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SSRN 2022年

作者： Nikravesh, Y. Latypov, Marat I. Frantziskonis, G. Muralidharan, Krishna Department of Civil and Architectural Engineering and Mechanics University of Arizona TucsonAZ85721 United States Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Lunar and Planetary Laboratory University of Arizona TucsonAZ85721 United States

Using classical molecular dynamics, we investigate the cold-spray additive manufacturing process involving copper particles impacting a copper substrate. Specifically, we develop fundamental insights into the interplay between particle size, particle velocity and ensuing penetration depth of the particle and the effective adhesion strength that binds the impinging particle with the substrate. Equally importantly, we also establish a quantitative constitutive relationship that governs the process variables (i.e., particle size, particle velocity), the resulting particle penetration depth and impact bonding energy. By examining the formation and evolution of adiabatic shear bands and dislocation densities within the particle and the substrate, as well as by examining the structural evolution of the impinging particle as a function of process variables in conjunction with observations of material jetting, we shed light on the deformation mechanisms that govern the cold spray process, and provide a fundamental basis for understanding the presence of a critical velocity that must be overcome in order to promote strong adhesion of the particle with the substrate. Further, by developing a comprehensive constitutive relationship that relates the process variables to the resulting penetration of the particle and the extent of impact bonding, we enable the ability to upscale information derived at the nanometric scales to experimental scales. This work thus serves as a steppingstone in not only answering fundamental interrelationships that govern the cold spray process, but also in the quest for developing comprehensive integrated computational materials engineering models for optimizing the process conditions underlying the cold spray process. © 2022, The Authors. All rights reserved.

关键词： Molecular dynamics

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ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

arXiv

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arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

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Stochastic Paleoclimatology: Modeling the EPICA Ice Core Climate Records

arXiv

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arXiv 2022年

作者： Keyes, N.D.B. Giorgini, L.T. Wettlaufer, J.S. Program in Applied Mathematics Yale University New HavenCT06520 United States Department of Earth & Planetary Sciences Yale University New HavenCT06520 United States Nordic Institute for Theoretical Physics Royal Institute of Technology Stockholm University Stockholm10691 Sweden Department of Physics Yale University New HavenCT06520 United States

We analyze and model the stochastic behavior of paleoclimate time series and assess the implications for the coupling of climate variables during the Pleistocene glacial cycles. We examine 800 kiloyears of carbon dioxide, methane, nitrous oxide and temperature proxy data from the EPICA Dome-C ice core, which are characterized by 100 ky glacial cycles overlain by fluctuations across a wide range of time scales. We quantify this behavior through multifractal time-weighted detrended fluctuation analysis, which distinguishes near-red-noise and white-noise behavior below and above the 100 ky glacial cycle respectively in all records. This allows us to model each time series as a one-dimensional periodic nonautonomous stochastic dynamical system, and assess the stability of physical processes and the fidelity of model-simulated time series. We extend this approach to a four-variable model with intervariable coupling terms, which we interpret in terms of possible interrelationships among the four time series. Within the framework of our coupling coefficients, we find that carbon dioxide and temperature act to stabilize each other and methane and nitrous oxide, whereas the latter two destabilize each other and carbon dioxide and temperature. We also compute the response function for each pair of variables to assess the model performance by comparison to the data and confirm the model predictions regarding stability amongst variables. Taken together, our results are consistent with glacial pacing dominated by carbon dioxide and temperature that is modulated by terrestrial biosphere feedbacks associated with methane and nitrous oxide emissions. © 2022, CC BY.

关键词： Carbon dioxide

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Image Recovery from Rotational And Translational Invariants

Image Recovery from Rotational And Translational Invariants

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Nicholas F. Marshall Ti-Yen Lan Tamir Bendory Amit Singer Department of Mathematics Princeton University Princeton NJ USA The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Electrical Engineering Tel Aviv University Tel Aviv Israel

ISBN: (数字)9781509066315

ISBN: (纸本)9781509066322

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotational and translational invariants and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.

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Characterizing the hyperuniformity of ordered and disordered two-phase media

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Physical Review E 2021年第1期103卷 012123-012123页

作者： Jaeuk Kim Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform two-phase heterogeneous media, which include composites, porous media, foams, cellular solids, colloidal suspensions, and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σV2(R) and the associated hyperuniformity order metrics B¯V. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements, and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered or irregular packings of circular disks, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have minimal values of the hyperuniformity order metrics B¯V across all volume fractions. On the other hand, for all packings of circular disks examined, the triangular-lattice packings have the smallest values of B¯V for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing of circular disks have the minimal values of the order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems with desirable bulk physical properties by inverse d

关键词： Patterns in complex systems

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Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

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Physical Review B 2021年第1期103卷 014118-014118页

作者： Amartya Bose Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the “τ order metric” of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the “τ order metric,” even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless

关键词： Long-range interactions Quantum phase transitions Spin chains

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Transcutaneous Vagus Nerve Stimulation: an Alternative Treatment of Chronic Migraine—a Systematic Review

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SN Comprehensive Clinical Medicine 2022年第1期4卷 1-13页

作者： de Carvalho, Ana Cláudia Marques, Aeska Lanary Cristino Ferreira, Lais Leite de Brito, Francisco Xavier Baptista, Abrahão Fontes da Silva, Marcelo Lourenço da Silva, Josie Resende Torres Federal University of Alfenas Alfenas Brazil Biosciences Applied to Health Program Federal University of Alfenas Alfenas Brazil Health and Function Study Nucleus Federal University of Bahia Salvador Bahia Brazil Center for Mathematics Computation and Cognition Federal University of ABC São Paulo Brazil Institute of Motricity Sciences Federal University of Alfenas Alfenas Brazil Federal University of Alfenas LANNED Laboratory of Neuroscience Neuromodulation and Study of Pain Alfenas Brazil

Migraine is a disabling condition that is currently underdiagnosed and undertreated. Transcutaneous vagus nerve stimulation (VNS) is among the most researched non-invasive brain stimulation techniques for migraine control. In this systematic review, we discuss the effects of VNS parameters (waveform, frequency, intensity, cycle, and current) and central and clinical mechanisms in auricular (taVNS) or cervical (tcVNS) transcutaneous VNS in the control of migraine pain. PubMed (National Library of Medicine), Cochrane Library, CAPES Journals (Portal of Journals of the Coordination for the Improvement of Higher Education Personnel), Virtual Health Library (VHL), and Google Scholar were searched by computer from the establishment of within the 10-year period (2011– 2021). Initially, a total of 10,017 articles were identified. After applying the exclusion criteria, 10,007 articles were excluded. The eligibility criteria were analyzed and only ten articles fulfilled the criteria. The most used parameters in this study for VNS were the frequencies of 1 Hz, 25 Hz, and 30 Hz. The 1-Hz stimulation caused a more significant reduction in the number of days with headache. The total stimulation time varies between studies, ranging from 2 to 240 min, and can be repeated for a period or a single session. Studies that used a longer treatment period showed clinical results in reducing pain and analyzed the scores. Moreover, studies have shown reduced intensity or severity of pain after taVNS. The studies performed taVNS or tcVNS, and both methods had positive effects on migraine control, pain reduction, and migraine score. An systematic literature review of transcutaneous vagus nerve stimulation (tVNS) on migraine pain management. The results indicate that auricular or cervical tVNS methods had positive effects on migraine control, pain reduction, and migraine score.

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Applications of mean field games in financial engineering and economic theory

arXiv

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arXiv 2020年

作者： Carmona, René DEPARTMENT OF OPERATIONS RESEARCH & FINANCIAL ENGINEERING BENDHEIM CENTER FOR FINANCE PROGRAM IN APPLIED & COMPUTATIONAL MATHEMATICS PRINCETON UNIVERSITY United States

This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront that several of the examples reviewed in this chapter were already discussed in book form. Still, they are here accompanied with discussions of, and references to, works which appeared over the last three years. Moreover, several completely new sections are added to show how recent developments in financial engineering and economics can benefit from being viewed through the lens of the Mean Field Game paradigm. The new financial engineering applications deal with bitcoin mining and the energy markets, while the new economic applications concern models offering a smooth transition between macro-economics and finance, and contract *** Codes 60, 91 © 2020, CC BY.

关键词： Finance

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Model of virus therapy and chemotherapy for cancer 3

Model of virus therapy and chemotherapy for cancer

引用

3rd International Conference on Natural and Environmental Sciences 2019, ICONES 2019

作者： Safitri, E. Tarmizi, T. Ramli, M. Wahyuni, S. Ikhwan, M. Mathematics Graduate Study Program Universitas Syiah Kuala Banda Aceh23111 Indonesia Department of Mathematics Universitas Syiah Kuala Banda Aceh23111 Indonesia Graduate School of Mathematics and Applied Science Universitas Syiah Kuala Banda Aceh23111 Indonesia

This article discusses the mathematical model of changes in the number of cancer cells as a result of the intervention. Here the effect of combination treatment, in the form of virus injection and chemotherapy on tumor cells, is presented in detail. There are two different tumor cells, uninfected tumor cells and infected tumor cells. Model simulations with different parameters were performed for 700 d. The initial values for the population of virus-infected tumor cells are divided into two categories. The number of tumor cells injected with the virus is 1/2 (half) and all tumor cells that are not infected. Based on the simulation results, it was concluded that the more the number of tumor cells injected with the virus, the faster the decrease in the number of tumor cell populations. It was also concluded that the reduced population of tumor cells reduces the amount of chemotherapy concentration used. © 2019 Published under licence by IOP Publishing Ltd.

关键词： Viruses

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Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit

引用

Open Journal of Modelling and Simulation 2021年第2期9卷 159-171页

作者： Camila de Andrade Kalil Maria Clícia Stelling de Castro Dilson Silva Célia Martins Cortez Postgraduate Program in Computational Sciences Rio de Janeiro State University Rio de Janeiro Brazil Department of Informatics and Computer Science Rio de Janeiro State University Rio de Janeiro Brazil Department of Applied Mathematics Rio de Janeiro State University Rio de Janeiro Brazil

The aim of the present study is to contribute to the knowledge about the functioning of the neuronal circuits. We built a mathematical-computational model using graph theory for a complex neurophysiological circuit consisting of a reverberating neuronal circuit and a parallel neuronal circuit, which could be coupled. Implementing our model in C++ and applying neurophysiological values found in the literature, we studied the discharge pattern of the reverberant circuit and the parallel circuit separately for the same input signal pattern, examining the influence of the refractory period and the synaptic delay on the respective output signal patterns. Then, the same study was performed for the complete circuit, in which the two circuits were coupled, and the parallel circuit could then influence the functioning of the reverberant. The results showed that the refractory period played an important role in forming the pattern of the output spectrum of a reverberating circuit. The inhibitory action of the parallel circuit was able to regulate the reverberation frequency, suggesting that parallel circuits may be involved in the control of reverberation circuits related to motive activities underlying precision tasks and perhaps underlying neural work processes and immediate memories.

关键词： Mathematical-Computational Modelling Neurophysiological Circuit Reverberating Circuit Parallel Circuit

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