Related papers: Change Detection: A functional analysis perspectiv…
Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…
In this paper a computationally efficient approach is suggested for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines, such as a single phase transformer (a…
Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--differential equations with uncertainties in the coefficient…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
We exploit the information derived from geographical coordinates to endogenously identify spatial regimes in technologies that are the result of a variety of complex, dynamic interactions among site-specific environmental variables and…
Detecting anomalous edges and nodes in dynamic networks is critical in various areas, such as social media, computer networks, and so on. Recent approaches leverage network embedding technique to learn how to generate node representations…
A Markov process is registered. At random moment $\theta$ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is…
We consider linearizations of stochastic differential equations with additive noise using the Karhunen-Lo\`eve expansion. We obtain our linearizations by truncating the expansion and writing the solution as a series of matrix-vector…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a…
Change point analyses are concerned with identifying positions of an ordered stochastic process that undergo abrupt local changes of some underlying distribution. When multiple processes are observed, it is often the case that information…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption,…
Structural change detection problems are often encountered in analytics and econometrics, where the performance of a model can be significantly affected by unforeseen changes in the underlying relationships. Although these problems have a…
Developing methods for detecting tipping phenomena at an early stage is an important problem in various fields such as ecology, medicine, and economics. A tipping phenomenon is characterized by a rapid transition resulting from the…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We consider the problem of online profile monitoring of random functions that admit basis expansions possessing random coefficients for the purpose of out-of-control state detection. Our approach is applicable to a broad class of random…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…