A classification of primitive permutation groups with finite stabilizers

We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.Comment: Accepted in J. Algebra. Various changes, some due to the author, some due to suggestions from readers and others due to the comments of anonymous referee

Microbial risk assessment for recreational use of the Kranji Reservoir, Singapore

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2009.Includes bibliographical references (leaves 69-72).The Public Utilities Board of Singapore is responsible for management of the Kranji drinking water reservoir and wishes to open the reservoir for recreational water use as part of their "Active, Beautiful, and Clean Waters Programme". A field campaign was conducted at the Kranji Reservoir to determine the microbial water and sediment quality of the reservoir for use in a model that predicts the risk of gastrointestinal illness due to recreational use of the reservoir. Water samples were collected at seven locations throughout the reservoir and sediment samples were collected at two locations located near the shore. The samples were then analyzed for Enterococci concentrations using a most probable number method. The measured geometric mean concentrations found during the field campaign were 13.3 Enterococci colony forming units (CFU) per 100 ml water and 1400 Enterococci CFU per gram sediment. Based on the strengths and weaknesses of available statistics-based risk models, a model by Wiedenmann was chosen based on the flexibility of the model and the quality of the underlying epidemiological study. Using the model, no-observed-adverse-effect-level guideline concentrations of 25 Enterococci CFU per 100 ml for swimming, 51 Enterococci CFU per 100 ml for kayaking and 860 Enterococci CFU per gram sediment for wading were calculated. Based on all available bacterial measurements of the Kranji Reservoir, an interim geometric mean guideline of 25 Enterococci CFU per 100 ml water and 860 Enterococci CFU per gram sediment is suggested.(cont.) Single-sample maximums for a monitoring program should be set to 96 Enterococci CFU per 100 ml water and 2,500 Enterococci CFU per gram sediment. These guidelines should be applied to the area of the reservoir open to recreation, which should be restricted to the northern main section of the reservoir. Entry and exit from the reservoir and wading should be restricted to a smaller area of shoreline until more sediment samples are taken to determine safe entry and exit areas. Final geometric mean and single-sample maximum guidelines should be based on a study of the pathogen-to-indicator-bacteria ratios in the Kranji Reservoir.by Cameron Chaffee Dixon.M.Eng

Effects of Trichinella Soluble Antigens on Macrophage Subpopulations

The immunomodulatory effects of Trichinella spiralis or Trichinella pseudospiralis soluble antigen extracts were examined in an effort to characterize the differences in immune responses seen during these Trichinella infections. The newborn larvae extracts of either parasite exhibited similar potency for stimulating macrophage PGE production; however, the muscle larvae extracts of T. pseudospiralis stimulated greater levels of PGE than did the muscle larvae extracts of T. spiralis. These data clearly indicate that Trichinella antigens possess immunomodulatory capabilities

Vasa Nervorum in rat major pelvic ganglion are innervated by nitrergic nerve fibers

INTRODUCTION The vasa nervorum comprises a network of small diameter blood vessels that provide blood supply to nerves and ganglia. The cell bodies of autonomic nerves innervating the urogenital organs are housed in the major pelvic ganglia (MPG) in rats. The vasa nervorum of rat MPG have not been characterized previously, and it is not known whether these blood vessels are innervated by neuronal nitric oxide synthase (nNOS) containing nitrergic nerves. AIM To characterize the blood vessels in and around the rat MPG and to assess their nitrergic innervation. MAIN OUTCOME MEASURES Characterization of small blood vessels in and around the rat MPG and expression of nNOS in nerve fibers around those blood vessels. METHODS MPG were obtained from healthy Sprague Dawley rats, fixed in paraformaldehyde, frozen and sectioned using a cryostat. The blood vessels and their nitrergic innervation were assessed with immunohistochemistry using antibodies against alpha-smooth muscle actin (smooth muscle marker), CD31 (endothelial marker), collagen IV (basal membrane marker) and nNOS. The immunofluorescence was imaged using a laser scanning confocal microscope. RESULTS The neuronal cell bodies were contained within a capsule in the MPG. Blood vessels were observed within the capsule of the MPG as well as outside the capsule. The blood vessels inside the capsule were CD31-positive capillaries with no smooth muscle staining. Outside the capsule capillaries, arterioles and venules were observed. The extra-capsular arterioles and venules, but not the capillaries were innervated by nNOS-positive nerve fibers. CONCLUSIONS This study, to our knowledge, is the first to demonstrate the blood vessel distribution pattern and their nitrergic innervation in the rat MPG. While similar studies in human pelvic plexus are warranted, these results suggest that the blood flow in the MPG may be regulated by nitrergic nerve fibers and reveal a reciprocal relationship between nerves and blood vessels. Beetson KA, Smith SF, Muneer A, Cameron NE, Cotter MA, and Cellek S. Vasa nervorum in rat major pelvic ganglion are innervated by nitrergic nerve fibers. J Sex Med **;**:**-**

Collineation group as a subgroup of the symmetric group

Let $\Psi$ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension $\ge 3$ over a field. Let $H$ be a closed (in the pointwise convergence topology) subgroup of the permutation group $\mathfrak{S}_{\Psi}$ of the set $\Psi$. Suppose that $H$ contains the projective group and an arbitrary self-bijection of $\Psi$ transforming a triple of collinear points to a non-collinear triple. It is well-known from \cite{KantorMcDonough} that if $\Psi$ is finite then $H$ contains the alternating subgroup $\mathfrak{A}_{\Psi}$ of $\mathfrak{S}_{\Psi}$. We show in Theorem \ref{density} below that $H=\mathfrak{S}_{\Psi}$, if $\Psi$ is infinite.Comment: 9 page

Steiner t-designs for large t

One of the most central and long-standing open questions in combinatorial design theory concerns the existence of Steiner t-designs for large values of t. Although in his classical 1987 paper, L. Teirlinck has shown that non-trivial t-designs exist for all values of t, no non-trivial Steiner t-design with t > 5 has been constructed until now. Understandingly, the case t = 6 has received considerable attention. There has been recent progress concerning the existence of highly symmetric Steiner 6-designs: It is shown in [M. Huber, J. Algebr. Comb. 26 (2007), pp. 453-476] that no non-trivial flag-transitive Steiner 6-design can exist. In this paper, we announce that essentially also no block-transitive Steiner 6-design can exist.Comment: 9 pages; to appear in: Mathematical Methods in Computer Science 2008, ed. by J.Calmet, W.Geiselmann, J.Mueller-Quade, Springer Lecture Notes in Computer Scienc

Tidal evolution of close-in giant planets : Evidence of Type II migration?

It is well accepted that 'hot Jupiters' did not form in situ, as the temperature in the protoplanetary disc at the radius at which they now orbit would have been too high for planet formation to have occurred. These planets, instead, form at larger radii and then move into the region in which they now orbit. The exact process that leads to the formation of these close-in planets is, however, unclear and it seems that there may be more than one mechanism that can produce these short-period systems. Dynamical interactions in multiple-planet systems can scatter planets into highly eccentric orbits which, if the pericentre is sufficiently close to the parent star, can be tidally circularised by tidal interactions between the planet and star. Furthermore, systems with distant planetary or stellar companions can undergo Kozai cycles which can result in a planet orbiting very close to its parent star. However, the most developed model for the origin of short period planets is one in which the planet exchanges angular momentum with the surrounding protoplanetary disc and spirals in towards the central star. In the case of 'hot Jupiters', the planet is expected to open a gap in the disc and migrate through Type II .migration. If this is the dominant mechanism for producing `hot Jupiters' then we would expect the currect properties of observed close-in giant planets to be consistent with an initial population resulting from Type II migration followed by evolution due to tidal interactions with the central star. We consider initial distributions that are consistent with Type II migration and find that after tidal evolution, the final distributions can be consistent with that observed. Our results suggest that a modest initial pile-up at a ~ 0.05 au is required and that the initial eccentricity distribution must peak at e \sim 0.Comment: 10 pages, 15 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ