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Functional connectivity estimates are highly sensitive to analysis choices and can be dominated by noise when the number of sampled time points is small relative to network dimensionality. This issue is particularly acute in fMRI, where…

It is shown how Adler's trace dynamics can be applied to stochastic mechanics and other complex classical dynamical systems. Emergent non-commutivity due to the fractal nature of sample trajectories is closely related to the fact that the…

We introduce a new phenomenological tool based on momentum region indicators to guide the analysis and interpretation of semi-inclusive deep-inelastic scattering measurements. The new tool, referred to as "affinity", is devised to help…

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…

Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a…

Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called…

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…

We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…

We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional…

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic and weakly confined granular material, using high-resolution $\gamma$-ray adsorption. In these experiments, the particle…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

We consider the influence of active speed fluctuations on the dynamics of a $d$-dimensional active Brownian particle performing a persistent stochastic motion. We use the Laplace transform of the Fokker-Planck equation to obtain exact…

This work presents a numerical investigation of different approximation techniques for the temporal weights used in the Dual Weighted Residual (DWR) method applied to a time-dependent convection-diffusion equation which is assumed to be…

In this article we explore how structural parameters of composites filled with one-dimensional, electrically conducting elements (such as sticks, needles, chains, or rods) affect the percolation properties of the system. To this end, we…

In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…

We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…

Active matter systems under confinement display persistent surface motion and a strong boundary affinity. However, despite extensive studies of their positional dynamics, much less attention has been given to the corresponding orientational…

Compressed deep learning models are crucial for deploying computer vision systems on resource-constrained devices. However, model compression may affect robustness, especially under natural corruption. Therefore, it is important to consider…

Constitutive models that describe the mechanical behavior of soft tissues have advanced greatly over the past few decades. These expert models are generalizable and require the calibration of a number of parameters to fit experimental data.…