Related papers: Multiscale Analysis of Information Dynamics for Li…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of…
Molecular dynamics (MD) simulations are powerful tools for elucidating the macroscopic physical properties of materials from microscopic atomic behaviors. However, the massive, high-dimensional datasets generated by MD simulations pose a…
Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…
The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
A powerful time series analysis modeling technique is presented to describe cycle-to-cycle variability in memristors. These devices show variability linked to the inherent stochasticity of device operation and it needs to be accurately…
Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…
Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as…
Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…
Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and non-living self-assembled systems. The arrays…
Data warehouse store and provide access to large volume of historical data supporting the strategic decisions of organisations. Data warehouse is based on a multidimensional model which allow to express user's needs for supporting the…
Many real-world problems in machine learning, signal processing, and communications assume that an unknown vector $x$ is measured by a matrix A, resulting in a vector $y=Ax+z$, where $z$ denotes the noise; we call this a single measurement…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…