The Spectra of Lamplighter Groups and Cayley Machines

We calculate the spectra and spectral measures associated to random walks on restricted wreath products of finite groups with the infinite cyclic group, by calculating the Kesten-von Neumann-Serre spectral measures for the random walks on Schreier graphs of certain groups generated by automata. This generalises the work of Grigorchuk and Zuk on the lamplighter group. In the process we characterise when the usual spectral measure for a group generated by automata coincides with the Kesten-von Neumann-Serre spectral measure.Comment: 36 pages, improved exposition, main results slightly strengthene

On the rational subset problem for groups

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automata subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership.Comment: 19 page

Instability of Supersonic Cold Streams Feeding Galaxies II. Nonlinear Evolution of Surface and Body Modes of Kelvin-Helmholtz Instability

As part of our long-term campaign to understand how cold streams feed massive galaxies at high redshift, we study the Kelvin-Helmholtz instability (KHI) of a supersonic, cold, dense gas stream as it penetrates through a hot, dilute circumgalactic medium (CGM). A linear analysis (Paper I) showed that, for realistic conditions, KHI may produce nonlinear perturbations to the stream during infall. Therefore, we proceed here to study the nonlinear stage of KHI, still limited to a two-dimensional slab with no radiative cooling or gravity. Using analytic models and numerical simulations, we examine stream breakup, deceleration and heating via surface modes and body modes. The relevant parameters are the density contrast between stream and CGM ($\delta$), the Mach number of the stream velocity with respect to the CGM ($M_{\rm b}$) and the stream radius relative to the halo virial radius ($R_{\rm s}/R_{\rm v}$). We find that sufficiently thin streams disintegrate prior to reaching the central galaxy. The condition for breakup ranges from $R_{\rm s} < 0.03 R_{\rm v}$ for $(M_{\rm b} \sim 0.75, \delta \sim 10)$ to $R_{\rm s} < 0.003 R_{\rm v}$ for $(M_{\rm b} \sim 2.25, \delta \sim 100)$. However, due to the large stream inertia, KHI has only a small effect on the stream inflow rate and a small contribution to heating and subsequent Lyman-$\alpha$ cooling emission.Comment: The main astrophysical results are Figure 22 and Figure 23. Final 7 pages are appendices. Accepted to MNRA

Tracking Giving Across Generations

In an article prepared for New Directions for Philanthropic Fundraising, Richard Steinberg and Mark Wilhelm summarize the type of data collected in COPPS and provide at least four areas of fundraising practice that can be improved with knowledge gained about donors from COPPS: targeting, predicting, benchmarking, and persuasion

Religious and Secular Giving, by Race and Ethnicity

In this article, the authors advance the literature on whether apparent differences in the giving and volunteering of black versus white, or Hispanic versus other families, are real. They employ new data, COPPS, that help to determine whether the differences are due to race and ethnicity themselves or a variety of factors that are correlated with these labels

Patterns of Giving in COPPS 2001

Serious researchers of philanthropy have bemoaned the lack of panel datasets for studying giving behavior. That gap is beginning to be filled with the start of the Center on Philanthropy Panel Study (COPPS). COPPS provides the first comprehensive panel study of giving and volunteering in the U.S., and one of the only such studies worldwide to date. Previous U.S. panels studies of giving have employed tax return data, which are limited to gifts of money and property by (in most years) itemizers and include only the financial and limited demographic data reported on those returns

Reduced glycogen availability is associated with increased AMPKα2 activity, nuclear AMPKα2 protein abundance, and GLUT4 mRNA expression in contracting human skeletal muscle

Glycogen availability can influence glucose transporter 4 (GLUT4) expression in skeletal muscle through unknown mechanisms. The multisubstrate enzyme AMP-activated protein kinase (AMPK) has also been shown to play an important role in the regulation of GLUT4 expression in skeletal muscle. During contraction, AMPK [alpha]2 translocates to the nucleus and the activity of this AMPK isoform is enhanced when skeletal muscle glycogen is low. In this study, we investigated if decreased pre-exercise muscle glycogen levels and increased AMPK [alpha]2 activity reduced the association of AMPK with glycogen and increased AMPK [alpha]2 translocation to the nucleus and GLUT4 mRNA expression following exercise. Seven males performed 60 min of exercise at ~70% [VO.sub.2] peak on 2 occasions: either with normal (control) or low (LG) carbohydrate pre-exercise muscle glycogen content. Muscle samples were obtained by needle biopsy before and after exercise. Low muscle glycogen was associated with elevated AMPK [alpha]2 activity and acetyl-CoA carboxylase [beta] phosphorylation, increased translocation of AMPK [alpha]2 to the nucleus, and increased GLUT4 mRNA. Transfection of primary human myotubes with a constitutively active AMPK adenovirus also stimulated GLUT4 mRNA, providing direct evidence of a role of AMPK in regulating GLUT4 expression. We suggest that increased activation of AMPK [alpha]2 under conditions of low muscle glycogen enhances AMPK [alpha]2 nuclear translocation and increases GLUT4 mRNA expression in response to exercise in human skeletal muscle. <br /