This article surveys all known fields of network coding theory and leads the reader through
the antecedents of the network coding theory to the most recent results, considering also …

Algebraic independence is a fundamental notion in commutative algebra that generalizes
independence of linear polynomials. Polynomials {f1,…, fm}⊂ K [x1,…, xn](over a field K) …

The present thesis deals with Gaussian conditional independence structures and their
inference problem. Conditional independence (CI) is a notion from statistics and information …

Newton iteration is an almost 350-year-old recursive formula that approximates a simple root
of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that …

In this article, we present a modern viewpoint on the Gordan algorithm for binary forms. The
symbolic method is recast in terms of SL (2, C) SL (2, C) equivariant homomorphisms. A …

We derive an implicit description of the image of a semialgebraic set under a birational map,
provided that the denominators of the map are positive on the set. For statistical models …

Bourgain and Chang recently showed that any subset of F _p F p of density≫ p− 1/15
contains a nontrivial progression x, x+ y, x+ y 2. We answer a question of theirs by proving …

We give an explicit presentation of the module of differentials of order n of a finitely
generated algebra via a higher-order Jacobian matrix. We use the presentation to study …

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a
simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) …

We show that the presentation of affine T-varieties of complexity one in terms of polyhedral
divisors holds over an arbitrary field. We also describe a class of multigraded algebras over …