Prior knowledge over arbitrary general sets is incorporated into
nonlinear support vector machine approximation and classification problems as linear constraints of a linear program. The key tool in this incorporation is a theorem of the alternative for convex functions that converts nonlinear prior knowledge implications into linear inequalities
without the need to kernelize these implications. Effectiveness of the
proposed formulation is demonstrated on synthetic examples and on
important breast cancer prognosis problems. All these problems
exhibit marked improvements upon the introduction of prior knowledge
over nonlinear kernel approaches that do not utilize
such knowledge.

We seek for the Hilbert series of the ring of invariant polynomials
in the $2n+n^2$ variables $\{u_i,v_j,x_{i,j}\}_{i,j=1}^n$ under the
action of $GL_n[C]$ by right multiplication on the row vector
$u=(u_1,u_2,\ldots ,u_n)$, left multiplication on the column vector
$v=(v_1,v_2,\ldots ,v_n)$ and by conjugation on the matrix $\|x_{i,j}\|_{i,j=1}^n$.
We reduce the computation of this Hilbert series to the evaluation of
the constant term of a certain rational function. Remarkably, the
final result hinges on the explicit evaluation of certain
Kostka-Foulkes polynomials.

The goal is to explain what a stack is and why people think they are interesting objects to study. I'll start by saying what people (who want to classify a certain class of mathematical objects, say triangles or elliptic curves or...) expect from a moduli space and why it can easily happen that such a moduli `space' doesn't exist. This is the situation in which stacks get their chance. They are some kind of a generalization of a the notion of a `space', where the meaning of space depends on what you are interested in (for example, in the context of algebraic geometry one might say that stacks are a generalization of the notion of a scheme). I'll then use an example to motivate the axioms appearing in the definition of a stack. Depending on how much time I have I will say what an algebraic stack is and maybe how Deligne and Mumford employed the notion to prove something interesting.