Related papers: Coupled-Cluster Imaginary-Time Evolution and the C…
Influence of surrounding matter on the properties of clusters is considered by an approach combining the methods of statistical and quantum mechanics. A cluster is treated as a bound N-particle system and surrounding matter as thermostat.…
We use elementary variational arguments to prove, and improve on, gap estimates which arise in simulating quantum circuits by adiabatic evolution.
We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
The high metallicity of the intra-cluster medium (ICM) is generally interpreted on the base of the galactic wind scenario for elliptical galaxies. In this framework, we develop a toy-model to follow the chemical evolution of the ICM,…
This paper extends the design-based framework to settings with multi-way cluster dependence, and shows how multi-way clustering can be justified when clustered assignment and clustered sampling occurs on different dimensions, or when either…
In this Letter we show how the nonlinear evolution of a resonant triad depends on the special combination of the modes' phases chosen according to the resonance conditions. This phase combination is called dynamical phase. Its evolution is…
Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the…
Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…
We consider a flat Universe filled with a vacuum energy coupled to matter and radiation by respectively positive coupling functions $Q_m$ and $Q_r$. We require that these functions be such as Universe exits from inflation to go to a…
Galaxies in clusters are gas-deficient and a number of possible explanations for this observation have been advanced, including galaxy-cluster tidal interactions, galaxy harassment, and ISM-ICM gas stripping. In this paper, we use a…
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an…
We propose ClusPath, a novel algorithm for detecting general evolution tendencies in a population of entities. We show how abstract notions, such as the Swedish socio-economical model (in a political dataset) or the companies fiscal…
Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical…
The formal consideration of the concept of interaction in thermodynamic analysis makes it possible to deduce, in the broadest terms, new results related to the coevolution of interacting systems, irrespective of their distance from…
In this paper we present a study of the cosmic flow from the point of view of how clusterings at different dynamical regimes in an expanding universe evolve according to a `coarse-grained' partitioning of their ranked energy distribution.…
A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…