6,054 research outputs found
Graph-Based Change-Point Detection
We consider the testing and estimation of change-points -- locations where
the distribution abruptly changes -- in a data sequence. A new approach, based
on scan statistics utilizing graphs representing the similarity between
observations, is proposed. The graph-based approach is non-parametric, and can
be applied to any data set as long as an informative similarity measure on the
sample space can be defined. Accurate analytic approximations to the
significance of graph-based scan statistics for both the single change-point
and the changed interval alternatives are provided. Simulations reveal that the
new approach has better power than existing approaches when the dimension of
the data is moderate to high. The new approach is illustrated on two
applications: The determination of authorship of a classic novel, and the
detection of change in a network over time
The Cauchy Operator for Basic Hypergeometric Series
We introduce the Cauchy augmentation operator for basic hypergeometric
series. Heine's transformation formula and Sears'
transformation formula can be easily obtained by the symmetric property of some
parameters in operator identities. The Cauchy operator involves two parameters,
and it can be considered as a generalization of the operator . Using
this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy
integral, Sears' two-term summation formula, as well as the -analogues of
Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for
the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big
-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic
Finite Form of the Quintuple Product Identity
The celebrated quintuple product identity follows surprisingly from an
almost-trivial algebraic identity, which is the limiting case of the
terminating q-Dixon formula.Comment: 1 pag
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