Invited Talks

The conference features three invited talks by Noriko Arai, David Stoutemyer and Bernd Sturmfels.

Noriko Arai,
National Institute of Informatics, Japan

Mathematics by Machine

Abstract: When David Hilbert began Hilbert's program (formalization of mathematics) in the early 20th century to give the solid foundation of mathematics, he unintentionally introduced the possibility of automatization of mathematics. Theoretically, the possibility was denied by Gödel's incompleteness theorem. However, an interesting question is still open. Is “mediocre mathematics” automizable? We are developing a system that solves a wide range of math problems written in natural language as a part of Todai Robot Project, an AI challenge to pass the university entrance examination. We report the overview and the progress of our project, and the theoretical and methodological difficulties to overcome.

David Stoutemyer,
University of Hawaii, USA

Fuzzy simplification of non-numeric expressions containing some numeric intervals and/or floating point numbers

Abstract: This article describes a Mathematica package that improves simplification of general non-numeric expressions containing any mixture of Gaussian rational numbers, symbolic constants, machine and arbitrary-precision floating-point numbers, together with intervals having any mixture of such endpoints. Such generalized numbers are not automatically all converted to floats or to intervals. Expressions can be multivariate and non-polynomial. Techniques include:

  • Recognition and unification of approximately similar and approximately proportional factors and terms.
  • The option of infinity-norm normalization that is more robust than monic normalization.
  • The option of a unit-normal quasi-primitive normalization that uses large rational approximate common divisors of mixed number types and intervals to nicely normalize sums.
  • A polynomial division algorithm tolerant of terms with coefficients that are float zeros or intervals containing 0.
  • The ability to round or underflow negligible terms while satisfying the inclusion property of interval arithmetic.
The package and a more detailed preprint of the ISSAC 2014 article will be posted at

Bernd Sturmfels,
University of California Berkeley, USA

Maximum Likelihood for Matrices with Rank Constraints

Abstract: Maximum likelihood estimation is a fundamental computational task in statistics. We address this problem for manifolds of low rank matrices. These represent mixtures of independent distributions of two discrete random variables. This non-convex optimization problems lead to some beautiful geometry, topology, and combinatorics. We discuss methods for finding the global maximum of the likelihood function, we present a duality theorem due to Draisma and Rodriguez, and we share recent work with Kubkas and Robeva concerning nonnegative rank and the EM algorithm.