Permanents, Pfaffian orientations, and even directed circuits

Given a 0-1 square matrix A, when can some of the 1's be changed to -1's in such a way that the permanent of A equals the determinant of the modified matrix? When does a real square matrix have the property that every real matrix with the same sign pattern (that is, the corresponding entries either have the same sign or are both zero) is nonsingular? When is a hypergraph with n vertices and n hyperedges minimally nonbipartite? When does a bipartite graph have a "Pfaffian orientation"? Given a digraph, does it have no directed circuit of even length? Given a digraph, does it have a subdivision with no even directed circuit? It is known that all of the above problems are equivalent. We prove a structural characterization of the feasible instances, which implies a polynomial-time algorithm to solve all of the above problems. The structural characterization says, roughly speaking, that a bipartite graph has a Pfaffian orientation if and only if it can be obtained by piecing together (in a specified way) planar bipartite graphs and one sporadic nonplanar bipartite graph.Comment: 47 pages, published versio

A shorter proof of the path-width theorem

A graph has {\em path-width} at most $w$ if it can be built from a sequence of graphs each with at most $w+1$ vertices, by overlapping consecutive terms. Every graph with path-width at least $w-1$ contains every $w$-vertex forest as a minor: this was originally proved by Bienstock, Robertson, Thomas and the author, and was given a short proof by Diestel. Here we give a proof even shorter and simpler than that of Diestel

Biological suppression of root-lesion nematodes in grain-growing soils

Root-lesion nematodes (RLNs) are found on 75% of grain farms in southern Queensland (QLD) and northern New South Wales (NSW) and are significant pests. This project confirmed that biological suppression of RLNs occurs in soils, examined what organisms are involved and how growers might enhance suppressiveness of soils. Field trials, and glasshouse and laboratory bioassays of soils from fields with contrasting management practices, showed suppressiveness is favoured with less tillage, more stubble and continuous intensive cropping, particularly in the top 15cm of soil. Through extensive surveys key organisms, Pasteuria bacteria, nematode-trapping fungi and predatory nematodes were isolated and identified as being present

Say It Again: A Case Study on Improving Communication in an Autistic Adolescent

Diagnoses of autism spectrum disorder (ASD) have increased significantly in recent years, necessitating a deeper understanding of its symptoms and how to improve on the resulting deficits in communication and social skills. This study examined the possibility of improving the communication of a thirteen-year-old boy with ASD. Within eight sessions, several methods of improving communication were tested, including using a computer to type messages, using pictures to guide conversations, and using simple, open-ended questions. Despite predictions that his communication would improve with the help of focused efforts to communicate and the implementation of these strategies, the participant’s communication skills did not demonstrate much change over the course of the study. However, some methods were found to be more effective in encouraging him to communicate. This study adds to the available data on how autistic individuals communicate and provides information on which methods are more effective for improving the communication of adolescents with ASD