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We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
The optimized effective potential (OEP) approach has so far mainly been used in benchmark studies and for the evaluation of band gaps. In this work, we extend the application of the OEP by determining the analytical ionic forces within the…
In many physical problems or applications one has to study functions that are invariant under the action of a symmetry group G and this is best done in the orbit space of G if one knows the equations and inequalities defining the orbit…
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the…
Rotations and poses are ubiquitous throughout many fields of science and engineering such as robotics, aerospace, computer vision and graphics. In this paper, we provide a complete characterization of rotations and poses in terms of the…
Posets are discrete mathematical structures which are ubiquitous in a broad range of data analysis and machine learning applications. Research connecting posets to the data science domain has been ongoing for many years. In this paper, a…
Photoemission orbital tomography (POT) from photoelectron momentum maps (PMMs) has enabled detailed analysis of the shape and energy of molecular orbitals in the adsorbed state. This study proposes a new POT method based on the PhaseLift.…
This paper investigates the qualitative behavior of a system of ordinary differential equations (ODEs) defined by a matrix operator derived from the algebraic structure of the Alpha Group. The system depends on a rotational parameter that…
In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The…
Two methods can be used to calculate explicitly the Killing form on the Lie algebras. The first one is a direct calculation of the traces of the generators in a matrix representation of the algebra, and the second one is the usage of the…
The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and domain-specific strengths. These tools…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even…
Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…
Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either…
An exponential polynomial is a finite linear sum of terms $P(z)e^{Q(z)}$, where $P(z)$ and $Q(z)$ are polynomials. The early results on the value distribution of exponential polynomials can be traced back to Georg P\'olya's paper published…
Equation of state (EOS) describes the thermodynamic properties of substances. It has important applications in many fields such as power mechanics, geophysics, astrophysics, and detonation physics. Currently, most EOSs have been constructed…
This paper concerns a class of orbital integrals in Lie algebras over p-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on varieties over finite fields. The construction, which is…
We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…