P-matrices and signed digraphs

We associate a signed digraph with a list of matrices whose dimensions permit them to be multiplied, and whose product is square. Cycles in this graph have a parity, that is, they are either even (termed e-cycles) or odd (termed o-cycles). The absence of e-cycles in the graph is shown to imply that the matrix product is a P0-matrix, i.e., all of its principal minors are nonnegative. Conversely, the presence of an e-cycle is shown to imply that there exists a list of matrices associated with the graph whose product fails to be a P0-matrix. The results generalise a number of previous results relating P- and P0-matrices to graphs

Graph-theoretic conditions for injectivity of functions on rectangular domains

This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and flows. Well-known results on systems with signed Jacobians are shown to be easy corollaries of more general results presented here.Comment: 16 pages, 5 figure

Everyday racism and "my tram experience": emotion, civic performance and learning on YouTube

Does the public expression and performance of shock, distress, anger, frustration and ideological disapproval of particular sorts of politics constitute a form of collective political expression from which individuals can learn about being citizens When it comes to the expression of feelings of racial and other types of prejudice, has political correctness led to a deepening of entrenched racist beliefs with no channel for discussion This article engages with such questions through a case study of YouTube responses to «My Tram Experience» a commuter-uploaded mobile-phone video of a racist diatribe on a tram in the UK. Using qualitative content analysis and thematic analysis, it describes how these performed, networked and distributed moments of citizen angst demonstrate a limited but interesting range of civic engagements with and positionings towards racism, immigration, class and nationalism. For one reason or another these are not allowed to occur in other public for a such as the mainstream media or schools. The article argues that these vlogs are both a wide-ranging potentially therapeutic resource for those needing validation for their racist or anti-racist views, or for those who wish to express and garner solidarity for discomfort and pain caused by racism; they are also a significant though currently uncurated resource for citizenship education both formal and informal because of their engagements with technology, social context, emotional context and political rhetoric