Motivated by the problem of predicting sleep states, we develop a mixed effects model for binary time series with a stochastic component represented by a Gaussian process. The fixed component captures the effects of c...
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We examine a continuum effect of a dynamic Wannier-Stark ladder (DWSL) driven by a cw laser—with Fac and ω as amplitude and frequency, respectively—by means of an excess density of states (DOS), ρ(ex)(E), closely ...
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We examine a continuum effect of a dynamic Wannier-Stark ladder (DWSL) driven by a cw laser—with Fac and ω as amplitude and frequency, respectively—by means of an excess density of states (DOS), ρ(ex)(E), closely related to the more familiar DOS and proportional to the lifetime of a resonance state. It is mathematically shown that ρ(ex)(E) is governed by three different physical mechanisms: the single-channel resonance mechanism, the multichannel nonresonance mechanism, and the multichannel resonance mechanism. The last mechanism becomes more important with the increase in Fac. The effect of the interchannel interaction is maximized when the ratio of a Bloch frequency to ω, represented as η, equals unity. In the actual calculations based on the R-matrix Floquet theory, it is revealed that, in a large-Fac region, ρ(ex)(E) for η=1 shows a complicated spectral structure composed of a couple of newly growing peaks, in contrast to ρ(ex)(E) for η=3 which just shows a monotonic change of a single spectral peak. It is speculated that the pronounced feature of the former spectra is attributed to the Fano-like multichannel resonance mechanism, whereas the feature of the latter case is attributed to the multichannel nonresonance mechanism.
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.
Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to address these challenges. This paper ta...
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Much work in the parimutuel betting literature has discussed estimating event outcome probabilities or developing optimal wagering strategies, particularly for horse race betting. Some betting pools, however, involve ...
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作者：
Torquato, S.Chen, D.Department of Chemistry
Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry
Princeton University PrincetonNJ08544 United States
Disordered hyperuniform heterogeneousmaterials are new, exotic amorphous states of matter that behave like crystals in themanner in which they suppress volume-fraction fluctuations at large length scales, and yet are ...
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Disordered hyperuniform heterogeneousmaterials are new, exotic amorphous states of matter that behave like crystals in themanner in which they suppress volume-fraction fluctuations at large length scales, and yet are statistically isotropic with no Bragg peaks. It has recently been shown that disordered hyperuniform dielectric two-dimensional (2D) cellular network solids possess complete photonic band gaps comparable in size to photonic crystals,while at the same timemaintaining statistical isotropy, enabling waveguide geometries not possible with photonic crystals. Motivated by these developments, we explore other functionalities of various 2D ordered and disordered hyperuniform cellular networks, including their effective thermal or electrical conductivities and *** the multifunctionality of a class of such low-density networks by demonstrating that theymaximize or virtually maximize the effective conductivities and elastic moduli. This is accomplished using themachinery of homogenization theory, including optimal bounds and cross-property bounds, and statistical *** rigorously prove that anisotropic networks consisting of sets of intersecting parallel channels in the low-density limit, ordered or disordered, possess optimal effective conductivity tensors. For a variety of different disordered networks,we showthatwhen short-range and long-range order increases, there is an increase in both the effective conductivity and elasticmoduli of the network. Moreover,we demonstrate that the effective conductivity and elasticmoduli of various disordered networks derived from disordered 'stealthy' hyperuniform point patterns possess virtually optimal *** note that the optimal networks for conductivity are also optimal for the fluid permeability associatedwith slow viscous flow through the channels as well as themean survival time associated with diffusioncontrolled reactions in the channels. In summary,we have identified ordered and disor
We formulate a 3 × 3 Riemann-Hilbert problem to solve the Cauchy problem for the Sasa-Satsuma equation on the line, which allows us to give a representation for the solution of Sasa-Satsuma equation. We then appl...
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In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniquen...
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Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of intere...
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