Related papers: Special Jordan subspaces in Coupled Cell Networks
We describe the ternary and the generalized superderivations of finite-dimensional semisimple Jordan superalgebras over an algebraically closed field of characteristic zero and of finite-dimensional simple Jordan superalgebras with…
We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential…
A basic problem for any class of nonassociative algebras is to determine the polynomial identities satisfied by the symmetrization and the skew-symmetrization of the original product. We consider the symmetrization of the product in the…
Network synchronization is an emerging phenomenon in complex networks. The spectrum of Laplacian matrix will be immensely helpful for getting the network dynamics information. Especially, network synchronizability is characterized by the…
Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer undergoes a synchronous evolution with all its replicas in other layers, irrespective of whether or not it is synchronized with…
We determine the isomorphism classes of Jordan algebras in dimension two over the field of real numbers. Using techniques of non-standard analysis we study the properties of the variety of Jordan algebras, and also the contractions among…
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…
The Lefschetz hyperplane section theorem asserts that an affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to describe attaching maps of these…
In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…
We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic groups (not necessarily affine) over fields of characteristic zero and some transformation groups of…
Conformal field theories with correlation functions which have logarithmic singularities are considered. It is shown that those singularities imply the existence of additional operators in the theory which together with ordinary primary…
We study circle valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…
The various types of retinal neurons are each positioned at their respective depths within the retina where they are believed to be assembled as orderly mosaics, in which like-type neurons minimize proximity to one another. Two common…
We study the relationship between cyclic homology of Jordan superalgebras and second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of bracket algebras.…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible…
Joint diagonalisation (JD) is a technique used to estimate an average eigenspace of a set of matrices. Whilst it has been used successfully in many areas to track the evolution of systems via their eigenvectors; its application in network…