Many, but not all

All-But-Many Lossy Trapdoor Functions

We put forward a generalization of lossy trapdoor functions (LTFs). Namely, all-but-many lossy trapdoor functions (ABM-LTFs) are LTFs that are parametrized with tags. Each tag can either be injective or lossy, which leads to an invertible or a lossy function. The interesting property of ABM-LTFs is that it is possible to generate an arbitrary number of lossy tags by means of a special trapdoor,...

An example of a structured proof by induction with many , but not all , gory details

How do you go about proving something like this in a convincing way, especially when you are a novice at writing proofs? The problem is that a proof that is “obvious” to an experienced mathematician, that is, the person standing at the front and teaching the course, is usually somewhat obscure to the beginner. The experienced mathematician, having done many hundreds of proofs, knows how to fill...

Ancestral T-box mutation is present in many, but not all, short-tailed dog breeds.

Dogs differ greatly in their morphological characteristics including various tail phenotypes. Congenitally short-tailed dogs are present in many breeds; however, the causative mutation located in the T-box transcription factor T gene (C189G) had only been described in the bobtailed Pembroke Welsh Corgis. We investigated here the presence of the T gene mutation in 23 other breeds (360 dogs, incl...

All-payer ratesetting: Down but not out

In the United States, when the cost-containment paradigm shifted from regulation to competition, all-payer hospital ratesetting went out of favor. After reviewing the published literature and supplementing the existing literature with more current information, the author concludes that all-payer ratesetting is able to meet its multiple objectives of cost containment, reduction of the amount of ...

The Irreducibility of All but Finitely Many Bessel Polynomials