Monomer-dimer tatami tilings of square regions

We prove that the number of monomer-dimer tilings of an $n\times n$ square grid, with $m<n$ monomers in which no four tiles meet at any point is $m2^m+(m+1)2^{m+1}$, when $m$ and $n$ have the same parity. In addition, we present a new proof of the result that there are $n2^{n-1}$ such tilings with $n$ monomers, which divides the tilings into $n$ classes of size $2^{n-1}$. The sum of these tilings over all monomer counts has the closed form $2^{n-1}(3n-4)+2$ and, curiously, this is equal to the sum of the squares of all parts in all compositions of $n$. We also describe two algorithms and a Gray code ordering for generating the $n2^{n-1}$ tilings with $n$ monomers, which are both based on our new proof.Comment: Expanded conference proceedings: A. Erickson, M. Schurch, Enumerating tatami mat arrangements of square grids, in: 22nd International Workshop on Combinatorial Al- gorithms (IWOCA), volume 7056 of Lecture Notes in Computer Science (LNCS), Springer Berlin / Heidelberg, 2011, p. 12 pages. More on Tatami tilings at http://alejandroerickson.com/joomla/tatami-blog/collected-resource

The impact of accretion disk winds on the X-ray spectrum of AGN: Part 1 - XSCORT

(abridged) The accretion disk in AGN is expected to produce strong outflows, in particular a UV-line driven wind. Despite providing a good fit to the data, current spectral models of the X-ray spectrum of AGN observed through an accretion disk wind are ad-hoc in their treatment of the properties of the wind material. In order to address these limitations we adopt a numerical computation method that links a series of radiative transfer calculations, incorporating the effect of a global velocity field in a self-consistent manner (XSCORT). We present a series of example spectra from the XSCORT code that allow us to examine the shape of AGN X-ray spectra seen through a wind, for a range of velocity and density distributions, total column densities and initial ionization parameters. These detailed spectral models clearly show considerable complexity and structure that is strongly affected by all these factors. The presence of sharp features in the XSCORT spectra contrasts strongly with both the previous models and with the smooth nature of the observed X-ray spectra of AGN with soft X-ray excesses, demonstrating that accretion disk winds are unlikely to be the origin of this mysterious spectral feature. The most significant parameter affecting the presence of the sharp features in the models is the terminal velocity of the wind. Increasing the terminal velocity of the absorbing material to ~c, and hence dramatically increasing the velocity dispersion across the wind, could potentially remove these features resulting in a spectrum similar to the previous models. Such a fast moving outflow cannot be associated with a radiatively driven accretion disk wind, however the presence of a highly relativistic jet may provide an origin for such material.Comment: 14 pages, 9 figures (colour), Accepted for publication in MNRAS (13th Aug 2007). Several significant changes to the text from v

Glückliche Fügung: Experiments' Potential to Integrate Disciplines

This essay reviews the discipline-connecting potential of experimentation. Two examples are used to illustrate how researchers in the first half of the twentieth century profitably combined resources from different disciplines in their experiments. These experiments were designed to test mechanism models describing chemical processes underlying the behavior of biological systems. The researchers had clear expectations about how certain interventions should affect the behavior of the organisms studied, if that behavior was indeed based on the presumed chemical processes. They manipulated the organisms in the relevant ways and determined how the behavior of the organisms changed as a result

Botulinumtoxin bei nichtneurogenen Blasenfunktionsstörungen

Zusammenfassung: Die nichtneurogene überaktive Harnblase mit oder ohne Detrusorüberaktivität und/oder Inkontinenz ist ein belastendes Symptom für viele Menschen, das bis vor wenigen Jahren nur mit anticholinergen Medikamenten oder operativ behandelt werden konnte. Intradetrusorinjektionen mit BotulinumtoxinTypA stellen eine minimal-invasive Alternative für Patienten dar, die auf Anticholinergika nicht ansprechen oder diese nicht vertragen. Dieser Übersichtsartikel fasst die relevanten Arbeiten der letzten 6Jahre zu diesem Thema zusammen und gibt Auskunft über die Wirksamkeit, die Nebenwirkungen, die verwendeten Dosierungen und Injektionstechniken. Insgesamt zeigte sich eine gute initiale Wirksamkeit, die etwa ab dem 4. Tag nach Injektion beginnt und durchschnittlich bis zu 31Wochen anhalten kann. Es ist allerdings je nach Dosis mit einer Erhöhung der Restharnmengen zu rechnen, die auch die Anwendung von intermittierendem Selbstkatheterismus notwendig machen können. Die Anwendung von Botulinumtoxin in der Harnblase ist noch immer keine offiziell zugelassene Therapi

OnabotulinumtoxinA and multiple sclerosis.

Lower urinary tract dysfunction is present in two of three patients with multiple sclerosis five years after the diagnosis. Most frequent symptoms are related to neurogenic detrusor overactivity, often associated with detrusor-sphincter dyssynergia. From the end of the 1990s, there is growing evidence that neurogenic detrusor overactivity can be effectively managed by intradetrusorial injections of botulinum toxin type A. This treatment has shown, in different randomised placebo-controlled trials, to be safe and effective on clinical and urodynamic parameters with significant improvement in quality of life. The median duration of effect is in mean nine months. The vast majority of studies have been conducted with onabotulinumtoxinA. The dose of onabotulinumtoxinA commonly used to treat neurogenic detrusor overactivity in patients with multiple sclerosis is 200 UI, even if in selected patients lower doses can be preferred. To be considered eligible for treatment, all patients should accept and be instructed to perform clean intermittent self-catheterisation, since the risk of increased post-void residual volume and/or urinary retention after injection is high, especially with 200 UI of onabotulinumtoxinA. However, quality of life and patient satisfaction seem not to be affected by the need of intermittent catheterisation. The risk of urinary infection after the procedure is to be kept in mind, mainly in patients with multiple sclerosis, so that adequate antibiotic prophylaxis is highly recommended

Orbital Period Determinations for Four SMC Be/X-ray Binaries

We present an optical and X-ray study of four Be/X-ray binaries located in the Small Magellanic Cloud (SMC). OGLE I-band data of up to 11 years of semi-continuous monitoring has been analysed for SMC X-2, SXP172 and SXP202B, providing both a measurement of the orbital period (Porb = 18.62, 68.90, and 229.9 days for the pulsars respectively) and a detailed optical orbital profile for each pulsar. For SXP172 this has allowed a direct comparison of the optical and X-ray emission seen through regular RXTE monitoring, revealing that the X-ray outbursts precede the optical by around 7 days. Recent X-ray studies by XMM-Newton have identified a new source in the vicinity of SXP15.3 raising doubt on the identification of the optical counterpart to this X-ray pulsar. Here we present a discussion of the observations that led to the proposal of the original counterpart and a detailed optical analysis of the counterpart to the new X-ray source, identifying a 21.7 d periodicity in the OGLE I-band data. The optical characteristics of this star are consistent with that of a SMC Be/X-ray binary. However, this star was rejected as the counterpart to SXP15.3 in previous studies due to the lack of H{\alpha} emission.Comment: Accepted for publication in MNRAS, 11 pages, 17 figure

Relativistic iron K X-ray Reverberation in NGC 4151

Recent X-ray observations have enabled the study of reverberation delays in AGN for the first time. All the detections so far are in sources with a strong soft excess, and the measured delay is between the hard (1-3 keV) direct continuum and the soft excess (0.5-1 keV), interpreted as the reflection continuum smeared by relativistic effects. There is however an inherent ambiguity in identifying and studying the details of the lines in the soft excess. Here we report the first detection of reverberation in the iron K band in any AGN. Using XMM-Newton observations of NGC 4151, we find delays of order 2000 s on time-scales of 10e5 s between the 5-6 keV band and 2-3 and 7-8 keV bands, with a broad lag profile resembling a relativistically-broadened iron line. The peak of the lag spectra shifts to lower energies at higher frequencies, consistent with the red wing of the line being emitted at smaller radii, as expected from reflection off the inner accretion disk. This is a first detection of a broad iron line using timing studies.Comment: final version, corrected small typo