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The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…
There are two approaches to time series approximate factor models: the static factor model, where the factors are loaded contemporaneously by the common component, and the Generalised Dynamic Factor Model, where the factors are loaded with…
We use a phenomenological Hamiltonian approach to derive a set of coupled mode equations that describe light propagation in waveguides that are periodically side-coupled to microcavities. The structure exhibits both Bragg gap and (polariton…
The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions.…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation.…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
We observe that the characteristic cycle of a D-module gives bounds for decomposition numbers of intersection cohomology complexes.
Reconfiguration paths express sequences of successive reconfiguration operations within a component-based approach allowing dynamic reconfigurations. We use constructs from regular expressions-pin particular, alternatives-to introduce…
On classes of functions defined on R^2n we introduce abstract composition laws modelled after the pseudodifferential product of symbols. We attach to these composition laws modulation mappings and spaces with useful algebraic and…
We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In…
We study the path realization of Demazure crystals related to solvable lattice models in statistical mechanics. Various characters are represented in a unified way as the sums over one dimensional configurations which we call unrestricted,…
Characteristic functions are shown to be useful for highly sensitive measurements. Redistributions of motional Fock states of a trapped atom can be directly monitored via the most fragile nonclassical part of the characteristic function.…
An expression describing the controlling parameters involved in short range nanoscale dissipation is proposed and supported by simulations and experimental findings. The expression is deconstructed into the geometrical, dynamic, chemical…
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions…