5,404 research outputs found
Centrally Image partition Regularity near 0
The notion of Image partition regularity near zero was first introduced by De
and Hindman. It was shown there that like image partition regularity over
the main source of infinite image partition regular matrices near
zero are Milliken- Taylor matrices. But Milliken- Taylor matrices are far apart
to have images in central sets. In this regard the notion of centrally image
partition regularity was introduced. In the present paper we propose the notion
centrally partition regular matrices near zero for dense sub semigroup of
(\ber^+,+) which are different from centrally partition regular matrices
unlike finite cases
Optimal transport with branching distance costs and the obstacle problem
We address the Monge problem in metric spaces with a geodesic distance: (X,
d) is a Polish space and dN is a geodesic Borel distance which makes (X,dN) a
possibly branching geodesic space. We show that under some assumptions on the
transference plan we can reduce the transport problem to transport problems
along family of geodesics. We introduce two assumptions on the transference
plan {\pi} which imply that the conditional probabilities of the first marginal
on each family of geodesics are continuous and that each family of geodesics is
a hourglass-like set. We show that this regularity is sufficient for the
construction of a transport map. We apply these results to the Monge problem in
d with smooth, convex and compact obstacle obtaining the existence of an
optimal map provided the first marginal is absolutely continuous w.r.t. the
d-dimensional Lebesgue measure.Comment: 27 pages, 1 figure; SIAM J. Math. Anal. 2012. arXiv admin note:
substantial text overlap with arXiv:1103.2796, arXiv:1103.279
A Nonparametric Ensemble Binary Classifier and its Statistical Properties
In this work, we propose an ensemble of classification trees (CT) and
artificial neural networks (ANN). Several statistical properties including
universal consistency and upper bound of an important parameter of the proposed
classifier are shown. Numerical evidence is also provided using various real
life data sets to assess the performance of the model. Our proposed
nonparametric ensemble classifier doesn't suffer from the `curse of
dimensionality' and can be used in a wide variety of feature selection cum
classification problems. Performance of the proposed model is quite better when
compared to many other state-of-the-art models used for similar situations
The Monge problem in Wiener Space
We address the Monge problem in the abstract Wiener space and we give an
existence result provided both marginal measures are absolutely continuous with
respect to the infinite dimensional Gaussian measure {\gamma}
The universal Glivenko-Cantelli property
Let F be a separable uniformly bounded family of measurable functions on a
standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest
number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are
equivalent:
1. F is a universal Glivenko-Cantelli class.
2. N_{[]}(F,\epsilon,\mu)0 and every probability
measure \mu.
3. F is totally bounded in L^1(\mu) for every probability measure \mu.
4. F does not contain a Boolean \sigma-independent sequence.
It follows that universal Glivenko-Cantelli classes are uniformity classes
for general sequences of almost surely convergent random measures.Comment: 26 page
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