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Discrete Euclidian Spaces (DESs) are the beginning of a journey without return towards the discretization of mathematics. Important mathematical concepts- such as the idea of number or the systems of numeration, whose formal definition is currently independent of Euclidean spaces -have in the Isodimensional Discrete Mathematics (IDM) their roots in the DESs. This mathematics, which arises largely from the discretization of traditional mathematics, presents its foundations and concepts differently from the orthodox way, so at first glance it may seem that the IDM could be an exotic tool, or perhaps just a simple curiosity. However, the IDM dis-crete approaches have a great theoretical repercussion on traditional mathematics.
In this paper we will relate hyperstructures and the general $mathscr{H}$-principle to known mathematical structures, and also discuss how they may give rise to new mathematical structures. The main purpose is to point out new ideas and directions of investigation.
Visualization, as a vibrant field for researchers, practitioners, and higher educational institutions, is growing and evolving very rapidly. Tremendous progress has been made since 1987, the year often cited as the beginning of data visualization as
We introduce the concept of a consistency space. The idea of the consistency space is motivated by the question, Given only the collection of sets of sentences which are logically consistent, is it possible to reconstruct their lattice structure?
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural deduction s
Numerous methods for crafting adversarial examples were proposed recently with high success rate. Since most existing machine learning based classifiers normalize images into some continuous, real vector, domain firstly, attacks often craft adversari