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"Transportation Miscellanea."
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ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS
The theory of optimal transportation has experienced a sharp increase in interest in many areas of economic research such as optimal matching theory and econometric identification. A particularly valuable tool, due to its convenient representation as the gradient of a convex function, has been the Brenier map: the matching obtained as the optimizer of the Monge–Kantorovich optimal transportation problem with the euclidean distance as the cost function. Despite its popularity, the statistical properties of the Brenier map have yet to be fully established, which impedes its practical use for estimation and inference. This article takes a first step in this direction by deriving a convergence rate for the simple plug-in estimator of the potential of the Brenier map via the semi-dual Monge–Kantorovich problem. Relying on classical results for the convergence of smoothed empirical processes, it is shown that this plug-in estimator converges in standard deviation to its population counterpart under the minimax rate of convergence of kernel density estimators if one of the probability measures satisfies the Poincaré inequality. Under a normalization of the potential, the result extends to convergence in the$L^2$norm, while the Poincaré inequality is automatically satisfied. The main mathematical contribution of this article is an analysis of the second variation of the semi-dual Monge–Kantorovich problem, which is of independent interest.
Journal Article
Airline Pilot Technical Interviews
This is not AI-generated content. The contents were written and verified by subject matter experts from Aviation Supplies & Academics, an 85-year-old aviation company. Look for the ASA wings to ensure you are purchasing a reliable publication. A study guide for a successful airline checkride All kinds of technical questions can be asked in an airline interview, yet there is a specific approach pilot applicants should take to successfully prepare for this part of the hiring process. In this expanded fourth edition of the book, author Ron McElroy gives readers an abundance of preparatory exercises in the areas of mental math, approach plates, regulations and procedures, weather, systems and aerodynamics, and cockpit situations to analyze and resolve. You will also be acquainted with 14 CFR Part 111 Pilot Records Database so that you are aware of the information sharing that occurs between employers. Using McElroy's tips and methods, aspiring professional pilots will be prepared to display their flying skills during the simulator ride as well as their aeronautical knowledge during the face-to-face oral questioning. This study and practice will not only ensure better performance during a technical interview or test but will help pilots fly the line a little better. Important note from the publisher: While AI-generated content can be helpful to identify resources for ongoing study, it is not a reliable resource for learning critical, safety-dependent topics such as aviation. AI content is sterile, often lacks important context, and is at risk of errors. ASA publishes only human-generated content to ensure it is accurate, reliable, comprehensive, and presented in context—so you can become a safe and effective aviator.
eBook
Guesstimation 2.0
Guesstimation 2.0reveals the simple and effective techniques needed to estimate virtually anything--quickly--and illustrates them using an eclectic array of problems. A stimulating follow-up toGuesstimation, this is the must-have book for anyone preparing for a job interview in technology or finance, where more and more leading businesses test applicants using estimation questions just like these.
The ability to guesstimate on your feet is an essential skill to have in today's world, whether you're trying to distinguish between a billion-dollar subsidy and a trillion-dollar stimulus, a megawatt wind turbine and a gigawatt nuclear plant, or parts-per-million and parts-per-billion contaminants. Lawrence Weinstein begins with a concise tutorial on how to solve these kinds of order of magnitude problems, and then invites readers to have a go themselves. The book features dozens of problems along with helpful hints and easy-to-understand solutions. It also includes appendixes containing useful formulas and more.
Guesstimation 2.0shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store, to the total length of all toilet paper used in the United States. It also enables readers to answer, once and for all, the most asked environmental question of our day: paper or plastic?
eBook
Backpacking with the Saints
Backpacking with the Saints is a captivating account of solo wilderness backpacking as spiritual practice. On his solitary hikes, Belden Lane has as companions the great spiritual texts of the world's religions. The wilderness, he argues, offers an enlightening approach to the texts, presenting the opportunity to explore the interior landscape and the spiritual realm of nature. The book thoughtfully examines the place of nature in the spiritual life and the dynamics of reading in the wild.
eBook
