Trace forms of Galois extensions in the presence of a fourth root of unity

We study quadratic forms that can occur as trace forms of Galois field extensions L/K, under the assumption that K contains a primitive 4th root of unity. M. Epkenhans conjectured that any such form is a scaled Pfister form. We prove this conjecture and classify the finite groups G which admit a G-Galois extension L/K with a non-hyperbolic trace form. We also give several applications of these results.Comment: 19 pages, to appear in International Math Research Notice

A Cautionary Note on Generalized Linear Models for Covariance of Unbalanced Longitudinal Data

Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome this and other challenges by embedding the covariance matrix of the observed data for each subject in a larger covariance matrix and employing the familiar EM algorithm to compute the maximum likelihood estimates of the parameters and their standard errors. We illustrate and assess the methodology using real data sets and simulations

A Qualitative Descriptive Study on Re-assessing the Mental Certification by FAA for Future Pilots

Mental illness becomes one of the main problems that most pilots do not usually address. It is not because pilots do not have the courage or are open enough to talk with someone, but because the Federal Aviation Administration (FAA) forces them to hide from mental depression. Most of the time, the pilots are not willing to declare such illnesses as they fear losing their job; simultaneously, the Federal Aviation Agencies across the world require pilots to be in peat health, including their mental condition, to operate the aircraft. While it can be said that the passengers’ and crews’ safety are in pilots’ hands, mental illness should not be viewed as a disease that cannot be cured. It can be treated with proper medical guidelines; however, the recovery journey can be long and exhausting. With the rising generation of younger pilots who have been dealing with 21st-century problems such as financial issues, family issues, and so on, depression rates among Generation Z have been drastically increased. The paper will analyze the FAA medical certification and whether it should be re-assessed and allowed pilots with long-term mental illness while giving them options for treatment. The paper will also discuss the new mental certification guidelines to a certain extent aligned with regulatory requirements for upcoming pilots to fly under certain circumstances. The Federal Aviation Administration (FAA) must be re-assessed its mental requirement in medical certification for future pilots

Scheme for remote implementation of partially unknown quantum operation of two qubits in cavity QED

By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits [An Min Wang: PRA, \textbf{74}, 032317(2006)], we present a scheme to implement it in cavity QED. Long-lived Rydberg atoms are used as qubits, and the interaction between the atoms and the field of cavity is a nonresonant one. Finally, we analyze the experimental feasibility of this scheme.Comment: 7 pages, 2 figure

Exploration of nonlocalities in ensembles consisting of bipartite quantum states

It is revealed that ensembles consisting of multipartite quantum states can exhibit different kinds of nonlocalities. An operational measure is introduced to quantify nonlocalities in ensembles consisting of bipartite quantum states. Various upper and lower bounds for the measure are estimated and the exact values for ensembles consisting of mutually orthogonal maximally entangled bipartite states are evaluated.Comment: The title and some contents changed, 4 pages, no figure

Generalized Point Set Registration with Fuzzy Correspondences Based on Variational Bayesian Inference

Point set registration (PSR) is an essential problem in surgical navigation and computer-assisted surgery (CAS). In CAS, PSR can be used to map the intra-operative surgical space with the pre-operative volumetric image space. The performances of PSR in real-world surgical scenarios are sensitive to noise and outliers. This paper proposes a novel point set registration approach where the additional features (i.e., the normal vectors) extracted from the point sets are utilized, and the convergence of the algorithm is guaranteed from the theoretical perspective. More specifically, we formulate the PSR with normal vectors by generalizing the Bayesian coherent point drift (BCPD) into the six-dimensional scenario. The proposed algorithm is more accurate and robust to noise and outliers, and the theoretical convergence of the proposed approach is guaranteed. Our contributions of this paper are summarized as follows. (1) The PSR problem with normal vectors is formally formulated through generalizing the BCPD approach; (2) The formulas for updating the parameters during the algorithm's iterations are given in closed forms; (3) Extensive experiments have been done to verify the proposed approach and specifically its significant improvements over the BCPD has been validated

Distributed feature selection for efficient economic big data analysis

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.With the rapidly increasing popularity of economic activities, a large amount of economic data is being collected. Although such data offers super opportunities for economic analysis, its low-quality, high-dimensionality and huge-volume pose great challenges on efficient analysis of economic big data. The existing methods have primarily analyzed economic data from the perspective of econometrics, which involves limited indicators and demands prior knowledge of economists. When embracing large varieties of economic factors, these methods tend to yield unsatisfactory performance. To address the challenges, this paper presents a new framework for efficient analysis of high-dimensional economic big data based on innovative distributed feature selection. Specifically, the framework combines the methods of economic feature selection and econometric model construction to reveal the hidden patterns for economic development. The functionality rests on three pillars: (i) novel data pre-processing techniques to prepare high-quality economic data, (ii) an innovative distributed feature identification solution to locate important and representative economic indicators from multidimensional data sets, and (iii) new econometric models to capture the hidden patterns for economic development. The experimental results on the economic data collected in Dalian, China, demonstrate that our proposed framework and methods have superior performance in analyzing enormous economic data.This work is supported by National Natural Science Foundation Project of China (U1301253), Science and Technology Planning Key Project of Guangdong Province, China (2015B010110006) and Research Office of Dalian Government in China