889 research outputs found
Metastability of Queuing Networks with Mobile Servers
We study symmetric queuing networks with moving servers and FIFO service
discipline. The mean-field limit dynamics demonstrates unexpected behavior
which we attribute to the meta-stability phenomenon. Large enough finite
symmetric networks on regular graphs are proved to be transient for arbitrarily
small inflow rates. However, the limiting non-linear Markov process possesses
at least two stationary solutions. The proof of transience is based on
martingale techniques
Markov chains, -trivial monoids and representation theory
We develop a general theory of Markov chains realizable as random walks on
-trivial monoids. It provides explicit and simple formulas for the
eigenvalues of the transition matrix, for multiplicities of the eigenvalues via
M\"obius inversion along a lattice, a condition for diagonalizability of the
transition matrix and some techniques for bounding the mixing time. In
addition, we discuss several examples, such as Toom-Tsetlin models, an exchange
walk for finite Coxeter groups, as well as examples previously studied by the
authors, such as nonabelian sandpile models and the promotion Markov chain on
posets. Many of these examples can be viewed as random walks on quotients of
free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth
birthday; 71 pages; final version to appear in IJA
Topology and energy transport in networks of interacting photosynthetic complexes
We address the role of topology in the energy transport process that occurs
in networks of photosynthetic complexes. We take inspiration from light
harvesting networks present in purple bacteria and simulate an incoherent
dissipative energy transport process on more general and abstract networks,
considering both regular structures (Cayley trees and hyperbranched fractals)
and randomly-generated ones. We focus on the the two primary light harvesting
complexes of purple bacteria, i.e., the LH1 and LH2, and we use
network-theoretical centrality measures in order to select different LH1
arrangements. We show that different choices cause significant differences in
the transport efficiencies, and that for regular networks centrality measures
allow to identify arrangements that ensure transport efficiencies which are
better than those obtained with a random disposition of the complexes. The
optimal arrangements strongly depend on the dissipative nature of the dynamics
and on the topological properties of the networks considered, and depending on
the latter they are achieved by using global vs. local centrality measures. For
randomly-generated networks a random arrangement of the complexes already
provides efficient transport, and this suggests the process is strong with
respect to limited amount of control in the structure design and to the
disorder inherent in the construction of randomly-assembled structures.
Finally, we compare the networks considered with the real biological networks
and find that the latter have in general better performances, due to their
higher connectivity, but the former with optimal arrangements can mimic the
real networks' behaviour for a specific range of transport parameters. These
results show that the use of network-theoretical concepts can be crucial for
the characterization and design of efficient artificial energy transport
networks.Comment: 14 pages, 16 figures, revised versio
Analysis of Absorbing Times of Quantum Walks
Quantum walks are expected to provide useful algorithmic tools for quantum
computation. This paper introduces absorbing probability and time of quantum
walks and gives both numerical simulation results and theoretical analyses on
Hadamard walks on the line and symmetric walks on the hypercube from the
viewpoint of absorbing probability and time.Comment: LaTeX2e, 14 pages, 6 figures, 1 table, figures revised, references
added, to appear in Physical Review
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