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Separate constituents of extended systems measure proper-times on different world-lines. Relating and comparing proper-time measurements along any two such world-lines requires that common simultaneity be possible, which in turn implies…
In this work we propose a novel approach for modeling spatio-temporal data characterized by group structures. In particular, we extend classical mixed effect regression models by introducing a space-time nonparametric component, regularized…
Estimating the covariance structure of multivariate time series is a fundamental problem with a wide-range of real-world applications -- from financial modeling to fMRI analysis. Despite significant recent advances, current state-of-the-art…
We present an adaptation of the standard Grassberger-Proccacia (GP) algorithm for estimating the Correlation Dimension of a time series in a non subjective manner. The validity and accuracy of this approach is tested using different types…
Understanding and distinguishing temporal patterns in time series data is essential for scientific discovery and decision-making. For example, in biomedical research, uncovering meaningful patterns in physiological signals can improve…
We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex…
Gravitational wave detectors produce time series of the gravitational wave strain co-added with instrument noise. For evenly sampled data, such as from laser interferometers, it has been traditional to Fourier transform the data and perform…
Spatially resolved transcriptomics (ST) measures gene expression along with the spatial coordinates of the measurements. The analysis of ST data involves significant computation complexity. In this work, we propose gene expression…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…
The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based…
The experimental and theoretical challenges posed by the study of dynamically inhomogeneous systems are outlined in the context of cuprates and other oxides. Considering the pitfalls in the single-component approach to the analysis of…
It has long been known that the excitation of fast motion in certain two-scale dynamical systems is linked to the singularity structure in complex time of the slow variables. We demonstrate, in the context of a fast harmonic oscillator…
Anomalies in univariate time series often refer to abnormal values and deviations from the temporal patterns from majority of historical observations. In multivariate time series, anomalies also refer to abnormal changes in the inter-series…