Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
We prove that for any 1-reduced simplicial set X, Adams' cobar construction, on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX, opening up the possibility of applying the to ...
This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of Fq6, for q≡1mod6. Our result arises from considering the Weil restriction of scalars of this group from Fq6 ...
We generalize the basic results of Vinberg's theta-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. To this end we clarify the relationship between the little Weyl group and the (standard) Weyl group. We ded ...
This work contains the study of the algebra called al-Badī‘ fī al-ḥisāb (literally : "the Wonderful on calculation"), written by the Persian mathematician Abu Bakr Muḥammad ibn al-Ḥusain al-Karaǧi (previously known as ...
We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic sur ...
This paper addresses the problem of distributed rate allocation for a class of multicast networks employing linear network coding. The goal is to minimize the cost (for example, the sum rates allocated to each link in the network) while satisfying a multic ...
We consider the following problem: Given a rational matrix A∈Qm×n and a rational polyhedron Q⊆Rm+p, decide if for all vectors b∈Rm, for which there exists an integral z∈Zp suc ...
A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts t ...
This paper addresses the problem of distributed rate allocation for a class of multicast networks employing linear network coding. The goal is to minimize the cost (for example, the sum rates allocated to each link in the network) while satisfying a multic ...
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common zero of the polynom ...
