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

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

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

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

Machine learning prediction models for mitral valve repairability and mitral regurgitation recurrence in patients undergoing surgical mitral valve repair

Background: Mitral valve regurgitation (MR) is the most common valvular heart disease and current variables associated with MR recurrence are still controversial. We aim to develop a machine learning-based prognostic model to predict causes of mitral valve (MV) repair failure and MR recurrence. Methods: 1000 patients who underwent MV repair at our institution between 2008 and 2018 were enrolled. Patients were followed longitudinally for up to three years. Clinical and echocardiographic data were included in the analysis. Endpoints were MV repair surgical failure with consequent MV replacement or moderate/severe MR (>2+) recurrence at one-month and mod-erate/severe MR recurrence after three years. Results: 817 patients (DS1) had an echocardiographic examination at one-month while 295 (DS2) also had one at three years. Data were randomly divided into training (DS1: n = 654; DS2: n = 206) and validation (DS1: n = 164; DS2 n = 89) cohorts. For intra-operative or early MV repair failure assessment, the best area under the curve (AUC) was 0.75 and the complexity of mitral valve prolapse was the main predictor. In predicting moderate/severe recurrent MR at three years, the best AUC was 0.92 and residual MR at six months was the most important predictor. Conclusions: Machine learning algorithms may improve prognosis after MV repair procedure, thus improving indications for correct candidate selection for MV surgical repair

A token-mixer architecture for CAD-RADS classification of coronary stenosis on multiplanar reconstruction CT images

Background and objective: In patients with suspected Coronary Artery Disease (CAD), the severity of stenosis needs to be assessed for precise clinical management. An automatic deep learning-based algorithm to classify coronary stenosis lesions according to the Coronary Artery Disease Reporting and Data System (CAD-RADS) in multiplanar reconstruction images acquired with Coronary Computed Tomography Angiography (CCTA) is proposed. Methods: In this retrospective study, 288 patients with suspected CAD who underwent CCTA scans were included. To model long-range semantic information, which is needed to identify and classify stenosis with challenging appearance, we adopted a token-mixer architecture (ConvMixer), which can learn structural relationship over the whole coronary artery. ConvMixer consists of a patch embedding layer followed by repeated convolutional blocks to enable the algorithm to learn long-range dependences between pixels. To visually assess ConvMixer performance, Gradient-Weighted Class Activation Mapping (Grad-CAM) analysis was used. Results: Experimental results using 5-fold cross-validation showed that our ConvMixer can classify significant coronary artery stenosis (i.e., stenosis with luminal narrowing ≥50%) with accuracy and sensitivity of 87% and 90%, respectively. For CAD-RADS 0 vs. 1–2 vs. 3–4 vs. 5 classification, ConvMixer achieved accuracy and sensitivity of 72% and 75%, respectively. Additional experiments showed that ConvMixer achieved a better trade-off between performance and complexity compared to pyramid-shaped convolutional neural networks. Conclusions: Our algorithm might provide clinicians with decision support, potentially reducing the interobserver variability for coronary artery stenosis evaluation

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

Development and testing of a deep learning-based strategy for scar segmentation on CMR-LGE images

Objective: The aim of this paper is to investigate the use of fully convolutional neural networks (FCNNs) to segment scar tissue in the left ventricle from cardiac magnetic resonance with late gadolinium enhancement (CMR-LGE) images. Methods: A successful FCNN in the literature (the ENet) was modified and trained to provide scar-tissue segmentation. Two segmentation protocols (Protocol 1 and Protocol 2) were investigated, the latter limiting the scar-segmentation search area to the left ventricular myocardial tissue region. CMR-LGE from 30 patients with ischemic-heart disease were retrospectively analyzed, for a total of 250 images, presenting high variability in terms of scar dimension and location. Segmentation results were assessed against manual scar-tissue tracing using one-patient-out cross validation. Results: Protocol 2 outperformed Protocol 1 significantly (p value < 0.05), with median sensitivity and Dice similarity coefficient equal to 88.07% [inter-quartile range (IQR) 18.84%] and 71.25% (IQR 31.82%), respectively. Discussion: Both segmentation protocols were able to detect scar tissues in the CMR-LGE images but higher performance was achieved when limiting the search area to the myocardial region. The findings of this paper represent an encouraging starting point for the use of FCNNs for the segmentation of nonviable scar tissue from CMR-LGE images

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