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

Tongue-surface movement patterns during speech and swallowing

The tongue has been frequently characterized as being composed of several functionally independent articulators. The question of functional regionality within the tongue was examined by quantifying the strength of coupling among four different tongue locations across a large number of consonantal contexts and participants. Tongue behavior during swallowing was also described. Vertical displacements of pellets affixed to the tongue were extracted from the x-ray microbeam database. Forty-six participants recited 20 vowel-consonant-vowel (VCV) combinations and swallowed 10 ccs of water. Tongue-surface movement patterns were quantitatively described by computing the covariance between the vertical time-histories of all possible pellet pairs. Phonemic differentiation in vertical tongue motions was observed as coupling varied predictably across pellet pairs with place of articulation. Moreover, tongue displacements for speech and swallowing clustered into distinct groups based on their coupling profiles. Functional independence of anterior tongue regions was evidenced by a wide range of movement coupling relations between anterior tongue pellets. The strengths and weaknesses of the covariance-based analysis for characterizing tongue movement are considered

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

Diversity and Paleodemography of the Addax (Addax nasomaculatus), a Saharan Antelope on the Verge of Extinction.

Since the 19th century, the addax (Addax nasomaculatus) has lost approximately 99% of its former range. Along with its close relatives, the blue antelope (Hippotragus leucophaeus) and the scimitar-horned oryx (Oryx dammah), the addax may be the third large African mammal species to go extinct in the wild in recent times. Despite this, the evolutionary history of this critically endangered species remains virtually unknown. To gain insight into the population history of the addax, we used hybridization capture to generate ten complete mitochondrial genomes from historical samples and assembled a nuclear genome. We found that both mitochondrial and nuclear diversity are low compared to other African bovids. Analysis of mitochondrial genomes revealed a most recent common ancestor ~32 kya (95% CI 11-58 kya) and weak phylogeographic structure, indicating that the addax likely existed as a highly mobile, panmictic population across its Sahelo-Saharan range in the past. PSMC analysis revealed a continuous decline in effective population size since ~2 Ma, with short intermediate increases at ~500 and ~44 kya. Our results suggest that the addax went through a major bottleneck in the Late Pleistocene, remaining at low population size prior to the human disturbances of the last few centuries

Diversity and Paleodemography of the Addax (<i>Addax nasomaculatus</i>), a Saharan Antelope on the Verge of Extinction.

Since the 19th century, the addax (Addax nasomaculatus) has lost approximately 99% of its former range. Along with its close relatives, the blue antelope (Hippotragus leucophaeus) and the scimitar-horned oryx (Oryx dammah), the addax may be the third large African mammal species to go extinct in the wild in recent times. Despite this, the evolutionary history of this critically endangered species remains virtually unknown. To gain insight into the population history of the addax, we used hybridization capture to generate ten complete mitochondrial genomes from historical samples and assembled a nuclear genome. We found that both mitochondrial and nuclear diversity are low compared to other African bovids. Analysis of mitochondrial genomes revealed a most recent common ancestor ~32 kya (95% CI 11-58 kya) and weak phylogeographic structure, indicating that the addax likely existed as a highly mobile, panmictic population across its Sahelo-Saharan range in the past. PSMC analysis revealed a continuous decline in effective population size since ~2 Ma, with short intermediate increases at ~500 and ~44 kya. Our results suggest that the addax went through a major bottleneck in the Late Pleistocene, remaining at low population size prior to the human disturbances of the last few centuries