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

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

A characterization of compact complex tori via automorphism groups

We show that a compact Kaehler manifold X is a complex torus if both the continuous part and discrete part of some automorphism group G of X are infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant fibration. Some applications to dynamics are given.Comment: title changed, to appear in Math. An

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

Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

Contains fulltext : 50308.pdf (publisher's version ) (Closed access)In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control

Virtual patients improve history-taking competence and confidence in medical students

Klark is a novel online medical education tool (www.klark-cases.com) where students take histories from virtual patients with common presentations from multiple specialities. We investigated whether Klark could enhance student confidence and competence in history-taking, and whether students find Klark helpful. A single cohort of first-year clinical medical students had access to Klark for three weeks. At both ends of the trial, participants were asked to complete feedback forms and participate in two mock Objective Structured Clinical Examination (OSCE) history stations. Outcome measures included self-reported confidence and competence in history-taking, performance in OSCE stations, and qualitative user experience data. Seventy participants successfully completed a case on Klark (mean 18.7), of which 63 (90% user retention) completed  ≥ 2 cases. Self-reported competence (p p p p  Klark improved competence and confidence in history-taking. Students found it helpful and chose to continue using the platform. By developing confidence and competence at their own pace in the Klark simulated environment, students can then maximise benefit from in-person clinical opportunities.</p