Related papers: Symbolic-numerical algorithm for generating cluste…
We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search…
We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…
A symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating'', preserves all dynamical…
The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single…
We consider a novel clustering task in which clusters can have compositional relationships, e.g., one cluster contains images of rectangles, one contains images of circles, and a third (compositional) cluster contains images with both…
We present an algorithm to solve very large one-dimensional disordered and interacting few-particle systems. Our approach exploits the localized nature of the eigenfunctions in real space to achieve a linear scaling with the total system…
Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…
Clustering is a difficult and widely-studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g. Euclidean distance) to…
The procedure for simulating the nuclear magnetic resonance spectrum linked to the spin system of a molecule for a certain nucleus entails diagonalizing the associated Hamiltonian matrix. As the dimensions of said matrix grow exponentially…
A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between classes. We introduce Self…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…
In the planted partition problem, the $n$ vertices of a random graph are partitioned into $k$ "clusters," and edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively…
This paper reports on constructive approximation methods for three classes of holomorphic functions on the unit disk which are closely connected each other: the class of starlike and spirallike functions, the class of semigroup generators,…
By applying a standard solution generating technique, we transform an arbitrary vacuum Mixmaster solution on $S^3 \times {\bf R}$ to a new solution which is spatially inhomogeneous. We thereby obtain a family of exact, spatially…
We consider programmable matter that consists of computationally limited devices (called particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention. We…
We study parallel algorithms for correlation clustering. Each pair among $n$ objects is labeled as either "similar" or "dissimilar". The goal is to partition the objects into arbitrarily many clusters while minimizing the number of…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
Algorithms are described and Maple implementations are provided for finding all quandles of order $n$, as well as computing all homomorphisms between two finite quandles or from a finitely presented quandle (e.g., a knot quandle) to a…
The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or…
We study numerically synchronization phenomena of spatiotemporal structures, including chimera states, in a two layer network of nonlocally coupled nonlinear chaotic discrete-time systems. Each of the interacting ensembles represents a one…