Geometry induced by flocks

Geometry Induced by a Diffusion Process

ABSTRACT: For nonlinear functions f of a random vector Y , E[ f ( Y )] and f (E[ Y ]) usually differ. Consequently the mathematical expectation of Y is not intrinsic: when we change coordinate systems, it is not invariant.This article is about a fundamental and hitherto neglected property of random vectors of the form , where X ( t ) is the value at time t of a diffusion process X : namely that...

Flocks of Cones: Star Flocks

The concept of a flock of a quadratic cone is generalized to arbitrary cones. Flocks whose planes contain a common point are called star flocks. Star flocks can be described in terms of their coordinate functions. If the cone is “big enough”, the star flocks it admits can be classified by means of a connection with certain blocking sets of Rédei type.

Hemangioma and Myelocytomas Induced by Avian Leukosis Virus Subgroup J in Commercial Layer Flocks

Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems

We construct three infinite families of partial flocks of sizes 12, 24 and 60 of the hyperbolic quadric of PG(3, q), for q congruent to -1 modulo 12, 24, 60 respectively, from the root systems of type D4, F4, H4, respectively. The smallest member of each of these families is an exceptional flock. We then characterise these partial flocks in terms of the rectangle condition of Benz and by not be...

Geometry-induced asymmetric diffusion.

Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two size...