The Adapted Ordering Method for Lie Algebras and Superalgebras and their Generalizations

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows: to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the Adapted Ordering Method for general Lie algebras and superalgebras, and their generalizations, provided they can be triangulated. We also review briefly the results obtained for the Virasoro algebra and for the N=2 and Ramond N=1 superconformal algebras.Comment: Many improvements in the redaction for pedagogical purposes. Latex, 11 page

Stochastic evolutions in superspace and superconformal field theory

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N=1 superspace with links to superconformal field theory and singular vectors of the N=1 superconformal algebra in the Neveu-Schwarz sector.Comment: 13 pages, LaTe

Superconformal Primary Fields on a Graded Riemann Sphere

Primary superfields for a two dimensional Euclidean superconformal field theory are constructed as sections of a sheaf over a graded Riemann sphere. The construction is then applied to the N=3 Neveu-Schwarz case. Various quantities in the N=3 theory are calculated and discussed, such as formal elements of the super-Mobius group, and the two-point function.Comment: LaTeX2e, 23 pages; fixed typos, sorted references, modified definition of primary superfield on page

Analytic Expressions for Singular Vectors of the N=2N=2 Superconformal Algebra

Using explicit expressions for a class of singular vectors of the $N=2$ (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent neutral singular vectors at the same grade. We construct this two dimensional space and we identify the singular vectors of the original Verma modules. We show that in some Verma modules these expressions lead to two linearly independent singular vectors which are at the same grade and have the same charge.Comment: 35 pages, LATE

An Introduction to Conformal Field Theory

A comprehensive introduction to two-dimensional conformal field theory is given.Comment: 69 pages, LaTeX; references adde

On the complete classification of the unitary N=2 minimal superconformal field theories

Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate of a partition function for such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments.Comment: 53 pages; Latex; minor changes in v2: intro expanded, references added, typos corrected, footnote added on p31; renumbering of sections; main theorem reformulated for clarity, but contents unchanged. Minor revisions in v3: typos corrected, footnotes 5, 6 added, lemma 1 and section 3.3.2 rewritten for greater generality, section 3.3 review removed. To appear in Comm. Math. Phy

A psycho-Geoinformatics approach for investigating older adults’ driving behaviours and underlying cognitive mechanisms

Introduction: Safe driving constantly challenges the driver’s ability to respond to the dynamic traffic scene under space and time constraints. It is of particular importance for older drivers to perform sufficient visual and motor actions with effective coordination due to the fact of age-related cognitive decline. However, few studies have been able to integrate drivers’ visual-motor behaviours with environmental information in a spatial-temporal context and link to the cognitive conditions of individual drivers. Little is known about the mechanisms that underpin the deterioration in visual-motor coordination of older drivers. Development: Based on a review of driving-related cognitive decline in older adults and the context of driver-vehicle-environment interactions, this paper established a conceptual framework to identify the parameters of driver’s visual and motor behaviour, and reveal the cognitive process from visual search to vehicle control in driving. The framework led to a psycho-geoinformatics approach to measure older drivers’ driving behaviours and investigate the underlying cognitive mechanisms. The proposed data collection protocol and the analysis and assessments depicted the psycho-geoinformatics approach on obtaining quantified variables and the key means of analysis, as well as outcome measures. Conclusions: Recordings of the driver and their interactions with the vehicle and environment at a detailed scale give a closer assessment of the driver’s behaviours. Using geoinformatics tools in driving behaviours assessment opens a new era of research with many possible analytical options, which do not have to rely on human observations. Instead, it receives clear indicators of the individual drivers’ interactions with the vehicle and the traffic environment. This approach should make it possible to identify lower-performing older drivers and problematic visual and motor behaviours, and the cognitive predictors of risky driving behaviours. A better targeted regulation and tailored intervention programs for older can be developed by further research

Does cycling infrastructure reduce stress biomarkers in commuting cyclists? A comparison of five European cities

There is substantial evidence that the environment has an important impact on the use of bicycles. Changes in the built environment, such as cycling infrastructure provision, usually aim at improving the efficiency, enjoyability and safety of cycling. They can also shape affective responses, for instance by triggering or preventing stress situations during cycling. The repeated occurrence of intensely stressful events may make actual cyclists more likely to abandon cycling and deter prospective cyclists from actually taking up this form of mobility. Therefore, using a novel approach, based on stress biomarker measurements obtained directly from cyclists, the objective of this study is to investigate the relationship between urban environment and cyclists' stress. It also investigates if different types of cycling infrastructures in the contexts of two different countries and in five different cities have different relationships with stress. Using a stress sensor, 70 young adults were invited to cycle along a standard route in Oxford, London (the United Kingdom), Amsterdam, Houten and Groningen (the Netherlands). These routes were around 6 km long and had a wide range of characteristics. Multilevel logistic regression analysis indicates that the probability of stressful events occurring is significantly lower on physically segregated cycle paths than on cycle paths on streets, with cycling on general use streets falling in-between these extremes. We also find higher probabilities of stress for primary roads compared to tertiary roads, at intersections than on straight roads, on cobbled and off-road surfaces compared to asphalt, and in noisier places. Models for the individual cities suggested that the relationship between cycling infrastructure and the likelihood of stressful events occurring may depend on the local context. Only for noise conditions, intersection types and cycling infrastructures were the effects consistent across the cities. These findings may be useful for urban infrastructure planning and management, indicating specific attributes that should be adjusted to make cycling less stressful