Dedicated to the memory of Bernard Dwork 1. Introduction In this series of two papers, we prove the p-adic meromorphic continuation of the pure slope L-functions arising from the slope decomposition of an overconvergent F-crystal, as conjectured by Dwork 6]. More precisely, we prove a suitable extension of Dwork's conjecture in our more general setting of-modules, see section 2 for precise deen...

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension i...

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by approximation theory, researchers have proposed a series of effective completion methods. However, most these methods directly consider the global low-rankness underlying tensors, which is not sufficient for low sampling rate; addition, single nuclear norm or its relaxation us...

The joint probability distribution of states of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence compositions, often follows Zipf's law, where a power law is observed on a rank-frequency plot. This behavior has been shown to imply that these systems reside near a unique critical point where the extensive parts of the entropy and ener...