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In this work we describe a novel statistical video representation and modeling scheme. Video representation schemes are needed to enable segmenting a video stream into meaningful video-objects, useful for later indexing and retrieval applications. In the proposed methodology, unsupervised clustering via Guassian mixture modeling extracts coherent space-time regions in feature space, and corresp...

This paper studies the possibility of representing lower previsions by continuous linear functionals. We prove the existence of a linear isomorphism between the linear space spanned by the coherent lower previsions and that of an appropriate space of continuous linear functionals. Moreover, we show that a lower prevision is coherent if and only if its transform is monotone. We also discuss the ...

In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique uppercontinuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinite...

A topology τ on a fixed nonempty set X is said to satisfy the weakly continuous representation property if every weakly continuous not necessarily total preorder on the topological space (X, τ) admits a continuous order preserving function. Such a property generalizes the well known continuous representation property of a topology τ on a set X (according to which every continuous total preorder...

Résumé en anglais This article introduces a continuous representation for controlled model and state jump hybrid systems. Such a representation is valuable in that it manages to cope with the difficulties related to discontinuities, by replacing the study of these systems by that of continuous ones, which is simple. The studied hybrid systems are first introduced, together with their associated...

In this paper, we present a clustering approach based on the combined use of a continuous vector space representation of sentences and the k-means algorithm. The principal motivation of this proposal is to split a big heterogeneous corpus into clusters of similar sentences. We use the word2vec toolkit for obtaining the representation of a given word as a continuous vector space. We provide empi...

(2) Let L, S, T be complete non empty posets, f be a CLHomomorphism of L, S, and g be a CLHomomorphism of S, T . Then g · f is a CLHomomorphism of L, T . (3) For every non empty relational structure L holds idL is infs-preserving. (4) For every non empty relational structure L holds idL is directed-sups-preserving. (5) For every complete non empty poset L holds idL is a CLHomomorphism of L, L. ...

in the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. the basic assumption is that the class of functions that we investigate here, except the verification of dirichlet's principles, is concurrently able to be expanded in taylor's representation, over a particular interval o...

Topological notions and methods are used in various areas of the physical sciences and engineering, and therefore computer processing of topological data is important. Separate from this, but closely related, are computer science uses of topology: applications to programming language semantics and computing with exact real numbers are important examples. The seminar concentrated on an important...