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A number of brown dwarfs are now known to be variable with observed amplitudes as large as 10-30% at some wavelengths. While spatial inhomogeneities in cloud coverage and thickness are likely responsible for much of the observed…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
Clinical data for ambulatory care, which accounts for 90% of the nations healthcare spending, is characterized by relatively small sample sizes of longitudinal data, unequal spacing between visits for each patient, with unequal numbers of…
Converting neutron scattering data to real-space time-dependent structures can only be achieved through suitable models, which is particularly challenging for geometrically disordered structures. We address this problem by introducing…
Time-reversal symmetry allows waves to retrace their paths through complex media and refocus at their origin. However, incomplete capture and reversal of scattered waves often limits pulse recompression. We address this challenge for…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
Drift diffusion models (DDMs) have found widespread use in computational neuroscience and other fields. They model evidence accumulation in simple decision tasks as a stochastic process drifting towards a decision barrier. In models where…
Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different…
This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
We propose a theoretical and computational approach to investigate temporal behavior of a nonlinear polarization in perturbative regime induced by an intense and ultrashort pulsed electric field. First-principles time-dependent density…
Materials with unusual optical properties are central to advanced control of light. Yet, in nature, such materials may be exceedingly rare and often difficult to obtain. To overcome this limitation, here we introduce the concept of temporal…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
Short planar glow discharges coupled to a resistive layer exhibit a wealth of spontaneous spatio-temporal patterns. Several authors have suggested effective reaction-diffusion-models to explore similarities with other pattern forming…
The Bou\'e-Dupuis variational formula gives a representation for log Laplace transforms of bounded measurable functions of a finite dimensional Brownian motion on a compact time interval as an infimum of a suitable cost over a collection of…
Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…
Multivariate time series have many applications, from healthcare and meteorology to life science. Although deep learning models have shown excellent predictive performance for time series, they have been criticised for being "black-boxes"…
In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new…
We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model…
Motivated by mixing processes in analytical laboratories, this work investigates enhanced dissipation in non-autonomous flows. We study the evolution of concentrations governed by the advection-diffusion equation, where the velocity field…