Variety of idempotents in nonassociative algebras

In this paper, we study the variety of all nonassociative (NA) algebras from the idempotent point of view. We are interested, in particular, in the spectral properties of idempotents when algebra is generic, i.e. idempotents are in general position. Our main result states that in this case, there exist at least $n-1$ nontrivial obstructions (syzygies) on the Peirce spectrum of a generic NA algebra of dimension $n$. We also discuss the exceptionality of the eigenvalue $\lambda=\frac12$ which appears in the spectrum of idempotents in many classical examples of NA algebras and characterize its extremal properties in metrised algebras.Comment: 27 pages, 1 figure, submitte

A Collection of Problems on Spectrally Bounded Operators

We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.Comment: 15 pages,; submitte

A local-global principle for linear dependence of noncommutative polynomials

A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to directional local linear dependence and evaluations in general algebras over fields of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.Comment: 8 page

β-admissibility of observation operators for hypercontractive semigroups

We prove a Weiss conjecture on β -admissibility of observation operators for discrete and continuous γ -hypercontractive semigroups of operators, by representing them in terms of shifts on weighted Bergman spaces and using a reproducing kernel thesis for Hankel operators. Particular attention is paid to the case γ=2 , which corresponds to the unweighted Bergman shift

Increased frequency of the immunoglobulin enhancer HS1,2 allele 2 in coeliac disease

Background: Coeliac disease ( CD) is characterized by increased immunological responsiveness to ingested gliadin in genetically predisposed individuals. This genetic predisposition is not completely defined. A dysregulation of immunoglobulins (Ig) is present in CD: since antiendomysium antibodies (anti-EMA) are of the IgA class. One polymorphic enhancer within the locus control region (LCR) of the immunoglobulin heavy chain cluster at the 3' of the C alpha-1 gene was investigated. The correlation of the penetrance of the four different alleles of the HS1,2-A enhancer of the LCR-1 3' to C alpha-1 in CD patients compared to a control population was analysed. Methods: A total of 115 consecutive CD outpatients, on a gluten-free diet, and 248 healthy donors, age- and sex-matched, from the same geographical area were enrolled in the study. HS1,2-A allele frequencies were investigated by nested polymerase chain reaction (PCR). Results: The frequency of allele 2 of the enhancer HS1,2-A gene was increased by 30.8% as compared to the control frequency. The frequency of homozygosity for allele 2 was significantly increased in CD patients. Crude odds ratio ( OR) showed that those with 2/2 and 2/4 ( OR 2.63, P < 0.001 and OR 2.01, P = 0.03) have a significantly higher risk of developing the disease. In contrast, allele 1/2 may represent a protective genetic factor against CD ( OR 0.52, P = 0.01). Conclusions: These data provide further evidence of a genetic predisposition in CD. Because of the Ig dysregulation in CD, the enhancer HS1,2-A may be involved in the pathogenesis

Position and sequence conservation in Amniota of polymorphic enhancer HS1.2 within the palindrome of IgH 3'Regulatory Region

<p>Abstract</p> <p>Background</p> <p>The Immunoglobulin heavy chain (IgH) 3' Regulatory Region (3'RR), located at the 3' of the constant alpha gene, plays a crucial role in immunoglobulin production. In humans, there are 2 copies of the 3'RR, each composed of 4 main elements: 3 enhancers and a 20 bp tandem repeat. The single mouse 3'RR differs from the two human ones for the presence of 4 more regulative elements with the double copy of one enhancer at the border of a palindromic region.</p> <p>Results</p> <p>We compared the 3'RR organization in genomes of vertebrates to depict the evolutionary history of the region and highlight its shared features. We found that in the 8 species in which the whole region was included in a fully assembled contig (mouse, rat, dog, rabbit, panda, orangutan, chimpanzee, and human), the shared elements showed synteny and a highly conserved sequence, thus suggesting a strong evolutionary constraint. In these species, the wide 3'RR (~30 kb in human) bears a large palindromic sequence, consisting in two ~3 kb complementary branches spaced by a ~3 kb sequence always including the HS1.2 enhancer. In mouse and rat, HS3 is involved by the palindrome so that one copy of the enhancer is present on each side. A second relevant feature of our present work concerns human polymorphism of the HS1.2 enhancer, associated to immune diseases in our species. We detected a similar polymorphism in all the studied Catarrhini (a primate parvorder). The polymorphism consists of multiple copies of a 40 bp element up to 12 in chimpanzees, 8 in baboons, 6 in macaque, 5 in gibbons, 4 in humans and orangutan, separated by stretches of Cytosine. We show specific binding of this element to nuclear factors.</p> <p>Conclusions</p> <p>The nucleotide sequence of the palindrome is not conserved among evolutionary distant species, suggesting pressures for the maintenance of two self-matching regions driving a three-dimensional structure despite of the inter-specific divergence at sequence level. The information about the conservation of the palindromic structure and the settling in primates of the polymorphic feature of HS1.2 show the relevance of these structures in the control and modulation of the Ig production through the formation of possible three-dimensional structures.</p

Precision Measurement of the Boron to Carbon Flux Ratio in Cosmic Rays from 1.9 GV to 2.6 TV with the Alpha Magnetic Spectrometer on the International Space Station

Knowledge of the rigidity dependence of the boron to carbon flux ratio (B/C) is important in understanding the propagation of cosmic rays. The precise measurement of the B/C ratio from 1.9 GV to 2.6 TV, based on 2.3 million boron and 8.3 million carbon nuclei collected by AMS during the first 5 years of operation, is presented. The detailed variation with rigidity of the B/C spectral index is reported for the first time. The B/C ratio does not show any significant structures in contrast to many cosmic ray models that require such structures at high rigidities. Remarkably, above 65 GV, the B/C ratio is well described by a single power law R[superscript Δ] with index Δ=-0.333±0.014(fit)±0.005(syst), in good agreement with the Kolmogorov theory of turbulence which predicts Δ=-1/3 asymptotically.National Science Foundation (U.S.) (Grants 1455202 and 1551980)Wyle Research (Firm) (Grant 2014/T72497)United States. National Aeronautics and Space Administration (NASA Earth and Space Science Fellowship Grant HELIO15F-0005

Antiproton Flux, Antiproton-to-Proton Flux Ratio, and Properties of Elementary Particle Fluxes in Primary Cosmic Rays Measured with the Alpha Magnetic Spectrometer on the International Space Station

International audienceA precision measurement by AMS of the antiproton flux and the antiproton-to-proton flux ratio inprimary cosmic rays in the absolute rigidity range from 1 to 450 GV is presented based on 3.49 × 105antiproton events and 2.42 × 109 proton events. The fluxes and flux ratios of charged elementary particlesin cosmic rays are also presented. In the absolute rigidity range ∼60 to ∼500 GV, the antiproton ¯p, protonp, and positron eþ fluxes are found to have nearly identical rigidity dependence and the electron e− fluxexhibits a different rigidity dependence. Below 60 GV, the ( ¯ p=p), ( ¯ p=eþ), and (p=eþ) flux ratios eachreaches a maximum. From ∼60 to ∼500 GV, the ( ¯ p=p), ( ¯ p=eþ), and (p=eþ) flux ratios show no rigiditydependence. These are new observations of the properties of elementary particles in the cosmos