Algebraic geometry of Poisson regression

On the Feasibility of Semi-algebraic Sets in Poisson Regression

Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. The local optimality approach is to study the regions in parameter space where a given design is optimal. In many situations these regions are semialgebraic. We investigate regions of optimality using computer tools such as yalmip, qepcad, and Mathematica.

Poisson Algebras via Model Theory and Differential-algebraic Geometry

Brown and Gordon asked whether the Poisson Dixmier-Moeglin equivalence holds for any complex affine Poisson algebra; that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry and model theory. In particular, it is sho...

Poisson Geometry

This paper is a survey of Poisson geometry, with an emphasis on global questions and the theory of Poisson Lie groups and groupoids.

Introductory Geometry: Algebraic Geometry

Algebraic Geometry the Fundamental Ideas of Abstract Algebraic Geometry

ALGEBRAIC GEOMETRY 79 It may be advisable to give a special name to those varieties which admit every (allowable) ground field as field of definition. Obviously, these are the varieties which are defined over the prime field of the given characteristic p. I propose to call them universal varieties. The projective space and the Grassmannian varieties are examples of universal varieties. Another ...