Regina Lectures on Fat Points

These notes are a record of lectures given in the Workshop on Connections Between Algebra and Geometry at the University of Regina, May 29--June 1, 2012. The lectures were meant as an introduction to current research problems related to fat points for an audience that was not expected to have much background in commutative algebra or algebraic geometry (although sections 8 and 9 of these notes demand somewhat more background than earlier sections).Comment: 32 pages, 3 figure

Matroid Configurations and Symbolic Powers of Their Ideals

Star configurations are certain unions of linear subspaces of projective space that have been studied extensively. We develop a framework for studying a substantial generalization, which we call matroid configurations, whose ideals generalize Stanley-Reisner ideals of matroids. Such a matroid configuration is a union of complete intersections of a fixed codimension. Relating these to the Stanley-Reisner ideals of matroids and using methods of liaison theory allows us, in particular, to describe the Hilbert function and minimal generators of the ideal of, what we call, a hypersurface configuration. We also establish that the symbolic powers of the ideal of any matroid configuration are Cohen-Macaulay. As applications, we study ideals coming from certain complete hypergraphs and ideals derived from tetrahedral curves. We also consider Waldschmidt constants and resurgences. In particular, we determine the resurgence of any star configuration and many hypersurface configurations. Previously, the only non-trivial cases for which the resurgence was known were certain monomial ideals and ideals of finite sets of points. Finally, we point out a connection to secant varieties of varieties of reducible forms

The changing UK careers landscape : tidal waves, turbulence and transformation

This article explores how the UK careers landscape in each of the four home nations is changing in response to neo-liberal policies. In this context, careers services are increasingly under pressure to demonstrate their added value, impact and returns on investment. As fiscal arrangements tighten and governments state their preferences and priorities for national careers services, differing strategic responses are beginning to emerge. A quasi-market, experimental approach is now the dominant discourse in England, in contrast to differing and complementary arrangements in Northern Ireland, Scotland and Wales. The article suggests that insofar as these developments are transforming national careers services, they are also creating significant challenges which require new forms of policy imagery and imagination for high-impact, all-age careers services

Sous-groupes alg\'ebriques du groupe de Cremona

We give a complete classification of maximal algebraic subgroups of the Cremona group of the plane and provide algebraic varieties that parametrize the conjugacy classes. ----- Nous donnons une classification compl\`ete des sous-groupes alg\'ebriques maximaux du groupe de Cremona du plan et explicitons les vari\'et\'es qui param\`etrent les classes de conjugaison.Comment: Text in French, Translated introduction, 35 pages, 1 figure, to appear in Transform. Group

Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics

We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of $N$ D-brane probes for both $N \to \infty$ and finite $N$. The techniques are applicable to generic singularities, orbifold, toric, non-toric, complete intersections, et cetera, even to geometries whose precise field theory duals are not yet known. The so-called ``Plethystic Exponential'' provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between gauge theory, algebraic geometry, combinatorics and number theory exhibit themselves in the form of plethystics and syzygies.Comment: 59+1 pages, 7 Figure

Approximate entropy detects the effect of a secondary cognitive task on postural control in healthy young adults: a methodological report

<p>Abstract</p> <p>Background</p> <p>Biomechanical measures of postural stability, while generally useful in neuroscience and physical rehabilitation research, may be limited in their ability to detect more subtle influences of attention on postural control. Approximate entropy (ApEn), a regularity statistic from nonlinear dynamics, recently has demonstrated relatively good measurement precision and shown promise for detecting subtle change in postural control after cerebral concussion. Our purpose was to further explore the responsiveness of ApEn by using it to evaluate the immediate, short-term effect of secondary cognitive task performance on postural control in healthy, young adults.</p> <p>Methods</p> <p>Thirty healthy, young adults performed a modified version of the Sensory Organization Test featuring single (posture only) and dual (posture plus cognitive) task trials. ApEn values, root mean square (RMS) displacement, and equilibrium scores (ES) were calculated from anterior-posterior (AP) and medial-lateral (ML) center of pressure (COP) component time series. For each sensory condition, we compared the ability of the postural control parameters to detect an effect of cognitive task performance.</p> <p>Results</p> <p>COP AP time series generally became more random (higher ApEn value) during dual task performance, resulting in a main effect of cognitive task (p = 0.004). In contrast, there was no significant effect of cognitive task for ApEn values of COP ML time series, RMS displacement (AP or ML) or ES.</p> <p>Conclusion</p> <p>During dual task performance, ApEn revealed a change in the randomness of COP oscillations that occurred in a variety of sensory conditions, independent of changes in the amplitude of COP oscillations. The finding expands current support for the potential of ApEn to detect subtle changes in postural control. Implications for future studies of attention in neuroscience and physical rehabilitation are discussed.</p

In vitro anti-HIV activity of some Indian medicinal plant extracts

Background Human Immunodeficiency Virus (HIV) persists to be a significant public health issue worldwide. The current strategy for the treatment of HIV infection, Highly Active Antiretroviral Therapy (HAART), has reduced deaths from AIDS related disease, but it can be an expensive regime for the underdeveloped and developing countries where the supply of drugs is scarce and often not well tolerated, especially in persons undergoing long term treatment. The present therapy also has limitations of development of multidrug resistance, thus there is a need for the discovery of novel anti-HIV compounds from plants as a potential alternative in combating HIV disease. Methods Ten Indian medicinal plants were tested for entry and replication inhibition against laboratory adapted strains HIV-1IIIB, HIV-1Ada5 and primary isolates HIV-1UG070, HIV-1VB59 in TZM-bl cell lines and primary isolates HIV-1UG070, HIV-1VB59 in PM1 cell lines. The plant extracts were further evaluated for toxicity in HEC-1A epithelial cell lines by transwell epithelial model. Results The methanolic extracts of Achyranthes aspera, Rosa centifolia and aqueous extract of Ficus benghalensis inhibited laboratory adapted HIV-1 strains (IC80 3.6–118 μg/ml) and primary isolates (IC80 4.8–156 μg/ml) in TZM-bl cells. Methanolic extract of Strychnos potatorum, aqueous extract of Ficus infectoria and hydroalcoholic extract of Annona squamosa inhibited laboratory adapted HIV-1 strains (IC80 4.24–125 μg/ml) and primary isolates (IC80 18–156 μg/ml) in TZM-bl cells. Methanolic extracts of Achyranthes aspera and Rosa centifolia, (IC801-9 μg/ml) further significantly inhibited HIV-1 primary isolates in PM1cells. Methanolic extracts of Tridax procumbens, Mallotus philippinensis, Annona reticulate, aqueous extract of Ficus benghalensis and hydroalcoholic extract of Albizzia lebbeck did not exhibit anti-HIV activity in all the tested strains. Methanolic extract of Rosa centifolia also demonstrated to be non-toxic to HEC-1A epithelial cells and maintained epithelial integrity (at 500 μg/ml) when tested in transwell dual-chamber. Conclusion These active methanolic extracts of Achyranthes aspera and Rosa centifolia, could be further subjected to chemical analysis to investigate the active moiety responsible for the anti-HIV activity. Methanolic extract of Rosa centifolia was found to be well tolerated maintaining the epithelial integrity of HEC-1A cells in vitro and thus has potential for investigating it further as candidate microbicide