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Abstract: The concept of the “risk environment” – defined as the “space … [where] factors exogenous to the individual interact to increase the chances of HIV transmission” – draws together the disciplines of public health and geography. Researchers have increasingly turned to geographic methods to quantify dimensions of the risk environment that are both structural and spatial (e.g., local poverty rates). The scientific power of the intersection between public health and geography, however, has yet to be fully mined. In particular, research on the risk environment has rarely applied geographic methods to create neighbourhood-based measures of syringe exchange programmes (SEPs) or of drug-related law enforcement activities, despite the fact that these interventions are widely conceptualized as structural and spatial in nature and are two of the most well-established dimensions of the risk environment. To strengthen research on the risk environment, this paper presents a way of using geographic methods to create neighbourhood-based measures of (1) access to SEP sites and (2) exposure to drug-related arrests, and then applies these methods to one setting (New York City [NYC]). NYC-based results identified substantial cross-neighbourhood variation in SEP site access and in exposure to drug-related arrest rates (even within the subset of neighbourhoods nominally experiencing the same drug-related police strategy). These geographic measures – grounded as they are in conceptualizations of SEPs and drug-related law enforcement strategies – can help develop new arenas of inquiry regarding the impact of these two dimensions of the risk environment on injectors’ health, including exploring whether and how neighbourhood-level access to SEP sites and exposure to drug-related arrests shape a range of outcomes among local injectors. [Copyright &y& Elsevier]

Abstract: We give necessary and sufficient conditions on a row-finite graph so that the Leavitt path algebra is purely infinite simple. This result provides the algebraic analog to the corresponding result for the Cuntz–Krieger -algebra given in [T. Bates, D. Pask, I. Raeburn, W. Szymański, The -algebras of row-finite graphs, New York J. Math. 6 (2000) 307–324]. [Copyright &y& Elsevier]