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

Infant EEG activity as a biomarker for autism: a promising approach or a false promise?

The ability to determine an infant's likelihood of developing autism via a relatively simple neurological measure would constitute an important scientific breakthrough. In their recent publication in this journal, Bosl and colleagues claim that a measure of EEG complexity can be used to detect, with very high accuracy, infants at high risk for autism (HRA). On the surface, this appears to be that very scientific breakthrough and as such the paper has received widespread media attention. But a close look at how these high accuracy rates were derived tells a very different story. This stems from a conflation between "high risk" as a population-level property and "high risk" as a property of an individual. We describe the approach of Bosl et al. and examine their results with respect to baseline prevalence rates, the inclusion of which is necessary to distinguish infants with a biological risk of autism from typically developing infants with a sibling with autism. This is an important distinction that should not be overlooked

A unified approach on Springer fibers in the hook, two-row and two-column cases

We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan basis and consider the standard torus relative to this. We deal with the problem to describe the flags fixed by the torus which belong to a given component of the Springer fiber. We solve the problem in the hook, two-row and two-column cases. We provide two main characterizations which are common to the three cases, and which involve dominance relations between Young diagrams and combinatorial algorithms. Then, for these three cases, we deduce topological properties of the components and their intersections.Comment: 42 page

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

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

Successful application of ancient DNA extraction and library construction protocols to museum wet collection specimens

Millions of scientific specimens are housed in museum collections, a large part of which are fluid preserved. The use of formaldehyde as fixative and subsequent storage in ethanol is especially common in ichthyology and herpetology. This type of preservation damages DNA and reduces the chance of successful retrieval of genetic data. We applied ancient DNA extraction and single stranded library construction protocols to a variety of vertebrate samples obtained from wet collections and of different ages. Our results show that almost all samples tested yielded endogenous DNA. Archival DNA extraction was successful across different tissue types as well as using small amounts of tissue. Conversion of archival DNA fragments into single-stranded libraries resulted in usable data even for samples with initially undetectable DNA amounts. Subsequent target capture approaches for mitochondrial DNA using homemade baits on a subset of 30 samples resulted in almost complete mitochondrial genome sequences in several instances. Thus, application of ancient DNA methodology makes wet collection specimens, including type material as well as rare, old or extinct species, accessible for genetic and genomic analyses. Our results, accompanied by detailed step-by-step protocols, are a large step forward to open the DNA archive of museum wet collections for scientific studies.publishedVersio