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- Grigoriy Blekherman, Reinhard C. Laubenbacher, +5 authors Vladimir Shulaev
- Metabolomics
- 2010

It is well known that significant metabolic change take place as cells are transformed from normal to malignant. This review focuses on the use of different bioinformatics tools in cancerâ€¦ (More)

We investigate the quantitative relationship between nonnegative polynomials and sums of squares of polynomials. We show that if the degree is fixed and the number of variables grows then there areâ€¦ (More)

A real polynomial in n variables is called nonnegative if it is greater than or equal to 0 at all points in R. It is a central question in real algebraic geometry whether a nonnegative polynomial canâ€¦ (More)

We study metric properties of convex bodies B and their polars B, where B is the convex hull of an orbit under the action of a compact group G. Examples include the Traveling Salesman Polytope inâ€¦ (More)

We study dimensions of the faces of the cone of nonnegative polynomials and the cone of sums of squares; we show that there are dimensional differences between corresponding faces of these cones.â€¦ (More)

An orbitope is the convex hull of an orbit of a point under the action of a compact group. We derive bounds on volumes of sections of polar bodies of orbitopes, extending methods developed in [BB03].â€¦ (More)

- Franziska Hinkelmann, Madison Brandon, +4 authors Reinhard C. Laubenbacher
- BMC Bioinformatics
- 2011

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding ofâ€¦ (More)

- Grigoriy Blekherman
- Discrete & Computational Geometry
- 2004

We study metric properties of the cone of homogeneous non-negative multivariate polynomials and the cone of sums of powers of linear forms, and the relationship between the two cones. We compute theâ€¦ (More)

- Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, Achill SchÃ¼rmann
- Experimental Mathematics
- 2009

In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optimaâ€¦ (More)

We study the geometry underlying the difference between nonnegative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quarticsâ€¦ (More)