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A Statistical Mechanics of Some Interconnection Networks
Despite intensive research on distributed processor interconnection architectures, relatively little work has been done on the performance analysis of such systems. The reason for this, besides the complexity of the behavior of such systems, is that Queueing Theory cannot easily handle systems consisting of many tightly interacting components. An alternate approach, based upon statistical mechanics, is used. We analyze interconnection structures such as crossbar, linear array, binary tree and ring
Probabilistic interconnection between interdependent networks promotes cooperation in the public goods game
Most previous works study the evolution of cooperation in a structured
population by commonly employing an isolated single network. However, realistic
systems are composed of many interdependent networks coupled with each other,
rather than the isolated single one. In this paper, we consider a system
including two interacting networks with the same size, entangled with each
other by the introduction of probabilistic interconnections. We introduce the
public goods game into such system, and study how the probabilistic
interconnection influences the evolution of cooperation of the whole system and
the coupling effect between two layers of interdependent networks. Simulation
results show that there exists an intermediate region of interconnection
probability leading to the maximum cooperation level in the whole system.
Interestingly, we find that at the optimal interconnection probability the
fraction of internal links between cooperators in two layers is maximal. Also,
even if initially there are no cooperators in one layer of interdependent
networks, cooperation can still be promoted by probabilistic interconnection,
and the cooperation levels in both layers can more easily reach an agreement at
the intermediate interconnection probability. Our results may be helpful in
understanding the cooperative behavior in some realistic interdependent
networks and thus highlight the importance of probabilistic interconnection on
the evolution of cooperation.Comment: 12 pages, 6 figures, submitted to Journal of Statistical Mechanics:
Theory and Experiment(JSTAT
Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems
Recently, significant attention has been dedicated to the models of opinion
dynamics in which opinions are described by real numbers, and agents update
their opinions synchronously by averaging their neighbors' opinions. The
neighbors of each agent can be defined as either (1) those agents whose
opinions are in its "confidence range," or (2) those agents whose "influence
range" contain the agent's opinion. The former definition is employed in
Hegselmann and Krause's bounded confidence model, and the latter is novel here.
As the confidence and influence ranges are distinct for each agent, the
heterogeneous state-dependent interconnection topology leads to a
poorly-understood complex dynamic behavior. In both models, we classify the
agents via their interconnection topology and, accordingly, compute the
equilibria of the system. Then, we define a positive invariant set centered at
each equilibrium opinion vector. We show that if a trajectory enters one such
set, then it converges to a steady state with constant interconnection
topology. This result gives us a novel sufficient condition for both models to
establish convergence, and is consistent with our conjecture that all
trajectories of the bounded confidence and influence models eventually converge
to a steady state under fixed topology.Comment: 22 pages, Submitted to SIAM Journal on Control and Optimization
(SICON
Computer architecture evaluation for structural dynamics computations: Project summary
The intent of the proposed effort is the examination of the impact of the elements of parallel architectures on the performance realized in a parallel computation. To this end, three major projects are developed: a language for the expression of high level parallelism, a statistical technique for the synthesis of multicomputer interconnection networks based upon performance prediction, and a queueing model for the analysis of shared memory hierarchies
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