Toric algebra of hypergraphs

The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their generators in terms of balanced walks on hypergraphs. Our results generalize those for the defining ideals of edge subrings of graphs, which are well-known in the commutative algebra community, and popular in the algebraic statistics community. One of the motivations for studying toric ideals of hypergraphs comes from algebraic statistics, where generators of the toric ideal give a basis for random walks on fibers of the statistical model specified by the hypergraph. Further, understanding the structure of the generators gives insight into the model geometry.Comment: Section 3 is new: it explains connections to log-linear models in algebraic statistics and to combinatorial discrepancy. Section 6 (open problems) has been moderately revise

Control strategies for a telerobot

One of the major issues impacting the utility of telerobotic systems for space is the development of effective control strategies. For near-term applications, telerobot control is likely to utilize teleoperation methodologies with integrated supervisory control capabilities to assist the operator. Two different approaches to telerobotic control are evaluated: bilateral force reflecting master controllers and proportional rate six degrees-of-freedom hand controllers. The controllers' performance of single manipulator arm tasks is compared. Simultaneous operation of both manipulator arms and complex multiaxis slave arm movements is investigated. Task times are significantly longer and fewer errors are committed with the hand controllers. The hand controllers are also rated significantly higher in cognitive and manual control workload on the two-arm task. The master controllers are rated significantly higher in physical workload. The implications of these findings for space teleoperations and higher levels of control are discussed

Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces

This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large-scale polynomial systems and finding small generating sets of graded ideals. The cornerstone of our work is showing that the theory of violator spaces of G\"artner et al.\ applies to polynomial ideal problems. To show this, one utilizes a Helly-type result for algebraic varieties. The resulting algorithms have expected runtime linear in the number of input polynomials, making the ideas interesting for handling systems with very large numbers of polynomials, but whose rank in the vector space of polynomials is small (e.g., when the number of variables and degree is constant).Comment: Minor edits, added two references; results unchange

From Pyscho to YouTube: how a generation lost the ability to be shocked (guest blog)

Thanks to the internet, digital technology and ‘citizen journalism’ the public can see a range of images and video footage unimaginable just 10 or 20 years ago. Some of this footage is shocking, haunting and desensitizing to a vast extent. Is it part of a wider trend towards a cultural loss of feeling? Polis Summer School student Stasi Georgieva reports