Related papers: An algorithm for evaluating Gram matrices in Verma…
In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $\Gamma$, where $\Gamma \subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We…
The formula-evaluation problem is defined recursively. A formula's evaluation is the evaluation of a gate, the inputs of which are themselves independent formulas. Despite this pure recursive structure, the problem is combinatorially…
I present a numerical algorithm for direct evaluation of multiple Grassmann integrals. The approach is exact and suffers no Fermion sign problems. Memory requirements grow exponentially with the interaction range and the transverse size of…
In this note we translate the pictorial description of Gulotta's efficient inverse algorithm (arXiv:0807.3012) into matrix operations, so that it can be implemented on a computer. As an application we point out that this in combination with…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
Computer algebra procedures to manipulate pseudo-differential operators are implemented to perform calculations with integrable models. We use lazy evaluation and streams to represent and operate with pseudo-differential operators. No order…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…
We present a computer algebra package based on Magma for performing computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general…
Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights…
We present some theorems and algorithms for calculating perpendicular categories and locally semi-simple decompositions. We implemented a computer program {\sc TETIVA} based on these algorithms and we offer this program for everybody's use.
A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented.
The devices designed for the Internet-of-Things encompass a large variety of distinct processor architectures, forming a highly heterogeneous zoo. In order to tackle this, we employ a simulator to estimate the performance of the…
This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…
Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The…
Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
Here we propose an evolutionary algorithm that self modifies its operators at the same time that candidate solutions are evolved. This tackles convergence and lack of diversity issues, leading to better solutions. Operators are represented…
We present a program for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes which supports the use of complex masses in the loop integrals. The program is built on an earlier…
Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and…