Related papers: The $k$-Compound of a Difference-Algebraic System
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…
The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…
We discuss $\mathcal{D}$-modules and dynamical systems in the \'etale topology. We introduce the differential scheme associated to a morphism $f: X\to S$ of schemes of the same dimension. We introduce differential inertia group $I_{diff}^i$…
In this work we derive important properties regarding matrix invariants which occur in the theory of differential equations with reflection.
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior…
In this work we present a novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems. It extends a classical subdivision technique [Dellnitz/Hohmann 1997] for the computation of such…
The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
k-frames were recently introduced by Gavruta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in Hilbert space which allows reproductions of arbitrary elements by…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
Deep Gaussian Processes (DGPs) leverage a compositional structure to model non-stationary processes. DGPs typically rely on local inducing point approximations across intermediate GP layers. Recent advances in DGP inference have shown that…
We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ordinary differentiable equations…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…