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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

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CONDITIONAL AVERAGES IN CONVECTIVE TURBULENCE

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PHYSICA A 1994年第1-4期204卷 341-345页

作者： KADANOFF, LP The Computational and Applied Math Program Ryerson Laboratory The University of Chicago 1100 East 58th Street Chicago IL 60637 USA

Two exact results are presented for the thermal dissipation in a Rayleigh-Benard geometry. The first result expresses the conditional dissipation at each value of theta within the entire volume of the system in terms of the thermal flux and the PDF for theta. The second gives the conditional dissipation in a region of the cell in terms of the conditional flux into the region. These results are used to argue that the observed stretched exponential PDF in the central region must be connected with the behavior near the boundary.

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KLF2 maintains lineage fidelity and suppresses CD8 T cell exhaustion during acute LCMV infection

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Science (New York, N.Y.) 2025年第6735期387卷 eadn2337页

作者： Fagerberg, Eric Attanasio, John Dien, Christine Singh, Jaiveer Kessler, Emily A. Abdullah, Leena Shen, Jian Hunt, Brian G. Connolly, Kelli A. De Brouwer, Edward He, Jiaming Iyer, Nivedita R. Buck, Jessica Borr, Emily R. Damo, Martina Foster, Gena G. Giles, Josephine R. Huang, Yina H. Tsang, John S. Krishnaswamy, Smita Cui, Weiguo Joshi, Nikhil S. Department of Immunobiology Yale University School of Medicine New Haven CT United States Program in Computational Biology & Bioinformatics Yale University New Haven CT United States Department of Microbiology and Immunology Geisel School of Medicine at Dartmouth NH United States Department of Pathology Feinberg School of Medicine at Northwestern University Chicago IL United States Department of Genetics and Computer Science Yale University School of Medicine New Haven CT United States Department of Medicine University of Chicago Chicago IL United States Section of Hematology Department of Internal Medicine Yale University School of Medicine New Haven CT United States Department of Systems Pharmacology and Translational Therapeutics University of Pennsylvania Philadelphia PA United States Institute for Immunology Perelman School of Medicine University of Pennsylvania Philadelphia PA United States Parker Institute for Cancer Immunotherapy Perelman School of Medicine University of Pennsylvania Philadelphia PA United States Yale Center for Systems and Engineering Immunology Yale University School of Medicine New Haven CT United States New Haven CT United States Department of Biomedical Engineering Yale University New Haven CT United States Computational Biology and Bioinformatics Program Yale University CT USA New Haven United States Applied Math Program Yale University New Haven CT United States

Naïve CD8 T cells have the potential to differentiate into a spectrum of functional states during an immune response. How these developmental decisions are made and what mechanisms exist to suppress differentiation toward alternative fates remains unclear. We employed in vivo CRISPR-Cas9-based perturbation sequencing to assess the role of ~40 transcription factors (TFs) and epigenetic modulators in T cell fate decisions. Unexpectedly, we found that knockout of the TF Klf2 resulted in aberrant differentiation to exhausted-like CD8 T cells during acute infection. KLF2 was required to suppress the exhaustion-promoting TF TOX and to enable the TF TBET to drive effector differentiation. KLF2 was also necessary to maintain a polyfunctional tumor-specific progenitor state. Thus, KLF2 provides effector CD8 T cell lineage fidelity and suppresses the exhaustion program.

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Exact solutions for the Saffman-Taylor problem with surface tension

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Physical Review Letters 1990年第24期65卷 2986-2986页

作者： Leo P. Kadanoff Computational and Applied Math Program Ryerson Laboratory The University of Chicago 1100 East 58th Street Chicago Illinois 60637

Solutions are reported for the problem of the motion of a two-dimensional interface between a viscous and a nonviscous fluid. The solution has the interface moving uniformly while the viscous fluid has a nontrivial potential flow. In an alternative interpretation, there are gravitational forces in the plane which allow the interface to be at rest while the fluid is in motion.

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On the non stationary Navier-Stokes equations with an external force

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Advances in Differential Equations 1999年第5期4卷 697-730页

作者： Cannone, Marco Planchon, Fabrice UMR 7599 du CNRS UFR Mathématiques Université Denis Diderot Paris VII 75251 Paris Cedex 05 2 Place Jussieu France Program for Applied and Computational Mathematics Princeton University Princeton NJ 08544-1000 United States

We present two different existence and uniqueness algorithms for constructing global mild solutions in C([0, T);L3(ℝ3)) to the Cauchy problem for the Navier-Stokes equations with an external force.

We present two different existence and uniqueness algorithms for constructing global mild solutions in C([0, T);L³(ℝ³)) to the Cauchy problem for the Navier-Stokes equations with an external force.

关键词： 35Q30 76D03 76D05

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Smooth graph signal interpolation for big data

arXiv

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arXiv 2018年

作者： Heimowitz, Ayelet Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Faculty of Math and Computer Science Weizmann Institute of Science Rehovot Israel

In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph signal interpolation. Our approach is based on diffusion embedding vectors and the connection between diffusion maps and signal processing on graphs. As diffusion embedding vectors may be expensive to compute for large graphs, we present a computationally efficient method, based on the Nyström extension, for interpolation of signals over a graph. We demonstrate our approach on the MNIST dataset and a dataset of daily average temperatures around the US. We show that our method outperforms state of the art graph signal interpolation methods on both datasets, and that our computationally efficient reconstruction achieves slightly reduced accuracy with a large speedup. Copyright © 2018, The Authors. All rights reserved.

关键词： computational efficiency

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Hyperbolic Diffusion Procrustes Analysis for Intrinsic Representation of Hierarchical Data Sets

Hyperbolic Diffusion Procrustes Analysis for Intrinsic Repre...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Ya-Wei Eileen Lin Yuval Kluger Ronen Talmon Viterbi Faculty of Electrical and Computer Engineering Technion Interdepartmental Program in Computational Biology and Bioinformatics Yale University Applied Math Program Yale University Department of Pathology School of Medicine Yale University

In this paper, we present Hyperbolic Diffusion Procrustes Analysis (HDPA), a new method for informative representation of hierarchical datasets based on hyperbolic geometry, diffusion geometry, and Procrustes analysis. Our method jointly embeds multiple datasets in a product manifold of hyperbolic spaces, where the data's hidden common hierarchical structure is provably recovered. In addition, our method generates an intrinsic embedding that accommodates the joint representation of multiple datasets with different features, acquired by different equipment, at different sites, or under different environmental conditions. Experimental results demonstrate the efficacy of HDPA on three biomedical datasets comprising heterogeneous gene expression and mass cytometry data.

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Graph Fourier MMD for Signals on Graphs

Graph Fourier MMD for Signals on Graphs

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2023 International Conference on Sampling Theory and Applications, SampTA 2023

作者： Leone, Samuel Venkat, Aarthi Huguet, Guillaume Tong, Alexander Wolf, Guy Krishnaswamy, Smita Applied Math Program New HavenCT United States Yale University Computational Biology & Bioinformatics Program New HavenCT United States Université de Montréal Mila - Quebec Ai Institute Dept. of Math. & Stat Montreal Canada Université de Montréal Mila-Quebec Ai Institute Dept. of Comp. Sci. & Oper. Res. Montreal Canada Yale University Department of Computer Science Department of Genetics New HavenCT United States

ISBN: (纸本)9798350328851

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes the difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization. © 2023 IEEE.

关键词： Genes

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Preconditioners for regularized image superresolution

Preconditioners for regularized image superresolution

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： N. Nguyan G. Golub P. Milanfar Sci. Comput. & Comput. Math. Program Stanford Univ. CA USA Scientific Computing and Computational Mathematics Program University of Stanford Stanford CA USA Applied Electromagnetics Lab SRI International Inc. Menlo Park CA USA

Superresolution reconstruction produces a high resolution image from a set of low resolution images. Previous work on superresolution had not adequately addressed the computational issues for this problem. In this paper, we propose efficient block circulant preconditioners for solving the regularized superresolution problem by conjugate gradients. The effectiveness of the preconditioners is demonstrated with superresolution results for a simulated image sequence and a FLIR image sequence.

关键词： Image resolution Layout Spatial resolution Pixel Image reconstruction Image sequences Motion estimation Solids Equations Scientific computing

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computational Methods for Single-Particle Electron Cryomicroscopy

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Biomedical Data Science 1000年第1期3卷 163-190页

作者： Amit Singer Fred J. Sigworth 1Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA email: amits@math.princeton.edu 2Departments of Cellular and Molecular Physiology Biomedical Engineering and Molecular Biophysics and Biochemistry Yale University New Haven Connecticut 06520 USA email: fred.sigworth@yale.edu

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the 3D molecular structure needs to be determined from many noisy 2D tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing, which also play a significant role in many other data science applications.

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