Period-magnitude relations for M giants in Baade's Window NGC6522

A large and complete sample of stars with K < 9.75 in the NGC6522 Baade's Window is examined using light curves from MACHO and IJK from DENIS. All 4 of the sequences ABCD in the K vs logP diagram of the LMC are seen in the Bulge. The Bulge sequences however show some differences from the Magellanic Clouds. The sequences may be useful as distance indicators. A new diagram of the frequency of late-type variables is presented. The catalogued SR variables of the solar nbd are found to be a subset of the total of SRs, biased towards large amplitude.Comment: 11 pages 11 fig

Long-term IR Photometry of Seyferts

Long-term (up to 10000d) monitoring has been undertaken for 41 Seyferts in the near-IR (JHKL). All but 2 showed variability, with K ampl in the range <0.1 to > 1.1 mags. The timescale for detectable change is from about one week to a few years. A simple cross-correlation study shows evidence for delays of up to several hundred days between the variations seen at the shortest wavelengths and the longest in many galaxies. In particular, the data for F9 now extend to twice the interval covered earlier and the delay between its UV and IR outputs persists. An analysis of the fluxes shows that, for any given galaxy, the colours of the variable component are usually independent of the level of activity. The state of activity can be parameterized. Taken over the whole sample, the colours of the variable components fall within moderately narrowly defined ranges. In particular, the H-K colour is appropriate to a black body of temperature 1600K. The H-K excess for a heavily reddened nucleus can be determined and used to find E_{B-V}, which can be compared to the values found from the visible region broad line fluxes. Using flux-flux diagrams, the flux within the aperture from the underlying galaxy can often be determined without the need for model surface brightness profiles. In many galaxies it is apparent that here must be an additional constant contribution from warm dust.Comment: Better quality available from ftp://ftp.saao.ac.za/pub/isg/seyf.pd

Generating Anisotropic Collapse and Expansion Solutions of Einstein's Equations

Analytic gravitational collapse and expansion solutions with anisotropic pressure are generated. Metric functions are found by requiring zero heat flow scalar. It emerges that a single function generates the anisotropic solutions. Each generating function contains an arbitrary function of time which can be chosen to fit various astrophysical time profiles. Two examples are provided: a bounded collapse metric and an expanding cosmological solutionComment: to appear in Gen. Rel. Gravi

PREP Workshop Report: Expository Writing

A significant part of the job of a mathematician involves writing - between research papers, expository writing, grant applications, letters of recommendation, and materials for our teaching, I know that I spend much of my days writing something or other. Yet most of us are never really trained to write mathematics, and even in our jobs we rarely find time to talk about the actual writing of the mathematics which has taken place. With this in mind, I chose to attend a PREP workshop held by the Mathematical Association of America at their headquarters in Washington, DC dedicated to the art of mathematical exposition. [excerpt

Critical Groups of Graphs with Dihedral Actions II

In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group Dn, extending earlier work by the author and Criel Merino. In particular, we show that the critical group of such a graph can be decomposed in terms of the critical groups of the quotients of the graph by certain subgroups of the automorphism group. This is analogous to a theorem of Kani and Rosen which decomposes the Jacobians of algebraic curves with a Dn-action

Fair-Weather Fans: The Correlation Between Attendance and Winning Percentage

In Rob Neyer\u27s chapter on San Francisco in his Big Book of Baseball Lineups, he speculates that there aren\u27t really good baseball cities, and that attendance more closely correlates with winning percentage than with any other factor. He also suggests that a statistically minded person look at this. I took the challenge and have been playing with a lot of data

Solving the Debt Crisis on Graphs - Solutions

We begin by noting that solutions to these puzzles are not unique. In particular, doing the `lending\u27 action from each of the vertices once brings us back to where we started. Moreover, the act of doing the `borrowing\u27 action from one vertex is equivalent to doing the`lending\u27 action from each of the other vertices. In particular, without loss of generality one can assume that there is (at least) one vertex for which you do neither action and for all other vertices you do the `lending\u27 action a nonnegative number of times. Below we give possible solutions to four of the puzzles by showing the number of times one lends from each vertex in order to eliminate all debt

Communal Partitions of Integers

There is a well-known formula due to Andrews that counts the number of incongruent triangles with integer sides and a fixed perimeter. In this note, we consider the analagous question counting the number of k-tuples of nonnegative integers none of which is more than 1/(k−1) of the sum of all the integers. We give an explicit function for the generating function which counts these k-tuples in the case where they are ordered, unordered, or partially ordered. Finally, we discuss the application to algebraic geometry which motivated this question

Glioma through the looking GLASS: molecular evolution of diffuse gliomas and the Glioma Longitudinal Analysis Consortium.

Adult diffuse gliomas are a diverse group of brain neoplasms that inflict a high emotional toll on patients and their families. The Cancer Genome Atlas and similar projects have provided a comprehensive understanding of the somatic alterations and molecular subtypes of glioma at diagnosis. However, gliomas undergo significant cellular and molecular evolution during disease progression. We review the current knowledge on the genomic and epigenetic abnormalities in primary tumors and after disease recurrence, highlight the gaps in the literature, and elaborate on the need for a new multi-institutional effort to bridge these knowledge gaps and how the Glioma Longitudinal Analysis Consortium (GLASS) aims to systemically catalog the longitudinal changes in gliomas. The GLASS initiative will provide essential insights into the evolution of glioma toward a lethal phenotype, with the potential to reveal targetable vulnerabilities and, ultimately, improved outcomes for a patient population in need