278 research outputs found
The Euler and Springer numbers as moment sequences
I study the sequences of Euler and Springer numbers from the point of view of
the classical moment problem.Comment: LaTeX2e, 30 pages. Version 2 contains some small clarifications
suggested by a referee. Version 3 contains new footnotes 9 and 10. To appear
in Expositiones Mathematica
Comparison of Channels: Criteria for Domination by a Symmetric Channel
This paper studies the basic question of whether a given channel can be
dominated (in the precise sense of being more noisy) by a -ary symmetric
channel. The concept of "less noisy" relation between channels originated in
network information theory (broadcast channels) and is defined in terms of
mutual information or Kullback-Leibler divergence. We provide an equivalent
characterization in terms of -divergence. Furthermore, we develop a
simple criterion for domination by a -ary symmetric channel in terms of the
minimum entry of the stochastic matrix defining the channel . The criterion
is strengthened for the special case of additive noise channels over finite
Abelian groups. Finally, it is shown that domination by a symmetric channel
implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality
for the original channel.Comment: 31 pages, 2 figures. Presented at 2017 IEEE International Symposium
on Information Theory (ISIT
Convex Relaxations for Permutation Problems
Seriation seeks to reconstruct a linear order between variables using
unsorted, pairwise similarity information. It has direct applications in
archeology and shotgun gene sequencing for example. We write seriation as an
optimization problem by proving the equivalence between the seriation and
combinatorial 2-SUM problems on similarity matrices (2-SUM is a quadratic
minimization problem over permutations). The seriation problem can be solved
exactly by a spectral algorithm in the noiseless case and we derive several
convex relaxations for 2-SUM to improve the robustness of seriation solutions
in noisy settings. These convex relaxations also allow us to impose structural
constraints on the solution, hence solve semi-supervised seriation problems. We
derive new approximation bounds for some of these relaxations and present
numerical experiments on archeological data, Markov chains and DNA assembly
from shotgun gene sequencing data.Comment: Final journal version, a few typos and references fixe
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