Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n=9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5,...,9 for the quadratic Casimir operator, in each case providing a formula (see eq. (11) to (15)) for the dimensions of the representations in the family as a function of D=dim g. This generalises previous results for powers j and Casimir eigenvalues j, j<=4. Many intriguing, perhaps puzzling, features of the dimension formulas are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered.Comment: 16 pages, LaTeX, 1 figure, 9 tables; v2: presentation improved, typos correcte

Ferromagnetic Ordering of Energy Levels for Uq(sl2)U_q(\mathfrak{sl}_2) Symmetric Spin Chains

We consider the class of quantum spin chains with arbitrary $U_q(\mathfrak{sl}_2)$-invariant nearest neighbor interactions, sometimes called $\textrm{SU}_q(2)$ for the quantum deformation of $\textrm{SU}(2)$, for $q>0$. We derive sufficient conditions for the Hamiltonian to satisfy the property we call {\em Ferromagnetic Ordering of Energy Levels}. This is the property that the ground state energy restricted to a fixed total spin subspace is a decreasing function of the total spin. Using the Perron-Frobenius theorem, we show sufficient conditions are positivity of all interactions in the dual canonical basis of Lusztig. We characterize the cone of positive interactions, showing that it is a simplicial cone consisting of all non-positive linear combinations of "cascade operators," a special new basis of $U_q(\mathfrak{sl}_2)$ intertwiners we define. We also state applications to interacting particle processes.Comment: 23 page

Reynolds-number Dependence of Streamwise Velocity Fluctuations in Turbulent Pipe Flow

Statistics of the streamwise velocity component in fully-developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 < Re_D < 5.7 x 10^6. The second moment exhibits two maxima: one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, is also Reynolds-number dependent and follows roughly the peak in Reynolds shear stress. The behaviour of both peaks is consistent with the concept of inactive motion which increases with increasing Reynolds number and decreasing distance from the wall. No simple scaling is apparent, and in particular, so-called "mixed" scaling is no better than wall scaling in the viscous sublayer and is actually worse than wall scaling in the outer region. The second moment is compared with empirical and theoretical scaling laws and some anomalies are apparent. The scaling of spectra using y, R and u_τ is examined. It appears that even at the highest Reynolds number, they exhibit incomplete similarity only: while spectra do collapse with either inner or outer scales for limited ranges of wave number, these ranges do not overlap. Thus similarity may not be described as complete and any apparent k_1^(-1) range does not attract any special significance and does not involve universal constants. It is suggested that this is because of the influence of inactive motion. Spectra also show the presence of very long structures close to the wall

Never Mind the Gap: Formative Assessment Confronted with Dewey’s and Gadamer’s Concept of Experience

The notion of “closing the learning gap” is widely used in the conceptualisation of formative assessment. It builds on an unarticulated assumption that students' learning can and should be controlled towards predefined outcomes. This article discusses this control assumption in the light of the concept of the American philosopher John Dewey and the German philosopher Hans‐Georg Gadamer. Their conceptualisation challenges the idea of learning as a linear and controllable process that results in stable and predictable outcomes. Using the concept of experience, we argue that learning follows a continuous circular movement where previous experiences condition future interpretations and that every experience changes the subject. This process of change is both unpredictable and diverse and requires that attention is paid to the uniqueness of each situation and to students as subjects. Following the discussion, we propose a model for considering the extensiveness and rigidity of formative assessment practices and that authors pay attention to whether they conceptualise formative assessment in a way that promotes student and teacher “gap closing” and control.publishedVersio

The Temperley-Lieb algebra and its generalizations in the Potts and XXZ models

We discuss generalizations of the Temperley-Lieb algebra in the Potts and XXZ models. These can be used to describe the addition of different types of integrable boundary terms. We use the Temperley-Lieb algebra and its one-boundary, two-boundary, and periodic extensions to classify different integrable boundary terms in the 2, 3, and 4-state Potts models. The representations always lie at critical points where the algebras becomes non-semisimple and possess indecomposable representations. In the one-boundary case we show how to use representation theory to extract the Potts spectrum from an XXZ model with particular boundary terms and hence obtain the finite size scaling of the Potts models. In the two-boundary case we find that the Potts spectrum can be obtained by combining several XXZ models with different boundary terms. As in the Temperley-Lieb case there is a direct correspondence between representations of the lattice algebra and those in the continuum conformal field theory.Comment: 49 page

Intratumoral Hydrogen Peroxide With Radiation Therapy in Locally Advanced Breast Cancer: Results From a Phase 1 Clinical Trial.

Purpose Hydrogen peroxide (H2O2) plays a vital role in normal cellular processes but at supraphysiological concentrations causes oxidative stress and cytotoxicity, a property that is potentially exploitable for the treatment of cancer in combination with radiation therapy (RT). We report the first phase 1 trial testing the safety and tolerability of intratumoral H2O2 + external beam RT as a novel combination in patients with breast cancer and exploratory plasma marker analyses investigating possible mechanisms of action.Methods and materials Twelve patients with breast tumors ≥3 cm (surgically or medically inoperable) received intratumoral H2O2 with either 36 Gy in 6 twice-weekly fractions (n = 6) or 49.5 Gy in 18 daily fractions (n = 6) to the whole breast ± locoregional lymph nodes in a single-center, nonrandomized study. H2O2 was mixed in 1% sodium hyaluronate gel (final H2O2 concentration 0.5%) before administration to slow drug release and minimize local discomfort. The mixture was injected intratumorally under ultrasound guidance twice weekly 1 hour before RT. The primary endpoint was patient-reported maximum intratumoral pain intensity before and 24 hours postinjection. Secondary endpoints included grade ≥3 skin toxicity and tumor response by ultrasound. Blood samples were collected before, during, and at the end of treatment for cell-death and immune marker analysis.Results Compliance with H2O2 and RT was 100%. Five of 12 patients reported moderate pain after injection (grade 2 Common Terminology Criteria for Adverse Events v4.02) with median duration 60 minutes (interquartile range, 20-120 minutes). Skin toxicity was comparable to RT alone, with maintained partial/complete tumor response relative to baseline in 11 of 12 patients at last follow-up (median 12 months). Blood marker analysis highlighted significant associations of TRAIL, IL-1β, IL-4, and MIP-1α with tumor response.Conclusions Intratumoral H2O2 with RT is well tolerated with no additional toxicity compared with RT alone. If efficacy is confirmed in a randomized phase 2 trial, the approach has potential as a cost-effective radiation response enhancer in multiple cancer types in which locoregional control after RT alone remains poor

Gain-of-Function Mutations in ZIC1 Are Associated with Coronal Craniosynostosis and Learning Disability

Human ZIC1 (zinc finger protein of cerebellum 1), one of five homologs of the Drosophila pair-rule gene odd-paired, encodes a transcription factor previously implicated in vertebrate brain development. Heterozygous deletions of ZIC1 and its nearby paralog ZIC4 on chromosome 3q25.1 are associated with Dandy-Walker malformation of the cerebellum, and loss of the orthologous Zic1 gene in the mouse causes cerebellar hypoplasia and vertebral defects. We describe individuals from five families with heterozygous mutations located in the final (third) exon of ZIC1 (encoding four nonsense and one missense change) who have a distinct phenotype in which severe craniosynostosis, specifically involving the coronal sutures, and variable learning disability are the most characteristic features. The location of the nonsense mutations predicts escape of mutant ZIC1 transcripts from nonsense-mediated decay, which was confirmed in a cell line from an affected individual. Both nonsense and missense mutations are associated with altered and/or enhanced expression of a target gene, engrailed-2, in a Xenopus embryo assay. Analysis of mouse embryos revealed a localized domain of Zic1 expression at embryonic days 11.5-12.5 in a region overlapping the supraorbital regulatory center, which patterns the coronal suture. We conclude that the human mutations uncover a previously unsuspected role for Zic1 in early cranial suture development, potentially by regulating engrailed 1, which was previously shown to be critical for positioning of the murine coronal suture. The diagnosis of a ZIC1 mutation has significant implications for prognosis and we recommend genetic testing when common causes of coronal synostosis have been excluded

A comparative analysis of the cultural representation of disability in school textbooks in Iran and England

The paper details the findings of a study which focused on the analysis of the cultural representation of disability in school textbooks in Iran and England. The paper argues that whilst inclusive education could facilitate the incorporating of disabled pupils into mainstream schools, there needs to be deeper examination as to how this transition should take place for children aged 3-13. The paper suggests that in such examinations school textbooks might be of significance in familiarizing non-disabled pupils, teachers and authorities with the issues related to disability and disabled pupils