One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). Most existing methods are tailored to spe...
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作者：
Salvatore TorquatoDepartment of Chemistry
Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA
Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering, and biology. Consider the time-dependent problem of mass tra...
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Understanding time-dependent diffusion processes in multiphase media is of great importance in physics, chemistry, materials science, petroleum engineering, and biology. Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, S(t), which we call the spreadability, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for S(t) in any Euclidean space dimension d in terms of the autocovariance function as well as corresponding Fourier representations of S(t) in terms of the spectral density, which are especially useful when scattering information is available experimentally or theoretically. These are singular results because they are rare examples of mass transport problems where exact solutions are possible. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of S(t) enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the “excess” spreadability, S(∞)−S(t), decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the “slowest” being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. We obtain exact results for S(t) for a variety of specific ordered and disordered model microstructures across dimensions that span from hyperuniform to antihyperuniform media. Moreover, we establish a remarkable connection between the spreadability
We develop new statistics for robustly filtering corrupted keypoint matches in the structure from motion pipeline. The statistics are based on consistency constraints that arise within the clustered structure of the g...
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ISBN:
(纸本)9781665426893
We develop new statistics for robustly filtering corrupted keypoint matches in the structure from motion pipeline. The statistics are based on consistency constraints that arise within the clustered structure of the graph of keypoint matches. The statistics are designed to give smaller values to corrupted matches and than uncorrupted matches. These new statistics are combined with an iterative reweighting scheme to filter keypoints, which can then be fed into any standard structure from motion pipeline. This filtering method can be efficiently implemented and scaled to massive datasets as it only requires sparse matrix multiplication. We demonstrate the efficacy of this method on synthetic and real structure from motion datasets and show that it achieves state-of-the-art accuracy and speed in these tasks.
We consider the Nernst-Planck equations describing the nonlinear time evolution of multiple ionic concentrations in a two-dimensional incompressible fluid. The velocity of the fluid evolves according to either the Eul...
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Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is ver...
Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms’ ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data.
作者：
Torquato, SalvatoreDepartment of Chemistry
Department of Physics Princeton Institute of Materials Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States
A variety of performance demands are being placed on material systems, including desirable mechanical, thermal, electrical, optical, acoustic and flow properties. The purpose of the present article is to review the em...
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Background and Objective: Wilson statistics describe well the power spectrum of proteins at high frequencies. Therefore, it has found several applications in structural biology, e.g., it is the basis for sharpening st...
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Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by a complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, an...
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Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by a complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, and lack of conventional long-range order, as in liquids and glasses. In this work, we begin a program to quantify the structural properties of nonhyperuniform and hyperuniform networks. In particular, large two-dimensional (2D) Voronoi networks (graphs) containing approximately 10,000 nodes are created from a variety of different point configurations, including the antihyperuniform hyperplane intersection process (HIP), nonhyperuniform Poisson process, nonhyperuniform random sequential addition (RSA) saturated packing, and both non-stealthy and stealthy hyperuniform point processes. We carry out an extensive study of the Voronoi-cell area distribution of each of the networks through determining multiple metrics that characterize the distribution, including their higher-cumulants (i.e., skewness 1 and excess kurtosis 2). We show that the HIP distribution is far from Gaussian, as evidenced by a high skewness (γ1 = 3.16) and large positive excess kurtosis (γ2 = 16.2). The Poisson (with γ1 = 1.07 and γ2 = 1.79) and non-stealthy hyperuniform (with γ1 = 0.257 and γ2 = 0.0217) distributions are Gaussian-like distributions, since they exhibit a small but positive skewness and excess kurtosis. The RSA (with γ1 = 0.450 and γ2 = -0.0384) and the highest stealthy hyperuniform distributions (with γ1 = 0.0272 and γ2 = -0.0626) are also non-Gaussian because of their low skewness and negative excess kurtosis, which is diametrically opposite non-Gaussian behavior of the HIP. The fact that the cell-area distributions of large, finite-sized RSA and stealthy hyperuniform networks (e.g., with N ≈ 10, 000 nodes) are narrower, have larger peaks, and smaller tails than a Gaussian distribution implies that in the thermodynamic limit the distributions should exhibit compact suppo
We present the first cosmological constraints using only the observed photometry of galaxies. Villaescusa-Navarro et al. (2022b) recently demonstrated that the internal physical properties of a single simulated galaxy...
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Building efficient, accurate, and generalizable reduced-order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagran...
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Building efficient, accurate, and generalizable reduced-order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and it investigates the effects of enforcing physical structure through smoothed particle hydrodynamics (SPH) versus relying on neural networks (NNs) as universal function approximators. Starting from NN parametrizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational, and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using automatic differentiation and sensitivity analysis. Each model within the hierarchy is trained on two data sets associated with weakly compressible homogeneous isotropic turbulence: (1) a validation set using weakly compressible SPH; and (2) a high-fidelity set from direct numerical simulations. Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.
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