12,095 research outputs found
Cantor Series Constructions Contrasting Two Notions of Normality
A. R\'enyi \cite{Renyi} made a definition that gives a generalization of
simple normality in the context of -Cantor series. In \cite{Mance}, a
definition of -normality was given that generalizes the notion of normality
in the context of -Cantor series. In this work, we examine both
-normality and -distribution normality, treated in \cite{Laffer} and
\cite{Salat}. Specifically, while the non-equivalence of these two notions is
implicit in \cite{Laffer}, in this paper, we give an explicit construction
witnessing the nontrivial direction. That is, we construct a base as well
as a real that is -normal yet not -distribution normal. We next
approach the topic of simultaneous normality by constructing an explicit
example of a base as well as a real that is both -normal and
-distribution normal
Two short proofs of the bounded case of S.B. Rao's degree sequence conjecture
S. B. Rao conjectured that graphic sequences are well-quasi-ordered under an
inclusion based on induced subgraphs. This conjecture has now been settled
completely by M. Chudnovsky and P. Seymour. One part of the proof proves the
result for the bounded case, a result proved independently by C. J. Altomare.
We give two short proofs of the bounded case of S. B. Rao's conjecture. Both
the proofs use the fact that if the number of entries in an integer sequence
(with even sum) is much larger than its highest term, then it is necessarily
graphic.Comment: 4 page
Ultra narrow AuPd and Al wires
In this letter we discuss a novel and versatile template technique aimed to
the fabrication of sub-10 nm wide wires. Using this technique, we have
successfully measured AuPd wires, 12 nm wide and as long as 20 m. Even
materials that form a strong superficial oxide, and thus not suited to be used
in combination with other techniques, can be successfully employed. In
particular we have measured Al wires, with lateral width smaller or comparable
to 10 nm, and length exceeding 10 m.Comment: 4 pages, 4 figures. Pubblished in APL 86, 172501 (2005). Added
erratum and revised Fig.
Objective Bayesian Search of Gaussian DAG Models with Non-local Priors
Directed Acyclic Graphical (DAG) models are increasingly employed in the study of physical and biological systems, where directed edges between vertices are used to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more reasonably tackled if the variables are assumed to satisfy a given ordering; in this case, we simply have to estimate the presence or absence of each possible edge, whose direction is established by the ordering of the variables. We propose an objective Bayesian methodology for model search over the space of Gaussian DAG models, which only requires default non-local priors as inputs. Priors of this kind are especially suited to learn sparse graphs, because they allow a faster learning rate, relative to ordinary local priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables. We apply our method to a variety of simulated and real data sets.Fractional Bayes factor; High-dimensional sparse graph; Moment prior; Non-local prior; Objective Bayes; Pathway based prior; Regulatory network; Stochastic search; Structural learning.
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