ترغب بنشر مسار تعليمي؟ اضغط هنا

Topology and Higher Concurrencies

54   0   0.0 ( 0 )
 نشر من قبل Nils Baas
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف Nils A. Baas




اسأل ChatGPT حول البحث

We formulate a general approach to higher concurrencies in general and neural codes in particular, and suggest how the higher order aspects may be dealt with in using topology.

قيم البحث

اقرأ أيضاً

47 - Nils A. Baas 2015
In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
186 - Jean Gallier 2008
Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics. This report may be viewed as a tutor ial and a set of notes on convex sets, polytopes, polyhedra, combinatorial topology, Voronoi Diagrams and Delaunay Triangulations. It is intended for a broad audience of mathematically inclined readers. I have included a rather thorough treatment of the equivalence of V-polytopes and H-polytopes and also of the equivalence of V-polyhedra and H-polyhedra, which is a bit harder. In particular, the Fourier-Motzkin elimination method (a version of Gaussian elimination for inequalities) is discussed in some detail. I also included some material on projective spaces, projective maps and polar duality w.r.t. a nondegenerate quadric in order to define a suitable notion of ``projective polyhedron based on cones. To the best of our knowledge, this notion of projective polyhedron is new. We also believe that some of our proofs establishing the equivalence of V-polyhedra and H-polyhedra are new.
55 - Nils A. Baas 2018
The purpose of this paper is to describe and elaborate the philosophical ideas behind hyperstructures and structure formation in general and emphasize the key ideas of the Hyperstructure Program.
76 - Nils A. Baas 2018
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.
The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface state s. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا