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Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…

A cornerstone of the smart grid is the advanced monitorability on its assets and operations. Increasingly pervasive installation of the phasor measurement units (PMUs) allows the so-called synchrophasor measurements to be taken roughly 100…

Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…

Mendelian Randomization is a widely used instrumental variable method for assessing causal effects of lifelong exposures on health outcomes. Many exposures, however, have causal effects that vary across the life course and often influence…

We propose a new estimation methodology to address the presence of covariate measurement error by exploiting the availability of spatial data. The approach uses neighboring observations as repeated measurements, after suitably controlling…

Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial…

Developmental transcriptional networks in plants and animals operate in both space and time. To understand these transcriptional networks it is essential to obtain whole-genome expression data at high spatiotemporal resolution. Substantial…

Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…

Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…

We introduce a method for manifold alignment of different modalities (or domains) of remote sensing images. The problem is recurrent when a set of multitemporal, multisource, multisensor and multiangular images is available. In these…

To ensure the safety of railroad operations, it is important to monitor and forecast track geometry irregularities. A higher safety requires forecasting with higher spatiotemporal frequencies, which in turn requires capturing spatial…

We propose a new methodology to estimate the spatial reuse of CSMA-like scheduling. Instead of focusing on spatial configurations of users, we model the interferences between users as a random graph. Using configuration models for random…

Modal analysis has become an essential tool to understand the coherent structure of complex flows. The classical modal analysis methods, such as dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD), rely on a…

Multi-subject fMRI studies are challenging due to the high variability of both brain anatomy and functional brain topographies across participants. An effective way of aggregating multi-subject fMRI data is to extract a shared…

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Phase imaging techniques extract the optical path-length information of a scene, whereas wavefront sensors provide the shape of an optical wavefront. Since these two applications have different technical requirements, they have developed…

Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…

A review on the main results concerning the algebraic and differential properties of the averaging and coordination operators and the properties of the space-time averages of macroscopic gravity is given. The algebraic and differential…

Time series forecasting is an important problem across many domains, playing a crucial role in multiple real-world applications. In this paper, we propose a forecasting architecture that combines deep autoregressive models with a Spectral…