4,929 research outputs found
Bethe free-energy approximations for disordered quantum systems
Given a locally consistent set of reduced density matrices, we construct
approximate density matrices which are globally consistent with the local
density matrices we started from when the trial density matrix has a tree
structure. We employ the cavity method of statistical physics to find the
optimal density matrix representation by slowly decreasing the temperature in
an annealing algorithm, or by minimizing an approximate Bethe free energy
depending on the reduced density matrices and some cavity messages originated
from the Bethe approximation of the entropy. We obtain the classical Bethe
expression for the entropy within a naive (mean-field) approximation of the
cavity messages, which is expected to work well at high temperatures. In the
next order of the approximation, we obtain another expression for the Bethe
entropy depending only on the diagonal elements of the reduced density
matrices. In principle, we can improve the entropy approximation by considering
more accurate cavity messages in the Bethe approximation of the entropy. We
compare the annealing algorithm and the naive approximation of the Bethe
entropy with exact and approximate numerical simulations for small and large
samples of the random transverse Ising model on random regular graphs.Comment: 23 pages, 4 figures, 4 appendice
Energy Efficient Ant Colony Algorithms for Data Aggregation in Wireless Sensor Networks
In this paper, a family of ant colony algorithms called DAACA for data
aggregation has been presented which contains three phases: the initialization,
packet transmission and operations on pheromones. After initialization, each
node estimates the remaining energy and the amount of pheromones to compute the
probabilities used for dynamically selecting the next hop. After certain rounds
of transmissions, the pheromones adjustment is performed periodically, which
combines the advantages of both global and local pheromones adjustment for
evaporating or depositing pheromones. Four different pheromones adjustment
strategies are designed to achieve the global optimal network lifetime, namely
Basic-DAACA, ES-DAACA, MM-DAACA and ACS-DAACA. Compared with some other data
aggregation algorithms, DAACA shows higher superiority on average degree of
nodes, energy efficiency, prolonging the network lifetime, computation
complexity and success ratio of one hop transmission. At last we analyze the
characteristic of DAACA in the aspects of robustness, fault tolerance and
scalability.Comment: To appear in Journal of Computer and System Science
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