38,812 research outputs found
The full replica symmetry breaking in the Ising spin glass on random regular graph
In this paper, we extend the full replica symmetry breaking scheme to the
Ising spin glass on a random regular graph. We propose a new martingale
approach, that overcomes the limits of the Parisi-M\'ezard cavity method,
providing a well-defined formulation of the full replica symmetry breaking
problem in random regular graphs. Finally, we define the order parameters of
the system and get a set of self-consistency equations for the order parameters
and the free energy. We face up the problem only from a technical point of
view: the physical meaning of this approach and the quantitative evaluation of
the solution of the self-consistency equations will be discussed in next works.Comment: 23 page
Byzantine Fault Tolerance for Nondeterministic Applications
All practical applications contain some degree of nondeterminism. When such
applications are replicated to achieve Byzantine fault tolerance (BFT), their
nondeterministic operations must be controlled to ensure replica consistency.
To the best of our knowledge, only the most simplistic types of replica
nondeterminism have been dealt with. Furthermore, there lacks a systematic
approach to handling common types of nondeterminism. In this paper, we propose
a classification of common types of replica nondeterminism with respect to the
requirement of achieving Byzantine fault tolerance, and describe the design and
implementation of the core mechanisms necessary to handle such nondeterminism
within a Byzantine fault tolerance framework.Comment: To appear in the proceedings of the 3rd IEEE International Symposium
on Dependable, Autonomic and Secure Computing, 200
Belief Propagation Algorithm for Portfolio Optimization Problems
The typical behavior of optimal solutions to portfolio optimization problems
with absolute deviation and expected shortfall models using replica analysis
was pioneeringly estimated by S. Ciliberti and M. M\'ezard [Eur. Phys. B. 57,
175 (2007)]; however, they have not yet developed an approximate derivation
method for finding the optimal portfolio with respect to a given return set. In
this study, an approximation algorithm based on belief propagation for the
portfolio optimization problem is presented using the Bethe free energy
formalism, and the consistency of the numerical experimental results of the
proposed algorithm with those of replica analysis is confirmed. Furthermore,
the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the
absolute deviation model and with the mean-variance model have the same typical
behavior, is verified using replica analysis and the belief propagation
algorithm.Comment: 5 pages, 2 figures, to submit to EP
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