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Identifying knot types of polymer conformations by machine learning

Physical Review E 2020年第2期101卷 022502-022502页

作者： Olafs Vandans Kaiyuan Yang Zhongtao Wu Liang Dai Department of Physics City University of Hong Kong 83 Tat Chee Avenue Kowloon Hong Kong China Department of Computer Science School of Computing National University of Singapore Singapore 117417 Singapore Department of Mathematics The Chinese University of Hong Kong Shatin NT Hong Kong China Shenzhen Research Institute City University of Hong Kong Shenzhen China

We investigate the use of artificial neural networks (NNs) as an alternative tool to current analytical methods for recognizing knots in a given polymer conformation. The motivation is twofold. First, it is of interest to examine whether NNs are effective at learning the global and sequential properties that uniquely define a knot. Second, knot classification is an important and unsolved problem in mathematical and physical sciences, and NNs may provide insights into this problem. Motivated by these points, we generate millions of polymer conformations for five knot types: 0, 31, 41, 51, and 52, and we design various NN models for classification. Our best model achieves a five-class classification accuracy of above 99% on a polymer of 100 monomers. We find that the sequential modeling ability of recurrent NNs is crucial for this result, as it outperforms feed-forward NNs and successfully generalizes to differently sized conformations as well. We present our methods and suggest that deep learning may be used in specific applications of knot detection where some error is permissible. Hopefully, with further development, NNs can offer an alternative computational method for knot identification and facilitate knot research in mathematical and physical sciences.

关键词： Polymer knots Polymers metropolis algorithm

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Large deviations of a random walk model with emerging territories

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Physical Review E 2020年第6期102卷 062141-062141页

作者： Hendrik Schawe Alexander K. Hartmann Laboratoire de Physique Théorique et Modélisation UMR-8089 CNRS CY Cergy Paris Université 95000 Cergy France Institut für Physik Universität Oldenburg 26111 Oldenburg Germany

We study an agent-based model of animals marking their territory and evading adversarial territory in one dimension with respect to the distribution of the size of the resulting territories. In particular, we use sophisticated sampling methods to determine it over a large part of territory sizes, including atypically small and large configurations, which occur with probability of less than 10−30. We find hints for the validity of a large deviation principle, the shape of the rate function for the right tail of the distribution, and insight into the structure of atypical realizations.

关键词： Random walks Organisms metropolis algorithm

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Biological Networks Regulating Cell Fate Choice Are Minimally Frustrated

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Physical Review Letters 2020年第8期125卷 088101-088101页

作者： Shubham Tripathi David A. Kessler Herbert Levine PhD Program in Systems Synthetic and Physical Biology Rice University Houston Texas 77005 USA Center for Theoretical Biological Physics Rice University Houston Texas 77005 USA Department of Physics Northeastern University Boston Massachusetts 02115 USA Department of Physics Bar-Ilan University Ramat-Gan 52900 Israel

Characterization of the differences between biological and random networks can reveal the design principles that enable the robust realization of crucial biological functions including the establishment of different cell types. Previous studies, focusing on identifying topological features that are present in biological networks but not in random networks, have, however, provided few functional insights. We use a Boolean modeling framework and ideas from the spin glass literature to identify functional differences between five real biological networks and random networks with similar topological features. We show that minimal frustration is a fundamental property that allows biological networks to robustly establish cell types and regulate cell fate choice, and that this property can emerge in complex networks via Darwinian evolution. The study also provides clues regarding how the regulation of cell fate choice can go awry in a disease like cancer and lead to the emergence of aberrant cell types.

关键词： Network structure Biological networks Gene regulatory networks metropolis algorithm

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Elastic-frustration-driven unusual magnetoelastic properties in a switchable core-shell spin-crossover nanostructure

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Physical Review B 2020年第5期101卷 054105-054105页

作者： Yogendra Singh Hassane Oubouchou Masamichi Nishino Seiji Miyashita Kamel Boukheddaden Groupe d'Etudes de la Matière Condensée Université de Versailles Université Paris-Saclay 78035 Versailles France Ecole Polytechnique d’Architecture and d’Urbanisme El Harrach 16000 Algeria Research Center for Advanced Measurement and Characterization National Institute for Materials Science Tsukuba Ibaraki 305-0047 Japan Elements Strategy Initiative Center for Magnetic Materials National Institute for Materials Science Tsukuba Ibaraki 305-0047 Japan Department of Physics Graduate School of Science The University of Tokyo Bunkyo-Ku Tokyo 113-0033 Japan

Spin-crossover (SCO) solids have been studied for their fascinating properties, exhibiting first-order phase transitions and macroscopic bistabilities, accompanied by significant magnetic, structural, and optical changes. These exceptional properties make these materials promising for applications as high-density information storage and optical switches. Recently, the critical progress made in chemistry allowed the design of spin-crossover nanocomposites, combining the properties of two types of spin-crossover solids having different properties, like different lattice parameters, bulk moduli, transition temperatures, ligand fields, etc. In this paper, we consider a microscopic electroelastic description of a SCO nanostructure made of a SCO active core surrounded by a SCO active shell, for which we impose an unconventional elastic frustration at the core-shell interface. The detailed examination of the thermodynamic properties of such a nanocomposite, as a function of the lattice parameter misfit between the two constituents, revealed that the frustration causes unexpected behaviors on the thermal dependence of the average bond lengths, such as the emergence of two- or three-step spin transitions, with self-organization of the spin states in the plateau regions. These results highlight the nontrivial character of the magnetoelastic properties in switchable SCO nanoparticles.

关键词： Classical statistical mechanics Elasticity Magnetic phase transitions Phase transitions Spin state transition Stress Thermodynamics Transition temperature 2-dimensional systems Interfaces Solid-solid interfaces Ising model metropolis algorithm Monte Carlo methods

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Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model

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Physical Review E 2020年第1期102卷 012131-012131页

作者： Hauke Fajen Alexander K. Hartmann A. P. Young Institut für Physik Universität Oldenburg 26111 Oldenburg Germany Physics Department University of California Santa Cruz Santa Cruz California 95064 USA

We apply generalizations of the Swendson-Wang and Wolff cluster algorithms, which are based on the construction of Fortuin-Kasteleyn clusters, to the three-dimensional ±1 random-bond Ising model. The behavior of the model is determined by the temperature T and the concentration p of negative (antiferromagnetic) bonds. The ground state is ferromagnetic for 0≤p0, our data suggest that the percolation transition is universal, irrespective of whether the ground state exhibits ferromagnetic or spin-glass order, and is in the universality class of standard percolation. This shows that correlations in the bond occupancy of the Fortuin-Kasteleyn clusters are irrelevant, except for p=0 where the clusters are strictly tied to Ising correlations so the percolation transition is in the Ising universality class.

关键词： Phase diagrams Phase transitions Classical spin models Spin glasses Ising model metropolis algorithm Monte Carlo methods

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Microscopic magnetic Hamiltonian for exotic spin textures in metals

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Physical Review B 2020年第7期102卷 075106-075106页

作者： Deepak S. Kathyat Arnob Mukherjee Sanjeev Kumar Department of Physical Sciences Indian Institute of Science Education and Research (IISER) Mohali Sector 81 S.A.S. Nagar Manauli PO 140306 India

We derive and study a microscopic spin Hamiltonian on a lattice for Rashba-coupled double exchange metals. The Hamiltonian consists of anisotropic interactions of the Dzyaloshinskii-Moriya and pseudodipolar form, in addition to the standard isotropic term. We validate the spin Hamiltonian by comparing results with those on the exact spin-fermion model, and present its phase diagram using large-scale Monte Carlo simulations. In addition to ferromagnetic, planar spiral, and flux states, the model hosts skyrmion crystal and classical spin-liquid states characterized, respectively, by multiple peaks and a diffuse ring pattern in the spin-structure factor. The filamentary domain-wall structures in the spin-liquid state are in remarkable agreement with experimental data on thin films of MnSi-type B20 metals and transition metals and their alloys.

关键词： Magnetic texture Magnetism Rashba coupling Chiral magnets Hybrid Monte Carlo algorithm Kondo lattice model metropolis algorithm

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Nonlocal stochastic-partial-differential-equation limits of spatially correlated noise-driven spin systems derived to sample a canonical distribution

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Physical Review E 2020年第5期102卷 052112-052112页

作者： Yuan Gao Jeremy L. Marzuola Jonathan C. Mattingly Katherine A. Newhall Department of Mathematics University of North Carolina at Chapel Hill CB 3250 Chapel Hill North Carolina 27599-3250 USA Department of Mathematics and Department of Statistical Sciences Duke University Box 90320 Durham North Carolina 27708-0320 USA

For a noisy spin system, we derive a nonlocal stochastic version of the overdamped Landau-Lipshitz equation designed to respect the underlying Hamiltonian structure and sample the canonical or Gibbs distribution while being driven by spatially correlated (colored) noise that regularizes the dynamics, making this Stochastic partial differential equation mathematically well-posed. We begin from a microscopic discrete-time model motivated by the metropolis-Hastings algorithm for a finite number of spins with periodic boundary conditions whose values are distributed on the unit sphere. We thus propose a future state of the system by adding to each spin colored noise projected onto the sphere, and then accept this proposed state with probability given by the ratio of the canonical distribution at the proposed and current states. For uncorrelated (white) noise this process is guaranteed to sample the canonical distribution. We demonstrate that for colored noise, the method used to project the noise onto the sphere and conserve the magnitude of the spins impacts the equilibrium distribution of the system, as coloring projected noise is not equivalent to projecting colored noise. In a specific scenario we show this break in symmetry vanishes with vanishing proposal size; the resulting continuous-time system of Stochastic differential equations samples the canonical distribution and preserves the magnitude of the spins while being driven by colored noise. Taking the continuum limit of infinitely many spins we arrive at the aforementioned version of the overdamped Landau-Lipshitz equation. Numerical simulations are included to verify convergence properties and demonstrate the dynamics.

关键词： Diffusion Random walks Spin dynamics Landau-Lifschitz-Gilbert equation Langevin equation metropolis algorithm Stochastic analysis

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One-dimensional model for chemotaxis with hard-core interactions

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Physical Review E 2020年第2期101卷 022419-022419页

作者： Tertius Ralph Stephen W. Taylor Maria Bruna Department of Mathematics University of Auckland Private Bag 92019 Auckland 1142 New Zealand Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences Wilberforce Road University of Cambridge Cambridge CB3 0WA United Kingdom

In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach is a systematic derivation for small occupied fraction of particles based on the method of matched asymptotic expansions. The second approach, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding noninteracting linear model as well as stochastic simulations of the underlying particle system.

关键词： Chemotaxis Excluded volume interaction Transport phenomena Collective dynamics Fokker–Planck equation metropolis algorithm

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Out-of-equilibrium Monte Carlo simulations of a classical gas with Bose-Einstein statistics

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Physical Review E 2020年第6期102卷 062125-062125页

作者： M. Di Pietro Martínez M. Giuliano M. Hoyuelos Instituto de Investigaciones Físicas de Mar del Plata CONICET Facultad de Ciencias Exactas y Naturales Universidad Nacional de Mar del Plata Funes 3350 7600 Mar del Plata Argentina

algorithms to determine transition probabilities in Monte Carlo simulations are tested using a system of classical particles with effective interactions which reproduce Bose-Einstein statistics. The system is appropriate for testing different Monte Carlo simulation methods in out-of-equilibrium situations since nonequivalent results are produced. We compare mobility numerical results obtained with transition probabilities derived from Glauber and metropolis algorithms. Then, we compare these with a recent method, the interpolation algorithm, appropriate for nonequilibrium systems in homogeneous substrata and without phase transitions. The results of mobility obtained from the interpolation algorithm are qualitatively verified with molecular dynamics simulations for low concentrations.

关键词： Diffusion Nonequilibrium statistical mechanics metropolis algorithm Molecular dynamics Monte Carlo methods

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New ordered phase in geometrically frustrated generalized XY model

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Physical Review E 2020年第3期102卷 032113-032113页

作者： M. Lach M. Žukovič Institute of Physics Faculty of Science P.J. Šafárik University Park Angelinum 9 041 54 Košice Slovakia

Critical properties of a geometrically frustrated generalized XY model with antiferromagnetic (AFM) and third-order antinematic (AN3) couplings on a triangular lattice are studied by Monte Carlo simulation. It is found that such a generalization leads to a phase diagram consisting of three different quasi-long-range ordered (QLRO) phases. Compared to the model with the second-order antinematic (AN2) coupling, besides the AFM and AN3 phases which appear in the limits of relatively strong AFM and AN3 interactions, respectively, it includes an additional complex canted antiferromagnetic (CAFM) phase. It emerges at lower temperatures, wedged between the AFM and AN3 phases as a result of the competition between the AFM and the AN3 couplings, which is absent in the model with the AN2 coupling. The AFM-CAFM and AN3-CAFM phase transitions are concluded to belong to the weak Ising and weak three-state Potts universality classes, respectively. Additionally, all three QLRO phases also feature true LRO of the standard and generalized chiralities, which both vanish simultaneously at second-order phase transitions with non-Ising critical exponents and the critical temperatures slightly higher than the magnetic and nematic order-disorder transition temperatures.

关键词： Classical statistical mechanics Critical phenomena Magnetic interactions Magnetic order Magnetic phase transitions Magnetism Order parameters Phase diagrams Phase separation Thermodynamics Topological phase transition Transition temperature XY model 2-dimensional systems Antiferromagnets Classical spin models Equilibrium lattice models Lattice models in statistical physics Magnetic systems Finite-size scaling metropolis algorithm Monte Carlo methods

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