Study of covering properties in fuzzy topology

This work is devoted to the study of covering properties both in L-fuzzy topological spaces and in smooth L-fuzzy topological spaces , that is the fuzzy spaces in Sostak's sense, where L is a fuzzy lattice . Based on the satisfactory theory of L-fuzzy compactness build up by Warner, McLean and Kudri, good definitions of feeble compactness and P-closedness are introduced and studied. A unification theory for good L-fuzzy covering axioms is provided. Following the lines of L-fuzzy compactness, we suggest two kinds of L-fuzzy relative compactness as in general topology, study some of their properties and prove that these notions are good extensions of the corresponding ordinary versions. We also present L-fuzzy versions of R-compactness , weak compactness and 0-rigidity and discuss some of their properties. By introducing 'a-Scott continuous functions', a 'goodness of extension' criterion for smooth fuzzy topological properties is established. We propose a good definition of compactness, which we call 'smooth compactness' in smooth L-fuzzy topological spaces. Smooth compactness turns out to be an extension of L-fuzzy compactness to smooth L-fuzzy topological spaces. We study some properties of smooth compactness and obtain different characterizations. As an extension of the fuzzy Hausdorffness defined by Warner and McLean, 'smooth Hausdorffness' is introduced in smooth L-fuzzy topological spaces. Good definitions of smooth countable compactness, smooth Lindelofness and smooth local compactness are introduced and some of their properties studied

Satiated economies with unbounded consumption sets : fuzzy core and equilibrium

For an exchange economy, under assumptions which did not bring about the existence of quasiequilibrium with dividends as yet, we prove the nonemptiness of the fuzzy rejective core. Then, via Konovalov (1998, 2005)'s equivalence result, we solve the equilibrium (with dividends) existence problem. In a last section, we show the existence of a Walrasian quasiequilibrium under a weak non-satiation condition which differs from the weak non-satiation assumption introduced by Allouch-Le Van (2009). This result, designed for exchange economies whose consumers' utility functions are not assumed to be upper semicontinuous, complements the one obtained by Martins-da-Rocha and Monteiro (2009).Exchange economy, satiation, equilibrium with dividends, rejective core, fuzzy rejective core, core equivalence.

Constraining scalar fields with stellar kinematics and collisional dark matter

The existence and detection of scalar fields could provide solutions to long-standing puzzles about the nature of dark matter, the dark compact objects at the centre of most galaxies, and other phenomena. Yet, self-interacting scalar fields are very poorly constrained by astronomical observations, leading to great uncertainties in estimates of the mass $m_\phi$ and the self-interacting coupling constant $\lambda$ of these fields. To counter this, we have systematically employed available astronomical observations to develop new constraints, considerably restricting this parameter space. In particular, by exploiting precise observations of stellar dynamics at the centre of our Galaxy and assuming that these dynamics can be explained by a single boson star, we determine an upper limit for the boson star compactness and impose significant limits on the values of the properties of possible scalar fields. Requiring the scalar field particle to follow a collisional dark matter model further narrows these constraints. Most importantly, we find that if a scalar dark matter particle does exist, then it cannot account for both the dark-matter halos and the existence of dark compact objects in galactic nucleiComment: 23 pages, 8 figures; accepted for publication by JCAP after minor change

Salient Object Detection via Augmented Hypotheses

In this paper, we propose using \textit{augmented hypotheses} which consider objectness, foreground and compactness for salient object detection. Our algorithm consists of four basic steps. First, our method generates the objectness map via objectness hypotheses. Based on the objectness map, we estimate the foreground margin and compute the corresponding foreground map which prefers the foreground objects. From the objectness map and the foreground map, the compactness map is formed to favor the compact objects. We then derive a saliency measure that produces a pixel-accurate saliency map which uniformly covers the objects of interest and consistently separates fore- and background. We finally evaluate the proposed framework on two challenging datasets, MSRA-1000 and iCoSeg. Our extensive experimental results show that our method outperforms state-of-the-art approaches.Comment: IJCAI 2015 pape