Related papers: Discrete dynamics in cluster integrable systems fr…
We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…
Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically…
We present simulations of a hard disc system and analyze the time evolution of the dynamic heterogeneities. We characterize the time evolution of slow regions and slow particles individually. The motion of slow clusters turns out to be very…
Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper…
Dynamic networks, especially those representing social networks, undergo constant evolution of their community structure over time. Nodes can migrate between different communities, communities can split into multiple new communities,…
It is proved that the generalized cluster complex defined by Fomin and Reading has a dihedral symmetry. Together with diagram symmetries, they generate its automorphism group. A consequence is a simple explicit formula for the order of this…
We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
Globular clusters (GCs) constitute a system which is evolving because of various interactions with the galactic environment. Evolution may be the explanation of many observed features of Globular Cluster Systems (GCSs); the different radial…
A new dynamical clustering algorithm for the identification of modules in complex networks has been recently introduced \cite{BILPR}. In this paper we present a modified version of this algorithm based on a system of chaotic Roessler…
Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as…
Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised…
Mixture models extend the toolbox of clustering methods available to the data analyst. They allow for an explicit definition of the cluster shapes and structure within a probabilistic framework and exploit estimation and inference…
In this paper we develop a theory of convexity for a free Abelian group M (the lattice of integer points), which we call theory of discrete convexity. We characterize those subsets X of the group M that could be call "convex". One property…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
We present recent theoretical investigations on the dynamics of metal clusters in contact with an environment, deposited of embedded. This concerns soft deposition as well as irradiation of the deposited/embedded clusters by intense laser…
We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain…
Dirac structures and Morse families are used to obtain a geometric formalism that unifies most of the scenarios in mechanics (constrained calculus, nonholonomic systems, optimal control theory, higher-order mechanics, etc.), as the examples…
It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular…