Enforcing social behavior in an Ising model with complex neighborhoods

Abstract

a b s t r a c tWe consider the problem of enforcing desired behavior in a population of individuals modeled by an Ising model. Although there is a large literature dealing with social interaction models, the problem of controlling behavior in a system modeled by the Ising model seems to be an unexplored field. First, we provide and analytically characterize an optimal policy that may be used to achieve this objective. Second, we show that complex neighborhoods highly influence the decision making process. Third, we use Lagrange multipliers associated to some constraints of a related problem to identify the role of individuals in the system.

An Ising Spin‐Based Model to Explore Efficient Flexibility in Distributed Power Systems

“…We can also associate with noise in customers' information channels; too much noise destroys the spontaneous magnetisation (max/min flexibility previously achieved) [15]. Also, when the "social temperature" [28] is high it destroys large domains (subpopulations) and hence it favours the mixing of options.…”

“…For low values the constraints are more stiff and the feasible space becomes fragmented. In the limit = 0 (maximum homogeneity of load split) we find that for combinations of {5, 6,10,13,14,15,22,23,24,25,26,27,28,29,30, 31} aggregators there are no optimal solutions (black dots). The reason for this is that for = 0 and, say, = 5, we are forcing to evenly distribute 32 buses among 5 aggregators so that at least one bus belongs to one aggregator.…”

Is there any connection between the network morphology and the fluctuations of the stock market index?

“…In real markets, the morphology of the trust network of the investors cannot be easily assessed [41,43]. To our knowledge, at the moment it is not possible to investigate or even to understand whether or how the morphology of the network plays any role on the oscillations of real stock market indices.…”

“…Besides, networks are essential for the spreading of information, and play a central role on social relations [40]. Recently, some works aimed to investigate the topology of trust economical networks [41][42][43][44][45] but there is no comprehensive study on this subject yet.…”

Accelerating the Simulations of the Ising Model by the GPU under the CUDA Environment

“…The Ising model, because of its rich content, became popular not only in physics but also in various interdisciplinary fields, i.e. biological systems [5], social sciences [6], biological physics [7], econophysics [8]. In the past 40 years, numerical simulations, represented by Monte Carlo (MC) method, have been used in the research of the Ising model, the performance of the MC method while dealing with large systems, however, is not satisfactory as lots of time is needed.…”