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DIFFUSION CURVATURE FOR ESTIMATING LOCAL CURVATURE IN HIGH DIMENSIONAL DATA

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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

A framework for relating neural activity to freely moving behavior

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A framework for relating neural activity to freely moving be...

Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

作者： Justin D. Foster Paul Nuyujukian Oren Freifeld Stephen I. Ryu Michael J. Black Krishna V. Shenoy Department of Electrical Engineering University of Stanford Stanford CA USA Bioengineering and Stanford Medical School University of Stanford Stanford CA USA Division of Applied Mathematics Brown University Providence RI USA Department of Neurosurgery Palo Alto Medical Foundation Palo Alto CA USA Department of Computer Science Brown University Providence RI USA Departments of Electrical Engineering Bioengineering and Neurobiology Neurosciences Program Neurosciences Program University of Stanford Stanford CA USA

Two research communities, motor systems neuroscience and motor prosthetics, examine the relationship between neural activity in the motor cortex and movement. The former community aims to understand how the brain controls and generates movement; the latter community focuses on how to decode neural activity as control signals for a prosthetic cursor or limb. Both have made progress toward understanding the relationship between neural activity in the motor cortex and behavior. However, these findings are tested using animal models in an environment that constrains behavior to simple, limited movements. These experiments show that, in constrained settings, simple reaching motions can be decoded from small populations of spiking neurons. It is unclear whether these findings hold for more complex, full-body behaviors in unconstrained settings. Here we present the results of freely-moving behavioral experiments from a monkey with simultaneous intracortical recording. We investigated neural firing rates while the monkey performed various tasks such as walking on a treadmill, reaching for food, and sitting idly. We show that even in such an unconstrained and varied context, neural firing rates are well tuned to behavior, supporting findings of basic neuroscience. Further, we demonstrate that the various behavioral tasks can be reliably classified with over 95% accuracy, illustrating the viability of decoding techniques despite significant variation and environmental distractions associated with unconstrained behavior. Such encouraging results hint at potential utility of the freely-moving experimental paradigm.

关键词： Legged locomotion Maximum likelihood decoding Kinematics Animals Educational institutions Cameras Neuroscience

Autonomous Electron Tomography Reconstruction with Machine Learning

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arXiv 2023年

作者： Millsaps, William Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Hovden, Robert Department of Nuclear Engineering & Radiological Sciences University of Michigan Ann ArborMI United States Department of Materials Science and Engineering University of Michigan Ann ArborMI United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States Advanced Photon Source Facility Argonne National Laboratory LemontIL United States Applied Physics Program University of Michigan Ann ArborMI United States

This manuscript is published in Microscopy and Microanalysis (DOI: 10.1093/micmic/ozad083). Modern electron tomography has progressed to higher resolution at lower doses by leveraging compressed sensing methods that minimize total variation (TV). However, these sparsity-emphasized reconstruction algorithms introduce tunable parameters that greatly influence the reconstruction quality. Here, Pareto front analysis shows that high-quality tomograms are reproducibly achieved when TV minimization is heavily weighted. However, in excess, compressed sensing tomography creates overly smoothed 3D reconstructions. Adding momentum to the gradient descent during reconstruction reduces the risk of over-smoothing and better ensures that compressed sensing is well behaved. For simulated data, the tedious process of tomography parameter selection is efficiently solved using Bayesian optimization with Gaussian processes. In combination, Bayesian optimization with momentum-based compressed sensing greatly reduces the required compute time-an 80% reduction was observed for the 3D reconstruction of SrTiO3 nanocubes. Automated parameter selection is necessary for large scale tomographic simulations that enable the 3D characterization of a wider range of inorganic and biological materials. © 2023, CC BY.

关键词： Compressed sensing

Cloud-AC-OPF: Model reduction technique for multi-scenario optimal power flow via chance-constrained optimization

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arXiv 2019年

作者： Frolov, Vladimir Roald, Line Chertkov, Michael Skolkovo Institute of Science and Technology Nobel Street 3 Moscow Region143026 Russia Electrical & Computer Engineering University of Wisconsin 1415 Engineering Drive MadisonWI53706 United States Center for Nonlinear Studies and Theoretical Division T-4 LANL Los AlamosNM87545 United States Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

—Many practical planning and operational applications in power systems require simultaneous consideration of a large number of operating conditions or Multi-Scenario AC-Optimal Power Flow (MS-AC-OPF) solution. However, when the number of exogenously prescribed conditions is large, solving the problem as a collection of single AC-OPFs may be time-consuming or simply intractable computationally. In this paper, we suggest a model reduction approach, coined Cloud-AC-OPF, which replaces a collection of samples by their compact representation in terms of mean and standard deviation. Instead of determining an optimal generation dispatch for each sample individually, we parametrize the generation dispatch as an affine function. The Cloud-AC-OPF is mathematically similar to a generalized Chance-Constrained AC-OPF (CC-AC-OPF) of the type recently discussed in the literature, but conceptually different as it discusses applications to long-term planning. We further propose a tractable formulation and implementation, and illustrate our construction on the example of 30-bus IEEE model. Copyright © 2019, The Authors. All rights reserved.

关键词： Acoustic generators

Dose Requirements for Fused Multi-Modal Electron Tomography

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 1968-1969页

作者： Manassa, Jason Schwartz, Jonathan Jiang, Yi Zheng, Huihuo Fessler, Jeffrey A. Wendy Di, Zichao Hovden, Robert Department of Materials Science and Engineering University of Michigan Ann Arbor MI United States Advanced Photon Source Facility Argonne National Laboratory Lemont IL United States Argonne Leadership Computing Facility Argonne National Laboratory Lemont IL United States Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor MI United States Mathematics and Computer Science Division Argonne National Laboratory Lemont IL United States Applied Physics Program University of Michigan Ann Arbor MI United States

Visualizing structure and transitions in high-dimensional biological data (vol 54, pg 781, 2019)

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NATURE BIOTECHNOLOGY 2020年第1期38卷 108-108页

作者： Moon, Kevin R. van Dijk, David Wang, Zheng Gigante, Scott Burkhardt, Daniel B. Chen, William S. Yim, Kristina van den Elzen, Antonia Hirn, Matthew J. Coifman, Ronald R. Ivanova, Natalia B. Wolf, Guy Krishnaswamy, Smita Department of Mathematics and Statistics Utah State University Logan USA Cardiovascular Research Center section Cardiology Department of Internal Medicine Yale University New Haven USA Department of Computer Science Yale University New Haven USA School of Basic Medicine Qingdao University Qingdao China Yale Stem Cell Center Department of Genetics Yale University New Haven USA Computational Biology and Bioinformatics Program Yale University New Haven USA Department of Genetics Yale University New Haven USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing USA Department of Mathematics Michigan State University East Lansing USA Applied Mathematics Program Yale University New Haven USA Department of Genetics Center for Molecular Medicine University of Georgia Athens USA Department of Mathematics and Statistics Université de Montréal Montréal Canada Mila—Quebec Artificial Intelligence Institute Montréal Canada

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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Neural FIM for learning Fisher information metrics from point cloud data

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arXiv 2023年

作者： Fasina, Oluwadamilola Huguet, Guillaume Tong, Alexander Zhang, Yanlei Wolf, Guy Nickel, Maximilian Adelstein, Ian Krishnaswamy, Smita Applied Math Program Yale University New HavenCT United States Mila - Quebec AI Institute MontrealQC Canada Department of Mathematics and Statistics Université de Montréal MontrealQC Canada Department of Computer Science and Operations Research Université de Montréal MontrealQC Canada FAIR Meta AI United States Department of Math Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States Department of Genetics Yale University New HavenCT United States

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells). Copyright © 2023, The Authors. All rights reserved.

关键词： Embeddings

K, T and D-like fuzzy Kripke models

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K, T and D-like fuzzy Kripke models

Conference of the North American Fuzzy Information Processing Society - NAFIPS

作者： Benjamin Bedregal Regivan H. N. Santiago Mario Benevides Petrúcio Viana Group of Logic Language Information Theory and Applications-LoLITA Department of Informatics and Applied Mathematics Federal University of Rio Grande do Norte Natal Rio Grande do Norte Brazil Program of Engineering of Systems and Computing-PESC Department of Computer Science Federal University of Rio de Janeiro Rio de Janeiro Rio de Janeiro Brazil Department of Analysis Fluminense Federal University (UFF) Niteroi Rio de Janeiro Brazil

The idea of a Kripke semantics endowed with possibility/plausibility information is not new; in fact there are different approaches for that; see: [6], [13], [16], [19]. This paper follows the approach found in [6], but whereas [6] provides a fixed interpretation for connectives into [0,1] here we provide a characterization of a fuzzy semantics for connectives in such a way that the resulting fuzzy frames: K, T and D, are described precisely by the set of statements which also describes, respectively, the usual modal systems K, T and D.

关键词： Semantics Fuzzy sets Fuzzy logic Bismuth Electronic mail Uncertainty Reliability

Collective behavior of active topological solitons, knotted streamlines, and transport of cargo in liquid crystals

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arXiv 2017年

作者： Sohn, Hayley R.O. Ackerman, Paul J. Boyle, Timothy J. Sheetah, Ghadah H. Fornberg, Bengt Smalyukh, Ivan I. Soft Materials Research Center and Materials Science and Engineering Program University of Colorado BoulderCO80309 United States Department of Physics Department of Electrical Computer and Energy Engineering University of Colorado BoulderCO80309 United States Department of Applied Mathematics University of Colorado BoulderCO80309 United States Renewable and Sustainable Energy Institute National Renewable Energy Laboratory University of Colorado BoulderCO80309 United States

Active colloids and liquid crystals are capable of locally converting the macroscopically-supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here we uncover how topological solitons in liquid crystals can locally transform electric energy to translational motion and allow for the transport of cargo along directions dependent on frequency of the applied electric field. By combining polarized optical video microscopy and numerical modeling that reproduces both the equilibrium structures of solitons and their temporal evolution in applied fields, we uncover the physical underpinnings behind this reconfigurable motion and study how it depends on the structure and topology of solitons. We show that, unexpectedly, the directional motion of solitons with and without the cargo arises mainly from the asymmetry in rotational dynamics of molecular ordering in liquid crystal rather than from the asymmetry of fluid flows, as in conventional active soft matter systems. Copyright © 2017, The Authors. All rights reserved.

关键词： Solitons