Analogs of Schur functions for rank two Weyl groups obtained from grid-like posets

In prior work, the authors, along with M. McClard, R. A. Proctor, and N. J. Wildberger, studied certain distributive lattice models for the "Weyl bialternants" (aka "Weyl characters") associated with the rank two root systems/Weyl groups. These distributive lattices were uniformly described as lattices of order ideals taken from certain grid-like posets, although the arguments connecting the lattices to Weyl bialternants were case-by-case depending on the type of the rank two root system. Using this connection with Weyl bialternants, these lattices were shown to be rank symmetric and rank unimodal, and their rank generating functions were shown to have beautiful quotient-of-products expressions. Here, these results are re-derived from scratch using completely uniform and elementary combinatorial reasoning in conjunction with some new combinatorial methodology developed elsewhere by the second listed author.Comment: 15 page

Hydrodynamic View of Wave-Packet Interference: Quantum Caves

Wave-packet interference is investigated within the complex quantum Hamilton-Jacobi formalism using a hydrodynamic description. Quantum interference leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display counterclockwise helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. The string of alternating stagnation and vortical tubes is sufficient to generate divergent trajectories. Moreover, the average wrapping time for trajectories and the rotational rate of the nodal line in the complex plane can be used to define the lifetime for interference features.Comment: 4 pages, 3 figures (major revisions with respect to the previous version have been carried out

Morphological and genetic analyses in the Melanoplus packardii group (Orthoptera: Acrididae)

Melanoplus packardii Scudder was described in 1897. Three additional closely-related species were later described and their status as species has been questioned on numerous occasions. We examined morphology from specimens collected in Nebraska which fit descriptions of three of the four forms and specimens that appeared to be hybrids. We found distinct morphological characters suggesting species status for M. foedus and M. packardii, but not for M. foedus fluviatilis. Examination of aedeagi of these three forms suggests that M. foedus and M. packardii are each distinct, but that the aedeagi of M. f. fluviatilis and M. f. foedus cannot be distinguished. Molecular analyses of the three groups did not produce clear separations and suggest gene exchange between these three forms may be ongoing. Together, these data suggest that M. foedus and M. packardii should be recognized as sibling species, but M. foedus fluviatilis is best considered a form of M. foedus, typically found in low lying areas

Morphological and genetic analyses in the Melanoplus packardii group (Orthoptera: Acrididae)

Melanoplus packardii Scudder was described in 1897. Three additional closely-related species were later described and their status as species has been questioned on numerous occasions. We examined morphology from specimens collected in Nebraska which fit descriptions of three of the four forms and specimens that appeared to be hybrids. We found distinct morphological characters suggesting species status for M. foedus and M. packardii, but not for M. foedus fluviatilis. Examination of aedeagi of these three forms suggests that M. foedus and M. packardii are each distinct, but that the aedeagi of M. f. fluviatilis and M. f. foedus cannot be distinguished. Molecular analyses of the three groups did not produce clear separations and suggest gene exchange between these three forms may be ongoing. Together, these data suggest that M. foedus and M. packardii should be recognized as sibling species, but M. foedus fluviatilis is best considered a form of M. foedus, typically found in low lying areas

6-[18F]Fluoro-L-DOPA and Cerebral Blood Flow in Unilaterally MPTP-Treated Monkeys

Intravenous administration of 15O-labeled water and 6-[18F]-L-fluorodopa were used to assess abnormal striatal activity in monkeys after long-term recovery of unilateral lesions of the dopaminergic nigro-striatal system induced by the neurotoxin MPTP. PET data were examined in relation to behavioral and biological parameters. Cerebral blood flow and 6-[18F]-L-DOPA uptake were found to be significantly reduced in the lesioned striatum, compared to the unaffected side and to normal controls. There was no correlation between cerebral blood flow and any of the behavioral parameters. The uptake rate constant of 18F-DOPA from blood to striatum and the ratios of striatum to occipital areas were highly correlated to the concentrations of homovanillic acid in the cerebrospinal fluid of the same animals but not to the rotational behavior. This MPTP-inducedmodei of striatal dopamine deficiency in primates presents similarities with idiopathic Parkinson's disease and may be used to evaluate the effects of dopaminergic lesions and transplants on brain function

e-Roster Policy: Insights and implications of codifying nurse scheduling

Following a decade of dissemination, particularly within the British National Health Service (NHS), electronic rostering systems were recently endorsed within the Carter Review. However, e-rostering necessitates the formal codification of the roster process. This research investigates that codification through the lens of the 'Roster Policy', a formal document specifying the rules and procedures used to prepare staff rosters. This study is based upon analysis of twenty-seven publicly available policies, each approved within a four-year period from January 2010 to July 2014. This research finds that, at an executive level, codified knowledge is used as a proxy for the common language and experience otherwise acquired on a ward through everyday interaction, while at ward level the nurse rostering problem continues to resist all efforts at simplification. Ultimately, it is imperative that executives recognise that e-rostering is not a silver-bullet and that information from such systems requires careful interpretation and circumspection

Distributive Lattices Defined for Representations of Rank Two Semisimple Lie Algebras

For a rank two root system and a pair of nonnegative integers, using only elementary combinatorics we construct two posets. The constructions are uniform across the root systems A1+A1, A2, C2, and G2. Examples appear in Figures 3.2 and 3.3. We then form the distributive lattices of order ideals of these posets. Corollary 5.4 gives elegant quotient-of-products expressions for the rank generating functions of these lattices (thereby providing answers to a 1979 question of Stanley). Also, Theorem 5.3 describes how these lattices provide a new combinatorial setting for the Weyl characters of representations of rank two semisimple Lie algebras. Most of these lattices are new; the rest of them (or related structures) have arisen in work of Stanley, Kashiwara, Nakashima, Littelmann, and Molev. In a future paper, one author shows that the posets constructed here form a Dynkin diagram-indexed answer to a combinatorially posed classification question. In a companion paper, some of these lattices are used to explicitly construct some representations of rank two semisimple Lie algebras. This implies that these lattices are strongly Sperner

Factors Associated With C5 Palsy Following Cervical Spine Surgery: A Systematic Review.

Study Design: Systematic review. Objectives: C5 palsy (C5P) is a not uncommon and disabling postoperative complication with a reported incidence varying between 0% and 30%. Among others, one explanation for its occurrence includes foraminal nerve root tethering. Although different risk factors have been reported, controversy about its causation and prevention persists. Inconsistent study findings contribute to the persistent ambiguity leading to an assumption of a multifactorial nature of the underlying C5P pathophysiology. Here, we report the results of a systematic review on C5P with narrow inclusion criteria in the hope of elucidating risk factors for C5P due to a common pathophysiological mechanism. Methods: Electronic databases from inception to March 9, 2019 and references of articles were searched. Narrow inclusion criteria were applied to identify studies investigating demographic, clinical, surgical, and radiographic factors associated with postoperative C5P. Results: Sixteen studies were included after initial screening of 122 studies. Eighty-four risk factors were analyzed; 27 in ≥2 studies and 57 in single studies. The pooled prevalence of C5P was 6.0% (range: 4.2%-24.1%) with no consistent evidence that C5P was associated with demographic, clinical, or specific surgical factors. Of the radiographic factors assessed, specifically decreased foraminal diameter and preoperative cord rotation were identified as risk factors for C5P. Conclusion: Although risk factors for C5P have been reported, ambiguity remains due to potentially multifactorial pathophysiology and study heterogeneity. We found foraminal diameter and cord rotation to be associated with postoperative C5P occurrence in our meta-analysis. These findings support the notion that factors contributing to, and acting synergistically with foraminal stenosis increase the risk of postoperative C5P

The macrophage inhibitory cytokine integrates AKT/PKB and MAP kinase signaling pathways in breast cancer cells

Macrophage inhibitory cytokine 1 (MIC-1), a divergent member of the transforming growth factor beta superfamily, plays a role in the progression of a number of cancers, including breast, gastric, prostate and colorectal carcinomas. Serum MIC-1 levels are elevated in patients with metastatic prostate, breast and colorectal carcinomas. In vitro studies have revealed a cell type-specific role for MIC-1 in senescence and apoptosis. MIC-1 activates the survival kinase AKT/PKB in neuronal cells. Depending on the cell type, it activates or represses the MAP kinases ERK1/2. Mechanisms responsible for an increased MIC-1 expression in cancers and the consequences of MIC-1 overexpression, however, are not known. In this study, we show that AKT/PKB directly regulates the expression of MIC-1 in breast cancer cells. Sequences within −88 to +30 of the MIC-1 promoter are required for the AKT-mediated induction of MIC-1. This region of the promoter contains two SP-1 binding sites (SP-1B and SP-1C), which bind to the SP-1 and SP-3 proteins. Mutation of SP-1C but not SP-1B reduced the AKT-mediated activation of MIC-1. MIC-1 increased the basal ERK1 phosphorylation and prolonged the estrogen-stimulated ERK1 phosphorylation in MCF-7 breast cancer cells without altering the phosphorylation status of AKT/PKB. Immunohistochemistry with MIC-1 antibody revealed an MIC-1 expression within the cancer cells of primary breast cancer and in the MCF-7 xenografts. Furthermore, a limited analysis of RNA from primary breast cancers revealed an overexpression of MIC-1 in tumors, compared with normal tissues. These results suggest that AKT/PKB through MIC-1 could regulate the ERK1 activity and the MIC-1 expression levels may serve as a surrogate marker for the AKT activation in tumors