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 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

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

Learning-Based Resource Allocation in Cloud Data Center Using Advantage Actor-Critic

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Due to the ever-changing system states and various user demands, resource allocation in cloud data center is faced with great challenges in dynamics and complexity. Although there are solutions that focus on this problem, they cannot effectively respond to the dynamic changes of system states and user demands since they depend on the prior knowledge of the system. Therefore, it is still an open challenge to realize automatic and adaptive resource allocation in order to satisfy diverse system requirements in cloud data center. To cope with this challenge, we propose an advantage actor-critic based reinforcement learning (RL) framework for resource allocation in cloud data center. First, the actor parameterizes the policy (allocating resources) and chooses continuous actions (scheduling jobs) based on the scores (evaluating actions) from the critic. Next, the policy is updated by gradient ascent and the variance of policy gradient can be significantly reduced with the advantage function. Simulations using Google cluster-usage traces show the effectiveness of the proposed method in cloud resource allocation. Moreover, the proposed method outperforms classic resource allocation algorithms in terms of job latency and achieves faster convergence speed than the traditional policy gradient method

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

Exploring the effects of car ownership and commuting on subjective well-being::a nationwide questionnaire study

How and to what extent household car ownership and commuting behavior affect individual subjective well-being (SWB) is of great interest for urban and transportation planning. Increasing attention has been paid to the associations between car ownership, commuting and SWB. However, only a limited number of studies examined the effects of travel-related factors on both cognitive and affective SWB aspects. This research empirically investigated the relationships from the two SWB aspects. Furthermore, we extend the modeling of generic cognitive SWB to several specific measures (e.g., satisfaction with life compared to a specific group of people, degree of free choice, social position, and social equality) to explore how car ownership and commuting behavior contribute to individual SWB. Drawing on the data derived from the 2014 China Labor-Force Dynamics Survey, a set of ordered probit models based on Bayesian inference are estimated. The findings point out that household car ownership has a significant effect on cognitive SWB but a limited influence on affective SWB. It appears that commuting time is significantly and negatively associated with individuals’ cognitive and affective well-being, whereas a positive correlation is found between the commuting by bicycle and affective SWB. The effects of commuting time and transportation modes on different measured satisfactions with life have no big differences. Finally, results of the Wald tests indicate that incorporating household car ownership and commuting behavior into the modeling framework can significantly improve the prediction accuracy of individual SWB

Generalized Point Set Registration with the Kent Distribution

Point set registration (PSR) is an essential problem in communities of computer vision, medical robotics and biomedical engineering. This paper is motivated by considering the anisotropic characteristics of the error values in estimating both the positional and orientational vectors from the PSs to be registered. To do this, the multi-variate Gaussian and Kent distributions are utilized to model the positional and orientational uncertainties, respectively. Our contributions of this paper are three-folds: (i) the PSR problem using normal vectors is formulated as a maximum likelihood estimation (MLE) problem, where the anisotropic characteristics in both positional and normal vectors are considered; (ii) the matrix forms of the objective function and its associated gradients with respect to the desired parameters are provided, which can facilitate the computational process; (iii) two approaches of computing the normalizing constant in the Kent distribution are compared. We verify our proposed registration method on various PSs (representing pelvis and femur bones) in computer-assisted orthopedic surgery (CAOS). Extensive experimental results demonstrate that our method outperforms the state-of-the-art methods in terms of the registration accuracy and the robustness

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