Abstract This paper contributes to answering the question how physicalism can be defined for a world without fundamental physical phenomena. In recent in this journal, Torin Alter, Sam Coleman, and Robert J. Howell propose necessary condition on physicalism. They argue that is true only if there no infinitely descending chain of mentally constituted I alleged faces counterexamples. An phenomena...

Let A be the ring of adeles a number field F. Given self-dual irreducible, automorphic, cuspidal representation ? GLn(A), with trivial central character, we construct its full inverse image under weak Langlands functorial lift from appropriate split classical group G. We do this by new automorphic descent method, namely double descent. This method is derived recent generalized doubling integral...

Nesterov's accelerated gradient descent (AGD), an instance of the general family of"momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior to GD in the nonconvex setting remains open. This paper studies a simple variant of AGD, and shows that it escapes saddle points and finds a second-order stat...

We learn recurrent neural network optimizers trained on simple synthetic functions by gradient descent. We show that these learned optimizers exhibit a remarkable degree of transfer in that they can be used to efficiently optimize a broad range of derivative-free black-box functions, including Gaussian process bandits, simple control objectives, global optimization benchmarks and hyper-paramete...

The purpose of this thesis is to give a new construction for central extensions of certain classes of infinite dimensional Lie algebras which include multiloop Lie algebras as motivating examples. The key idea of this construction is to view multiloop Lie algebras as twisted forms. This perspective provides a beautiful bridge between infinite dimensional Lie theory and descent theory and is cru...