Concave functions play a fundamental role in the structure of and minimization of badness-of-fit functions used in data analysis when extreme values of either parameters or data need to be penalized. This paper summarizes my findings about this role. I also describe three examples where concave functions are useful: building measures of badness-of-fit, building robust M -estimators, and buildin...

The notions of union-soft semigroups, union-soft l-ideals, and union-soft r-ideals are introduced, and related properties are investigated. Characterizations of a union-soft semigroup, a union-soft l-ideal, and a union-soft r-ideal are provided. The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-soft l-ideals and union-so...

In this paper we study a class of non linear diffusion equations in a Hilbert space X, ∂tμt −∇ · (∇(L ◦ ρt)γ) = 0 in X × (0,+∞), with respect to a log-concave reference probability measure γ. We obtain existence, uniqueness and stability properties, in the framework of gradient flows in spaces of probability measures.

During the late stages of cranial neurulation in mammalian embryos, the neural epithelium becomes concave. A thick subapical band of microfilament bundles, attached to junctions which are both vertical and horizontal in orientation, can be seen by TEM. Prior to this the neural epithelium is first biconvex and then V-shaped in transverse section, microfilament bundles are absent, and the subapic...

We introduce a design strategy to maximize the Near Field (NF) enhancement near plasmonic antennas. We start by identifying and studying the basic electromagnetic effects that contribute to the electric near field enhancement. Next, we show how the concatenation of a convex and a concave surface allows merging all the effects on a single, continuous nanoantenna. As an example of this NF maximiz...

Nanopillar films of Al-Nb alloys have been fabricated on substrates with a regular concave cell structure by oblique angle physical vapor deposition. The concave cell structure of substrate increases the shadow region for the flux of depositing atoms, assisting the formation of an isolated nanopillar on each cell. Depending upon the alloy composition and deposition angle, the pillar shape chang...

Nanopillar films of Al-Nb alloys have been fabricated on substrates with a regular concave cell structure by oblique angle physical vapor deposition. The concave cell structure of the substrate increases the shadow region for the flux of depositing atoms, assisting the formation of an isolated nanopillar on each cell. Depending upon the alloy composition and deposition angle, the pillar shape c...

In this paper, we discuss the properties of the hyperfibonacci numbers F [r] n and hyperlucas numbers L [r] n . We investigate the log-concavity (log-convexity) of hyperfibonacci numbers and hyperlucas numbers. For example, we prove that {F [r] n }n≥1 is log-concave. In addition, we also study the log-concavity (log-convexity) of generalized hyperfibonacci numbers and hyperlucas numbers.