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Minimal lattice model of lipid membranes with liquid-ordered domains

Physical Review Research 2021年第4期3卷 L042030-L042030页

作者： Tanmoy Sarkar Oded Farago Department of Biomedical Engineering Ben Gurion University of the Negev Be'er Sheva 84105 Israel

Mixtures of lipids and cholesterol are commonly used as model systems for studying the formation of liquid-ordered (Lo) domains in heterogeneous biological membranes. The simplest model system exhibiting coexistence between Lo domains and a liquid-disordered (Ld) matrix is that of a binary mixture of saturated lipids such as DPPC and cholesterol (Chol). DPPC/Chol mixtures have been investigated for decades both experimentally, theoretically, and recently also by means of atomistic simulations. Here, we present a minimal lattice model that captures the correct behavior of this mixture across multiple scales. On the macroscopic scales, we present simulation results of mixtures of thousands of lipids and Chol molecules which show excellent agreement with the phase diagram of the system. The simulations are conducted on timescales of hundreds of microseconds and show the morphologies and dynamics of the domains. On the molecular scales, the simulations reveal local structures similar to those recently seen in atomistic simulations, including the formation of gel-like nanodomains (∼1–10 nm) within larger Chol-rich Lo domains (∼10–100 nm). The observed multiscale behavior is related to the tendency of Chol to induce ordering of acyl chains on the one hand, and disrupt their packing with each other, on the other hand.

关键词： Membranes Phase diagrams Phase transitions Cell membrane Lipids metropolis algorithm

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K-Means Clustering algorithm Based on Chaotic Adaptive Artificial Bee Colony

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algorithmS 2021年第2期14卷 53页

作者： Jin, Qibing Lin, Nan Zhang, Yuming Beijing Univ Chem Technol Sch Informat Sci & Technol Beijing 100029 Peoples R China

K-Means Clustering is a popular technique in data analysis and data mining. To remedy the defects of relying on the initialization and converging towards the local minimum in the K-Means Clustering (KMC) algorithm, a chaotic adaptive artificial bee colony algorithm (CAABC) clustering algorithm is presented to optimally partition objects into K clusters in this study. This algorithm adopts the max-min distance product method for initialization. In addition, a new fitness function is adapted to the KMC algorithm. This paper also reports that the iteration abides by the adaptive search strategy, and Fuch chaotic disturbance is added to avoid converging on local optimum. The step length decreases linearly during the iteration. In order to overcome the shortcomings of the classic ABC algorithm, the simulated annealing criterion is introduced to the CAABC. Finally, the confluent algorithm is compared with other stochastic heuristic algorithms on the 20 standard test functions and 11 datasets. The results demonstrate that improvements in CAABA-K-means have an advantage on speed and accuracy of convergence over some conventional algorithms for solving clustering problems.

关键词： artificial bee colony (ABC) algorithm K-means clustering (KMC) algorithm chaos algorithm metropolis algorithm simulated annealing

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Field percolation-switching in soft ternary anisotropic system

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 520卷 11-25页

作者： Ambrozic, M. Kralj, S. Univ Maribor Fac Math & Nat Sci Koroska 160 Maribor Slovenia Jozef Stefan Inst Jamova 39 Ljubljana Slovenia Fac Ind Engn Segova 112 Novo Mesto Slovenia

We study numerically external electric or magnetic field driven switching between percolated and non-percolated configuration of nanoparticles in soft matter ternary systems. The system consists of nematic liquid crystal, impurities and elongated nanoparticles. We use the Lebwohl-Lasher lattice-type modeling to determine the orientational order of nanoparticles and consequently the metropolis algorithm to find the percolation threshold. In our model the external field acts directly only on the liquid crystal component, which in turn tends to reorient nanoparticles. We determine regimes where an external field relatively robustly switches between percolated and non-percolated states. The main variable physical parameters are volume concentration and length-to-width ratio of nanoparticles, concentration of impurities and temperature. We have revealed that impurities imposing static orientational disorder are a significant part of the system. A possible application is also proposed. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Nematic liquid crystals Nanoparticles Lebwohl-Lasher model metropolis algorithm Percolation threshold

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On the Analysis of Trajectory-Based Search algorithms: When is it Beneficial to Reject Improvements?

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algorithmICA 2019年第2期81卷 858-885页

作者： Nallaperuma, Samadhi Oliveto, Pietro S. Perez Heredia, Jorge Sudholt, Dirk Univ Sheffield Sheffield S1 4DP S Yorkshire England Basque Ctr Appl Math Bilbao 48009 Spain

We investigate popular trajectory-based algorithms inspired by biology and physics to answer a question of general significance: when is it beneficial to reject improvements? A distinguishing factor of SSWM (strong selection weak mutation), a popular model from population genetics, compared to the metropolis algorithm (MA), is that the former can reject improvements, while the latter always accepts them. We investigate when one strategy outperforms the other. Since we prove that both algorithms converge to the same stationary distribution, we concentrate on identifying a class of functions inducing large mixing times, where the algorithms will outperform each other over a long period of time. The outcome of the analysis is the definition of a function where SSWM is efficient, while metropolis requires at least exponential time. The identified function favours algorithms that prefer high quality improvements over smaller ones, revealing similarities in the optimisation strategies of SSWM and metropolis respectively with best-improvement (BILS) and first-improvement (FILS) local search. We conclude the paper with a comparison of the performance of these algorithms and a (1,lambda) RLS on the identified function. The algorithm favours the steepest gradient with a probability that increases with the size of its offspring population. The results confirm that BILS excels and that the (1,lambda) RLS is efficient only for large enough population sizes.

关键词： Theory Evolutionary algorithms Non-elitism metropolis algorithm Strong selection weak mutation regime

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Generating Synthetic Power Grids Using Exponential Random Graph Models

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PRX Energy 2024年第2期3卷 023005-023005页

作者： Francesco Giacomarra Gianmarco Bet Alessandro Zocca

Synthetic power grids enable real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power grids using exponential random graph (ERG) models. Our two main contributions are (1) the formulation of an ERG model tailored specifically for capturing the topological nuances of power grids and (2) a general procedure for estimating the parameters of such a model conditioned on working with connected graphs. From a modeling perspective, we identify edge counts per bus type and k-triangles as crucial topological characteristics for synthetic power-grid generation. From a technical perspective, we develop a rigorous methodology to estimate the parameters of an ERG constrained to the space of connected graphs. The proposed model is flexible, easy to implement, and successfully captures the desired topological properties of power grids.

关键词： Electric power transmission Network structure Power grid networks Random graphs Entropic sampling methods Graph theory metropolis algorithm

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Random walks on the BMW monoid: an algebraic approach

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JOURNAL OF ALGEBRAIC COMBINATORICS 2019年第3期50卷 347-361页

作者： Wolff, Sarah Denison Univ Granville OH 43023 USA

We consider metropolis-based systematic scan algorithms for generating Birman-Murakami-Wenzl (BMW) monoid basis elements of the BMW algebra. As the BMW monoid consists of tangle diagrams, these scanning strategies can be rephrased as random walks on links and tangles. We also consider the Brauer algebra and use metropolis-based scans to generate Brauer diagrams, giving rise to random walks on perfect matchings. Taking an algebraic perspective, we translate these walks into left multiplication operators in the BMW algebra and so give an algebraic interpretation of the metropolis algorithm in this setting.

关键词： metropolis algorithm Systematic scans Random walks Representation theory Semisimple algebras

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An evolutionary approach for structural reliability

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STRUCTURAL ENGINEERING AND MECHANICS 2019年第4期71卷 329-339页

作者： Garakaninezhad, Alireza Bastami, Morteza Iranian Acad Ctr Educ Culture & Res Kerman *** Iran IIEES 26 Arghavan StPOB 19395-3913 Tehran Iran

Assessment of failure probability, especially for a complex structure, requires a considerable number of calls to the numerical model. Reliability methods have been developed to decrease the computational time. In this approach, the original numerical model is replaced by a surrogate model which is usually explicit and much faster to evaluate. The current paper proposed an efficient reliability method based on Monte Carlo simulation (MCS) and multi-gene genetic programming (MGGP) as a robust variant of genetic programming (GP). GP has been applied in different fields;however, its application to structural reliability has not been tested. The current study investigated the performance of MGGP as a surrogate model in structural reliability problems and compares it with other surrogate models. An adaptive metropolis algorithm is utilized to obtain the training data with which to build the MGGP model. The failure probability is estimated by combining MCS and MGGP. The efficiency and accuracy of the proposed method were investigated with the help of five numerical examples.

关键词： reliability genetic programming surrogate model metropolis algorithm failure probability Monte Carlo

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Sub-dominant Cogrowth Behavior and the Viability of Deciding Amenability Numerically

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EXPERIMENTAL MATHEMATICS 2019年第1期28卷 67-80页

作者： Elder, Murray Rogers, Cameron Univ Technol Sydney Sch Math & Phys Sci Ultimo Australia Launceston Church Grammar Sch Launceston Tas Australia

We critically analyze a recent numerical method due to the first author, Rechnitzer, and van Rensburg, which attempts to detect amenability in a finitely generated group by numerically estimating its asymptotic cogrowth rate. We identify two potential sources of error. We then propose a modification of the method that enables it to easily compute surprisingly accurate estimates for initial terms of the cogrowth sequence.

关键词： amenable group cogrowth function Folner function Kesten's criterion return probability metropolis algorithm R Thompson's group F

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Quantitative contraction rates for Markov chains on general state spaces

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ELECTRONIC JOURNAL OF PROBABILITY 2019年第none期24卷 1-36页

作者： Eberle, Andreas Majka, Mateusz B. Univ Bonn Inst Angew Math Endenicher Allee 60 D-53115 Bonn Germany Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England

We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich (L-1 Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently been derived by combining appropriate couplings with carefully designed Kantorovich distances. In this paper, we partially carry over this approach from diffusions to Markov chains. We derive quantitative lower bounds on contraction rates for Markov chains on general state spaces that are powerful if the dynamics is dominated by small local moves. For Markov chains on R(d )with isotropic transition kernels, the general bounds can be used efficiently together with a coupling that combines maximal and reflection coupling. The results are applied to Euler discretizations of stochastic differential equations with non-globally contractive drifts, and to the metropolis adjusted Langevin algorithm for sampling from a class of probability measures on high dimensional state spaces that are not globally log-concave.

关键词： Markov chains Wasserstein distances quantitative bounds couplings Euler schemes metropolis algorithm

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Nonequilibrium phase transition in an Ising model without detailed balance

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Physical Review E 2020年第5期102卷 052111-052111页

作者： Manoj Kumar Chandan Dasgupta Centre for Fluid and Complex Systems Coventry University Coventry CV1 5FB United Kingdom International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bengaluru 560089 India Department of Physics Indian Institute of Science Bengaluru 560012 India

We study a two-dimensional ferromagnetic Ising model in which spins are updated using modified versions of the metropolis and Glauber algorithms. These update rules do not obey the detailed balance condition. The steady-state behavior of the model is studied using molecular field theory and Monte Carlo simulations. This model is found to exhibit a nonequilibrium phase transition from a “paramagnetic” state with zero magnetization to a “ferromagnetic” state with nonzero magnetization as the variable that plays the role of temperature in the spin updates is decreased. From detailed Monte Carlo simulations using the modified metropolis algorithm, we demonstrate explicitly the nonequilibrium nature of the transition and show that it cannot be described as an equilibrium transition with an effective temperature different from the temperature used in the spin updates. The critical exponents that characterize the singular behavior near this continuous phase transition are calculated from finite size scaling of specific heat, magnetization, susceptibility, and correlation length. We find that the values of these exponents are the same (within error bars) as those of the equilibrium Ising model in two dimensions.

关键词： Classical statistical mechanics Critical exponents Critical phenomena Phase transitions Finite-size scaling Heatbath algorithm Ising model Mean field theory metropolis algorithm

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