On Functions with a Conjugate

Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a conjugate.Comment: To appear: Annales de l'Institut Fourier, vol. 64 (2014

State and green crimes related to water pollution and ecological disorganization: water pollution from publicly owned treatment works (POTW) facilities across US states

Green criminologists often refer to water pollution as an example of a green crime, but have yet to produce much research on this subject. The current article addresses the need for green criminological analyses of water pollution problems, and draws attention to an overlooked issue: water pollution emissions from state owned public water treatment facilities or POTWs. Legally, POTWs may emit certain quantities and kinds of pollutants to waterways following treatment. This does not mean, however, that those emissions have no adverse ecological or public health impacts, or that those emissions cannot also be employed as examples of green crimes or green-state crimes. Indeed, from the perspective of environmental sociology and ecological Marxism, those emissions generate ecological disorganization. Moreover, POTW emissions contain numerous pollutants that generate different forms of ecological disorganization. The current study uses POTW emissions data drawn from the US EPA’s Discharge Monitoring Report system for 2014 to illustrate the extent of pollution emitted by POTWs in and across US states as one dimension of ecological disorganization. To contextualize the meaning of those data, we review US water pollution regulations, review the health and ecological impacts of chemicals emitted by POTWs, and situate those emissions within green criminological discussions of green crime and green-state crimes

Generalized Direct Sampling for Hierarchical Bayesian Models

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models involving large data sets. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. Additionally, the method can be used to compute marginal likelihoods