相关论文: Polynomial Lie algebra methods in solving the seco…

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…

Clustering is an important task with applications in many fields of computer science. We study the fully dynamic setting in which we want to maintain good clusters efficiently when input points (from a metric space) can be inserted and…

The Lie-algebraic method approximates differential operators that are formal polynomials of {1,x,d/dx} by linear operators acting on a finite dimensional space of polynomials. In this paper we prove that the rank of the n-dimensional…

We propose a simple method to identify a continuous Lie algebra symmetry in a dataset through regression by an artificial neural network. Our proposal takes advantage of the $ \mathcal{O}(\epsilon^2)$ scaling of the output variable under…

We introduce families of quasi-rectifiable vector fields and study their geometric and algebraic aspects. Then, we analyse their applications to systems of partial differential equations. Our results explain, in a simpler manner, previous…

The growth of evolutionary computing (EC) methods in the exploration of complex potential energy landscapes of atomic and molecular clusters, as well as crystals over the last decade or so is reviewed. The trend of growth indicates that…

We implement two algorithms in MATHEMATICA for classifying automorphisms of lower-dimensional non-commutative Lie algebras. The first algorithm is a brute-force approach whereas the second is an evolutionary strategy. These algorithms are…

In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums…

An equivalence between an integro-differential operator M and an evolution operator Ln is determined. From this equivalence the fundamental solution of Ln is estimated in terms of the fundamental solution related to the third-order operator…

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…

In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and…

The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for…

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…

Let $\mathrm{R}$ be a real closed field and $\mathrm{D} \subset \mathrm{R}$ an ordered domain. We consider the algorithmic problem of computing the generalized Euler-Poincar\'e characteristic of real algebraic as well as semi-algebraic…

We give a new analysis of a tuning problem in music theory, pertaining specifically to the approximation of harmonics on a two-dimensional keyboard. We formulate the question as a linear programming problem on families of constraints and…

We establish sufficient conditions of exact and almost full recovery of the node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time algorithms. First, we improve upon the known conditions of almost full recovery by…

Cluster algebras are a recent topic of study and have been shown to be a useful tool to characterize structures in several knowledge fields. An important problem is to establish whether or not a given cluster algebra is of finite type.…

We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.

We discuss the nearest neighbor distribution of the eigenvalues for hermitian generators in the Lie algebra of a semisimple complex Lie Group along a sequence of irreducible representations. After the basic definitions a limit theorem for…