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For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in…
We present a general framework for classification of sparse and irregularly-sampled time series. The properties of such time series can result in substantial uncertainty about the values of the underlying temporal processes, while making…
Water availability is a major environmental driver affecting riparian and wetland vegetation. The interaction between water table fluctuations and vegetation in a stochastic environment contributes to the complexity of the dynamics of these…
This article develops a continuous-time asymptotic framework for analyzing adaptive experiments -- settings in which data collection and treatment assignment evolve dynamically in response to incoming information. A key challenge in…
Being spontaneous, micro-expressions are useful in the inference of a person's true emotions even if an attempt is made to conceal them. Due to their short duration and low intensity, the recognition of micro-expressions is a difficult task…
We consider the problem of estimating the sparse time-varying parameter vectors of a point process model in an online fashion, where the observations and inputs respectively consist of binary and continuous time series. We construct a novel…
Local climate information is crucial for impact assessment and decision-making, yet coarse global climate simulations cannot capture small-scale phenomena. Current statistical downscaling methods infer these phenomena as temporally…
Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or…
There exists a correlation between geospatial activity temporal patterns and type of land use. A novel self-supervised approach is proposed to stratify landscape based on mobility activity time series. First, the time series signal is…
Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…
Time-series Foundation Models (TSFMs) have recently emerged as a universal paradigm for learning across diverse temporal domains. However, despite their empirical success, the internal mechanisms by which these models represent fundamental…
We develop a timescale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a…
Mobile communication channels are often modeled as linear time-varying filters or, equivalently, as time-frequency integral operators with finite support in time and frequency. Such a characterization inherently assumes the signals are…
Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we…
We present measurements of the complete spatio-temporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a new absorption technique…
The trade-off in remote sensing instruments that balances the spatial resolution and temporal frequency limits our capacity to monitor spatial and temporal dynamics effectively. The spatiotemporal data fusion technique is considered as a…
Random advection of Lagrangian tracer scalar field $\theta (t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…