mortality. Our aim was to assess quantitatively the presence of scar tissue from cardiac-magnetic-resonance (CMR) with late-Gadolinium-enhancement (LGE) images using a deep-learning (DL) approach. Methods. Scar segmentation was performed automatically with a DL approach based on ENet, a deep fully-convolutional neural network (FCNN). We investigated three different ENet configurations. The first configuration (C1) exploited ENet to retrieve directly scar segmentation from the CMR-LGE images. The second (C2) and third (C3) configurations performed scar segmentation in the myocardial region, which was previously obtained in a manual or automatic way with a state-of-the-art DL method, respectively. Results. When tested on 250 CMR-LGE images from 30 patients, the best-performing configuration (C2) achieved 97% median accuracy (inter-quartile (IQR) range = 4%) and 71% median Dice similarity coefficient (IQR = 32%). Conclusions. DL approaches using ENet are promising in automatically segmenting scars in CMR-LGE images, achieving higher performance when limiting the search area to the manually-defined myocardial region

A Novel Approach Based on Spatio-temporal Features and Random Forest for Scar Detection Using Cine Cardiac Magnetic Resonance Images

Aim. To identify the presence of scar tissue in the left ventricle from Gadolinium (Gd)-free magnetic resonance cine sequences using a learning-based approach relying on spatio-temporal features. Methods. The spatial and temporal features were extracted using local binary patterns from (i) cine end-diastolic frame and (ii) two parametric images of amplitude and phase wall motion, respectively, and classified with Random Forest. Results. When tested on 328 cine sequences from 40 patients, a recall of 70% was achieved, improving significantly the classification resulting from spatial and temporal features processed separately. Conclusions. The proposed approach showed promising results, paving the way for scar identification from Gd-free images

Aging at Criticality in Model C Dynamics

We study the off-equilibrium two-point critical response and correlation functions for the relaxational dynamics with a coupling to a conserved density (Model C) of the O(N) vector model. They are determined in an \epsilon=4-d expansion for vanishing momentum. We briefly discuss their scaling behaviors and the associated scaling forms are determined up to first order in epsilon. The corresponding fluctuation-dissipation ratio has a non trivial large time limit in the aging regime and, up to one-loop order, it is the same as that of the Model A for the physically relevant case N=1. The comparison with predictions of local scale invariance is also discussed.Comment: 13 pages, 1 figur

Symmetries of microcanonical entropy surfaces

Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the microcanonical order parameter in the high energy and in the low energy phases are investigated. In particular the breaking of the symmetry of the microcanonical entropy in the low energy regime is considered. The general statements are corroborated by investigations of various examples of classical spin systems.Comment: 15 pages, 5 figures include