We study how the learning rate affects the performance of a relaxed randomized Kaczmarz algorithm for solving Ax ≈ b + Ε, where Ax = b is a consistent linear system and Ε has independent mean zero random entries. W...
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We prove that the power-law vortex ω¯ (x) = β|x|−α, which explicitly solves the stationary unforced incompressible Euler equations in R2 in both physical and self-similar coordinates, is exponentially linearly...
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The implementation of titanium dioxide (TiO2) as a photocatalyst material in hydrogen (H2) evolution reaction (HER) has embarked renewed interest in the past decade. Rapid electron-hole pairs recombination and wide ba...
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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.
This work is devoted to the efficient solution of variational-monolithic fluid-structure interaction (FSI) initial-boundary value problems. Solvers for such monolithic systems were developed, e.g., in [2, 3, 5, 7, 9,...
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We report on an extensive study of the viscosity of liquid water at near-ambient conditions,performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics(AIMD),based on density...
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We report on an extensive study of the viscosity of liquid water at near-ambient conditions,performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics(AIMD),based on density-functional theory(DFT).In order to cope with the long simulation times necessary to achieve an acceptable statistical accuracy,our ab initio approach is enhanced with deep-neural-network potentials(NNP).This approach is first validated against AIMD results,obtained by using the Perdew–Burke–Ernzerhof(PBE)exchange-correlation functional and paying careful attention to crucial,yet often overlooked,aspects of the statistical data ***,we train a second NNP to a dataset generated from the Strongly Constrained and Appropriately Normed(SCAN)*** the error resulting from the imperfect prediction of the melting line is offset by referring the simulated temperature to the theoretical melting one,our SCAN predictions of the shear viscosity of water are in very good agreement with experiments.
We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settin...
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This article considers fluid structure interaction describing the motion of a fluid contained in a porous medium. The fluid is modelled by Navier-Stokes equations and the coupling between fluid and the porous medium i...
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In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times tha...
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In this article we consider Bayesian parameter inference for a type of partially observed stochastic Volterra equation (SVE). SVEs are found in many areas such as physics and mathematical finance. In the latter field ...
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