اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDiscrete Euclidian Spaces: a starting point toward the discretization of mathematics
195
0
0.0
(
0
)
تأليف
Ricardo Ramos-Montero
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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
a distinct field. As such, the number of visualization resources and the demand for those resources are increasing at a very fast pace. We present a collection of open visualization resources for all those with an interest in interactive data visualization and visual analytics. Because the number of resources is so large, we focus on collections of resources, of which there are already very many ranging from literature collections to collections of practitioner resources. We develop a novel classification of visualization resource collections based on the resource type, e.g. literature-based, web-based, etc. The result is a helpful overview and details-on-demand of many useful resources. The collection offers a valuable jump-start for those seeking out data visualization resources from all backgrounds spanning from beginners such as students to teachers, practitioners, and researchers wishing to create their own advanced or novel visual designs.
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
ystem ``a la Prawitz. The rest of the material is more or less traditional but I emphasize partial functions more than usual (after all, programs may not terminate for all input) and I provide a fairly complete account of the basic concepts of graph theory.
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
al examples in such domain. However, adversarial examples may become benign after denormalizing them back into the discrete integer domain, known as the discretization problem. This problem was mentioned in some work, but has received relatively little attention. In this work, we first conduct a comprehensive study of existing methods and tools for crafting. We theoretically analyze 34 representative methods and empirically study 20 representative open source tools for crafting adversarial images. Our study reveals that the discretization problem is far more serious than originally thought. This suggests that the discretization problem should be taken into account seriously when crafting adversarial examples and measuring attack success rate. As a first step towards addressing this problem in black-box scenario, we propose a black-box method which reduces the adversarial example searching problem to a derivative-free optimization problem. Our method is able to craft adversarial images by derivative-free search in the discrete integer domain. Experimental results show that our method is comparable to recent white-box methods (e.g., FGSM, BIM and C&W) and achieves significantly higher success rate in terms of adversarial examples in the discrete integer domain than recent black-box methods (e.g., ZOO, NES-PGD and Bandits). Moreover, our method is able to handle models that is non-differentiable and successfully break the winner of NIPS 2017 competition on defense with 95% success rate. Our results suggest that discrete optimization algorithms open up a promising area of research into effective black-box attacks.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
