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BPS2025 - Learning the conformational ensemble from cryo-EM

Biophysical Journal 2025年第3期124卷 310a-310a页

作者： Jeffrey Xiang Jake Moomaw Kawamura Diego Sanchez Joshua Rhodes Erik H. Thiede Department of Chemistry and Chemical Biology Cornell University Ithaca NY USA Biophysics Program Cornell University Ithaca NY USA Center for Applied Mathematics Cornell University Ithaca NY USA

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DIFFUSION CURVATURE FOR ESTIMATING LOCAL CURVATURE IN HIGH DIMENSIONAL DATA

arXiv

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arXiv 2022年

作者： Bhaskar, Dhananjay MacDonald, Kincaid Fasina, Oluwadamilola Thomas, Dawson Rieck, Bastian Adelstein, Ian Krishnaswamy, Smita Department of Genetics Yale School of Medicine New HavenCT United States Department of Mathematics Yale University New HavenCT United States Program for Applied Mathematics Yale University New HavenCT United States Department of Physics Yale University New HavenCT United States Institute of AI for Health Helmholtz Pioneer Campus Munich Germany Department of Computer Science Yale University New HavenCT United States Program for Computational Biology and Bioinformatics Yale University New HavenCT United States

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes. © 2022, CC BY.

关键词： Geometry

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A Deep Learning Approach for Nerve Injury Classification in Brachial Plexopathies Using Magnetic Resonance Neurography with Modified Hiking Optimization Algorithm

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Academic Radiology 2025年

作者： Dahou, Abdelghani Elaziz, Mohamed Abd Khattap, Mohamed G. Hassan, Hend Galal Eldeen Mohamed Ali School of Computer Science and Technology Zhejiang Normal University Jinhua 321004 China Mathematics and Computer Science department University of Ahmed DRAIA Adrar 01000 Algeria Department of Mathematics Faculty of Science Zagazig University Zagazig 44519 Egypt Faculty of Computer Science and Engineering Galala University Suez 435611 Egypt Artificial Intelligence Research Center (AIRC) Ajman University Ajman 346 United Arab Emirates Department of Diagnostic Interventional Radiology and Molecular Imaging Faculty of Medicine Ain Shams University Cairo 11591 Egypt Technology of Radiology and Medical Imaging Program Faculty of Applied Health Sciences Technology Galala University Suez 435611 Egypt

Rationale and Objectives: Brachial plexopathies (BPs) encompass a complex spectrum of nerve injuries affecting motor and sensory function in the upper extremities. Diagnosis is challenging due to the intricate anatomy and symptom overlap with other neuropathies. Magnetic Resonance Neurography (MRN) provides advanced imaging but requires specialized interpretation. This study proposes an AI-based framework that combines deep learning (DL) with the modified Hiking Optimization Algorithm (MHOA) enhanced by a Comprehensive Learning (CL) technique to improve the classification of nerve injuries (neuropraxia, axonotmesis, neurotmesis) using MRN data. Materials and Methods: The framework utilizes MobileNetV4 for feature extraction and MHOA for optimized feature selection across different MRI sequences (STIR, T2, T1, and DWI). A dataset of 39 patients diagnosed with BP was used. The framework classifies injuries based on Seddon's criteria, distinguishing between normal and abnormal conditions as well as injury severity. Results: The model achieved excellent performance, with 1.0000 accuracy in distinguishing normal from abnormal conditions using STIR and T2 sequences. For injury severity classification, accuracy was 0.9820 in STIR, outperforming the original HOA and other metaheuristic algorithms. Additionally, high classification accuracy (0.9667) was observed in DWI. The proposed framework outperformed traditional methods and demonstrated high sensitivity and specificity. Conclusion: The proposed AI-based framework significantly improves the diagnosis of BP by accurately classifying nerve injury types. By integrating DL and optimization techniques, it reduces diagnostic variability, making it a valuable tool for clinical settings with limited specialized neuroimaging expertise. This framework has the potential to enhance clinical decision-making and optimize patient outcomes through precise and timely diagnoses. © 2025 The Association of University Radiologists

关键词： Brachial Plexopathy (BP) Comprehensive Learning (CL) Deep Learning (DL) Feature Selection (FS) Hiking Optimization Algorithm (HOA) Magnetic Resonance Neurography (MRN) MobileNetV4

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ZERO KINETIC UNDERCOOLING LIMIT IN THE SUPERCOOLED STEFAN PROBLEM

arXiv

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arXiv 2020年

作者： Baker, Graeme Shkolnikov, Mykhaylo Program in Applied & Computational Mathematics Princeton University PrincetonNJ08544 United States ORFE Department Bendheim Center for Finance Program in Applied & Computational Mathematics Princeton University PrincetonNJ08544 United States

We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium freezing point and the characteristic invariant temperature throughout the liquid our main theorem shows that, as the kinetic undercooling parameter tends to zero, the free boundary converges to the (possibly irregular) free boundary in the supercooled Stefan problem without kinetic undercooling, whose uniqueness has been recently established in [DNS19], [LS18b]. The key tools in the proof are a Feynman-Kac formula, which expresses the free boundary in the problem with kinetic undercooling through a local time of a reflected process, and a resulting comparison principle for the free boundaries with different kinetic undercooling *** Codes 80A22, 35B44, 60H30 Copyright © 2020, The Authors. All rights reserved.

关键词： Supercooling

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The Jacobi theta distribution

arXiv

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arXiv 2021年

作者： Bastian, Caleb Deen Rempala, Grzegorz A. Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Division of Biostatistics The Ohio State University ColumbusOH United States Department of Mathematics The Ohio State University ColumbusOH United States Department of Chemistry Princeton University PrincetonNJ United States

We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the positive reals, has a single positive parameter, is unimodal, positively skewed, and leptokurtic. Its cumulative distribution and density functions are expressed in terms of the Jacobi theta function. We describe asymptotic and log-normal approximations, inference, and a few applications of such distributions to *** Codes 60E05, 60G57 © 2021, CC BY.

关键词： Laplace transforms

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Surrogate approximation of the grad-shafranov free boundary problem via stochastic collocation on sparse grids

arXiv

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arXiv 2021年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Applied Mathematics & Statistics and Scientific Computing Program University of Maryland College Park United States Courant Institute of Mathematical Sciences New York University Department of Mathematics The University of Arizona

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. The use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over *** Codes 65C30, 65C05, 65N35, 65N99, 65Z05 Copyright © 2021, The Authors. All rights reserved.

关键词： Monte Carlo methods

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A deep potential model with long-range electrostatic interactions

arXiv

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arXiv 2021年

作者： Zhang, Linfeng Wang, Han Muniz, Maria Carolina Panagiotopoulos, Athanassios Z. Car, Roberto Weinan, E. DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei+core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the deep potential long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples, the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal. © 2021, CC BY.

关键词： Electrostatics

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Enhanced removal of crystal violet using rawfava bean peels, its chemically activated carbon compared with commercial activated carbon

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Case Studies in Chemical and Environmental Engineering 2024年 9卷

作者： Sh, Husien El-taweel, Reem M. Alrefaey, KhloodA. Labena, Ahmed Fahim, Irene Samy Said, Lobna A. Radwan, Ahmed G. School of Engineering and Applied Sciences Nile University Giza Egypt Industrial Engineering Program SESC Research Center Nile University Giza Egypt Egyptian Petroleum Research Institute (EPRI) Nasr City Cairo Egypt Nanoelectronics Integrated Systems Center (NISC) Nile University Giza Egypt Engineering Mathematics and Physics Dept. Faculty of Engineering Cairo University Giza 12613 Egypt

Crystal violet is a basic dye that is widely used by various industries, such as textiles and paints. These industries discharge their effluents, contaminated with crystal violet, into water streams, and these effluents have an adverse effect on aquatic organisms, the environment, and human health. Crystal violet is a basic dye that is widely used by various industries, such as textiles and paints. These industries discharge their effluents, contaminated with crystal violet, into water streams, and these effluents have an adverse effect on aquatic organisms, the environment, and human health. Hence, this paper is directed at studying the removal of crystal violet using environmentally friendly, cost-effective adsorbent materials such as raw fava bean (RFP-H₃F), and chemically activated carbon (H3F) in comparison to commercial activated carbon (CAC).Various characterization techniques are applied, such as XRD, FT-IR,and SEM analyses. Then, the process of optimizing is shown through some preliminary experiments and a Response Surface Methodology (RSM) experiment to find the best conditions for removing crystal violet efficiently. Results revealed that the raw fava bean peels and the commercial activated carbon have the maximum removal efficiency of 95 %, and 83 % respectively, after 180 min of contact time. It is hypothesized that raw fava bean peels (RFP) and chemically activated carbon using phosphoric acid RFP-H₃F will exhibit comparable efficiency in removing crystal violet when compared to commercial activated carbon (CAC). Various characterization techniques, including X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FT-IR),and scanning electron microscopy (SEM), are applied to analyze the properties of the adsorbent materials. Afterwards, the optimization process is displayed through some preliminary experiments followed by a Response Surface Methodology (RSM) experiment to obtain the optimum conditions, which achieve high

关键词： Adsorption ANN Crystal violet Dyes Fava bean Peels RSM

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Algebraic constraints and algorithms for common lines in cryo-EM

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Biological imaging 2024年 4卷 e9页

作者： Tommi Muller Adriana L Duncan Eric J Verbeke Joe Kileel Mathematical Institute University of Oxford Oxford UK. Department of Mathematics University of Texas at Austin Austin TX USA. Program in Applied and Computational Mathematics Princeton University Princeton NJ USA. Oden Institute University of Texas at Austin Austin TX USA.

We revisit the topic of common lines between projection images in single-particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2 × matrix storing properly scaled basis vectors for the common lines between projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated with the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental datasets.

关键词： ADMM common lines cryo-electron microscopy discrete heterogeneity group synchronization low-rank matrix

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On the Parameter Combinations that Matter and on Those that do Not

arXiv

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arXiv 2021年

作者： Evangelou, Nikolaos Wichrowski, Noah J. Kevrekidis, George A. Dietrich, Felix Kooshkbaghi, Mahdi McFann, Sarah Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Johns Hopkins University United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Department of Mathematics and Statistics University of Massachusetts Amherst United States Department of Informatics Technical University of Munich Germany The Program in Applied and Computational Mathematics Princeton University United States Department of Chemical and Biological Engineering Princeton University United States Lewis-Sigler Institute for Integrative Genomics Princeton University United States

We present a data-driven approach to characterizing nonidentifiability of a model’s parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established *** Codes 37E99 (Primary), 68T07 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： Parameter estimation

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