We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufticient statistic. Examples include contingency tables, logistic regression, and spectral… (More)

What do you do to start reading algorithms in invariant theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference… (More)

Of the 18 chapters in the book, we will only cover the 5 listed below and thus allow for a more leisurely pace. There is also some supplementary material in the bibliography to expand upon if needed.… (More)

We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy methods) are… (More)

Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to… (More)

A continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations. We introduce mixed subdivisions of Newton polytopes, and we apply them to… (More)

The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of… (More)