On a nonlinear recurrent relation

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.Comment: to appear in Journal of Statistical Physic

The n-tangle of odd n qubits

Coffman, Kundu and Wootters presented the 3-tangle of three qubits in [Phys. Rev. A 61, 052306 (2000)]. Wong and Christensen extended the 3-tangle to even number of qubits, known as $n$-tangle [Phys. Rev. A 63, 044301 (2001)]. In this paper, we propose a generalization of the 3-tangle to any odd $n$-qubit pure states and call it the $n$-tangle of odd $n$ qubits. We show that the $n$-tangle of odd $n$ qubits is invariant under permutations of the qubits, and is an entanglement monotone. The $n$-tangle of odd $n$ qubits can be considered as a natural entanglement measure of any odd $n$-qubit pure states.Comment: 7 pages, no figure

Freshness-Aware Thompson Sampling

To follow the dynamicity of the user's content, researchers have recently started to model interactions between users and the Context-Aware Recommender Systems (CARS) as a bandit problem where the system needs to deal with exploration and exploitation dilemma. In this sense, we propose to study the freshness of the user's content in CARS through the bandit problem. We introduce in this paper an algorithm named Freshness-Aware Thompson Sampling (FA-TS) that manages the recommendation of fresh document according to the user's risk of the situation. The intensive evaluation and the detailed analysis of the experimental results reveals several important discoveries in the exploration/exploitation (exr/exp) behaviour.Comment: 21st International Conference on Neural Information Processing. arXiv admin note: text overlap with arXiv:1409.772