A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Refined conformal spectra in the dimer model

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu-Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c=-2.Comment: 44 page

Critical exponents for the homology of Fortuin-Kasteleyn clusters on a torus

A Fortuin-Kasteleyn cluster on a torus is said to be of type $\{a,b\}, a,b\in\mathbb Z$, if it possible to draw a curve belonging to the cluster that winds $a$ times around the first cycle of the torus as it winds $-b$ times around the second. Even though the $Q$-Potts models make sense only for $Q$ integers, they can be included into a family of models parametrized by $\beta=\sqrt{Q}$ for which the Fortuin-Kasteleyn clusters can be defined for any real $\beta\in (0,2]$. For this family, we study the probability $\pi({\{a,b\}})$ of a given type of clusters as a function of the torus modular parameter $\tau=\tau_r+i\tau_i$. We compute the asymptotic behavior of some of these probabilities as the torus becomes infinitely thin. For example, the behavior of $\pi(\{1,0\})$ is studied along the line $\tau_r=0$ and $\tau_i\to\infty$. Exponents describing these behaviors are defined and related to weights $h_{r,s}$ of the extended Kac table for $r,s$ integers, but also half-integers. Numerical simulations are also presented. Possible relationship with recent works and conformal loop ensembles is discussed.Comment: References and one figure adde

New ground ice maps for Canada using a paleogeographic modelling approach

Ground ice melt caused by climate-induced permafrost degradation may trigger significant ecological change, damage infrastructure, and alter biogeochemical cycles. The fundamental ground ice mapping for Canada is now &gt;20 years old and does not include significant new insights gained from recent field- and remote-sensing-based studies. New modelling incorporating paleogeography is presented in this paper to depict the distribution of three ground ice types (relict ice, segregated ice, and wedge ice) in northern Canada. The modelling uses an expert-system approach in a geographic information system (GIS), founded in conceptual principles gained from empirically based research, to predict ground ice abundance in near-surface permafrost. Datasets of surficial geology, deglaciation, paleovegetation, glacial lake and marine limits, and modern permafrost distribution allow representations in the models of paleoclimatic shifts, tree line migration, marine and glacial lake inundation, and terrestrial emergence, and their effect on ground ice abundance. The model outputs are generally consistent with field observations, indicating abundant relict ice in the western Arctic, where it has remained preserved since deglaciation in thick glacigenic sediments in continuous permafrost. Segregated ice is widely distributed in fine-grained deposits, occurring in the highest abundance in glacial lake and marine sediments. The modelled abundance of wedge ice largely reflects the exposure time of terrain to low air temperatures in tundra environments following deglaciation or marine/glacial lake inundation and is thus highest in the western Arctic. Holocene environmental changes result in reduced ice abundance where the tree line advanced during warmer periods. Published observations of thaw slumps and massive ice exposures, segregated ice and associated landforms, and ice wedges allow a favourable preliminary assessment of the models, and the results are generally comparable with the previous ground ice mapping for Canada. However, the model outputs are more spatially explicit and better reflect observed ground ice conditions in many regions. Synthetic modelling products that incorporated the previous ground ice information may therefore include inaccuracies. The presented modelling approach is a significant advance in permafrost mapping, but additional field observations and volumetric ice estimates from more areas in Canada are required to improve calibration and validation of small-scale ground ice modelling. The ground ice maps from this paper are available in the supplement in GeoTIFF format.</p

Effet de l'exercice aigu sur la synthèse et dégradation protéique du muscle squelettique chez les personnes atteintes de dystrophie myotonique de type 1: Étude de séries de cas / Effect of acute eccentric exercise on skeletal muscle hypertrophy and atrophy signalling pathways in men with myotonic dystrophy type 1

INTRODUCTION: La dystrophie myotonique de type 1 (DM1) est une maladie génétique multisystémique. L'atrophie musculaire constitue un symptôme majeur et le renforcement musculaire est souvent utilisé pour contrer sa progression qui évolue au fil des ans. Toutefois, il demeure inconnu si ce stimulus déclenche des mécanismes cellulaires et moléculaires menant à l'hypertrophie, tels qu'observés chez une population saine. OBJECTIF: Évaluer l’effet de l'exercice aigu en résistance sur les adaptations musculaires chez les DM1. MÉTHODOLOGIE: Dix hommes atteints de DM1 ont participé à une séance unique d'exercice excentrique en résistance des muscles extenseurs du genou sur biodex. Une biopsie musculaire a été prélevée une semaine avant et 24 heures après l’intervention. Certains acteurs de la cascade de synthèse (AKT et mTOR) et de dégradation (Atrogin-1 et MuRF) protéique du muscle ont été évalués par immunobuvardage. RÉSULTATS: Nos résultats préliminaires démontrent que les patients présentent une grande variabilité dans la réponse à l'exercice. Les formes totales des protéines activées par phosphorylation (AKT et mTOR) varient. De plus, la forme phosphorylée d'AKT semble absente, ce qui concorde avec les altérations du récepteur à l'IGF déjà connues chez la DM1. Les protéines ne nécessitant pas de phosphorylation (Atrogin-1 et MuRF) présentent aussi une variation hétérogène post exercice. Finalement, pour les 10 patients étudiés, il n’y a pas de corrélation entre la réponse à l'exercice et la sévérité de la maladie. CONCLUSION: L'augmentation du nombre de patients (N=20) permettra une meilleure compréhension de la réponse à l'entraînement chez les DM1 et une clarification potentielle quant à la pertinence d'individualiser les protocoles d'entraînement à chaque patient

Has education lost sight of children?

The reflections presented in this chapter are informed by clinical and personal experiences of school education in the UK. There are many challenges for children and young people in the modern education system and for the professionals who support them. In the UK, there are significant gaps between the highly selective education provided to those who pay privately for it and to the majority of those educated in the state-funded system. Though literacy rates have improved around the world, many children, particularly boys, do not finish their education for reasons such as boredom, behavioural difficulties or because education does not ‘pay’. Violence, bullying, and sexual harassment are issues faced by many children in schools and there are disturbing trends of excluding children who present with behavioural problems at school whose origins are not explored. Excluded children are then educated with other children who may also have multiple problems which often just make the situation worse. The experience of clinicians suggests that school-related mental health problems are increasing in severity. Are mental health services dealing with the consequences of an education system that is not meeting children’s needs? An education system that is testing- and performance-based may not be serving many children well if it is driving important decisions about them at increasingly younger ages. Labelling of children and setting them on educational career paths can occur well before they reach secondary schools, limiting potential very early on in their developmental trajectory. Furthermore, the emphasis at school on testing may come at the expense of creativity and other forms of intelligence, which are also valuable and important. Meanwhile the employment marketplace requires people with widely different skills, with an emphasis on innovation, creativity, and problem solving. Is education losing sight of the children it is educating