Many representative graph neural networks, $ eg $, GPR-GNN and ChebNet, approximate
graph convolutions with graph spectral filters. However, existing work either applies …

Graduate Texts in Mathematics bridge the gap between passive study and creative
understanding, offering graduate-level introductions to advanced topics in mathematics. The …

Many important applications in global optimization, algebra, probability and statistics,
applied mathematics, control theory, financial mathematics, inverse problems, etc. can be …

We consider the problem of minimizing a polynomial over a semialgebraic set defined by
polynomial equations and inequalities, which is NP-hard in general. Hierarchies of …

Moment and polynomial optimization has received high attention in recent decades. It has
beautiful theory and efficient methods, as well as broad applications for various …

A few words on the second edition. By a nice coincidence, Springer's proposal to revise the
book came when I was giving a serious thought to the idea. Ten years have passed and my …

Let R [X]≔ R [x 1,…, xn] and let and Δn denote the simplex {(x1,…, xn)| xi≥ 0,∑ ixi= 1}.
Pólya's Theorem says that if f∈ R [X] is homogeneous and positive on Δn, then for …

Let β≡ β (2n) be an N-dimensional real multi-sequence of degree 2n, with associated
moment matrix 𝓜 (n)≡ 𝓜 (n)(β), and let r:= rank 𝓜 (n). We prove that if 𝓜 (n) is positive …

We consider the generalized problem of moments (GPM) from a computational point of view
and provide a hierarchy of semidefinite programming relaxations whose sequence of …

A bstract We explore the correspondence between geometric function theory (GFT) and
quantum field theory (QFT). The crossing symmetric dispersion relation provides the …