Machine Learning Topological Invariants with Neural Networks

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.Comment: 6 pages, 4 figures and 1 table + 2 pages of supplemental materia

学会抄録

THP-1 cell viability after exposure to U-MWCNTs or Z-MWCNTs. (PDF 423 kb

High-Intensity Interval Training Elicits Higher Enjoyment than Moderate Intensity Continuous Exercise

<div><p>Exercise adherence is affected by factors including perceptions of enjoyment, time availability, and intrinsic motivation. Approximately 50% of individuals withdraw from an exercise program within the first 6 mo of initiation, citing lack of time as a main influence. Time efficient exercise such as high intensity interval training (HIIT) may provide an alternative to moderate intensity continuous exercise (MICT) to elicit substantial health benefits. This study examined differences in enjoyment, affect, and perceived exertion between MICT and HIIT. Twelve recreationally active men and women (age = 29.5 ± 10.7 yr, VO₂max = 41.4 ± 4.1 mL/kg/min, BMI = 23.1 ± 2.1 kg/m²) initially performed a VO₂max test on a cycle ergometer to determine appropriate workloads for subsequent exercise bouts. Each subject returned for two additional exercise trials, performing either HIIT (eight 1 min bouts of cycling at 85% maximal workload (Wmax) with 1 min of active recovery between bouts) or MICT (20 min of cycling at 45% Wmax) in randomized order. During exercise, rating of perceived exertion (RPE), affect, and blood lactate concentration (BLa) were measured. Additionally, the Physical Activity Enjoyment Scale (PACES) was completed after exercise. Results showed higher enjoyment (p = 0.013) in response to HIIT (103.8 ± 9.4) versus MICT (84.2 ± 19.1). Eleven of 12 participants (92%) preferred HIIT to MICT. However, affect was lower (p<0.05) and HR, RPE, and BLa were higher (p<0.05) in HIIT versus MICT. Although HIIT is more physically demanding than MICT, individuals report greater enjoyment due to its time efficiency and constantly changing stimulus.</p><p><b><i>Trial Registration</i>:</b><a href="https://clinicaltrials.gov/ct2/show/NCT:02981667" target="_blank">NCT:02981667</a>.</p></div

Flow chart describing participant recruitment.

<p>Flow chart describing participant recruitment.</p

Physical characteristics of participants (N = 12).

<p>Physical characteristics of participants (N = 12).</p