Related papers: Symbolic-numerical algorithm for generating cluste…
We describe identical particles through their extrinsic physical properties and operationally with an operator of selective measure Mm. The operator Mm is formed through non-symmetrized tensor product of one-particle measurement operators,…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
A variety of coherent states of the harmonic oscillator is considered. It is formed by a particular superposition of canonical coherent states. In the simplest case, these superpositions are eigenfunctions of the annihilation operator…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
Cluster states are an essential component in one-way quantum computation protocols. We present two schemes to generate addressable continuous-variable cluster states from quadrature squeezed cylindrically polarized modes. By including…
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…
Factorization method is developed for a family of discretely spiked harmonic oscillators. Two sets of intertwining and ladder operators are presented to algebraically generate eigenstates with energies isomorphic to those of the ordinary…
Manipulating the way in which colloidal particles self-organise is a central challenge in the design of functional soft materials. Meeting this challenge requires the use of building blocks that interact with one another in a highly…
We present a geometric design rule for size-controlled clustering of self-propelled particles. We show that active particles that tend to rotate under an external force have an intrinsic, signed parameter with units of curvature which we…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we…
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…
We present a detailed algorithm to construct symbolic encodings for chaotic attractors of three-dimensional flows. It is based on a topological analysis of unstable periodic orbits embedded in the attractor and follows the approach proposed…
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these…
In the past few years there has been a tumultuous activity aimed at introducing novel conceptual schemes for quantum computing. The approach proposed in (Marzuoli A and Rasetti M 2002, 2005a) relies on the (re)coupling theory of SU(2)…
The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…
Distributed synchronization is known to occur at several scales in the brain, and has been suggested as playing a key functional role in perceptual grouping. State-of-the-art visual grouping algorithms, however, seem to give comparatively…
Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wave functions obtained by dividing particles into multiple clusters, constructing a readily evaluable wave…
We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract…
Calculating interactions or correlations between pairs of particles is typically the most time-consuming task in particle simulation or correlation analysis. Straightforward implementations using a double loop over particle pairs have…
We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models. In the special case of $S=1/2$, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$ model in…