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Challenges in control of Covid-19: Short doubling time and long delay to effect of interventions

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arXiv 2020年

作者： Pellis, Lorenzo Scarabel, Francesca Stage, Helena B. Overton, Christopher E. Chappell, Lauren H.K. Lythgoe, Katrina A. Fearon, Elizabeth Bennett, Emma Curran-Sebastian, Jacob Das, Rajenki Fyles, Martyn Lewkowicz, Hugo Pang, Xiaoxi Vekaria, Bindu Webb, Luke House, Thomas Hall, Ian Department of Mathematics University of Manchester United Kingdom LIAM - Laboratory of Industrial and Applied Mathematics Department of Mathematics and Statistics York University TorontoON Canada CDLab - Computational Dynamics Laboratory Department of Mathematics Computer Science and Physics University of Udine Italy Department of Plant Sciences University of Oxford United Kingdom Big Data Institute University of Oxford United Kingdom Department of Global Health and Development London School of Hygiene and Tropical Medicine United Kingdom Emergency Response Department Public Health England United Kingdom IBM Research Hartree Centre SciTech Daresbury Warrington United Kingdom

Early assessments of the spreading rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but more reliable inferences can now be made. Here, we estimate from European data that COVID-19 cases are expected to double initially every three days, until social distancing interventions slow this growth, and that the impact of such measures is typically only seen nine days - i.e. three doubling times - after their implementation. We argue that such temporal patterns are more critical than precise estimates of the basic reproduction number for initiating interventions. This observation has particular implications for the low- and middle-income countries currently in the early stages of their local epidemics. Copyright © 2020, The Authors. All rights reserved.

关键词： Cell proliferation

Kinetic Frustration Effects on Dense Two-Dimensional Packings of Convex Particles and Their Structural Characteristics

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arXiv 2021年

作者： Maher, Charles Emmett Stillinger, Frank H. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The study of hard-particle packings is of fundamental importance in physics, chemistry, cell biology, and discrete geometry. Much of the previous work on hard-particle packings concerns their densest possible arrangements. By contrast, we examine kinetic effects inevitably present in both numerical and experimental packing protocols. Specifically, we determine how changing the compression/shear rate of a two-dimensional packing of noncircular particles causes it to deviate from its densest possible configuration, which is always periodic. The adaptive shrinking cell (ASC) optimization scheme maximizes the packing fraction of a hard-particle packing by first applying random translations and rotations to the particles and then isotropically compressing and shearing the simulation box repeatedly until a possibly jammed state is reached. We use a stochastic implementation of the ASC optimization scheme to mimic different effective time scales by varying the number of particle moves between compressions/shears. We generate dense, effectively jammed, monodisperse, two-dimensional packings of obtuse scalene triangle, rhombus, curved triangle, lens, and "ice cream cone" (a semicircle grafted onto an isosceles triangle) shaped particles, with a wide range of packing fractions and degrees of order. To quantify these kinetic effects, we introduce the kinetic frustration index K, which measures the deviation of a packing from its maximum possible packing fraction. To investigate how kinetics affect short- and long-range ordering in these packings, we compute their spectral densities χV (k) and characterize their contact networks. We find that kinetic effects are most significant when the particles have greater asphericity, less curvature, and less rotational symmetry. This work may be relevant to the design of laboratory packing protocols. Copyright © 2021, The Authors. All rights reserved.

关键词： Kinetic theory

Effective Elastic Wave Characteristics of Composite Media

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arXiv 2020年

作者： Kim, Jaeuk Torquato, S. Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the "strong-contrast" expansion formalism that was previously applied to the static problem. These strong-contrast expansions explicitly incorporate complete microstructural information of the composite via an infinite set of n-point correlation functions. Utilizing the rapid-convergence properties of these series expansions (even for extreme contrast ratios), we extract accurate approximations that depend on the microstructure via the spectral density, which is easy to compute or measure for any composite. We also investigate the predictive power of modifications of such approximation formulas postulated elsewhere [J. Kim and S. Torquato, Proc. Nat. Acad. Sci. 117, 8764 (2020)] to extend their applicability beyond the quasistatic regime. The accuracy of these nonlocal microstructure-dependent approximations is validated by comparison to full-waveform simulation results for certain models of dispersions. We apply our formulas to a variety of models of nonhyperuniform and hyperuniform disordered composites. We demonstrate that hyperuniform systems are less lossy than their nonhyperuniform counterparts in the quasistatic regime, and stealthy hyperuniform media can be perfectly transparent for a wide range of wavenumbers. Finally, we discuss how to utilize our approximations for engineering composites with prescribed elastic wave characteristics. Copyright © 2020, The Authors. All rights reserved.

关键词： Microstructure

Modeling Global Dynamics from Local Snapshots with Deep Generative Neural Networks

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Modeling Global Dynamics from Local Snapshots with Deep Gene...

International Conference on Sampling Theory and Applications (SampTA)

作者： Scott Gigante David van Dijk Kevin R. Moon Alexander Strzalkowski Guy Wolf Smita Krishnaswamy Computational Biology and Bioinformatics Program Yale University New Haven CT USA Department of Genetics Yale University New Haven CT USA Department of Mathematics and Statistics Utah State University Logan UT USA Department of Computer Science Princeton University Princeton NJ USA Department of Mathematics and Statistics Université de Montréal Montéal QC Canada

ISBN: (数字)9781728137414

ISBN: (纸本)9781728137421

Complex high dimensional stochastic dynamic systems arise in many applications in the natural sciences and especially biology. However, while these systems are difficult to describe analytically, "snapshot" measurements that sample the output of the system are often available. In order to model the dynamics of such systems given snapshot data, or local transitions, we present a deep neural network framework we call Dynamics Modeling Network or DyMoN. DyMoN is a neural network framework trained as a deep generative Markov model whose next state is a probability distribution based on the current state. DyMoN is trained using samples of current and next-state pairs, and thus does not require longitudinal measurements. We show the advantage of DyMoN over shallow models such as Kalman filters and hidden Markov models, and other deep models such as recurrent neural networks in its ability to embody the dynamics (which can be studied via perturbation of the neural network) and generate longitudinal hypothetical trajectories. We perform three case studies in which we apply DyMoN to different types of biological systems and extract features of the dynamics in each case by examining the learned model.

关键词： Hidden Markov models Trajectory Neural networks Biological system modeling Data models Markov processes

A fluctuating boundary integral method for brownian suspensions

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arXiv 2017年

作者： Bao, Yuanxun Rachh, Manas Keaveny, Eric E. Greengard, Leslie Donev, Aleksandar Courant Institute of Mathematical Sciences New York University 251 Mercer Street New YorkNY United States Applied Mathematics Program Yale University New HavenCT06511 United States Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom Center for Computational Biology Flatiron Institute New YorkNY United States

We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green’s function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation-dissipation balance relation (DFDB). Based on a recently-developed Positively Split Ewald method [A. M. Fiore, F. Balboa Usabiaga, A. Donev and J. W. Swan, J. Chem. Phys., 146, 124116, 2017], near-field contributions to the Brownian displacements are efficiently approximated by iterative methods in real space, while far-field contributions are rapidly generated by fast Fourier-space methods based on fluctuating hydrodynamics. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator. Copyright © 2017, The Authors. All rights reserved.

关键词： Boundary integral equations

Multifunctional Composites for Elastic and Electromagnetic Wave Propagation

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arXiv 2019年

作者： Kim, Jaeuk Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Composites are ideally suited to achieve desirable multifunctional effective properties, since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish the first cross-property relations for two-phase composite media that link effective elastic and electromagnetic wave characteristics to one another, including effective wave speeds and attenuation coefficients. This is achieved by deriving accurate formulas for the effective elastodynamic properties that depend on the microstructure via the spectral density and utilizing previous analogous results for effective electromagnetic properties. Our formulas enable us to explore the wave characteristics of a broad class of disordered microstructures, including exotic disordered "hyperuniform" varieties, that can have advantages over crystalline ones, such as nearly optimal, direction-independent properties and robustness against defects. We specifically show that disordered "stealthy" hyperuniform/nonhyperuniform microstructures exhibit novel elastic wave characteristics that have the potential for future applications, e.g., low-pass or narrow-band-pass (using negative Poisson ratio materials) filters that transmit or absorb elastic waves "isotropically" for a range of wavenumbers. We also demonstrate that two-phase media with engineered disorder and phase properties can exhibit "anomalous dispersion" with resonance-like attenuation. Our cross-property relations for effective wave characteristics can be applied to design multifunctional composites via inverse techniques, including exterior components of spacecraft or building materials that require both excellent stiffness and electromagnetic absorption, and heat-sinks for CPUs that have to efficiently emit thermal radiation and suppress mechanical vibrations, and nondestructive evaluation of the elastic moduli of materials from the effective dielectric response. DR Copyright © 2019, The Authors. All rights res

关键词： Microstructure

Documentation and 3D modeling of railway industrial heritage: Study of the Cajo-Santander locomotive shed 2

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Documentation and 3D modeling of railway industrial heritage...

2nd Digital Heritage International Congress: Analysis and Interpretation - Theory, Methodologies, Preservation and Standards - Digital Heritage Projects and Applications, Digital Heritage 2015

作者： Cobos, Óscar J. Cosido Soto, José Luis Lalana Vega, Leticia Terán Campi, Massimiliano Catuogno, Raffaele Ramirez, Lucía Hernández Llamas, José Pereda Vidal, Esteban Sainz Department of Applied Mathematics and Computational Sciences University of Cantabria Santander39006 Spain University Institute of Urban Superior Technical School of Architecture of the University of Valladolid Valladolid47014 Spain CEFEM Santander City Council Santander39009 Spain 3DIntelligence Santander39008 Spain DiARC Department of Architecture University of Naples FEDERICO II Naples80134 Italy Dpto. C.A.I.T. Mechanics of Continuous Media and the Theory of Structures University of Valladolid Spain

ISBN: (纸本)9781509000487

The works of three-dimensional documentation of the industrial heritage of Santander, which are carried out under the initiative of the authors of the article had the cooperation of the University of Cantabria, University of Naples 'Federico II', University of Valladolid and the 3DIntelligence company. Within this project, it has been made the documentation of locomotive shed and the roundabout structure, key piece of industrial railway heritage in Santander. For this project we used the fusion of data (point clouds) from the Scanner-Laser and data from convergent photogrammetry. This initiative has enjoyed the cooperation of the RENFE company, who allowed access to their infrastructure. Both structures are currently in use, making complex the data collection phase. © 2015 IEEE.

关键词： Photogrammetry

Data-driven molecular modeling with the generalized Langevin equation

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arXiv 2019年

作者： Grogan, Francesca Lei, Huan Li, Xiantao Baker, Nathan A. Pacific Northwest National Laboratory RichlandWA99352 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Statistics and Probability Michigan State University East LansingMI48824 United States Department of Mathematics Pennsylvania State University State College PA16801 United States Division of Applied Mathematics Brown University ProvidenceRI02912 United States

The complexity of molecular dynamics simulations necessitates dimension reduction and coarsegraining techniques to enable tractable computation. The generalized Langevin equation (GLE) describes coarse-grained dynamics in reduced dimensions. In spite of playing a crucial role in non-equilibrium dynamics, the memory kernel of the GLE is often ignored because it is difficult to characterize and expensive to solve. To address these issues, we construct a data-driven rational approximation to the GLE. Building upon previous work leveraging the GLE to simulate simple systems, we extend these results to more complex molecules, whose many degrees of freedom and complicated dynamics require approximation methods. We demonstrate the effectiveness of our approximation by testing it against exact methods and comparing observables such as autocorrelation and transition rates. Copyright © 2019, The Authors. All rights reserved.

关键词： Molecular dynamics

The Assessment of Vibrational Non-equilibrium Effect on Detonation

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The Assessment of Vibrational Non-equilibrium Effect on Deto...

第二届高温气体动力学国际会议

作者： Lisong Shi Hua Shen Peng Zhang Deliang Zhang Chihyung Wen Department of Mechanical Engineering The Hong Kong Polytechnic University Applied Mathematics and Computational Science King Abdullah University of Science and Technology State Key Laboratory of High Temperature Gas Dynamics Institute of Mechanics Chinese Academy of sciences

Published simulations indicated that the calculated detonation cell sizes are significantly smaller compared to the experimental *** research targets to narrow down this discrepancy,by accounting the non-equilibrium effect between vibrational energy and translational-rotational energy,and the influence on reaction rates.A series of 1D and 2D numerical investigation are

关键词： The Assessment of Vibrational Non-equilibrium Effect on Detonation