11,765 research outputs found
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that
We report on some recent developments in the search for optimal network
topologies. First we review some basic concepts on spectral graph theory,
including adjacency and Laplacian matrices, and paying special attention to the
topological implications of having large spectral gaps. We also introduce
related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we
discuss two different dynamical feautures of networks: synchronizability and
flow of random walkers and so that they are optimized if the corresponding
Laplacian matrix have a large spectral gap. From this, we show, by developing a
numerical optimization algorithm that maximum synchronizability and fast random
walk spreading are obtained for a particular type of extremely homogeneous
regular networks, with long loops and poor modular structure, that we call
entangled networks. These turn out to be related to Ramanujan and Cage graphs.
We argue also that these graphs are very good finite-size approximations to
Bethe lattices, and provide almost or almost optimal solutions to many other
problems as, for instance, searchability in the presence of congestion or
performance of neural networks. Finally, we study how these results are
modified when studying dynamical processes controlled by a normalized (weighted
and directed) dynamics; much more heterogeneous graphs are optimal in this
case. Finally, a critical discussion of the limitations and possible extensions
of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted
for pub. in JSTA
From Packet to Power Switching: Digital Direct Load Scheduling
At present, the power grid has tight control over its dispatchable generation
capacity but a very coarse control on the demand. Energy consumers are shielded
from making price-aware decisions, which degrades the efficiency of the market.
This state of affairs tends to favor fossil fuel generation over renewable
sources. Because of the technological difficulties of storing electric energy,
the quest for mechanisms that would make the demand for electricity
controllable on a day-to-day basis is gaining prominence. The goal of this
paper is to provide one such mechanisms, which we call Digital Direct Load
Scheduling (DDLS). DDLS is a direct load control mechanism in which we unbundle
individual requests for energy and digitize them so that they can be
automatically scheduled in a cellular architecture. Specifically, rather than
storing energy or interrupting the job of appliances, we choose to hold
requests for energy in queues and optimize the service time of individual
appliances belonging to a broad class which we refer to as "deferrable loads".
The function of each neighborhood scheduler is to optimize the time at which
these appliances start to function. This process is intended to shape the
aggregate load profile of the neighborhood so as to optimize an objective
function which incorporates the spot price of energy, and also allows
distributed energy resources to supply part of the generation dynamically.Comment: Accepted by the IEEE journal of Selected Areas in Communications
(JSAC): Smart Grid Communications series, to appea
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