相关论文: Special Jordan subspaces in Coupled Cell Networks

We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…

Synchronization across long neural distances is a functionally important phenomenon. In order to access the mechanistic basis of long-range synchrony, we constructed an experimental model that enables monitoring of spiking activities over…

We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest…

Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetry called \emph{latent symmetry}, which is an extension of the standard notion of symmetry.…

The theories of $\pi$-points and modules of constant Jordan type have been a topic of much recent interest in the field of finite group scheme representation theory. These theories allow for a finite group scheme module $M$ to be restricted…

In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms''…

In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network…

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…

We consider some distinguished classes of elements of a multiplicative lattice endowed with coarse lower topologies, and call them lower spaces. The primary objective of this paper is to study the topological properties of these lower…

Two type of superization of the Jordanian r-matrix for the Lie algebra sl(2) are considered. One type is associated with the Lie superalgebra sl(1|1) and another type is associated with the orthosymplectic Lie superalgebra osp(1|2).…

We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian…

Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial…

Adjacency polytopes, a.k.a. symmetric edge polytopes, associated with undirected graphs have been defined and studied in several seemingly independent areas including number theory, discrete geometry, and dynamical systems. In particular,…

A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism, economical networks... It consists in a directed graph $G$, each node (or cell) representing an agent of the network and each…

A classical result of singularity theory states that the spectrum of an isolated hypersurface singularity is symmetric with respect to $n/2$, where $n$ is the dimension of the enclosing space. We prove a similar result for the…

In this paper we consider the definition of " monodromy of an angle valued map" based on linear relations as proposed in Burghelea-Haller (3). This definition provides an alternative treatment of monodromy and computationally an alternative…

Inter-layer synchronization is a dynamical state occurring in multi-layer networks composed of identical nodes. The state corresponds to have all layers synchronized, with nodes in each layer which do not necessarily evolve in unison. So…

By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3 and the relation to the super-Ehlers symmetry in D = 5, we elucidate the massless multiplet structure of the spectrum of a broad class of D = 5 supergravity…

This paper provides synchronization conditions for networks of nonlinear systems. The components of the network (referred to as "compartments'' in this paper) are made up of an identical interconnection of subsystems, each represented as an…

Nonlinear dynamics has an important role when designing modern synchrotron lattices. In this letter, we introduce a new method of using a square matrix to analyze periodic nonlinear dynamical systems [1, 2]. Applying the method to the…