Related papers: Synchronicity phenomenon in cluster patterns
The possibility for detuned spins to display synchronous oscillations in local observables is analyzed in the presence of collective dissipation and incoherent pumping. We show that there exist two distinct mechanisms that can give rise to…
Considered as commutative algebras, cluster algebras can be very unpleasant objects. However, the first author introduced a condition known as "local acyclicity" which implies that cluster algebras behave reasonably. One of the earliest and…
We establish certain fundamental properties of $f$-vectors and $F$-matrices for generalized cluster algebras, including the initial and final seed mutation formulas, the compatibility property and the symmetry property. Along the way, we…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
We present a new algorithm for clustering longitudinal data. Data of this type can be conceptualized as consisting of individuals and, for each such individual, observations of a time-dependent variable made at various times. Generically,…
Synchronization is a fundamental phenomenon in dynamical systems, occurring in a wide range of contexts such as mechanical, chemical, biological, and social systems. In this work, we explore a novel manifestation of synchronization in…
In the theory of generalized cluster algebras, we build the so-called cluster formula and $D$-matrix pattern. Then as applications, some fundamental conjectures of generalized cluster algebras are solved affirmatively.
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
Social media are transforming global communication and coordination and provide unprecedented opportunities for studying socio-technical domains. Here we study global dynamical patterns of communication on Twitter across many scales.…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
An approach for understanding the behavior of multiplicity distributions in restricted phase-space intervals derived on the basis of global observables is proposed. We obtain a unifying connection between local multiparticle clusters and…
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of certain Laurent polynomial rings.…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network…
We initiate a systematic study of the cohomology of cluster varieties. We introduce the Louise property for cluster algebras that holds for all acyclic cluster algebras, and for most cluster algebras arising from marked surfaces. For…
A network of chaotic systems can be designed in such a way that the cluster patterns formed by synchronous nodes can be controlled through the coupling parameters. We present a novel approach to exploit such a network for covert…
We propose a novel model-based clustering approach for samples of time series. We assume as a unique commonality that two observations belong to the same group if structural changes in their behaviours happen at the same time. We resort to…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…