Related papers: Synchronicity phenomenon in cluster patterns
Pattern comparison represents a fundamental and crucial aspect of scientific modeling, artificial intelligence, and pattern recognition. Three main approaches have typically been applied for pattern comparison: (i) distances; (ii)…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
Motivated by a construction in the theory of cluster algebras (Fomin and Zelevinsky), one associates to each acyclic directed graph a family of sequences of natural integers, one for each vertex; this construction is called a {\em frieze};…
We introduce a class of commutative superalgebras generalizing cluster algebras. A cluster superalgebra is defined by a hypergraph called an "extended quiver", and transformations called mutations. We prove the super analog of the "Laurent…
The open quantum system eigenstate in the vicinity of low-energy decay channel may mimic its features, in particular the characteristic clustering properties of the decay channel. This generic mechanism of clusterization, the so-called…
The goal of this note is to study quantum clusters in which cluster variables (not coefficients) commute which each other. It turns out that this property is preserved by mutations. Remarkably, this is equivalent to the celebrated sign…
We have previously defined synchronization (Gomez, E. and K. Schubert 2011) as a relation between the times at which a pair of events can happen, and introduced an algebra that covers all possible relations for such pairs. In this work we…
The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…
In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar…
Synchronization is a widespread phenomenon encountered in many natural and engineered systems with nonlinear classical dynamics. How synchronization concepts and mechanisms transfer to the quantum realm and whether features are universal or…
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…
Generalized chaotic synchronization regime is observed in the unidirectionally coupled one-dimensional Ginzburg-Landau equations. The mechanism resulting in the generalized synchronization regime arising in the coupled spatially extended…