8,490 research outputs found
Adaptive Complex Contagions and Threshold Dynamical Systems
A broad range of nonlinear processes over networks are governed by threshold
dynamics. So far, existing mathematical theory characterizing the behavior of
such systems has largely been concerned with the case where the thresholds are
static. In this paper we extend current theory of finite dynamical systems to
cover dynamic thresholds. Three classes of parallel and sequential dynamic
threshold systems are introduced and analyzed. Our main result, which is a
complete characterization of their attractor structures, show that sequential
systems may only have fixed points as limit sets whereas parallel systems may
only have period orbits of size at most two as limit sets. The attractor states
are characterized for general graphs and enumerated in the special case of
paths and cycle graphs; a computational algorithm is outlined for determining
the number of fixed points over a tree. We expect our results to be relevant
for modeling a broad class of biological, behavioral and socio-technical
systems where adaptive behavior is central.Comment: Submitted for publicatio
Distributed Graph Automata and Verification of Distributed Algorithms
Combining ideas from distributed algorithms and alternating automata, we
introduce a new class of finite graph automata that recognize precisely the
languages of finite graphs definable in monadic second-order logic. By
restricting transitions to be nondeterministic or deterministic, we also obtain
two strictly weaker variants of our automata for which the emptiness problem is
decidable. As an application, we suggest how suitable graph automata might be
useful in formal verification of distributed algorithms, using Floyd-Hoare
logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's
Master's thesis arXiv:1404.6503. (This version of the article (v2) is
identical to the previous one (v1), except for minor changes in phrasing.
The Least-core and Nucleolus of Path Cooperative Games
Cooperative games provide an appropriate framework for fair and stable profit
distribution in multiagent systems. In this paper, we study the algorithmic
issues on path cooperative games that arise from the situations where some
commodity flows through a network. In these games, a coalition of edges or
vertices is successful if it enables a path from the source to the sink in the
network, and lose otherwise. Based on dual theory of linear programming and the
relationship with flow games, we provide the characterizations on the CS-core,
least-core and nucleolus of path cooperative games. Furthermore, we show that
the least-core and nucleolus are polynomially solvable for path cooperative
games defined on both directed and undirected network
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