Remarks on the geometry of coordinate projections in R^n

We study geometric properties of coordinate projections. Among other results, we show that if a body K in R^n has an "almost extremal" volume ratio, then it has a projection of proportional dimension which is close to the cube. We compare type 2 and infratype 2 constant of a Banach space. This follows from a comparison lemma for Rademacher and Gaussian averages. We also establish a sharp estimate on the shattering dimension of the convex hull of a class of functions in terms of the shattering dimension of the class itself.Comment: Israel Journal of Mathematics, to appea

Entropy, dimension and the Elton-Pajor Theorem

The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a number of consequences, including the optimal Elton's theorem and a uniform central limit theorem in the real valued case

Taking Away the Tightrope: Fixing the National Flood Insurance Program Circus via Eminent Domain

As Harvey, Irma, Maria and other major 2017 storms washed upon the shores of the United States, millions of people across the nation in major cities and rural areas alike found their possessions, their homes, and sadly in many cases their lives, washed away with the storms. The destructive hurricane season came just as Congress began to consider the reauthorization of the National Flood Insurance Program (NFIP), a federal system of subsidized flood insurance created to fill a void left by private insurers in the 1960s. Extreme weather events such as these illustrate the need for such a program and pressure politicians to continue providing coverage in high-risk area; yet, the growing number and intensity of storms as a result of climate change also underscores the need for NFIP reform. The continued provision of coverage at subsidized premium rates under the NFIP have not only contributed to the program’s long-term insolvency, but also have created perverse incentives to develop in high-risk areas that will only grow riskier over time. The most egregious example of this comes in the form of severe repetitive loss properties—homes that flood dozens of times, yet continue to receive insurance benefits many times the value of the underlying property. Rather than maintaining the status quo, this note proposes the institution of a system of “involuntary buyouts,” whereby federal, state, and local governmental actors can exercise their existing authority under the Takings Clause. This approach would improve the solvency of the NFIP, prevent redevelopment in high-risk areas, and create natural barriers to safeguard communities against future disasters

The Extrapolation of Families of Curves by Recurrence Relations, with Application to Creep-Rupture Data

A method using finite-difference recurrence relations is presented for direct extrapolation of families of curves. The method is illustrated by applications to creep-rupture data for several materials and it is shown that good results can be obtained without the necessity for any of the usual parameter concepts

Practical Solution of Plastic Deformation Problems in Elastic-Plastic Range

A practical method for solving plastic deformation problems in the elastic-plastic range is presented. The method is one of successive approximations and is illustrated by four examples which include a flat plate with temperature distribution across the width. a thin shell with axial temperature distribution, a solid cylinder with radial temperature distribution, and a rotating disk with radial temperature distribution

Atypical pneumonia in adults in southern Africa

The true incidence of Legionella pneumophilia, Mycoplasma pneumoniae, Chlamydophila pneumoniae and Coxiella burnetti, the so-called atypical pathogens that cause adult community-acquired pneumonia in southern Africa, is unknown. Although there are a lack of community-based studies, hospital-based studies suggest that the incidence may be as high as 30% in patients admitted to, but not requiring, an intensive care unit. A lack of specific clinical features that differentiate atypical pathogens, plus the lack of reliable, simple diagnostics, compound the uncertainty regarding the contribution of atypical pathogens to the sum total of community-acquired pneumonia in southern Africa. Without reliable diagnostic tests, macrolide or azalide antibiotics are widely used for in-patients with pneumonia, potentially fuelling the rise of antibiotic resistance to macrolides in other bacteria