From the quantum transfer matrix to the quench action: the Loschmidt echo in XXZ Heisenberg spin chains

We consider the computation of the Loschmidt echo after quantum quenches in the interacting XXZ Heisenberg spin chain both for real and imaginary times. We study two-site product initial states, focusing in particular on the N\ue9el and tilted N\ue9el states. We apply the Quantum Transfer Matrix (QTM) approach to derive generalized TBA equations, which follow from the fusion hierarchy of the appropriate QTM's. Our formulas are valid for arbitrary imaginary time and for real times at least up to a time t0, after which the integral equations have to be modified. In some regimes, t0 is seen to be either very large or infinite, allowing to explore in detail the post-quench dynamics of the system. As an important part of our work, we show that for the N\ue9el state our imaginary time results can be recovered by means of the quench action approach, unveiling a direct connection with the quantum transfer matrix formalism. In particular, we show that in the zero-time limit, the study of our TBA equations allows for a simple alternative derivation of the recently obtained Bethe ansatz distribution functions for the N\ue9el, tilted N\ue9el and tilted ferromagnet states

Dynamical phase transitions and Loschmidt echo in the infinite-range XY model

We compare two different notions of dynamical phase transitions in closed quantum systems. The first is identified through the time-averaged value of the equilibrium-order parameter, whereas the second corresponds to non-analyticities in the time behaviour of the Loschmidt echo. By exactly solving the dynamics of the infinite-range XY model, we show that in this model non-analyticities of the Loschmidt echo are not connected to standard dynamical phase transitions and are not robust against quantum fluctuations. Furthermore, we show that the existence of either of the two dynamical transitions is not necessarily connected to the equilibrium quantum phase transition. \ua9 2016 The Author(s) Published by the Royal Society. All rights reserved

Disease Progression of Hypertrophic Cardiomyopathy: Modeling Using Machine Learning

Background: Cardiovascular disorders in general are responsible for 30% of deaths worldwide. Among them, hypertrophic cardiomyopathy (HCM) is a genetic cardiac disease that is present in about 1 of 500 young adults and can cause sudden cardiac death (SCD). Objective: Although the current state-of-the-art methods model the risk of SCD for patients, to the best of our knowledge, no methods are available for modeling the patient's clinical status up to 10 years ahead. In this paper, we propose a novel machine learning (ML)-based tool for predicting disease progression for patients diagnosed with HCM in terms of adverse remodeling of the heart during a 10-year period. Methods: The method consisted of 6 predictive regression models that independently predict future values of 6 clinical characteristics: left atrial size, left atrial volume, left ventricular ejection fraction, New York Heart Association functional classification, left ventricular internal diastolic diameter, and left ventricular internal systolic diameter. We supplemented each prediction with the explanation that is generated using the Shapley additive explanation method. Results: The final experiments showed that predictive error is lower on 5 of the 6 constructed models in comparison to experts (on average, by 0.34) or a consortium of experts (on average, by 0.22). The experiments revealed that semisupervised learning and the artificial data from virtual patients help improve predictive accuracies. The best-performing random forest model improved R2 from 0.3 to 0.6. Conclusions: By engaging medical experts to provide interpretation and validation of the results, we determined the models' favorable performance compared to the performance of experts for 5 of 6 targets

A machine learning-based risk stratification model for ventricular tachycardia and heart failure in hypertrophic cardiomyopathy

Background: Machine learning (ML) and artificial intelligence are emerging as important components of precision medicine that enhance diagnosis and risk stratification. Risk stratification tools for hypertrophic cardiomyopathy (HCM) exist, but they are based on traditional statistical methods. The aim was to develop a novel machine learning risk stratification tool for the prediction of 5-year risk in HCM. The goal was to determine if its predictive accuracy is higher than the accuracy of the state-of-the-art tools. Method: Data from a total of 2302 patients were used. The data were comprised of demographic characteristics, genetic data, clinical investigations, medications, and disease-related events. Four classification models were applied to model the risk level, and their decisions were explained using the SHAP (SHapley Additive exPlanations) method. Unwanted cardiac events were defined as sustained ventricular tachycardia occurrence (VT), heart failure (HF), ICD activation, sudden cardiac death (SCD), cardiac death, and all-cause death. Results: The proposed machine learning approach outperformed the similar existing risk-stratification models for SCD, cardiac death, and all-cause death risk-stratification: it achieved higher AUC by 17%, 9%, and 1%, respectively. The boosted trees achieved the best performing AUC of 0.82. The resulting model most accurately predicts VT, HF, and ICD with AUCs of 0.90, 0.88, and 0.87, respectively. Conclusions: The proposed risk-stratification model demonstrates high accuracy in predicting events in patients with hypertrophic cardiomyopathy. The use of a machine-learning risk stratification model may improve patient management, clinical practice, and outcomes in general

Disease Progression of Hypertrophic Cardiomyopathy: Modeling Using Machine Learning

Background: Cardiovascular disorders in general are responsible for 30% of deaths worldwide. Among them, hypertrophic cardiomyopathy (HCM) is a genetic cardiac disease that is present in about 1 of 500 young adults and can cause sudden cardiac death (SCD). Objective: Although the current state-of-the-art methods model the risk of SCD for patients, to the best of our knowledge, no methods are available for modeling the patient's clinical status up to 10 years ahead. In this paper, we propose a novel machine learning (ML)-based tool for predicting disease progression for patients diagnosed with HCM in terms of adverse remodeling of the heart during a 10-year period. Methods: The method consisted of 6 predictive regression models that independently predict future values of 6 clinical characteristics: left atrial size, left atrial volume, left ventricular ejection fraction, New York Heart Association functional classification, left ventricular internal diastolic diameter, and left ventricular internal systolic diameter. We supplemented each prediction with the explanation that is generated using the Shapley additive explanation method. Results: The final experiments showed that predictive error is lower on 5 of the 6 constructed models in comparison to experts (on average, by 0.34) or a consortium of experts (on average, by 0.22). The experiments revealed that semisupervised learning and the artificial data from virtual patients help improve predictive accuracies. The best-performing random forest model improved R2 from 0.3 to 0.6. Conclusions: By engaging medical experts to provide interpretation and validation of the results, we determined the models' favorable performance compared to the performance of experts for 5 of 6 targets

A machine learning-based risk stratification model for ventricular tachycardia and heart failure in hypertrophic cardiomyopathy

Background: Machine learning (ML) and artificial intelligence are emerging as important components of precision medicine that enhance diagnosis and risk stratification. Risk stratification tools for hypertrophic cardiomyopathy (HCM) exist, but they are based on traditional statistical methods. The aim was to develop a novel machine learning risk stratification tool for the prediction of 5-year risk in HCM. The goal was to determine if its predictive accuracy is higher than the accuracy of the state-of-the-art tools. Method: Data from a total of 2302 patients were used. The data were comprised of demographic characteristics, genetic data, clinical investigations, medications, and disease-related events. Four classification models were applied to model the risk level, and their decisions were explained using the SHAP (SHapley Additive exPlanations) method. Unwanted cardiac events were defined as sustained ventricular tachycardia occurrence (VT), heart failure (HF), ICD activation, sudden cardiac death (SCD), cardiac death, and all-cause death. Results: The proposed machine learning approach outperformed the similar existing risk-stratification models for SCD, cardiac death, and all-cause death risk-stratification: it achieved higher AUC by 17%, 9%, and 1%, respectively. The boosted trees achieved the best performing AUC of 0.82. The resulting model most accurately predicts VT, HF, and ICD with AUCs of 0.90, 0.88, and 0.87, respectively. Conclusions: The proposed risk-stratification model demonstrates high accuracy in predicting events in patients with hypertrophic cardiomyopathy. The use of a machine-learning risk stratification model may improve patient management, clinical practice, and outcomes in general