Related papers: Symbolic-numerical algorithm for generating cluste…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
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…
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…
The many-identical-particle quantum correlations are revisited utilizing the machinery of basic group theory, especially that of the group of permutations. It is done with the purpose to obtain precise definitions of effective distinct…
Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard,…
In this article, we present a $T$-matrix method for numerical computation of second-harmonic generation from clusters of arbitrarily distributed spherical particles made of centrosymmetric optical materials. The electromagnetic fields at…
Identification of the clusters from an unlabeled data set is one of the most important problems in Unsupervised Machine Learning. The state of the art clustering algorithms are based on either the statistical properties or the geometric…
We introduce the Neural Collaborative Subspace Clustering, a neural model that discovers clusters of data points drawn from a union of low-dimensional subspaces. In contrast to previous attempts, our model runs without the aid of spectral…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as represents of their respective symmetry groups: O(2), O(3), and O(2,1). Solving the Schrodinger equation by…
Reflections are omnipresent tools in quantum algorithms. We consider the task of reflecting through the eigenspace of an implementable unitary. Such reflections are generally designed using phase estimation or linear combination of…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
We consider geometric numerical integration algorithms for differential equations evolving on symmetric spaces. The integrators are constructed from canonical operations on the symmetric space, its Lie triple system (LTS), and the…
Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It…
In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…
Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
Cluster algorithms for classical and quantum spin systems are discussed. In particular, the cluster algorithm is applied to classical O(N) lattice actions containing interactions of more than two spins. The performance of the multi-cluster…