Series of nilpotent orbits

We organize the nilpotent orbits in the exceptional complex Lie algebras into series using the triality model and show that within each series the dimension of the orbit is a linear function of the natural parameter a=1,2,4,8, respectively for f_4,e_6,e_7,e_8. We also obtain explicit representatives in a uniform manner. We observe similar regularities for the centralizers of nilpotent elements in a series and graded components in the associated grading of the ambient Lie algebra. More strikingly, for a greater than one, the degrees of the unipotent characters of the corresponding Chevalley groups, associated to these series through the Springer correspondance are given by polynomials which have uniform expressions in terms of a.Comment: 20 pages, revised version with more formulas for unipotent character

On the exact evaluation of spin networks

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs

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

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

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

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

What drives sound symbolism? Different acoustic cues underlie sound-size and sound-shape mappings

Sound symbolism refers to the non-arbitrary mappings that exist between phonetic properties of speech sounds and their meaning. Despite there being an extensive literature on the topic, the acoustic features and psychological mechanisms that give rise to sound symbolism are not, as yet, altogether clear. The present study was designed to investigate whether different sets of acoustic cues predict size and shape symbolism, respectively. In two experiments, participants judged whether a given consonant-vowel speech sound was large or small, round or angular, using a size or shape scale. Visual size judgments were predicted by vowel formant F1 in combination with F2, and by vowel duration. Visual shape judgments were, however, predicted by formants F2 and F3. Size and shape symbolism were thus not induced by a common mechanism, but rather were distinctly affected by acoustic properties of speech sounds. These findings portray sound symbolism as a process that is not based merely on broad categorical contrasts, such as round/unround and front/back vowels. Rather, individuals seem to base their sound-symbolic judgments on specific sets of acoustic cues, extracted from speech sounds, which vary across judgment dimensions

The neurochemical basis of human cortical auditory processing: combining proton magnetic resonance spectroscopy and magnetoencephalography

BACKGROUND: A combination of magnetoencephalography and proton magnetic resonance spectroscopy was used to correlate the electrophysiology of rapid auditory processing and the neurochemistry of the auditory cortex in 15 healthy adults. To assess rapid auditory processing in the left auditory cortex, the amplitude and decrement of the N1m peak, the major component of the late auditory evoked response, were measured during rapidly successive presentation of acoustic stimuli. We tested the hypothesis that: (i) the amplitude of the N1m response and (ii) its decrement during rapid stimulation are associated with the cortical neurochemistry as determined by proton magnetic resonance spectroscopy. RESULTS: Our results demonstrated a significant association between the concentrations of N-acetylaspartate, a marker of neuronal integrity, and the amplitudes of individual N1m responses. In addition, the concentrations of choline-containing compounds, representing the functional integrity of membranes, were significantly associated with N1m amplitudes. No significant association was found between the concentrations of the glutamate/glutamine pool and the amplitudes of the first N1m. No significant associations were seen between the decrement of the N1m (the relative amplitude of the second N1m peak) and the concentrations of N-acetylaspartate, choline-containing compounds, or the glutamate/glutamine pool. However, there was a trend for higher glutamate/glutamine concentrations in individuals with higher relative N1m amplitude. CONCLUSION: These results suggest that neuronal and membrane functions are important for rapid auditory processing. This investigation provides a first link between the electrophysiology, as recorded by magnetoencephalography, and the neurochemistry, as assessed by proton magnetic resonance spectroscopy, of the auditory cortex

Phonological and orthographic influences in the bouba–kiki effect

We examine a high-profile phenomenon known as the bouba–kiki effect, in which non-word names are assigned to abstract shapes in systematic ways (e.g. rounded shapes are preferentially labelled bouba over kiki). In a detailed evaluation of the literature, we show that most accounts of the effect point to predominantly or entirely iconic cross-sensory mappings between acoustic or articulatory properties of sound and shape as the mechanism underlying the effect. However, these accounts have tended to confound the acoustic or articulatory properties of non-words with another fundamental property: their written form. We compare traditional accounts of direct audio or articulatory-visual mapping with an account in which the effect is heavily influenced by matching between the shapes of graphemes and the abstract shape targets. The results of our two studies suggest that the dominant mechanism underlying the effect for literate subjects is matching based on aligning letter curvature and shape roundedness (i.e. non-words with curved letters are matched to round shapes). We show that letter curvature is strong enough to significantly influence word–shape associations even in auditory tasks, where written word forms are never presented to participants. However, we also find an additional phonological influence in that voiced sounds are preferentially linked with rounded shapes, although this arises only in a purely auditory word–shape association task. We conclude that many previous investigations of the bouba–kiki effect may not have given appropriate consideration or weight to the influence of orthography among literate subjects