Pretrial Detention in the Ninth Circuit

In 1992, the Judicial Conference of the United States ( JCUS ) adopted a resolution encouraging the examination of bias based on race, ethnicity, gender, age and disability in the federal judiciary. The Ninth Circuit responded to the JCUS resolution with a study of gender bias, completed in 1993.2 Subsequently, the Ninth Circuit Judicial Conference authorized a second study, establishing the Task Force on Racial, Religious, and Ethnic Fairness in 1993.\u27 This study of pretrial detention in the Ninth Circuit was undertaken as part of the research commissioned by the Task Force

A natural stochastic extension of the sandpile model on a graph

We introduce a new model of a stochastic sandpile on a graph $G$ containing a sink. When unstable, a site sends one grain to each of its neighbours independently with probability $p \in (0,1]$. For $p=1$, this coincides with the standard Abelian sandpile model. In general, for $p\in(0,1)$, the set of recurrent configurations of this sandpile model is different from that of the Abelian sandpile model. We give a characterisation of this set in terms of orientations of the graph $G$. We also define the lacking polynomial $L_G$ as the generating function counting this set according to the number of grains, and show that this polynomial satisfies a recurrence which resembles that of the Tutte polynomial