Loop-Cluster Coupling and Algorithm for Classical Statistical Models.

Potts spin systems play a fundamental role in statistical mechanics and quantum field theory and can be studied within the spin, the Fortuin-Kasteleyn (FK) bond or the q-flow (loop) representation. We introduce a Loop-Cluster (LC) joint model of bond-occupation variables interacting with q-flow variables and formulate an LC algorithm that is found to be in the same dynamical universality as the celebrated Swendsen-Wang algorithm. This leads to a theoretical unification for all the representations, and numerically, one can apply the most efficient algorithm in one representation and measure physical quantities in others. Moreover, by using the LC scheme, we construct a hierarchy of geometric objects that contain as special cases the q-flow clusters and the backbone of FK clusters, the exact values of whose fractal dimensions in two dimensions remain as an open question. Our work not only provides a unified framework and an efficient algorithm for the Potts model but also brings new insights into the rich geometric structures of the FK clusters.

Geometric Explanation of Anomalous Finite-Size Scaling in High Dimensions.

We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on five-dimensional hypercubic lattices with free and periodic boundary conditions, by using geometric representations and recently introduced Markov-chain Monte Carlo algorithms. We show that previously observed anomalous behavior for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.

Fragmentation of fractal random structures.

We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads to broad distributions of fragment sizes. The resulting power laws are shown to encode characteristic fingerprints of the fragmented objects.

Sweeny dynamics for the random-cluster model with small Q.

The Sweeny algorithm for the Q-state random-cluster model in two dimensions is shown to exhibit a rich mixture of critical dynamical scaling behaviors. As Q decreases, the so-called critical speeding-up for nonlocal quantities becomes more and more pronounced. However, for some quantity of a specific local pattern, e.g., the number of half faces on the square lattice, we observe that, as Q→0, the integrated autocorrelation time τ diverges as Q^{-ζ}, with ζ≃1/2, leading to the nonergodicity of the Sweeny method for Q→0. Such Q-dependent critical slowing-down, attributed to the peculiar form of the critical bond weight v=sqrt[Q], can be eliminated by a combination of the Sweeny and the Kawasaki algorithm. Moreover, by classifying the occupied bonds into bridge bonds and backbone bonds, and the empty bonds into internal-perimeter bonds and external-perimeter bonds, one can formulate an improved version of the Sweeny-Kawasaki method such that the autocorrelation time for any quantity is of order O(1).

Environmental and genetic predictors of human cardiovascular ageing.

Cardiovascular ageing is a process that begins early in life and leads to a progressive change in structure and decline in function due to accumulated damage across diverse cell types, tissues and organs contributing to multi-morbidity. Damaging biophysical, metabolic and immunological factors exceed endogenous repair mechanisms resulting in a pro-fibrotic state, cellular senescence and end-organ damage, however the genetic architecture of cardiovascular ageing is not known. Here we use machine learning approaches to quantify cardiovascular age from image-derived traits of vascular function, cardiac motion and myocardial fibrosis, as well as conduction traits from electrocardiograms, in 39,559 participants of UK Biobank. Cardiovascular ageing is found to be significantly associated with common or rare variants in genes regulating sarcomere homeostasis, myocardial immunomodulation, and tissue responses to biophysical stress. Ageing is accelerated by cardiometabolic risk factors and we also identify prescribed medications that are potential modifiers of ageing. Through large-scale modelling of ageing across multiple traits our results reveal insights into the mechanisms driving premature cardiovascular ageing and reveal potential molecular targets to attenuate age-related processes.

Deep learning on resting electrocardiogram to identify impaired heart rate recovery.

Background and Objective: Postexercise heart rate recovery (HRR) is an important indicator of cardiac autonomic function and abnormal HRR is associated with adverse outcomes. We hypothesized that deep learning on resting electrocardiogram (ECG) tracings may identify individuals with impaired HRR. Methods: We trained a deep learning model (convolutional neural network) to infer HRR based on resting ECG waveforms (HRRpred) among UK Biobank participants who had undergone exercise testing. We examined the association of HRRpred with incident cardiovascular disease using Cox models, and investigated the genetic architecture of HRRpred in genome-wide association analysis. Results: Among 56,793 individuals (mean age 57 years, 51% women), the HRRpred model was moderately correlated with actual HRR (r = 0.48, 95% confidence interval [CI] 0.47-0.48). Over a median follow-up of 10 years, we observed 2060 incident diabetes mellitus (DM) events, 862 heart failure events, and 2065 deaths. Higher HRRpred was associated with lower risk of DM (hazard ratio [HR] 0.79 per 1 standard deviation change, 95% CI 0.76-0.83), heart failure (HR 0.89, 95% CI 0.83-0.95), and death (HR 0.83, 95% CI 0.79-0.86). After accounting for resting heart rate, the association of HRRpred with incident DM and all-cause mortality were similar. Genetic determinants of HRRpred included known heart rate, cardiac conduction system, cardiomyopathy, and metabolic trait loci. Conclusion: Deep learning-derived estimates of HRR using resting ECG independently associated with future clinical outcomes, including new-onset DM and all-cause mortality. Inferring postexercise heart rate response from a resting ECG may have potential clinical implications and impact on preventive strategies warrants future study.

Lifted worm algorithm for the Ising model.

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energylike observable on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energylike observable on the complete graph and leads to a significant constant improvement on toroidal grids.

Efficient simulation of the random-cluster model.

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.