5,707 research outputs found
Weight Distribution for Non-binary Cluster LDPC Code Ensemble
In this paper, we derive the average weight distributions for the irregular
non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we
give the exponential growth rate of the average weight distribution in the
limit of large code length. We show that there exist -regular
non-binary cluster LDPC code ensembles whose normalized typical minimum
distances are strictly positive.Comment: 12pages, 6 figures, To be presented in ISIT2013, Submitted to IEICE
Trans. Fundamental
Local and Global Trust Based on the Concept of Promises
We use the notion of a promise to define local trust between agents
possessing autonomous decision-making. An agent is trustworthy if it is
expected that it will keep a promise. This definition satisfies most
commonplace meanings of trust. Reputation is then an estimation of this
expectation value that is passed on from agent to agent.
Our definition distinguishes types of trust, for different behaviours, and
decouples the concept of agent reliability from the behaviour on which the
judgement is based. We show, however, that trust is fundamentally heuristic, as
it provides insufficient information for agents to make a rational judgement. A
global trustworthiness, or community trust can be defined by a proportional,
self-consistent voting process, as a weighted eigenvector-centrality function
of the promise theoretical graph
Universality of the Distribution Functions of Random Matrix Theory. II
This paper is a brief review of recent developments in random matrix theory.
Two aspects are emphasized: the underlying role of integrable systems and the
occurrence of the distribution functions of random matrix theory in diverse
areas of mathematics and physics.Comment: 17 pages, 3 figure
Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition
We consider a family of random matrix ensembles (RME) invariant under
similarity transformations and described by the probability density . Dyson's mean field theory (MFT) of the
corresponding plasma model of eigenvalues is generalized to the case of weak
confining potential, . The
eigenvalue statistics derived from MFT are shown to deviate substantially from
the classical Wigner-Dyson statistics when . By performing systematic
Monte Carlo simulations on the plasma model, we compute all the relevant
statistical properties of the RME with weak confinement. For
the distribution function of the energy-level spacings (LSDF) of this RME
coincides in a large energy window with the LSDF of the three dimensional
Anderson model at the metal-insulator transition. For the same , the
variance of the number of levels, , in
an interval containing levels on average, grows linearly
with , and its slope is equal to , which is
consistent with the value found for the Anderson model at the critical point.Comment: 32 pages, REVTEX 3.0, 10 postscript (uuencoded) figures include
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