Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group

Categorification of skew-symmetrizable cluster algebras

We propose a new framework for categorifying skew-symmetrizable cluster algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with the action of a finite group G, we construct a G-equivariant mutation on the set of maximal rigid G-invariant objects of C. Using an appropriate cluster character, we can then attach to these data an explicit skew-symmetrizable cluster algebra. As an application we prove the linear independence of the cluster monomials in this setting. Finally, we illustrate our construction with examples associated with partial flag varieties and unipotent subgroups of Kac-Moody groups, generalizing to the non simply-laced case several results of Gei\ss-Leclerc-Schr\"oer.Comment: 64 page

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde

Hilbert Series for Moduli Spaces of Two Instantons

The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where G is a simple gauge group, is studied in detail. For a given G, the moduli space is a singular hyperKahler cone with a symmetry group U(2) \times G, where U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli space transform in irreducible representations of the symmetry group and hence the Hilbert series admits a character expansion. For cases that G is a classical group (of type A, B, C, or D), there is an ADHM construction which allows us to compute the HS explicitly using a contour integral. For cases that G is of E-type, recent index results allow for an explicit computation of the HS. The character expansion can be expressed as an infinite sum which lives on a Cartesian lattice that is generated by a small number of representations. This structure persists for all G and allows for an explicit expressions of the HS to all simple groups. For cases that G is of type G_2 or F_4, discrete symmetries are enough to evaluate the HS exactly, even though neither ADHM construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure

Selected reactive oxygen species and antioxidant enzymes in common bean after Pseudomonas syringae pv. phaseolicola and Botrytis cinerea infection

Phaseolus vulgaris cv. Korona plants were inoculated with the bacteria Pseudomonas syringae pv. phaseolicola (Psp), necrotrophic fungus Botrytis cinerea (Bc) or with both pathogens sequentially. The aim of the experiment was to determine how plants cope with multiple infection with pathogens having different attack strategy. Possible suppression of the non-specific infection with the necrotrophic fungus Bc by earlier Psp inoculation was examined. Concentration of reactive oxygen species (ROS), such as superoxide anion (O2 -) and H2O2 and activities of antioxidant enzymes such as superoxide dismutase (SOD), catalase (CAT) and peroxidase (POD) were determined 6, 12, 24 and 48 h after inoculation. The measurements were done for ROS cytosolic fraction and enzymatic cytosolic or apoplastic fraction. Infection with Psp caused significant increase in ROS levels since the beginning of experiment. Activity of the apoplastic enzymes also increased remarkably at the beginning of experiment in contrast to the cytosolic ones. Cytosolic SOD and guaiacol peroxidase (GPOD) activities achieved the maximum values 48 h after treatment. Additional forms of the examined enzymes after specific Psp infection were identified; however, they were not present after single Bc inoculation. Subsequent Bc infection resulted only in changes of H2O2 and SOD that occurred to be especially important during plant–pathogen interaction. Cultivar Korona of common bean is considered to be resistant to Psp and mobilises its system upon infection with these bacteria. We put forward a hypothesis that the extent of defence reaction was so great that subsequent infection did not trigger significant additional response

Appropriate disclosure of a diagnosis of dementia : identifying the key behaviours of 'best practice'

Background: Despite growing evidence that many people with dementia want to know their diagnosis, there is wide variation in attitudes of professionals towards disclosure. The disclosure of the diagnosis of dementia is increasingly recognised as being a process rather than a one-off behaviour. However, the different behaviours that contribute to this process have not been comprehensively defined. No intervention studies to improve diagnostic disclosure in dementia have been reported to date. As part of a larger study to develop an intervention to promote appropriate disclosure, we sought to identify important disclosure behaviours and explore whether supplementing a literature review with other methods would result in the identification of new behaviours. Methods: To identify a comprehensive list of behaviours in disclosure we conducted a literature review, interviewed people with dementia and informal carers, and used a consensus process involving health and social care professionals. Content analysis of the full list of behaviours was carried out. Results: Interviews were conducted with four people with dementia and six informal carers. Eight health and social care professionals took part in the consensus panel. From the interviews, consensus panel and literature review 220 behaviours were elicited, with 109 behaviours over-lapping. The interviews and consensus panel elicited 27 behaviours supplementary to the review. Those from the interviews appeared to be self-evident but highlighted deficiencies in current practice and from the panel focused largely on balancing the needs of people with dementia and family members. Behaviours were grouped into eight categories: preparing for disclosure; integrating family members; exploring the patient's perspective; disclosing the diagnosis; responding to patient reactions; focusing on quality of life and well-being; planning for the future; and communicating effectively. Conclusion: This exercise has highlighted the complexity of the process of disclosing a diagnosis of dementia in an appropriate manner. It confirms that many of the behaviours identified in the literature (often based on professional opinion rather than empirical evidence) also resonate with people with dementia and informal carers. The presence of contradictory behaviours emphasises the need to tailor the process of disclosure to individual patients and carers. Our combined methods may be relevant to other efforts to identify and define complex clinical practices for further study.This project is funded by UK Medical Research Council, Grant reference number G0300999

Variability and change in the Canadian cryosphere

Abstract During the International Polar Year (IPY), comprehensive observational research programs were undertaken to increase our understanding of the Canadian polar cryosphere response to a changing climate. Cryospheric components considered were snow, permafrost, sea ice, freshwater ice, glaciers and ice shelves. Enhancement of conventional observing systems and retrieval algorithms for satellite measurements facilitated development of a snapshot of current cryospheric conditions, providing a baseline against which future change can be assessed. Key findings include: 1. surface air temperatures across the Canadian Arctic exhibit a warming trend in all seasons over the past 40 years. A consistent pan-cryospheric response to these warming temperatures is evident through the analysis of multi-decadal datasets; 2. in recent years (including the IPY period) a higher rate of change was observed compared to previous decades including warming permafrost, reduction in snow cover extent and duration, reduction in summer sea ice extent, increased mass loss from glaciers, and thinning and break-up of the remaining Canadian ice shelves. These changes illustrate both a reduction in the spatial extent and mass of the cryosphere and an increase in the temporal persistence of melt related parameters. The observed changes in the cryosphere have important implications for human activity including the close ties of northerners to the land, access to northern regions for natural resource development, and the integrity of northern infrastructure

Predicting mental imagery based BCI performance from personality, cognitive profile and neurophysiological patterns

Mental-Imagery based Brain-Computer Interfaces (MI-BCIs) allow their users to send commands to a computer using their brain-activity alone (typically measured by ElectroEncephaloGraphy— EEG), which is processed while they perform specific mental tasks. While very promising, MI-BCIs remain barely used outside laboratories because of the difficulty encountered by users to control them. Indeed, although some users obtain good control performances after training, a substantial proportion remains unable to reliably control an MI-BCI. This huge variability in user-performance led the community to look for predictors of MI-BCI control ability. However, these predictors were only explored for motor-imagery based BCIs, and mostly for a single training session per subject. In this study, 18 participants were instructed to learn to control an EEG-based MI-BCI by performing 3 MI-tasks, 2 of which were non-motor tasks, across 6 training sessions, on 6 different days. Relationships between the participants’ BCI control performances and their personality, cognitive profile and neurophysiological markers were explored. While no relevant relationships with neurophysiological markers were found, strong correlations between MI-BCI performances and mental-rotation scores (reflecting spatial abilities) were revealed. Also, a predictive model of MI-BCI performance based on psychometric questionnaire scores was proposed. A leave-one-subject-out cross validation process revealed the stability and reliability of this model: it enabled to predict participants’ performance with a mean error of less than 3 points. This study determined how users’ profiles impact their MI-BCI control ability and thus clears the way for designing novel MI-BCI training protocols, adapted to the profile of each user