Every day, the Centers for Disease Control and Pre­ vention (CDC) focuses the world’s attention on issues that deserve to be in the public health spotlight. Visitors to the CDC Web site know that this spotlighting is not only a metaphor but also a prominent physical feature on the agency’s Internet home page. Through its Spot­ light section, the CDC summarizes at a glance the most important thi...

Are P and NP provably inseparable ? Take a look at some unorthodox, guilty mentioned folklore and related unpublished results.

The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus not shellable. Nevertheless, there seem to be large classes of intervals that are shellable and thus have the homotopy type ...

A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of non-complemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable problems is new; the approach allows us to relax the hypotheses under which the results were originally pr...

The split version of the Freudenthal-Tits magic square stems from Lie theory and constructs a Lie algebra starting from two split composition algebras [5, 20, 21]. The geometries appearing in the second row are Severi varieties [24]. We provide an easy uniform axiomatization of these geometries and related ones, over an arbitrary field. In particular we investigate the entry A2 × A2 in the magi...

We propose a simple and fast algorithm called PatchLift for computing distances between patches (contiguous block of samples) extracted from a given one-dimensional signal. PatchLift is based on the observation that the patch distances can be efficiently computed from a matrix that is derived from the one-dimensional signal using lifting; importantly, the number of operations required to comput...

The low energy three nucleon problem with two particle separable potentials is solved. The formalism of Faddeev in recasting the three body equations into Fredholm form and subsequent angular momentum reductions are carried out. Upon searching for a bound state two poles of the amplitude are found. Upon further examination one of the poles is found to have a residue of the wrong sign. This diff...

We study nonlinear Boolean functions that are used in cryptography, especially in block and stream ciphers. We point out possible cryptographic weaknesses of the so-called separable functions. A characteristic of these functions is that they can be transformed into ones that are composed of two “sub-functions” with disjoint variables. We then proceed to construct non-separable functions that ex...

We answer a question of Shelah and Steprāns [6] by producing a model of ZFC where there are no strongly separable almost disjoint families. The notion of a strongly separable almost disjoint family is a natural variation on the well known notion of a completely separable almost disjoint family, and is closely related to the metrization problem for countable Fréchet groups.

We construct an example of conjugacy separable group possessing a not conjugacy separable subgroup of finite index. We give also a sufficient condition for a conjugacy separable group to preserve this property when passing to subgroups of finite index. We establish also conjugacy separability of finitely presented residually free groups using impressive results of Bridson and Wilton [BW-07].