Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin

Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website

A Systematic Review of Non-Invasive Pharmacologic Neuroprotective Treatments for Acute Spinal Cord Injury

An increasing number of therapies for spinal cord injury (SCI) are emerging from the laboratory and seeking translation into human clinical trials. Many of these are administered as soon as possible after injury with the hope of attenuating secondary damage and maximizing the extent of spared neurologic tissue. In this article, we systematically review the available pre-clinical research on such neuroprotective therapies that are administered in a non-invasive manner for acute SCI. Specifically, we review treatments that have a relatively high potential for translation due to the fact that they are already used in human clinical applications, or are available in a form that could be administered to humans. These include: erythropoietin, NSAIDs, anti-CD11d antibodies, minocycline, progesterone, estrogen, magnesium, riluzole, polyethylene glycol, atorvastatin, inosine, and pioglitazone. The literature was systematically reviewed to examine studies in which an in-vivo animal model was utilized to assess the efficacy of the therapy in a traumatic SCI paradigm. Using these criteria, 122 studies were identified and reviewed in detail. Wide variations exist in the animal species, injury models, and experimental designs reported in the pre-clinical literature on the therapies reviewed. The review highlights the extent of investigation that has occurred in these specific therapies, and points out gaps in our knowledge that would be potentially valuable prior to human translation