686 research outputs found
Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems
In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons
Coordination of passive systems under quantized measurements
In this paper we investigate a passivity approach to collective coordination
and synchronization problems in the presence of quantized measurements and show
that coordination tasks can be achieved in a practical sense for a large class
of passive systems.Comment: 40 pages, 1 figure, submitted to journal, second round of revie
Consensus with Linear Objective Maps
A consensus system is a linear multi-agent system in which agents communicate
to reach a so-called consensus state, defined as the average of the initial
states of the agents. Consider a more generalized situation in which each agent
is given a positive weight and the consensus state is defined as the weighted
average of the initial conditions. We characterize in this paper the weighted
averages that can be evaluated in a decentralized way by agents communicating
over a directed graph. Specifically, we introduce a linear function, called the
objective map, that defines the desired final state as a function of the
initial states of the agents. We then provide a complete answer to the question
of whether there is a decentralized consensus dynamics over a given digraph
which converges to the final state specified by an objective map. In
particular, we characterize not only the set of objective maps that are
feasible for a given digraph, but also the consensus dynamics that implements
the objective map. In addition, we present a decentralized algorithm to design
the consensus dynamics
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Group Field Theory: An overview
We give a brief overview of the properties of a higher dimensional
generalization of matrix model which arises naturally in the context of a
background independent approach to quantum gravity, the so called group field
theory. We show that this theory leads to a natural proposal for the physical
scalar product of quantum gravity. We also show in which sense this theory
provides a third quantization point of view on quantum gravity.Comment: 10 page
Hamiltonian theory of gaps, masses and polarization in quantum Hall states: full disclosure
I furnish details of the hamiltonian theory of the FQHE developed with Murthy
for the infrared, which I subsequently extended to all distances and apply it
to Jain fractions \nu = p/(2ps + 1). The explicit operator description in terms
of the CF allows one to answer quantitative and qualitative issues, some of
which cannot even be posed otherwise. I compute activation gaps for several
potentials, exhibit their particle hole symmetry, the profiles of charge
density in states with a quasiparticles or hole, (all in closed form) and
compare to results from trial wavefunctions and exact diagonalization. The
Hartree-Fock approximation is used since much of the nonperturbative physics is
built in at tree level. I compare the gaps to experiment and comment on the
rough equality of normalized masses near half and quarter filling. I compute
the critical fields at which the Hall system will jump from one quantized value
of polarization to another, and the polarization and relaxation rates for half
filling as a function of temperature and propose a Korringa like law. After
providing some plausibility arguments, I explore the possibility of describing
several magnetic phenomena in dirty systems with an effective potential, by
extracting a free parameter describing the potential from one data point and
then using it to predict all the others from that sample. This works to the
accuracy typical of this theory (10 -20 percent). I explain why the CF behaves
like free particle in some magnetic experiments when it is not, what exactly
the CF is made of, what one means by its dipole moment, and how the comparison
of theory to experiment must be modified to fit the peculiarities of the
quantized Hall problem
Scalings of domain wall energies in two dimensional Ising spin glasses
We study domain wall energies of two dimensional spin glasses. The scaling of
these energies depends on the model's distribution of quenched random
couplings, falling into three different classes. The first class is associated
with the exponent theta =-0.28, the other two classes have theta = 0, as can be
justified theoretically. In contrast to previous claims, we find that theta=0
does not indicate d=d_l but rather d <= d_l, where d_l is the lower critical
dimension.Comment: Clarifications and extra reference
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