84 research outputs found
Subset sum phase transitions and data compression
We propose a rigorous analysis approach for the subset sum problem in the
context of lossless data compression, where the phase transition of the subset
sum problem is directly related to the passage between ambiguous and
non-ambiguous decompression, for a compression scheme that is based on
specifying the sequence composition. The proposed analysis lends itself to
straightforward extensions in several directions of interest, including
non-binary alphabets, incorporation of side information at the decoder
(Slepian-Wolf coding), and coding schemes based on multiple subset sums. It is
also demonstrated that the proposed technique can be used to analyze the
critical behavior in a more involved situation where the sequence composition
is not specified by the encoder.Comment: 14 pages, submitted to the Journal of Statistical Mechanics: Theory
and Experimen
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
We extend the mathematical theory of quantum hypothesis testing to the
general -algebraic setting and explore its relation with recent
developments in non-equilibrium quantum statistical mechanics. In particular,
we relate the large deviation principle for the full counting statistics of
entropy flow to quantum hypothesis testing of the arrow of time.Comment: 60 page
Non differentiable large-deviation functionals in boundary-driven diffusive systems
We study the probability of arbitrary density profiles in conserving
diffusive fields which are driven by the boundaries. We demonstrate the
existence of singularities in the large-deviation functional, the direct analog
of the free-energy in non-equilibrium systems. These singularities are unique
to non-equilibrium systems and are a direct consequence of the breaking of
time-reversal symmetry. This is demonstrated in an exactly-solvable model and
also in numerical simulations on a boundary-driven Ising model. We argue that
this singular behavior is expected to occur in models where the compressibility
has a deep enough minimum. The mechanism is explained using a simple model.Comment: 5 pages, 3 figure
Objective Bayesian Analysis of the Yule-Simon Distribution with Applications
The Yule-Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, has ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule--Simon distribution. In particular, we discuss the Jeffreys prior and a loss-based prior, which has recently appeared in the literature. We illustrate the performance of the derived priors through a simulation study and the analysis of real datasets
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