Related papers: On Robust $\beta$-Spectra Shape Parameter Extracti…
We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g.…
The two-matrix model can be solved by introducing bi-orthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of bi-orthogonal polynomials (called "windows") satisfy polynomial ODEs as well as…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
Statistical power estimation for studies with multiple model parameters is inherently a multivariate problem. Power for individual parameters of interest cannot be reliably estimated univariately since correlation and variance explained…
Complete orthonormal sets of exponential-type orbitals with non-integer principal quantum numbers are discussed as basis functions in non-relativistic Hartree-Fock-Roothaan electronic structure calculations of atoms. A method is proposed to…
In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating function, the associated continued fraction, the orthogonality…
In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a…
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…
Given a bivariate weight function defined on the positive quadrant of $\mathbb{R}^2$, we study polynomials in two variables orthogonal with respect to varying measures obtained by special modifications of this weight function. In…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…
The efforts associated with parametrization of continuum-based models for crystal plasticity are a significant obstacle for the routine use of these models in materials science and engineering. While phenomenological constitutive…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
The weighted Euler characteristic transform (WECT) is a new tool for extracting shape information from data equipped with a weight function. Image data may benefit from the WECT where the intensity of the pixels are used to define the…
A major obstacle for computing optical spectra of solids is the lack of reliable approximations for capturing excitonic effects within time-dependent density-functional theory. We show that the trustful prediction of strongly bound…
The baryonic features in the galaxy power spectrum offer tight, time-resolved constraints on the expansion history of the Universe but complicate the measurement of the broadband shape of the power spectrum, which also contains precious…
Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}. In the present paper…
We introduce a family of weight matrices $W$ of the form $T(t)T^*(t)$, $T(t)=e^{\mathscr{A}t}e^{\mathscr{D}t^2}$, where $\mathscr{A}$ is certain nilpotent matrix and $\mathscr{D}$ is a diagonal matrix with negative real entries. The weight…
We draw attention on the procedure, where Standard Model predictions and experimental results are compared and certain new physics scenarios are ruled out, that requires great attention, since there is still a room for new physics,…