3,815 research outputs found
Classification methods for Hilbert data based on surrogate density
An unsupervised and a supervised classification approaches for Hilbert random
curves are studied. Both rest on the use of a surrogate of the probability
density which is defined, in a distribution-free mixture context, from an
asymptotic factorization of the small-ball probability. That surrogate density
is estimated by a kernel approach from the principal components of the data.
The focus is on the illustration of the classification algorithms and the
computational implications, with particular attention to the tuning of the
parameters involved. Some asymptotic results are sketched. Applications on
simulated and real datasets show how the proposed methods work.Comment: 33 pages, 11 figures, 6 table
A decomposition theorem for fuzzy set-valued random variables and a characterization of fuzzy random translation
Let be a fuzzy set--valued random variable (\frv{}), and \huku{X} the
family of all fuzzy sets for which the Hukuhara difference X\HukuDiff B
exists --almost surely. In this paper, we prove that can be
decomposed as X(\omega)=C\Mink Y(\omega) for --almost every
, is the unique deterministic fuzzy set that minimizes
as is varying in \huku{X}, and is a centered
\frv{} (i.e. its generalized Steiner point is the origin). This decomposition
allows us to characterize all \frv{} translation (i.e. X(\omega) = M \Mink
\indicator{\xi(\omega)} for some deterministic fuzzy convex set and some
random element in \Banach). In particular, is an \frv{} translation if
and only if the Aumann expectation is equal to up to a
translation.
Examples, such as the Gaussian case, are provided.Comment: 12 pages, 1 figure. v2: minor revision. v3: minor revision;
references, affiliation and acknowledgments added. Submitted versio
Minimum sensitivity design of attitude control systems Final report
Minimum sensitivity design of attitude control systems for spacecraf
Lineability of non-differentiable Pettis primitives
Let X be an infinite-dimensional Banach space. In 1995, settling a long
outstanding problem of Pettis, Dilworth and Girardi constructed an X-valued
Pettis integrable function on [0; 1] whose primitive is nowhere weakly
differentiable. Using their technique and some new ideas we show that ND, the
set of strongly measurable Pettis integrable functions with nowhere weakly
differentiable primitives, is lineable, i.e., there is an infinite dimensional
vector space whose nonzero vectors belong to ND
Rolewicz-type chaotic operators
In this article we introduce a new class of Rolewicz-type operators in l_p,
. We exhibit a collection F of cardinality continuum of
operators of this type which are chaotic and remain so under almost all finite
linear combinations, provided that the linear combination has sufficiently
large norm. As a corollary to our main result we also obtain that there exists
a countable collection of such operators whose all finite linear combinations
are chaotic provided that they have sufficiently large norm.Comment: 15 page
Metric differentiability of Lipschitz maps
An extension of Rademacher’s theorem is proved for Lipschitz mappings between Banach spaces without the Radon–Nikodým property
Classes of regular Sobolev mappings
We prove that a slight modi\ufb01cation of the notion of \u3b1-absolute continuity introduced in [D. Bongiorno, Absolutely continuous
functions in Rn, J. Math. Anal. Appl. 303 (2005) 119\u2013134] is equivalent to the notion of n, \u3bb-absolute continuity given by S. Hencl
in [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175\u2013189]
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