33,620 research outputs found
A Phase Transition in a Quenched Amorphous Ferromagnet
Quenched thermodynamic states of an amorphous ferromagnet are studied. The
magnet is a countable collection of point particles chaotically distributed
over , . Each particle bears a real-valued spin with
symmetric a priori distribution; the spin-spin interaction is pair-wise and
attractive. Two spins are supposed to interact if they are neighbors in the
graph defined by a homogeneous Poisson point process. For this model, we prove
that with probability one: (a) quenched thermodynamic states exist; (b) they
are multiple if the particle density (i.e., the intensity of the underlying
point process) and the inverse temperature are big enough; (c) there exist
multiple quenched thermodynamic states which depend on the realizations of the
underlying point process in a measurable way
Graph rigidity and distributed formation stabilization of multi-vehicle systems
We provide a graph theoretical framework that allows us to formally define formations of multiple vehicles and the issues arising in uniqueness of graph realizations and its connection to stability of formations. The notion of graph rigidity is crucial in identifying the shape variables of a formation and an appropriate potential function associated with the formation. This allows formulation of meaningful optimization or nonlinear control problems for formation stabilization/tacking, in addition to formal representation of split, rejoin, and reconfiguration maneuvers for multi-vehicle formations. We introduce an algebra that consists of performing some basic operations on graphs which allow creation of larger rigid-by-construction graphs by combining smaller rigid subgraphs. This is particularly useful in performing and representing rejoin/split maneuvers of multiple formations in a distributed fashion
Repeat-Until-Success quantum computing using stationary and flying qubits
We introduce an architecture for robust and scalable quantum computation
using both stationary qubits (e.g. single photon sources made out of trapped
atoms, molecules, ions, quantum dots, or defect centers in solids) and flying
qubits (e.g. photons). Our scheme solves some of the most pressing problems in
existing non-hybrid proposals, which include the difficulty of scaling
conventional stationary qubit approaches, and the lack of practical means for
storing single photons in linear optics setups. We combine elements of two
previous proposals for distributed quantum computing, namely the efficient
photon-loss tolerant build up of cluster states by Barrett and Kok [Phys. Rev.
A 71, 060310(R) (2005)] with the idea of Repeat-Until-Success (RUS) quantum
computing by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)]. This idea can be
used to perform eventually deterministic two-qubit logic gates on spatially
separated stationary qubits via photon pair measurements. Under non-ideal
conditions, where photon loss is a possibility, the resulting gates can still
be used to build graph states for one-way quantum computing. In this paper, we
describe the RUS method, present possible experimental realizations, and
analyse the generation of graph states.Comment: 14 pages, 7 figures, minor changes, references and a discussion on
the effect of photon dark counts adde
Filtering Random Graph Processes Over Random Time-Varying Graphs
Graph filters play a key role in processing the graph spectra of signals
supported on the vertices of a graph. However, despite their widespread use,
graph filters have been analyzed only in the deterministic setting, ignoring
the impact of stochastic- ity in both the graph topology as well as the signal
itself. To bridge this gap, we examine the statistical behavior of the two key
filter types, finite impulse response (FIR) and autoregressive moving average
(ARMA) graph filters, when operating on random time- varying graph signals (or
random graph processes) over random time-varying graphs. Our analysis shows
that (i) in expectation, the filters behave as the same deterministic filters
operating on a deterministic graph, being the expected graph, having as input
signal a deterministic signal, being the expected signal, and (ii) there are
meaningful upper bounds for the variance of the filter output. We conclude the
paper by proposing two novel ways of exploiting randomness to improve (joint
graph-time) noise cancellation, as well as to reduce the computational
complexity of graph filtering. As demonstrated by numerical results, these
methods outperform the disjoint average and denoise algorithm, and yield a (up
to) four times complexity redution, with very little difference from the
optimal solution
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability
Distributed consensus and other linear systems with system stochastic
matrices emerge in various settings, like opinion formation in social
networks, rendezvous of robots, and distributed inference in sensor networks.
The matrices are often random, due to, e.g., random packet dropouts in
wireless sensor networks. Key in analyzing the performance of such systems is
studying convergence of matrix products . In this paper, we
find the exact exponential rate for the convergence in probability of the
product of such matrices when time grows large, under the assumption that
the 's are symmetric and independent identically distributed in time.
Further, for commonly used random models like with gossip and link failure, we
show that the rate is found by solving a min-cut problem and, hence, easily
computable. Finally, we apply our results to optimally allocate the sensors'
transmission power in consensus+innovations distributed detection
Distributed Random Convex Programming via Constraints Consensus
This paper discusses distributed approaches for the solution of random convex
programs (RCP). RCPs are convex optimization problems with a (usually large)
number N of randomly extracted constraints; they arise in several applicative
areas, especially in the context of decision under uncertainty, see [2],[3]. We
here consider a setup in which instances of the random constraints (the
scenario) are not held by a single centralized processing unit, but are
distributed among different nodes of a network. Each node "sees" only a small
subset of the constraints, and may communicate with neighbors. The objective is
to make all nodes converge to the same solution as the centralized RCP problem.
To this end, we develop two distributed algorithms that are variants of the
constraints consensus algorithm [4],[5]: the active constraints consensus (ACC)
algorithm, and the vertex constraints consensus (VCC) algorithm. We show that
the ACC algorithm computes the overall optimal solution in finite time, and
with almost surely bounded communication at each iteration. The VCC algorithm
is instead tailored for the special case in which the constraint functions are
convex also w.r.t. the uncertain parameters, and it computes the solution in a
number of iterations bounded by the diameter of the communication graph. We
further devise a variant of the VCC algorithm, namely quantized vertex
constraints consensus (qVCC), to cope with the case in which communication
bandwidth among processors is bounded. We discuss several applications of the
proposed distributed techniques, including estimation, classification, and
random model predictive control, and we present a numerical analysis of the
performance of the proposed methods. As a complementary numerical result, we
show that the parallel computation of the scenario solution using ACC algorithm
significantly outperforms its centralized equivalent
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