Related papers: On a New Algorithm for the Computation of Enclosur…
Embedding Calculus, as described by Weiss, is a calculus of functors, suitable for studying contravariant functors from the poset of open subsets of a smooth manifold M, denoted O(M), to a category of topological spaces (of which the…
Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving…
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems…
We present a method to calculate integrals over monomials of matrix elements with invariant measures in terms of Wick contractions. The method gives exact results for monomials of low order. For higher--order monomials, it leads to an error…
A new method is proposed to calculate wave functions in $k_T$-factorization in \cite{LiMi} as a comment about our paper \cite{FMW}. We point out that the results obtained with the method are in conflict with the translation invariance and…
A new version of the Hadwiger theorem on convex functions is established and an explicit representation of functional intrinsic volumes is found using new functional Cauchy-Kubota formulas. In addition, connections between functional…
Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…
We propose an algorithm to determine Maximally Localized Wannier Functions (MLWFs). This algorithm, based on recent theoretical developments, does not require any physical input such as initial guesses for the Wannier functions, unlike…
Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…
We discuss how to compute certified enclosures for the eigenvalues of benchmark linear magnetohydrodynamics operators in the plane slab and cylindrical pinch configurations. For the plane slab, our method relies upon the formulation of an…
Weyl groups are ubiquitous, and efficient algorithms for them -- especially for the exceptional algebras -- are clearly desirable. In this paper we provide several of these, addressing practical concerns arising naturally for instance in…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for computing Wannier functions in one-dimensional…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
Being encouraged by [AKRS] that provides an amazing bridge between Statistics and Invariant Theory, and especially by [FM], where quiver semi-invariant techniques apply to verify the existence of MLE for a recent iPCA model, we provide an…
I suggest an enhancement of the procedure of Chiong, Hsieh, and Shum (2017) for calculating bounds on counterfactual demand in semiparametric discrete choice models. Their algorithm relies on a system of inequalities indexed by cycles of a…
Let $\left( W,\sigma \right) $ be a symplectic vector space and let $% T:W\rightarrow W$ be a linear map that satisfies a certain condition of non-degeneracy. We define the Schur multiplier $\omega _{\sigma ,T}$ on $W$. To this multiplier…
The weight distribution of error correction codes is a critical determinant of their error-correcting performance, making enumeration of utmost importance. In the case of polar codes, the minimum weight $\wm$ (which is equal to minimum…
We develop algorithms for certifying an approximation to a nonsingular solution of a square system of equations built from univariate analytic functions. These algorithms are based on the existence of oracles for evaluating basic data about…