54 research outputs found
Configuration-like spaces and coincidences of maps on orbits
In this paper we study the spaces of -tuples of points in a Euclidean
space, without -wise coincidences (configuration-like spaces). A transitive
group action by permuting these points is considered, and some new upper bounds
on the genus (in the sense of Krasnosel'skii--Schwarz and Clapp--Puppe) for
this action are given. Some theorems of Cohen--Lusk type for coincidence points
of continuous maps to Euclidean spaces are deduced
Asymptotic behaviour of random Markov chains with tridiagonal generators
Continuous-time discrete-state random Markov chains generated by a random
linear differential equation with a random tridiagonal matrix are shown to have
a random attractor consisting of singleton subsets, essentially a random path,
in the simplex of probability vectors. The proof uses comparison theorems for
Carath\'eodory random differential equations and the fact that the linear
cocycle generated by the Markov chain is a uniformly contractive mapping of the
positive cone into itself with respect to the the Hilbert projective metric. It
does not involve probabilistic properties of the sample path and is thus
equally valid in the nonautonomous deterministic context of Markov chains with,
say, periodically varying transitions probabilities, in which case the
attractor is a periodic path.Comment: 11 pages, 15 bibliography references, added bibliography, minor
change
New generalized fuzzy metrics and fixed point theorem in fuzzy metric space
In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature
An introduction to continuous optimization for imaging
International audienceA large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification
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