Related papers: The Heider balance - a continuous approach
A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational…
We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by…
Since the 1940's there has been an interest in the question why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This note provides an…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical evolution of the leaf volume along local unstable manifolds.…
We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We…
In the recent period of time with a lot of social platforms emerging, the relationships among various units can be framed with respect to either positive, negative or no relation. These units can be individuals, countries or others that…
We give an explicit description of the homomorphism group H_n(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups H_i(q) are trivial for i at least 2 but less than n. The…
A distributed algorithm is described for solving a linear algebraic equation of the form $Ax=b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of…
In this article, we compute both the algebraic and the analytic Brauer groups of a homogeneous space under the action of a connected, simply connected, semisimple complex algebraic group, where the stabilizer subgroup is closed and…
We introduce a method to predict which correlation matrix coefficients are likely to change their signs in the future in the high-dimensional regime, i.e. when the number of features is larger than the number of samples per feature. The…
It is known that individuals in social networks tend to exhibit homophily (a.k.a. assortative mixing) in their social ties, which implies that they prefer bonding with others of their own kind. But what are the reasons for this phenomenon?…
We give formulas for calculating the unramified Brauer group of a homogeneous space $X$ of a semisimple simply connected group $G$ with finite geometric stabilizer $\bar F$ over a wide family of fields of characteristic 0. When $k$ is a…
In this paper, some notes of the homogeneous balance (HB) method are discussed by a kind of general fifth-order KdV (fKdV) equation. Frist, the auto-B\"acklund transformation and lax represents of the higher-order KdV equation(a specific…
Real-world complex systems are often better modeled as hypergraphs, where edges represent group interactions involving multiple entities. Understanding and quantifying homophily (similarity-driven association) in such networks is essential…
Random exchange kinetic models are widely employed to describe the conservative dynamics of large interacting systems. Due to their simplicity and generality, they are quite popular in several fields, from statistical mechanics to…
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…
We study the convergence properties of Social Hegselmann-Krause dynamics, a {variant} of the Hegselmann-Krause (HK) model of opinion dynamics where a physical connectivity graph that accounts for the extrinsic factors that could prevent…
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…