Related papers: Clustering dynamics in globally coupled map lattic…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
Clustering, or transitivity has been observed in real networks and its effects on their structure and function has been discussed extensively. The focus of these studies has been on clustering of single networks while the effect of…
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Many real-world networks display a natural bipartite structure. It is necessary and important to study the bipartite networks by using the bipartite structure of the data. Here we propose a modification of the clustering coefficient given…
The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents…
Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…
Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…
Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we…
Critical phase transitions have proven to be a powerful concept to capture the phenomenology of many systems, including deeply non-equilibrium ones like living systems. The study of these phase transitions has overwhelmingly relied on…
Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in…
A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state…
The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…
An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
The structure of defect clusters formed in a displacement cascade plays a significant role in the micro-structural evolution during irradiation. Molecular dynamics simulations have been widely used to study collision cascades and subsequent…
Within network data analysis, bipartite networks represent a particular type of network where relationships occur between two disjoint sets of nodes, formally called sending and receiving nodes. In this context, sending nodes may be…