Transition Operators Assigned to Physical Systems

From torsion theories to closure operators and factorization systems

Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].

Furberg assigned to them ?

L-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS

The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

Opacity Generalized to Transition Systems

Recently, opacity has proved to be a very promising technique for describing security properties. Much of the work has been couched in terms of Petri nets. Here, we extend the notion of opacity to the model of labelled transition systems and generalize opacity in order to be able to represent information flow security as well as protocol security. We give precise links between opacity and other...

Transition thresholds and transition operators for binarization and edge detection

The transition method for image binarization is based on the concept of t-transition pixels, a generalization of edge pixels, and t-transition sets. We introduce a novel unsupervised thresholding for unimodal histograms to estimate the transition sets. We also present dilation and incidence transition operators to refine the transition set. Afterward, we propose the simple edge transition opera...