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Accuracy of a one-dimensional reduction of dynamical systems on networks

Physical Review E 2022年第2期105卷 024305-024305页

作者： Prosenjit Kundu Hiroshi Kori Naoki Masuda Department of Mathematics State University of New York at Buffalo Buffalo New York 14260-2900 USA Department of Complexity Science and Engineering The University of Tokyo Chiba 277-8561 Japan Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo Buffalo New York 14260-5030 USA

Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on three approximations in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.

关键词： Complex systems Dynamics of networks Network resilience

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An Improved Unbiased Particle Filter

arXiv

引用

arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

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Nonuniform 3D finite difference elastic wave simulation on staggered grids

arXiv

引用

arXiv 2020年

作者： Gao, Longfei Ghattas, Omar Keyes, David Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX78712 United States Oden Institute for Computational Engineering and Sciences Jackson School of Geosciences Department of Mechanical Engineering The University of Texas at Austin AustinTX78712 United States Applied Mathematics and Computational Science Program Extreme Computing Research Center King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with different grid spacings, separated by nonconforming interfaces. We demonstrate that this layer-wise finite difference discretization has the potential to significantly reduce the simulation cost, compared to its fully uniform counterpart. Stability of such a discretization is achieved by using specially designed difference operators, which are variants of the standard difference operators with adaptations near boundaries or interfaces, and penalty terms, which are appended to the discretized wave system to weakly impose boundary or interface conditions. Combined with specially designed interpolation operators, the discretized wave system is shown to preserve the energy conserving property of the continuous elastic wave equation, and a fortiori ensure the stability of the simulation. Numerical examples are presented to demonstrate the efficacy of the proposed simulation approach. © 2020, CC BY.

关键词： Elastic waves

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Mechanism, catalysis and predictions of 1,3,2-diazaphospholenes: Theoretical insight into highly polarized P-X bonds

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Organic Chemistry Frontiers 2016年第4期3卷 423-433页

作者： Liu, Liu Wu, Yile Chen, Peng Chan, Chinglin Xu, Ji Zhu, Jun Zhao, Yufen Department of Chemistry and Chemical Biology College of Chemistry and Chemical Engineering Key Laboratory for Chemical Biology of Fujian Province China Department of Chemistry National Tsing Hua University Hsinchu 30013 Taiwan Materials Science and Engineering Program University of California San Diego San Diego 92093 CA United States State Key Laboratory of Physical Chemistry of Solid Surfaces Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry College of Chemistry and Chemical Engineering Xiamen University Xiamen Fujian 361005 China

Density functional theory (DFT) calculations were carried out to investigate the hydridic character of several main group hydrides. A P-hydrido-1,3,2-diazaphospholene 1f with two π-electron donor amino groups on the heterocyclic skeleton framework performs as a strong hydride donor owing to the significant n(N)-σ∗(P-H) hyperconjugation. The natural bond orbital analysis reveals that high π-electron delocalization exists in both 1f and the corresponding stable phosphenium E_f ⁺. In addition, 1f is calculated to have a similar catalytic ability for the hydroboration of acetone with pinacolborane, compared to 1e. Thus, a variety of organic substrates activated by 1f are explored, including ketone, imine, isocyanate, CO₂, diazene, alkene, alkyne and epoxide. The results show that the highly polarized and electron-deficient bonds such as CO π bonds are readily activated, whereas 1f seems difficult to react with electron-rich unsaturated bonds of propene and propyne. More importantly, 1,3,2-diazaphospholene-based compounds, featuring an extremely polarized P-X bond (X = CCMe, NMe₂, PMe₂ and SMe), are predicted to have a useful catalytic ability. The preliminary computational results suggest that these P-X compounds could catalyze the silylamination, silylphosphination and silylsulfenylation of acetone with TMSNMe₂, TMSPMe₂ and TMSSMe, respectively. The products are silylethers, which are equivalent to the corresponding alcohols since they easily undergo hydrolysis. Our computational study opens a new avenue to the design of novel main group organocatalysts. © 2016 the Partner Organisations.

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Relative magnetic field and slipping effect on Casson dusty fluid of two phase fluctuating flow over inclined parallel plate

引用

South African Journal of Chemical engineering 2023年 44卷 135-146页

作者： khan, Dolat Kumam, Poom Kumam, Wiyada Suttiarporn, Panawan Rehman, Ali Fixed Point Research Laboratory Fixed Point Theory and Applications Research Group Center of Excellence in Theoretical and Computational Science (TaCS-CoE) Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd. Bang Mod Bangkok Thung Khru 10140 Thailand Center of Excellence in Theoretical and Computational Science (TaCS-CoE) Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd. Bang Mod Bangkok Thung Khru 10140 Thailand Applied Mathematics for Science and Engineering Research Unit (AMSERU) Program in Applied Statistics Department of Mathematics and Computer Science Faculty of Science and Technology Rajamangala University of Technology Thanyaburi (RMUTT) Pathum Thani 12110 Thailand Faculty of Science Energy and Environment King Mongkut's University of Technology North Bangkok Rayong Campus Rayong 21120 Thailand Special Interest Group for Modelling and Data Analytics Faculty of Ocean Engineering Technology and Informatics Universiti Malaysia Terengganu Terengganu Kuala Nerus 21030 Malaysia

Due to its significant applications in magnetic devices for cell separation, magnetic drugs for cancer tumor treatment, blood flow adjustment during surgery, magnetic endoscopy, and fluid pumping in industrial and engineering processes, magnetohydrodynamics (MHD) has a wide range of applications. Therefore, the aim of this study to investigate the Relative Magnetic Field and slipping effect on Casson dusty fluid of two-phase fluctuating flow over inclined parallel plate. More exactly, the relative magnetic phenomena are fixed relatively to the plate (MFFRP) or fixed relatively to the fluid (MFFRF). The mathematical modeling was established as the set of partial differential equations for dusty Casson fluid. Buckingham's pi theorem is used to find out the dimensionless variables, to make our system dimensionless. The solution in perturb form is to find out by incorporating Poincare–Lighthill perturbation technique (PLPT). To know in-depth different parameters the graphical results for both velocities are plotted with the help of software Mathcad- 15. It is clearly detected that the relative magnetic field performs a vital part in the fluid as well as particle motion. Moreover, the relative magnetic field play a vital role in the decreasing of skin friction of both plates. © 2023

关键词： Brinkman fluid Dust particles Fluctuating vertical plate Inclined relative magnetic field PLPT

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Compaction and Tensile Forces Determine the Accuracy of Folding Landscape Parameters from Single Molecule Pulling Experiments

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Physical Review Letters 2011年第13期106卷 138102-138102页

作者： Greg Morrison Changbong Hyeon Michael Hinczewski D. Thirumalai School of Engineering and Applied Science Harvard University Cambridge Massachusetts 02138 USA Biophysics Program Institute For Physical Science and Technology University of Maryland College Park Maryland 20742 USA School of Computational Sciences Korea Institute for Advanced Study Seoul 130-722 Republic of Korea

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (Pfold=0.5). Using results for the forced unfolding of a RNA hairpin, an exactly soluble model, and an analytic theory, we show that Pfold is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and a leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles.

关键词： Free energy

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Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming

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Physical Review E 2010年第6期82卷 061302-061302页

作者： S. Torquato Y. Jiao Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive-shrinking cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in d-dimensional Euclidean space Rd, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential-linear-programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in Rd for d=2, 3, 4, 5, and 6 with a diversity of disorder and densities up to the respective maximal densities. A novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures (locally maximally dense and mechanically stable packings), besides the usual disordered ones (such as the maximally random jammed state), with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere. For example, in three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range [0.6, 0.7408…], where π/18=0.7408… corresponds to the density of the densest packing. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for d=2, 4, 5, and 6. Our jammed sphere packings are characterized and compared to the corresponding packings generated by the well-known Lubachevsky-Stillinger (LS) molecular-dynamics packing algorithm. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust an

关键词： Packing

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Applying the MVC EA-IRPM to reporting-guidelines in medicine: A strategy that is a web system 4

Applying the MVC EA-IRPM to reporting-guidelines in medicine...

引用

4th IEEE EMBS International Conference on Biomedical and Health Informatics, BHI 2017

作者： Letouze, Patrick De Souza, J.I.M. Silva, Valeria Martins Climaco, Glaubos Chagas, F.B. Ishihara, Joao Y. Graduate Program of Computational Modeling of Systems Universidade Federal Do Tocantins Quadra 109 Norte Avenida NS-15 Palmas77001-090 Brazil Graduate Program of Systems' Engineering and Computation - PESC Universidade Federal Do Rio de Janeiro Rio de Janeiro Brazil Department of Informatics at the Universidade Federal Do Maranh/ Ao - UFMA Brazil Faculty of Computer Science Faculdade Pitagoras Imperatriz Imperatriz Brazil Faculty of Electrical Engineering Universidade de Brasília Brasília Brazil

ISBN: (纸本)9781509041794

Reporting-Guidelines in Medicine play an important role in promoting the quality of reports in health-related research. For instance, a poorly reported research may induce misinterpretation and inappropriate clinical settings. Basically, three major issues regarding Reporting-Guidelines in Medicine has to be addressed: (1) the existence of lots of reporting guidelines covering a broad spectrum of medical research increases the difficulties when reporting a medical research because it may not be clear which guidelines are applicable, or if all related guidelines are considered;(2) most guideline developers have not described how their guidance was developed, consequently tracking guidelines and features for evaluation, or even for correcting, may be not possible;(3) few guideline developers have evaluated the effectiveness of their guidance, then the real value that the guideline brings to reporting the research is not assured. Hence, we propose a solution to these three issues based on the Model-View-Controller Evolutionary Acquisition Interdisciplinary Research Project Management (MVC EA-IRPM) that is simultaneously a strategy and a web system for the development and management of reporting guidelines. © 2017 IEEE.

关键词： Clinical research

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CAUCHY MARKOV RANDOM FIELD PRIORS FOR BAYESIAN INVERSION

arXiv

引用

arXiv 2021年

作者： Suuronen, Jarkko Chada, Neil K. Roininen, Lassi School of Engineering Science Lappeenranta-Lahti University of Technology PO Box 20 LappeenrantaFI-53851 Finland Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed In order to use such priors successfully, sophisticated optimization and Markov chain Monte Carlo (MCMC) methods are usually required In this paper, our focus is largely on reviewing recently developed Cauchy difference priors, while introducing interesting new variants, whilst providing a comparison We firstly propose a one-dimensional second order Cauchy difference prior, and construct new first and second order two-dimensional isotropic Cauchy difference priors Another new Cauchy prior is based on the stochastic partial differential equation approach, derived from Matérn type Gaussian presentation The comparison also includes Cauchy sheets Our numerical computations are based on both maximum a posteriori and conditional mean estimation We exploit state-of-the-art MCMC methodologies such as Metropolis-within-Gibbs, Repelling-Attracting Metropolis, and No-U-Turn sampler variant of Hamiltonian Monte Carlo We demonstrate the models and methods constructed for one-dimensional and two-dimensional deconvolution problems Thorough MCMC statistics are provided for all test cases, including potential scale reduction factors. Copyright © 2021, The Authors. All rights reserved.

关键词： Bayesian networks

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Edge-Stress-Induced Warping of Graphene Sheets and Nanoribbons

引用

Physical Review Letters 2008年第24期101卷 245501-245501页

作者： V. B. Shenoy C. D. Reddy A. Ramasubramaniam Y. W. Zhang Division of Engineering Brown University Providence Rhode Island 02912 USA Institute of High Performance Computing Singapore 138632 Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Materials Science and Engineering National University of Singapore Singapore 119260

We show that edge stresses introduce intrinsic ripples in freestanding graphene sheets even in the absence of any thermal effects. Compressive edge stresses along zigzag and armchair edges of the sheet cause out-of-plane warping to attain several degenerate mode shapes. Based on elastic plate theory, we identify scaling laws for the amplitude and penetration depth of edge ripples as a function of wavelength. We also demonstrate that edge stresses can lead to twisting and scrolling of nanoribbons as seen in experiments. Our results underscore the importance of accounting for edge stresses in thermal theories and electronic structure calculations for freestanding graphene sheets.

关键词： Nanoribbons

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