Descent sets for oscillating tableaux

The descent set of an oscillating (or up-down) tableau is introduced. This descent set plays the same role in the representation theory of the symplectic groups as the descent set of a standard tableau plays in the representation theory of the general linear groups. In particular, we show that the descent set is preserved by Sundaram's correspondence. This gives a direct combinatorial interpretation of the branching rules for the defining representations of the symplectic groups; equivalently, for the Frobenius character of the action of a symmetric group on an isotypic subspace in a tensor power of the defining representation of a symplectic group

Protease-activated receptor 4 variant p.Tyr157Cys reduces platelet functional responses and alters receptor trafficking

OBJECTIVE—: Protease-activated receptor 4 (PAR4) is a key regulator of platelet reactivity and is encoded by F2RL3, which has abundant rare missense variants. We aimed to provide proof of principle that rare F2LR3 variants potentially affect on platelet reactivity and responsiveness to PAR1 antagonist drugs and to explore underlying molecular mechanisms. APPROACH AND RESULTS—: We identified 6 rare F2RL3 missense variants in 236 cardiac patients, of which the variant causing a tyrosine 157 to cysteine substitution (Y157C) was predicted computationally to affect most on PAR4 structure. Y157C platelets from 3 cases showed reduced responses to PAR4-activating peptide and to α-thrombin compared with controls, but no reduction in responses to PAR1-activating peptide. Pretreatment with the PAR1 antagonist vorapaxar caused lower residual α-thrombin responses in Y157C platelets than in controls, indicating greater platelet inhibition. HEK293 cells transfected with a PAR4 Y157C expression construct had reduced PAR4 functional responses, unchanged total PAR4 expression but reduced surface expression. PAR4 Y157C was partially retained in the endoplasmic reticulum and displayed an expression pattern consistent with defective N-glycosylation. Mutagenesis of Y322, which is the putative hydrogen bond partner of Y157, also reduced PAR4 surface expression in HEK293 cells. CONCLUSIONS—: Reduced PAR4 responses associated with Y157C result from aberrant anterograde surface receptor trafficking, in part, because of disrupted intramolecular hydrogen bonding. Characterization of PAR4 Y157C establishes that rare F2RL3 variants have the potential to markedly alter platelet PAR4 reactivity particularly after exposure to therapeutic PAR1 antagonists

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

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

Ecological Interactions of the Sexually Deceptive Orchid Orchis Galilaea

Plant species dependent on highly specific interactions with pollinators are vulnerable to environmental change. Conservation strategies therefore require a detailed understanding of pollination ecology. This two-year study examined the interactions between the sexually deceptive orchid, Orchis galilaea, and its pollinator Lasioglossum marginatum. Relationships were investigated across three different habitats known to support O. galilaea (garrigue, oak woodland, and mixed oak/pine woodland) in Lebanon. Visitation rates to flowers were extremely low and restricted to male bees. The reproductive success of O. galilaea under ambient conditions was 29.3% (±2.4), compared to 89.0% (±2.1) in plants receiving cross-pollination by hand. No difference in reproductive success was found between habitat types, but values of reproductive success were positively correlated to the abundance of male bees. Pollination limitation can have negative impacts on the population growth of orchids, and this study provides clear evidence for more holistic approaches to habitat conservation to support specific interactions