presents a series of informal talks o " Mathematics is the process of turning coffee into theorems " –Paul Erdös inference, e.g. hypothesis testing, has been used to examine new therapeutic drugs. In the use of Bayesian analysis to enhance inference. will talk about va assigned to the concept of "straightness" so that it will be meaningful on curved surfac… (More)
The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relax-ations. In this paper, we characterize Gomory… (More)
This paper concerns the associated primes and primary decompositions of the monomial initial ideals of lattice ideals. For a xed initial ideal, we show that the multiplicities of its associated primes and its arithmetic degree are the cardinalities of sets of polytopes in which the origin is the unique lattice point. The associated primes are shown to… (More)
We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible decomposition of monomial ideals. The gap can be computed in polynomial time when the dimension is fixed.
The purpose of this exposition 1 is to give a simple treatment of Knutson and Tao's recent proof of the saturation conjecture . A finite dimensional irreducible polynomial representation of GL n (C) is determined by its highest weight, which is a weakly decreasing sequence of n non-negative integers, also called a partition [5, §8]. The irreducible… (More)
Given a model in algebraic statistics and data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying the local maxima in the probability simplex. Applications include models specified by rank conditions on matrices and the… (More)
We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist of elements of Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We… (More)