Related papers: An algorithm for evaluating Gram matrices in Verma…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse…
The GVW algorithm is a signature-based algorithm for computing Gr\"obner bases. If the input system is not homogeneous, some J-pairs with higher signatures but lower degrees are rejected by GVW's Syzygy Criterion, instead, GVW have to…
The Grade of Membership (GoM) model, which allows subjects to belong to multiple latent classes, is a powerful tool for inferring latent classes in categorical data. However, its application is limited to categorical data with nonnegative…
The evaluation mechanism of pattern matching with dynamic patterns is modelled in the Pure Pattern Calculus by one single meta-rule. This contribution presents a refinement which narrows the gap between the abstract calculus and its…
We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free…
Matrix transformations in terms of triangular matrices is the easiest method of evaluating matrix-variate gamma and beta integrals in the real and complex cases. Here we give several procedures of explicit evaluation of gamma and beta…
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…
In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…
We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order…
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…
This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m,n in (1/T)Z_+, an A_{g,n}(V)-A_{g,m}(V)-bimodule A_{g,n,m}(V) is…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step towards the classification of finite dimensional irreducible modules. Motivated by known results in type A, we…
We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…
Algorithms for the numerical evaluation of the incomplete gamma function ratios $P(a,x)=\gamma(a,x)/\Gamma(a)$ and $Q(a,x)=\Gamma(a,x)/\Gamma(a)$ are described for positive values of $a$ and $x$. Also, inversion methods are given for…
In the present paper we continue the project of systematic classification and construction of invariant differential operators for non-compact semisimple Lie groups. This time we make the stress on one of the main building blocks, namely…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…