172,575 research outputs found
Function and form in networks of interacting agents
The main problem we address in this paper is whether function determines form
when a society of agents organizes itself for some purpose or whether the
organizing method is more important than the functionality in determining the
structure of the ensemble. As an example, we use a neural network that learns
the same function by two different learning methods. For sufficiently large
networks, very different structures may indeed be obtained for the same
functionality. Clustering, characteristic path length and hierarchy are
structural differences, which in turn have implications on the robustness and
adaptability of the networks. In networks, as opposed to simple graphs, the
connections between the agents are not necessarily symmetric and may have
positive or negative signs. New characteristic coefficients are introduced to
characterize this richer connectivity structure.Comment: 27 pages Latex, 11 figure
Equation-Free Multiscale Computations in Social Networks: from Agent-based Modelling to Coarse-grained Stability and Bifurcation Analysis
We focus at the interface between multiscale computations, bifurcation theory
and social networks. In particular we address how the Equation-Free approach, a
recently developed computational framework, can be exploited to systematically
extract coarse-grained, emergent dynamical information by bridging detailed,
agent-based models of social interactions on networks, with macroscopic,
systems-level, continuum numerical analysis tools. For our illustrations we use
a simple dynamic agent-based model describing the propagation of information
between individuals interacting under mimesis in a social network with private
and public information. We describe the rules governing the evolution of the
agents emotional state dynamics and discover, through simulation, multiple
stable stationary states as a function of the network topology. Using the
Equation-Free approach we track the dependence of these stationary solutions on
network parameters and quantify their stability in the form of coarse-grained
bifurcation diagrams
From continuous to discontinuous transitions in social diffusion
Models of social diffusion reflect processes of how new products, ideas or
behaviors are adopted in a population. These models typically lead to a
continuous or a discontinuous phase transition of the number of adopters as a
function of a control parameter. We explore a simple model of social adoption
where the agents can be in two states, either adopters or non-adopters, and can
switch between these two states interacting with other agents through a
network. The probability of an agent to switch from non-adopter to adopter
depends on the number of adopters in her network neighborhood, the adoption
threshold and the adoption coefficient , two parameters defining a Hill
function. In contrast, the transition from adopter to non-adopter is
spontaneous at a certain rate . In a mean-field approach, we derive the
governing ordinary differential equations and show that the nature of the
transition between the global non-adoption and global adoption regimes depends
mostly on the balance between the probability to adopt with one and two
adopters. The transition changes from continuous, via a transcritical
bifurcation, to discontinuous, via a combination of a saddle-node and a
transcritical bifurcation, through a supercritical pitchfork bifurcation. We
characterize the full parameter space. Finally, we compare our analytical
results with Montecarlo simulations on annealed and quenched degree regular
networks, showing a better agreement for the annealed case. Our results show
how a simple model is able to capture two seemingly very different types of
transitions, i.e., continuous and discontinuous and thus unifies underlying
dynamics for different systems. Furthermore the form of the adoption
probability used here is based on empirical measurements.Comment: 7 pages, 3 figure
Reaction networks as systems for resource allocation: A variational principle for their non-equilibrium steady states
Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at stationarity the system minimizes a global function of the reaction fluxes with the form of a Hopfield Hamiltonian with Hebbian couplings, that is explicitly seen to correspond to the rate of decay of entropy production over time. Guided by this analogy, we show that reaction networks can be formally re-cast as systems of interacting reactions that optimize the use of the available compounds by competing for substrates, akin to agents competing for a limited resource in an optimal allocation problem. As an illustration, we analyze the scenario that emerges in two simple cases: that of toy (random) reaction networks and that of a metabolic network model of the human red blood cell. © 2012 De Martino et al
Social network dynamics of face-to-face interactions
The recent availability of data describing social networks is changing our
understanding of the "microscopic structure" of a social tie. A social tie
indeed is an aggregated outcome of many social interactions such as
face-to-face conversations or phone-calls. Analysis of data on face-to-face
interactions shows that such events, as many other human activities, are
bursty, with very heterogeneous durations. In this paper we present a model for
social interactions at short time scales, aimed at describing contexts such as
conference venues in which individuals interact in small groups. We present a
detailed anayltical and numerical study of the model's dynamical properties,
and show that it reproduces important features of empirical data. The model
allows for many generalizations toward an increasingly realistic description of
social interactions. In particular in this paper we investigate the case where
the agents have intrinsic heterogeneities in their social behavior, or where
dynamic variations of the local number of individuals are included. Finally we
propose this model as a very flexible framework to investigate how dynamical
processes unfold in social networks.Comment: 20 pages, 25 figure
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