The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (resp. cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (resp. weak cone-quasiconvexity), i.e. the notions obtained by replacing in the classical definitions the conditions of type ”for all x, y in the domain and for all t ...

In this paper, we apply the combination method of bagging which has been developed in the context of supervised learning of classifiers and regressors to the unsupervised artificial neural network known as the Self Organising Map. We show that various initialisation techniques can be used to create maps which are comparable by humans by eye. We then use a semi-supervised version of the SOM to c...

PROPRE is a generic and semi-supervised neural learning paradigm that extracts meaningful concepts of multimodal data flows based on predictability across modalities. It consists on the combination of two computational paradigms. First, a topological projection of each data flow on a self-organizing map (SOM) to reduce input dimension. Second, each SOM activity is used to predict activities in ...

This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps de…ned on spaces of random variables, possibly with the so-called Fatou property. We show …rst that the celebrated Namioka-Klee theorem for linear, positive functionals holds also for convex monotone maps on Frechet lattices. It is well-known among the specialists th...

Quantitative analysis of brain lesions and ischemic infarcts is becoming very important due to their association with cardiovascular disease and normal aging. In this paper, we present a semi-supervised segmentation methodology that detects and classifies cerebrovascular disease in multi-channel magnetic resonance (MR) images. The method combines intensity based fuzzy c-means (FCM) segmentation...

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172–6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp. 4733–4736] with a modified semi-implicit Euler iterative scheme and seeding with periodic orbits of neighbouring periods, has been shown to be highly efficient when appl...

We examine the problem of extending, in a natural way, order-preserving maps that are de ̄ned on the interior of a closed cone K1 (taking values in another closed cone K2 ) to the whole of K1 . We give conditions, in considerable generality (for cones in both ̄niteand in ̄nite-dimensional spaces), under which a natural extension exists and is continuous. We also give weaker conditions under which ...