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A Portable Multiscopic Camera for Novel View and Time Synthesis in Dynamic Scenes

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arXiv 2022年

作者： Zhang, Tianjia Lau, Yuen-Fui Chen, Qifeng The Hong Kong University of Science and Technology Hong Kong The Individualized Interdisciplinary Program The Robotics Institute Hong Kong The Department of Mathematics Hong Kong The Department of Computer Science and Engineering The Department of Electronic and Computer Engineering Hong Kong

We present a portable multiscopic camera system with a dedicated model for novel view and time synthesis in dynamic scenes. Our goal is to render high-quality images for a dynamic scene from any viewpoint at any time using our portable multiscopic camera. To achieve such novel view and time synthesis, we develop a physical multiscopic camera equipped with five cameras to train a neural radiance field (NeRF) in both time and spatial domains for dynamic scenes. Our model maps a 6D coordinate (3D spatial position, 1D temporal coordinate, and 2D viewing direction) to view-dependent and time-varying emitted radiance and volume density. Volume rendering is applied to render a photo-realistic image at a specified camera pose and time. To improve the robustness of our physical camera, we propose a camera parameter optimization module and a temporal frame interpolation module to promote information propagation across time. We conduct experiments on both real-world and synthetic datasets to evaluate our system, and the results show that our approach outperforms alternative solutions qualitatively and quantitatively. Our code and dataset are available at https://***/. Copyright © 2022, The Authors. All rights reserved.

关键词： Cameras

BRAIN-TO-TEXT BENCHMARK’24: LESSONS LEARNED

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arXiv 2024年

作者： Willett, Francis R. Li, Jingyuan Le, Trung Fan, Chaofei Chen, Mingfei Shlizerman, Eli Chen, Yue Zheng, Xin Okubo, Tatsuo S. Benster, Tyler Lee, Hyun Dong Kounga, Maxwell Buchanan, E. Kelly Zoltowski, David Linderman, Scott W. Henderson, Jaimie M. Department of Neurosurgery Stanford University United States Department of Electrical & Computer Engineering University of Washington United States Department of Computer Science Stanford University United States Department of Applied Mathematics University of Washington United States China Neurosciences Phd Program Stanford University United States Wu Tsai Neurosciences Institute Department of Statistics Stanford University United States

Speech brain-computer interfaces aim to decipher what a person is trying to say from neural activity alone, restoring communication to people with paralysis who have lost the ability to speak intelligibly. The Brain-to-Text Benchmark’24 and associated competition was created to foster the advancement of decoding algorithms that convert neural activity to text. Here, we summarize the lessons learned from the competition ending on June 1, 2024 (the top 4 entrants also presented their experiences in a recorded webinar). The largest improvements in accuracy were achieved using an ensembling approach, where the output of multiple independent decoders was merged using a fine-tuned large language model (an approach used by all 3 top entrants). Performance gains were also found by improving how the baseline recurrent neural network (RNN) model was trained, including by optimizing learning rate scheduling and by using a diphone training objective. Improving upon the model architecture itself proved more difficult, however, with attempts to use deep state space models or transformers not yet appearing to offer a benefit over the RNN baseline. The benchmark will remain open indefinitely to support further work towards increasing the accuracy of brain-to-text algorithms. © 2024, CC BY.

关键词： Recurrent neural networks

Multidomain Model for Optic Nerve Potassium Clearance: Roles of Glial Cells and Perivascular Spaces

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arXiv 2024年

作者： Xiao, Shanfeng Huang, Huaxiong Eisenberg, Robert Song, Zilong Xu, Shixin School of Mathematical Sciences Soochow University 1 Shi-Zi Street Jiangsu Province Suzhou215006 China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International College Zhuhai519088 China Laboratory of Mathematics and Complex Systems MOE Beijing China Normal University Beijing100875 China Department of Mathematics and Statistics York University TorontoONM3J 1P3 Canada Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States Math and Statistics Department Utah State University Old Main Hill LoganUT84322 United States Zu Chongzhi Center for Mathematics and Computational Sciences Duke Kunshan University 8 Duke Ave Kunshan China

The accumulation of potassium in the extracellular space surrounding nerve cells is a fundamental aspect of biophysics that has garnered significant attention in recent research. This phenomenon holds implications for various neurological conditions, including spreading depression, migraine, certain types of epilepsy, and potentially, learning processes. A quantitative analysis is essential for understanding the dynamics of potassium clearance following a series of action potentials. This clearance process involves multiple structures along the nerve, including glia, the extracellular space, axons, and the perivascular space, necessitating a spatially distributed systems approach akin to the cable equations of nerve physiology. In this study, we propose a multi-domain model for the optic nerve to investigate potassium accumulation and clearance dynamics. The model accounts for the convection, diffusion, and electrical migration of fluid and ions, revealing the significant roles of glia and the perivascular space in potassium buffering. Specifically, our findings suggest that potassium clearance primarily occurs through convective flow within the syncytia of glia, driven by osmotic pressure differences. Additionally, the perivascular space serves as a crucial pathway for potassium buffering and fluid circulation, further contributing to the overall clearance process. Importantly, our model’s adaptability allows for its application to diverse structures with distinct channel and transporter distributions across the six compartments, extending its utility beyond the optic nerve. © 2024, CC BY-SA.

关键词： Neurons

Marginally stable thermal equilibria of Rayleigh-Bénard convection

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Physical Review Fluids 2021年第9期6卷 093501-093501页

作者： Liam O'Connor Daniel Lecoanet Evan H. Anders Department of Engineering Sciences and Applied Mathematics Northwestern University Evanston Illinois 60208 USA Center for Interdisciplinary Exploration and Research in Astrophysics Northwestern University Evanston Illinois 60201 USA

Natural convection exhibits turbulent flows which are difficult or impossible to resolve in direct numerical simulations. In this work we investigate a quasilinear form of the Rayleigh-Bénard problem which describes the bulk one-dimensional properties of convection without resolving the turbulent dynamics. We represent perturbations away from the mean using a sum of marginally stable eigenmodes. By constraining the perturbation amplitudes, the marginal stability criterion allows us to evolve the background temperature profile under the influence of multiple eigenmodes representing flows at different length scales. We find the quasilinear system evolves to an equilibrium state where advective and diffusive fluxes sum to a constant. These marginally stable thermal equilibria (MSTE) are exact solutions of the quasilinear equations. The mean MSTE temperature profiles have thinner boundary layers and larger Nusselt numbers than thermally equilibrated two- and three-dimensional simulations of the full nonlinear equations. MSTE solutions exhibit a classic boundary-layer scaling of the Nusselt number Nu with the Rayleigh number Ra of Nu∼Ra1/3. When MSTE are used as initial conditions for a two-dimensional simulation, we find that Nu quickly equilibrates without the burst of turbulence often induced by purely conductive initial conditions, but we also find that the kinetic energy is too large and viscously attenuates on a long, viscous timescale.

关键词： Rayleigh-Bénard convection Structure & turbulence of boundary layers Navier-Stokes equation

Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks

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arXiv 2024年

作者： Maher, Charles Emmett Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Jammed (mechanically rigid) polydisperse circular-disk packings in two dimensions (2D) are popular models for structural glass formers. Maximally random jammed (MRJ) states, which are the most disordered packings subject to strict jamming, have been shown to be hyperuniform. The characterization of the hyperuniformity of MRJ circular-disk packings has covered only a very small part of the possible parameter space for the disk-size distributions. Hyperuniform heterogeneous media are those that anomalously suppress large-scale volume-fraction fluctuations compared to those in typical disordered systems, i.e., their spectral densities χV (k) tend to zero as the wavenumber k ≡ |k| tends to zero and are often described by the power-law χV (k) ∼ kα as k → 0 where α is the so-called hyperuniformity scaling exponent. In this work, we generate and characterize the structure of strictly jammed binary circular-disk packings with a size ratio β = DL/DS, where DL and DS are the large and small disk diameters, respectively, and molar ratio of the two disk sizes is 1:1. In particular, by characterizing the rattler fraction φR, the fraction of configurations in an ensemble with fixed β that are isostatic, and the n-fold orientational order metrics n of ensembles of packings with a wide range of size ratios β, we show that size ratios 1.2 β 2.0 produce maximally random jammed (MRJ)-like states, which we show are the most disordered strictly jammed packings according to several criteria. Using the large-R scaling of the volume fraction variance σ2 V (R) associated with a spherical sampling window of radius R, we extract the hyperuniformity scaling exponent α from these packings, and find the function α (β) is maximized at β = 1.4 (with α = 0.450±0.002) within the range 1.2 ≤ β ≤ 2.0. Just outside of this range of β values, α (β) begins to decrease more quickly, and far outside of this range the packings are nonhyperuniform, i.e., α = 0. Moreover, we compute the spectral density χV (k

关键词： Disks (structural components)

GRAMMCell: Docking-based Cell Modeling Resource

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Journal of Molecular Biology 2025年 169085页

作者： Singh, Amar Tytarenko, Andrii M. Ambati, Vineeth Kumar Copeland, Matthew M. Kundrotas, Petras J. Kasyanov, Pavlo O. Feinberg, Eugene A. Vakser, Ilya A. Computational Biology Program The University of Kansas Lawrence 66045 KS United States Institute for Applied System Analysis at the Igor Sikorsky Kyiv Polytechnic Institute Kyiv 03056 Ukraine Department of Applied Mathematics and Statistics Stony Brook University Stony Brook 11794 NY United States Department of Molecular Biosciences The University of Kansas Lawrence 66045 KS United States

The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecular interactions. Computational approaches to cell modeling, such as molecular dynamics, provide details of macromolecular behavior in concentrated solutions. However, such simulations are either slow, when carried out at atomic resolution, or significantly coarse-grained. Protein docking has been widely used for predicting structures of protein complexes. Systematic docking approaches, such as those based on Fast Fourier Transform (FFT), map the entire intermolecular energy landscape by determining the position and depth of the energy minima. The GRAMMCell web server implements docking-based approach for simulating cell crowded environment by sampling the intermolecular energy landscape generated by GRAMM (Global RAnge Molecular Matching). GRAMM systematically maps the landscape by a spectrum of docking poses corresponding to stable (deep energy minima) and transient (shallow minima) protein interactions. The sampling of these energy landscapes of a large system of proteins is performed in GRAMMCell using highly optimized Markov Chain Monte Carlo protocol. The procedure allows simulation of extra-long trajectories of large, crowded protein systems with atomic resolution accuracy. GRAMMCell is available at https://***. © 2025 The Author(s)

关键词： cell-modelling energy landscape protein docking protein–protein interactions web-based resource

Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

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Gaussian Process Port-Hamiltonian Systems: Bayesian Learning...

IEEE Conference on Decision and Control

作者： Thomas Beckers Jacob Seidman Paris Perdikaris George J. Pappas Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA USA graduate program in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA USA Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia PA USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GPPHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

关键词： Uncertainty Gaussian processes Probabilistic logic Data models Bayes methods Behavioral sciences Kernel

A qualitative study of the dynamic behavior for adaptive gradient algorithms

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arXiv 2020年

作者： Ma, Chao Wu, Lei Weinan, E. Department of Mathematics Stanford University Program in Applied and Computational Mathematics Princeton University Program in Applied and Computational Mathematics Department of Mathematics Princeton University

The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss curve: fast initial convergence, oscillations, and large spikes in the late phase. The sign gradient descent (signGD) flow, which is the limit of Adam when taking the learning rate to 0 while keeping the momentum parameters fixed, is used to explain the fast initial convergence. For the late phase of Adam, three different types of qualitative patterns are observed depending on the choice of the hyper-parameters: oscillations, spikes, and divergence. In particular, Adam converges much smoother and even faster when the values of the two momentum factors are close to each other. This observation is particularly important for scientific computing tasks, for which the training process usually proceeds into the high precision regime. Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

Epidemics from the Eye of the Pathogen

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arXiv 2021年

作者： Sahneh, Faryad Darabi Fries, William Watkins, Joseph C. Lega, Joceline Department of Mathematics University of Arizona United States Interdisciplinary Program in Applied Mathematics University of Arizona United States Department of Epidemiology and Biostatistics University of Arizona United States BIO5 Institute University of Arizona TucsonAZ85721 United States

While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic SIR (Susceptible, Infected, Recovered) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona. Copyright © 2021, The Authors. All rights reserved.

关键词： COVID-19