325,161 research outputs found
Mass Media and Polarisation Processes in the Bounded Confidence Model of Opinion Dynamics
This paper presents a social simulation in which we add an additional layer of mass media communication to the social network \'bounded confidence\' model of Deffuant et al (2000). A population of agents on a lattice with continuous opinions and bounded confidence adjust their opinions on the basis of binary social network interactions between neighbours or communication with a fixed opinion. There are two mechanisms for interaction. \'Social interaction\' occurs between neighbours on a lattice and \'mass communication,\' adjusts opinions based on an agent interacting with a fixed opinion. Two new variables are added, polarisation: the degree to which two mass media opinions differ, and broadcast ratio: the number of social interactions for each mass media communication. Four dynamical regimes are observed, fragmented, double extreme convergence, a state of persistent opinion exchange leading to single extreme convergence and a disordered state. Double extreme convergence is found where agents are less willing to change opinion and mass media communications are common or where there is moderate willingness to change opinion and a high frequency of mass media communications. Single extreme convergence is found where there is moderate willingness to change opinion and a lower frequency of mass media communication. A period of persistent opinion exchange precedes single extreme convergence, it is characterized by the formation of two opposing groups of opinion separated by a gradient of opinion exchange. With even very low frequencies of mass media communications this results in a move to central opinions followed by a global drift to one extreme as one of the opposing groups of opinion dominates. A similar pattern of findings is observed for Neumann and Moore neighbourhoods.Opinion Dynamics, Mass Media, Polarisation, Extremists, Consensus
Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication
This paper proposes a novel class of distributed continuous-time coordination
algorithms to solve network optimization problems whose cost function is a sum
of local cost functions associated to the individual agents. We establish the
exponential convergence of the proposed algorithm under (i) strongly connected
and weight-balanced digraph topologies when the local costs are strongly convex
with globally Lipschitz gradients, and (ii) connected graph topologies when the
local costs are strongly convex with locally Lipschitz gradients. When the
local cost functions are convex and the global cost function is strictly
convex, we establish asymptotic convergence under connected graph topologies.
We also characterize the algorithm's correctness under time-varying interaction
topologies and study its privacy preservation properties. Motivated by
practical considerations, we analyze the algorithm implementation with
discrete-time communication. We provide an upper bound on the stepsize that
guarantees exponential convergence over connected graphs for implementations
with periodic communication. Building on this result, we design a
provably-correct centralized event-triggered communication scheme that is free
of Zeno behavior. Finally, we develop a distributed, asynchronous
event-triggered communication scheme that is also free of Zeno with asymptotic
convergence guarantees. Several simulations illustrate our results.Comment: 12 page
Adiabatic corrections for velocity-gauge simulations of electron dynamics in periodic potentials
We show how to significantly reduce the number of energy bands required to
model the interaction of light with crystalline solids in the velocity gauge.
We achieve this by deriving analytical corrections to the electric current
density. These corrections depend only on band energies, the matrix elements of
the momentum operator, and the macroscopic vector potential. Thus, the
corrections can be evaluated independently from modeling the interaction with
light. In addition to improving the convergence of velocity-gauge calculations,
our analytical approach overcomes the long-standing problem of divergences in
expressions for linear and nonlinear susceptibilities.Comment: Submitted to Computer Physics Communication
On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay
This paper studies the robustness of a dynamic average consensus algorithm to
communication delay over strongly connected and weight-balanced (SCWB)
digraphs. Under delay-free communication, the algorithm of interest achieves a
practical asymptotic tracking of the dynamic average of the time-varying
agents' reference signals. For this algorithm, in both its continuous-time and
discrete-time implementations, we characterize the admissible communication
delay range and study the effect of the delay on the rate of convergence and
the tracking error bound. Our study also includes establishing a relationship
between the admissible delay bound and the maximum degree of the SCWB digraphs.
We also show that for delays in the admissible bound, for static signals the
algorithms achieve perfect tracking. Moreover, when the interaction topology is
a connected undirected graph, we show that the discrete-time implementation is
guaranteed to tolerate at least one step delay. Simulations demonstrate our
results
Welfare Maximization with Limited Interaction
We continue the study of welfare maximization in unit-demand (matching)
markets, in a distributed information model where agent's valuations are
unknown to the central planner, and therefore communication is required to
determine an efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed
that if the market size is , then rounds of interaction (with
logarithmic bandwidth) suffice to obtain an -approximation to the
optimal social welfare. In particular, this implies that such markets converge
to a stable state (constant approximation) in time logarithmic in the market
size.
We obtain the first multi-round lower bound for this setup. We show that even
if the allowable per-round bandwidth of each agent is , the
approximation ratio of any -round (randomized) protocol is no better than
, implying an lower bound on the
rate of convergence of the market to equilibrium.
Our construction and technique may be of interest to round-communication
tradeoffs in the more general setting of combinatorial auctions, for which the
only known lower bound is for simultaneous () protocols [DNO14]
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