37,273 research outputs found
Asynchronous Networks and Event Driven Dynamics
Real-world networks in technology, engineering and biology often exhibit
dynamics that cannot be adequately reproduced using network models given by
smooth dynamical systems and a fixed network topology. Asynchronous networks
give a theoretical and conceptual framework for the study of network dynamics
where nodes can evolve independently of one another, be constrained, stop, and
later restart, and where the interaction between different components of the
network may depend on time, state, and stochastic effects. This framework is
sufficiently general to encompass a wide range of applications ranging from
engineering to neuroscience. Typically, dynamics is piecewise smooth and there
are relationships with Filippov systems. In the first part of the paper, we
give examples of asynchronous networks, and describe the basic formalism and
structure. In the second part, we make the notion of a functional asynchronous
network rigorous, discuss the phenomenon of dynamical locks, and present a
foundational result on the spatiotemporal factorization of the dynamics for a
large class of functional asynchronous networks
Distributed Computing with Adaptive Heuristics
We use ideas from distributed computing to study dynamic environments in
which computational nodes, or decision makers, follow adaptive heuristics (Hart
2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly
"best replying" to others' actions, and minimizing "regret", that have been
extensively studied in game theory and economics. We explore when convergence
of such simple dynamics to an equilibrium is guaranteed in asynchronous
computational environments, where nodes can act at any time. Our research
agenda, distributed computing with adaptive heuristics, lies on the borderline
of computer science (including distributed computing and learning) and game
theory (including game dynamics and adaptive heuristics). We exhibit a general
non-termination result for a broad class of heuristics with bounded
recall---that is, simple rules of behavior that depend only on recent history
of interaction between nodes. We consider implications of our result across a
wide variety of interesting and timely applications: game theory, circuit
design, social networks, routing and congestion control. We also study the
computational and communication complexity of asynchronous dynamics and present
some basic observations regarding the effects of asynchrony on no-regret
dynamics. We believe that our work opens a new avenue for research in both
distributed computing and game theory.Comment: 36 pages, four figures. Expands both technical results and discussion
of v1. Revised version will appear in the proceedings of Innovations in
Computer Science 201
Abstracting Asynchronous Multi-Valued Networks: An Initial Investigation
Multi-valued networks provide a simple yet expressive qualitative state based
modelling approach for biological systems. In this paper we develop an
abstraction theory for asynchronous multi-valued network models that allows the
state space of a model to be reduced while preserving key properties of the
model. The abstraction theory therefore provides a mechanism for coping with
the state space explosion problem and supports the analysis and comparison of
multi-valued networks. We take as our starting point the abstraction theory for
synchronous multi-valued networks which is based on the finite set of traces
that represent the behaviour of such a model. The problem with extending this
approach to the asynchronous case is that we can now have an infinite set of
traces associated with a model making a simple trace inclusion test infeasible.
To address this we develop a decision procedure for checking asynchronous
abstractions based on using the finite state graph of an asynchronous
multi-valued network to reason about its trace semantics. We illustrate the
abstraction techniques developed by considering a detailed case study based on
a multi-valued network model of the regulation of tryptophan biosynthesis in
Escherichia coli.Comment: Presented at MeCBIC 201
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