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arXiv 2018年

作者： Chu, Ran Endeve, Eirik Hauck, Cory D. Mezzacappa, Anthony Computational and Applied Mathematics Group Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996-1200 United States Joint Institute for Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37831-6354 United States Department of Mathematics University of Tennessee KnoxvilleTN37996-1320 United States

Building on the framework of Zhang & Shu [1, 2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f. The two-moment model is closed using algebraic moment closures;e.g., as proposed by Cernohorsky & Bludman [3] and Banach & Larecki [4]. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli's exclusion principle, which demands a bounded distribution function (i.e., f ∈ [0, 1]). This realizability-preserving scheme combines a suitable CFL condition, a realizability-enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combined with a backward Euler step. The IMEX scheme is formally only first-order accurate, but works well in the diffusion limit, and - without interactions with the background - reduces to the optimal second-order strong stability-preserving explicit Runge-Kutta scheme of Shu & Osher [5]. Numerical results demonstrate the realizability-preserving properties of the scheme. We also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport. Copyright © 2018, The Authors. All rights reserved.

关键词： Galerkin methods

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Dynamics, scaling behavior, and control of nuclear wrinkling

arXiv

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arXiv 2022年

作者： Jackson, Jonathan A. Romeo, Nicolas Mietke, Alexander Burns, Keaton J. Totz, Jan F. Martin, Adam C. Dunkel, Jörn Alsous, Jasmin Imran Department of Biology Massachusetts Institute of Technology United States Graduate Program in Biophysics Harvard University United States Department of Mathematics Massachusetts Institute of Technology United States Department of Physics Massachusetts Institute of Technology United States School of Mathematics University of Bristol United Kingdom Center for Computational Biology Flatiron Institute Simons Foundation United States

The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. Here, we combine live-imaging experiments, theory, and simulations to characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly, Drosophila melanogaster, when nurse cell nuclei increase in size and display stereotypical wrinkling behavior. A spectral analysis of three-dimensional high-resolution data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing mechanical properties of the nuclear envelope. Our findings advance the biophysical understanding of nuclear membrane fluctuations during early multicellular development. Copyright © 2022, The Authors. All rights reserved.

关键词： Spectrum analysis

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N-ACT: An Interpretable Deep Learning Model for Automatic Cell Type and Salient Gene Identification

arXiv

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arXiv 2022年

作者： Ali Heydari, A. Davalos, Oscar A. Hoyer, Katrina K. Sindi, Suzanne S. Department of Applied Mathematics University of California United States Health Sciences Research Institute Quantitative and Systems Biology Graduate Program Department of Molecular and Cell Biology University of California Merced United States

Single-cell RNA sequencing (scRNAseq) is rapidly advancing our understanding of cellular composition within complex tissues and organisms. A major limitation in most scRNAseq analysis pipelines is the reliance on manual annotations to determine cell identities, which are time consuming, subjective, and require expertise. Given the surge in cell sequencing, supervised methods–especially deep learning models–have been developed for automatic cell type identification (ACTI), which achieve high accuracy and scalability. However, all existing deep learning frameworks for ACTI lack interpretability and are used as "black-box" models. We present N-ACT (Neural-Attention for Cell Type identification): the first-of-its-kind interpretable deep neural network for ACTI utilizing neural attention to detect salient genes for use in cell-types identification. We compare N-ACT to conventional annotation methods on two previously manually annotated data sets, demonstrating that N-ACT accurately identifies marker genes and cell types in an unsupervised manner, while performing comparably on multiple data sets to current state-of-the-art model in traditional supervised ACTI. © 2022, CC BY.

关键词： Genes

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Feature selection using stochastic gates

arXiv

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arXiv 2018年

作者： Yamada, Yutaro Lindenbaum, Ofir Negahban, Sahand Kluger, Yuval Statistics Department Yale University New HavenCT United States Applied Mathematics Program Yale University New HavenCT United States Computational Biology and Bioinformatics Yale University New HavenCT United States Department of Pathology Yale University New HavenCT United States

Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection in high-dimensional non-linear function estimation problems. The new procedure is based on minimizing the `0 norm of the vector of indicator variables that represent if a feature is selected or not. Our approach relies on the continuous relaxation of Bernoulli distributions, which allows our model to learn the parameters of the approximate Bernoulli distributions via gradient descent. This general framework simultaneously minimizes a loss function while selecting relevant features. Furthermore, we provide an information-theoretic justification of incorporating Bernoulli distribution into our approach and demonstrate the potential of the approach on synthetic and real-life applications. Copyright © 2018, The Authors. All rights reserved.

关键词： Feature extraction

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Inferring solar differential rotation through normal-mode coupling using bayesian statistics

arXiv

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arXiv 2021年

作者： Kashyap, Samarth Ganesh Bharati Das, Srijan Hanasoge, Shravan M. Woodard, Martin F. Tromp, Jeroen Department of Astronomy and Astrophysics Tata Institute of Fundamental Research Mumbai India Department of Geosciences Princeton University PrincetonNJ United States NorthWest Research Associates Boulder Office 3380 Mitchell Lane BoulderCO United States Department of Geosciences and Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

Normal-mode helioseismic data analysis uses observed solar oscillation spectra to infer perturbations in the solar interior due to global and local-scale flows and structural asphericity. Differential rotation, the dominant global-scale axisymmetric perturbation, has been tightly constrained primarily using measurements of frequency splittings via "a-coefficients". However, the frequency-splitting formalism invokes the approximation that multiplets are isolated. This assumption is inaccurate for modes at high angular degrees. Analysing eigenfunction corrections, which respect cross coupling of modes across multiplets, is a more accurate approach. However, applying standard inversion techniques using these cross-spectral measurements yields a-coefficients with a significantly wider spread than the well-constrained results from frequency splittings. In this study, we apply Bayesian statistics to infer a-coefficients due to differential rotation from cross spectra for both f-modes and p-modes. We demonstrate that this technique works reasonably well for modes with angular degrees ` = 50 − 291. The inferred a3−coefficients are found to be within 1 nHz of the frequency splitting values for ` > 200. We also show that the technique fails at ` © 2021, CC BY.

关键词： Eigenvalues and eigenfunctions

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A new phase-field approach to variational implicit solvation of charged molecules with the coulomb-field approximation

arXiv

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arXiv 2017年

作者： Zhao, Yanxiang Ma, Yanping Sun, Hui Li, Bo Du, Qiang Department of Mathematics George Washington University 801 22nd St. NW Phillips 739 WashingtonDC20052 United States Department of Mathematics Loyola Marymount University 1 LMU drive Los AngelesCA90045 United States Department of Mathematics and Statistics California State University Long BeachCA90840-1001 United States Department of Mathematics and Quantitative Biology Graduate Program University of California San Diego 9500 Gilman Drive Mail code: 0112 La JollaCA92093-0112 United States Department of Applied Physics and Applied Mathematics Columbia University NY10027 United States

We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and electrostatic interaction energy that is described by the Coulomb-field approximation, all coupled together self-consistently through a phase field. By introducing a new phase-field term in the description of the solute-solvent van der Waals and electrostatic interactions, we can keep the phase-field values closer to those describing the solute and solvent regions, respectively, making it more accurate in the free-energy estimate. We first prove that our phase-field functionals Γ-converge to the corresponding sharp-interface limit. We then develop and implement an efficient and stable numerical method to solve the resulting gradient-flow equation to obtain equilibrium conformations and their associated free energies of the underlying charged molecular system. Our numerical method combines a linear splitting scheme, spectral discretization, and exponential time differencing Runge-Kutta approximations. Applications to the solvation of single ions and a two-plate system demonstrate that our new phase-field implementation improves the previous ones by achieving the localization of the system forces near the solute-solvent interface and maintaining more robustly the desirable hyperbolic tangent profile for even larger interfacial width. This work provides a scheme to resolve the possible unphysical feature of negative values in the phase-field function found in the previous phase-field modeling (cf. H. Sun, et al. J. Chem. Phys., 2015) of charged molecules with the Poisson-Boltzmann equation for the electrostatic interaction. Copyright © 2017, The Authors. All rights reserved.

关键词： Free energy

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No treeline shift despite climate change over the last 70 years

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Forest Ecosystems 2022年第1期9卷 13-22页

作者： Mirela Beloiu Dimitris Poursanidis Antonis Tsakirakis Nektarios Chrysoulakis Samuel Hoffmann Petros Lymberakis Antonis Barnias David Kienle Carl Beierkuhnlein Department of Biogeography University of BayreuthUniversitatsstraaße 3095447BayreuthGermany Remote Sensing Lab Institute of Applied and Computational MathematicsFoundation for Research and Technology Hellas100 N.Plastira Str.Vassilika VoutonHeraklion70013Greece Samaria National Park Management BodyOld National Road Chanion-KissamouAgioi ApostoloiChaniaCreteGreece Natural History Museum of Crete University of CreteKnossou Av.71409IrakleioCreteGreece GIB Department of Geography University of Bayreuth95447BayreuthGermany BayCEER Bayreuth Center of Ecology and Environmental Research University of Bayreuth95448BayreuthGermany

Background:The recent rise in temperature and shifting precipitation regimes threaten ecosystems around the globe to different *** are expected to respond to climate warming by shifting to higher elevations,but it is unclear whether they can track temperature ***,we integrated high-resolution aerial imagery with local climatic and topographic characteristics to study the treeline dynamic from 1945 to 2015 on the semiarid Mediterranean island of Crete,***:During the study period,the mean annual temperature at the treeline increased by 0.81℃,while the average precipitation decreased by 170 *** treeline is characterized by a diffuse form,with trees growing on steep limestone slopes(>50°)and shallow ***,the treeline elevation decreases with increasing distance from the coast and with aspect(south>north).Yet,we found no shift in the treeline over the past 70 years,despite an increase in temperature in all four study ***,the treeline elevation correlated strongly with topographic exposure to wind(R^(2)=0.74,p<0.001).Therefore,the temporal lag in treeline response to warming could be explained by a combination of topographic and microclimatic factors,such as the absence of a shelter effect and a decrease in ***:Although there was no treeline shift over the last 70 years,climate change has already started shifting the treeline altitudinal ***,the lack of climate-mediated migration at the treeline should raise concerns about the threats posed by warming,such as drought damages,and wildfire,especially in the Mediterranean ***,conservation management should discuss options and needs to support adaptive management.

关键词： Aerial imagery Protected area Continental island Mediterranean region High mountains Temperature Precipitation Climate change Forest dynamics

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Coarse-grained descriptions of dynamics for networks with both intrinsic and structural heterogeneities

arXiv

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arXiv 2017年

作者： Bertalan, Tom Wu, Yan Laing, Carlo William Gear, C. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University PrincetonNJ United States Department of Bioengineering University of California San DiegoCA United States Institute of Natural and Mathematical Sciences Massey University Auckland New Zealand Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and, ultimately, design. Here we propose and illustrate a systematic and powerful approach to obtaining good collective coarse-grained observables-variables successfully summarizing the detailed state of such networks. Finding such variables can naturally lead to successful reduced dynamic models for the networks. The main premise enabling our approach is the assumption that the behavior of a node in the network depends (after a short initial transient) on the node identity: a set of descriptors that quantify the node properties, whether intrinsic (e.g. parameters in the node evolution equations) or structural (imparted to the node by its connectivity in the particular network structure). The approach creates a natural link with modeling and "computational enabling technology" developed in the context of Uncertainty Quantification. In our case, however, we will not focus on ensembles of different realizations of a problem, each with parameters randomly selected from a distribution. We will instead study many coupled heterogeneous units, each characterized by randomly assigned (heterogeneous) parameter value(s). One could then coin the term Heterogeneity Quantification for this approach, which we illustrate through a model dynamic network consisting of coupled oscillators with one intrinsic heterogeneity (oscillator individual frequency) and one structural heterogeneity (oscillator degree in the undirected network). The computational implementation of the approach, its shortcomings and possible extensions are also discussed. Copyright © 2017, The Authors. All rights reserved.

关键词： Data mining

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Bayesian multinomial logistic normal models through marginally latent matrix-T processes

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 255-296页

作者： Justin D. Silverman Kimberly Roche Zachary C. Holmes Lawrence A. David Sayan Mukherjee College of Information Science and Technology Department of Statistics and Institute for Computational and Data Science Penn State University University Park PA Program in Computational Biology and Bioinformatics Duke University Durham NC Department of Molecular Genetics and Microbiology Duke University Durham NC Department of Molecular Genetics and Microbiology and Center for Genomic and Computational Biology Duke University Durham NC Departments of Statistical Science Mathematics Computer Science Biostatistics & Bioinformatics Duke University Durham NC

Bayesian multinomial logistic-normal (MLN) models are popular for the analysis of sequence count data (e.g., microbiome or gene expression data) due to their ability to model multivariate count data with complex covariance structure. However, existing implementations of MLN models are limited to small datasets due to the non-conjugacy of the multinomial and logistic-normal distributions. Motivated by the need to develop efficient inference for Bayesian MLN models, we develop two key ideas. First, we develop the class of Marginally Latent Matrix-T Process (Marginally LTP) models. We demonstrate that many popular MLN models, including those with latent linear, non-linear, and dynamic linear structure are special cases of this class. Second, we develop an efficient inference scheme for Marginally LTP models with specific accelerations for the MLN subclass. Through application to MLN models, we demonstrate that our inference scheme are both highly accurate and often 4-5 orders of magnitude faster than MCMC.

关键词： Bayesian statistics multivariate analysis count data microbiome gene expression

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Charge-Transfer-Induced Cesium Superlattices on Graphene

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Physical Review Letters 2012年第15期108卷 156803-156803页

作者： Can-Li Song Bo Sun Yi-Lin Wang Ye-Ping Jiang Lili Wang Ke He Xi Chen Ping Zhang Xu-Cun Ma Qi-Kun Xue Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing 100190 China State Key Laboratory of Low-Dimensional Quantum Physics Department of Physics Tsinghua University Beijing 100084 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We investigate cesium (Cs) adsorption on graphene formed on a 6H-SiC(0001) substrate by a combined scanning tunneling microscopy and density functional theory study. Individual Cs atoms adsorb preferentially at the rim region of the well-defined 6×6 substrate superstructure and on multilayer graphene. By finely controlling the graphene thickness and Cs coverages (1/3 ML and 1 ML), we here demonstrate two intriguing and well-ordered Cs superlattices on bilayer and multilayer graphene (<6 layers). Statistical analysis of the Cs-Cs interatomic distance reveals a hitherto unobserved Cs-Cs long-range electrostatic potential caused by charge transfer from Cs to graphene, which couples with the inhomogeneous substrate potential to stabilize the observed Cs superlattices. The present study provides a new avenue to fabricate atomic and molecular superlattices for applications in high-density recording and data storage.

关键词： CESIUM GRAPHENE CHARGE transfer SUPERLATTICES ADSORPTION SCANNING tunneling microscopy DENSITY functionals

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