Related papers: A simple algorithm for orbit classification
In this paper we investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on a simple Lie algebras of type $E_6$, $F_4$ and $G_2$. The methods for classifying the orbits for…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
This paper is a continuation of arXiv:1201.1102. We investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on the simple Lie algebra of type $E_7$. The methods for…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
We introduce analysis of orbital parities as a concept and a tool for understanding radicals. Based on fundamental reduced one- and two-electron density matrices, our approach allows us to evaluate a total measure of radical character and…
We exhibit algorithms for calculating Tits' buildings and orbits of vectors in a lattice $L$ for certain subgroups of $\operatorname{O}(L)$. We discuss how these algorithms can be applied to understand the configuration of boundary…
In this work, applying general results from averaging theory, we find periodic orbits for a class of Hamiltonian systems $H$ whose potential models the motion of elliptic galaxies.
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
Grouping elements into families to analyse them separately is a standard analysis procedure in many areas of sciences. We propose herein a new algorithm based on the simple idea that members from a family look like each other, and don't…
The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are…
Discovering "good" algorithms for an operation is often considered an art best left to experts. What if there is a simple methodology, an algorithm, for systematically deriving a family of algorithms as well as their cost analyses, so that…
This research paper focuses on the implementation of radial Basis Function (RBF) Support Vector Machines (SVM) for classifying asteroid orbits. Asteroids are important astronomical objects, and their orbits play a crucial role in…
One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the…
We compute the mapping class group orbits in the homotopy set of framings of a compact connected oriented surface with non-empty boundary. In the case $g > 1$ the computation is some modification of Johnson's results and certain arguments…
We construct and analyze families of periodic delay orbits for a class of delay differential equations in two dimensions depending on two real-valued functions. These families are parametrized by the delay parameter. It is possible to…
We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…
This paper introduces a novel and general algorithm for approximately counting the number of orbits under group actions. The method is based on combining the Burnside process and importance sampling. Specializing to unitriangular groups…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems…