Related papers: Synchronicity phenomenon in cluster patterns
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets…
Based on the construction of polytope functions and several results about them in [LP], we take a deep look on their mutation behaviors to find a link between a face of a polytope and a sub-cluster algebra of the corresponding cluster…
We extend the notion of $y$-variables (coefficients) in cluster algebras to cluster scattering diagrams. Accordingly, we extend the dilogarithm identity associated with a period in a cluster pattern to the one associated with a loop in a…
Using the APM cluster data we investigate whether the dynamical status of clusters is related to the large-scale structure of the Universe. We find that cluster substructure is strongly correlated with the tendency of clusters to be aligned…
Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered…
We study Newton polytopes for cluster variables in cluster algebras $\mathcal{A}(\Sigma)$ of types A and D. A famous property of cluster algebras is the Laurent phenomenon: each cluster variable can be written as a Laurent polynomial in the…
In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work…
This work introduces the phenomenon of Collective Almost Synchronization (CAS), which describes a universal way of how patterns can appear in complex networks even for small coupling strengths. The CAS phenomenon appears due to the…
In this paper, we provide a Hodge-theoretic interpretation of Laurent phenomenon for general skew-symmetric quantum cluster algebras, using Donaldson-Thomas theory for a quiver with potential. It turns out that the positivity conjecture…
We establish a combinatorial realization of continued fractions as quotients of cardinalities of sets. These sets are sets of perfect matchings of certain graphs, the snake graphs, that appear naturally in the theory of cluster algebras. To…
A coupled cell network is a type of ordinary differential equation $\dot x(t)=f(x(t))$, with structural constraints on the vector field $f$, encoded in a directed graph, whose cells and arrows are labeled by type. The generated dynamics can…
We consider the phenomenon of mutual synchronization in a fundamental quantum system of two detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to this spontaneous phenomenon showing…
Clustering bifurcations are investigated by considering models of globally coupled map lattices. Typical classes of clustering bifurcations are revealed. The clustering bifurcation thresholds of the coupled system are closely related to the…
We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than…
Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the…
This paper proposes an early detection method for cluster structural changes. Cluster structure refers to discrete structural characteristics, such as the number of clusters, when data are represented using finite mixture models, such as…
In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in…
We study the phase synchronized clusters in the diffusively coupled maps on the Cayley tree networks for heterogeneous delay values. Cayley tree networks comprise of two parts: the inner nodes and the boundary nodes. We find that…
We study the relationship between synchronization and the rate with which information is exchanged between nodes in a spatio-temporal network that describes the dynamics of classical particles under a substrate Remoissenet-Peyrard…