Non-disturbance criteria of quantum measurements

Using the general sequential product proposed by Shen and Wu in [J. Phys. A: Math. Theor. 42, 345203, 2009], we derive three criteria for describing non-disturbance between quantum measurements that may be unsharp with such new sequential products, which generalizes Gudder's results

Achieving non-discrimination in prediction

Discrimination-aware classification is receiving an increasing attention in data science fields. The pre-process methods for constructing a discrimination-free classifier first remove discrimination from the training data, and then learn the classifier from the cleaned data. However, they lack a theoretical guarantee for the potential discrimination when the classifier is deployed for prediction. In this paper, we fill this gap by mathematically bounding the probability of the discrimination in prediction being within a given interval in terms of the training data and classifier. We adopt the causal model for modeling the data generation mechanism, and formally defining discrimination in population, in a dataset, and in prediction. We obtain two important theoretical results: (1) the discrimination in prediction can still exist even if the discrimination in the training data is completely removed; and (2) not all pre-process methods can ensure non-discrimination in prediction even though they can achieve non-discrimination in the modified training data. Based on the results, we develop a two-phase framework for constructing a discrimination-free classifier with a theoretical guarantee. The experiments demonstrate the theoretical results and show the effectiveness of our two-phase framework

Faster Information Propagation on Highways: a Virtual MIMO Approach

In vehicular communications, traffic-related information should be spread over the network as quickly as possible to maintain a safe and reliable transportation system. This motivates us to develop more efficient information propagation schemes. In this paper, we propose a novel cluster-based cooperative information forwarding scheme, in which the vehicles opportunistically form virtual antenna arrays to boost one-hop transmission range and therefore accelerate information propagation along the highway. Both closed-form results of the transmission range gain and the improved Information Propagation Speed (IPS) are derived and verified by simulations. It is observed that the proposed scheme demonstrates the most significant IPS gain in moderate traffic scenarios, whereas too dense or too sparse vehicle density results in less gain. Moreover, it is also shown that increased mobility offers more contact opportunities and thus facilitates information propagation.Comment: IEEE 2014 Global Telecommunications Conference (GLOBECOM 2014) - Communication Theory Symposiu

Relationship between Nichols braided Lie algebras and Nichols algebras

We establish the relationship among Nichols algebras, Nichols braided Lie algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra $\mathfrak B(V)$ is finite-dimensional if and only if Nichols braided Lie algebra $\mathfrak L(V)$ is finite-dimensional if there does not exist any $m$-infinity element in $\mathfrak B(V)$; (ii) Nichols Lie algebra $\mathfrak L^-(V)$ is infinite dimensional if $D^-$ is infinite. We give the sufficient conditions for Nichols braided Lie algebra $\mathfrak L(V)$ to be a homomorphic image of a braided Lie algebra generated by $V$ with defining relations.Comment: LeTex 18 pages, need JOLT-macros to compile. To appear in Journal of Lie Theor