Reflections on the Impact of Devolution in California

Provides a definition of devolution, an overview of the context of recent policy changes, a review of recent policy changes, an overview of significant upcoming policy debates, and a discussion of the implications of devolution for California

Passage of L\'evy Processes across Power Law Boundaries at Small Times

We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow 0}|X_t|/t^{\kappa}$, $\limsup_{t\downarrow 0}X_t/t^{\kappa}$ and/or $\liminf_{t\downarrow 0}X_t/t^{\kappa}$ are almost surely (a.s.) finite or infinite. Necessary and sufficient conditions are given for these possibilities for all values of $\kappa>0$. Often (for many values of $\kappa$), when the limsups are finite a.s., they are in fact zero, as we show, but the limsups may in some circumstances take finite, nonzero, values, a.s. In general, the process crosses one or two-sided boundaries in quite different ways, but surprisingly this is not so for the case $\kappa=1/2$. An integral test is given to distinguish the possibilities in that case. Some results relating to other norming sequences for $X$, and when $X$ is centered at a nonstochastic function, are also given

Passage of Lévy Processes across Power Law Boundaries at Small Times

We wish to characterize when a Lévy process Xt crosses boundaries like tκ, κ > 0, in a one- or two-sided sense, for small times t; thus, we inquire when lim.supt↓0 |Xt|/tκ, lim supt↓0, Xt/tκ and/or lim inft↓0 Xt/tκ are almost surely (a.s.) finite or infinite. Necessary and sufficient conditions are given for these possibilities for all values of κ > 0. This completes and extends a line of research, going back to Blumenthal and Getoor in the 1960s. Often (for many values of κ), when the lim sups are finite a.s., they are in fact zero, but the lim sups may in some circumstances take finite, nonzero, values, a.s. In general, the process crosses one- or two-sided boundaries in quite different ways, but surprisingly this is not so for the case κ = 1/2, where a new kind of analogue of an iterated logarithm law with a square root boundary is derived. An integral test is given to distinguish the possibilities in that case.Supported in part by ARC Grants DP0210572 and DP0664603

Every plane graph of maximum degree 8 has an edge-face 9-colouring

An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \cup F$ such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree $\Delta\ge10$ can be edge-face coloured with $\Delta+1$ colours. Borodin's bound was recently extended to the case where $\Delta=9$. In this paper, we extend it to the case $\Delta=8$.Comment: 29 pages, 1 figure; v2 corrects a contraction error in v1; to appear in SIDM

Child Witness Policy: Law Interfacing with Social Science

The number of children testifying in court has posed serious practical and legal problems for the judicial system. One problem confronting the courts is how to protect children from experiencing the psychological trauma resulting from face-to-face confrontation with a defendant who may have physically harmed the child or threatened future harm to the child