Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte

On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.Comment: Latex2e file, 22 pages. Final version appeared in IJT

Measurement of the production of charged pions by protons on a tantalum target

A measurement of the double-differential cross-section for the production of charged pions in proton--tantalum collisions emitted at large angles from the incoming beam direction is presented. The data were taken in 2002 with the HARP detector in the T9 beam line of the CERN PS. The pions were produced by proton beams in a momentum range from 3 \GeVc to 12 \GeVc hitting a tantalum target with a thickness of 5% of a nuclear interaction length. The angular and momentum range covered by the experiment (100 \MeVc \le p < 800 \MeVc and 0.35 \rad \le \theta <2.15 \rad) is of particular importance for the design of a neutrino factory. The produced particles were detected using a small-radius cylindrical time projection chamber (TPC) placed in a solenoidal magnet. Track recognition, momentum determination and particle identification were all performed based on the measurements made with the TPC. An elaborate system of detectors in the beam line ensured the identification of the incident particles. Results are shown for the double-differential cross-sections ${{\mathrm{d}^2 \sigma}} / {{\mathrm{d}p\mathrm{d}\theta}}$ at four incident proton beam momenta (3 \GeVc, 5 \GeVc, 8 \GeVc and 12 \GeVc). In addition, the pion yields within the acceptance of typical neutrino factory designs are shown as a function of beam momentum. The measurement of these yields within a single experiment eliminates most systematic errors in the comparison between rates at different beam momenta and between positive and negative pion production.Comment: 49 pages, 31 figures. Version accepted for publication on Eur. Phys. J.

Novel genetic loci associated with hippocampal volume

The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg =-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness

Measurement of the production of charged pions by protons on a tantalum target

A measurement of the double-differential cross-section for the production of charged pions in proton--tantalum collisions emitted at large angles from the incoming beam direction is presented. The data were taken in 2002 with the HARP detector in the T9 beam line of the CERN PS. The pions were produced by proton beams in a momentum range from 3 \GeVc to 12 \GeVc hitting a tantalum target with a thickness of 5% of a nuclear interaction length. The angular and momentum range covered by the experiment (100 \MeVc \le p < 800 \MeVc and 0.35 \rad \le \theta <2.15 \rad) is of particular importance for the design of a neutrino factory. The produced particles were detected using a small-radius cylindrical time projection chamber (TPC) placed in a solenoidal magnet. Track recognition, momentum determination and particle identification were all performed based on the measurements made with the TPC. An elaborate system of detectors in the beam line ensured the identification of the incident particles. Results are shown for the double-differential cross-sections d2σ/dpdθ at four incident proton beam momenta (3 \GeVc, 5 \GeVc, 8 \GeVc and 12 \GeVc). In addition, the pion yields within the acceptance of typical neutrino factory designs are shown as a function of beam momentum. The measurement of these yields within a single experiment eliminates most systematic errors in the comparison between rates at different beam momenta and between positive and negative pion production

Nonthermal phenomena in clusters of galaxies

Recent observations of high energy (> 20 keV) X-ray emission in a few clusters of galaxies broaden our knowledge of physical phenomena in the intracluster space. This emission is likely to be nonthermal, probably resulting from Compton scattering of relativistic electrons by the cosmic microwave background (CMB) radiation. Direct evidence for the presence of relativistic electrons in some 50 clusters comes from measurements of extended radio emission in their central regions. We briefly review the main results from observations of extended regions of radio emission, and Faraday rotation measurements of background and cluster radio sources. The main focus of the review are searches for nonthermal X-ray emission conducted with past and currently operating satellites, which yielded appreciable evidence for nonthermal emission components in the spectra of a few clusters. This evidence is clearly not unequivocal, due to substantial observational and systematic uncertainties, in addition to virtually complete lack of spatial information. If indeed the emission has its origin in Compton scattering of relativistic electrons by the CMB, then the mean magnetic field strength and density of relativistic electrons in the cluster can be directly determined. Knowledge of these basic nonthermal quantities is valuable for the detailed description of processes in intracluster gas and for the origin of magnetic fields.Comment: 23 pages, 7 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 5; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Reproducibility in the absence of selective reporting : An illustration from large-scale brain asymmetry research

Altres ajuts: Max Planck Society (Germany).The problem of poor reproducibility of scientific findings has received much attention over recent years, in a variety of fields including psychology and neuroscience. The problem has been partly attributed to publication bias and unwanted practices such as p-hacking. Low statistical power in individual studies is also understood to be an important factor. In a recent multisite collaborative study, we mapped brain anatomical left-right asymmetries for regional measures of surface area and cortical thickness, in 99 MRI datasets from around the world, for a total of over 17,000 participants. In the present study, we revisited these hemispheric effects from the perspective of reproducibility. Within each dataset, we considered that an effect had been reproduced when it matched the meta-analytic effect from the 98 other datasets, in terms of effect direction and significance threshold. In this sense, the results within each dataset were viewed as coming from separate studies in an "ideal publishing environment," that is, free from selective reporting and p hacking. We found an average reproducibility rate of 63.2% (SD = 22.9%, min = 22.2%, max = 97.0%). As expected, reproducibility was higher for larger effects and in larger datasets. Reproducibility was not obviously related to the age of participants, scanner field strength, FreeSurfer software version, cortical regional measurement reliability, or regional size. These findings constitute an empirical illustration of reproducibility in the absence of publication bias or p hacking, when assessing realistic biological effects in heterogeneous neuroscience data, and given typically-used sample sizes

The genetic architecture of the human cerebral cortex

INTRODUCTION The cerebral cortex underlies our complex cognitive capabilities. Variations in human cortical surface area and thickness are associated with neurological, psychological, and behavioral traits and can be measured in vivo by magnetic resonance imaging (MRI). Studies in model organisms have identified genes that influence cortical structure, but little is known about common genetic variants that affect human cortical structure. RATIONALE To identify genetic variants associated with human cortical structure at both global and regional levels, we conducted a genome-wide association meta-analysis of brain MRI data from 51,665 individuals across 60 cohorts. We analyzed the surface area and average thickness of the whole cortex and 34 cortical regions with known functional specializations. RESULTS We identified 306 nominally genome-wide significant loci (P < 5 × 10−8) associated with cortical structure in a discovery sample of 33,992 participants of European ancestry. Of the 299 loci for which replication data were available, 241 loci influencing surface area and 14 influencing thickness remained significant after replication, with 199 loci passing multiple testing correction (P < 8.3 × 10−10; 187 influencing surface area and 12 influencing thickness). Common genetic variants explained 34% (SE = 3%) of the variation in total surface area and 26% (SE = 2%) in average thickness; surface area and thickness showed a negative genetic correlation (rG = −0.32, SE = 0.05, P = 6.5 × 10−12), which suggests that genetic influences have opposing effects on surface area and thickness. Bioinformatic analyses showed that total surface area is influenced by genetic variants that alter gene regulatory activity in neural progenitor cells during fetal development. By contrast, average thickness is influenced by active regulatory elements in adult brain samples, which may reflect processes that occur after mid-fetal development, such as myelination, branching, or pruning. When considered together, these results support the radial unit hypothesis that different developmental mechanisms promote surface area expansion and increases in thickness. To identify specific genetic influences on individual cortical regions, we controlled for global measures (total surface area or average thickness) in the regional analyses. After multiple testing correction, we identified 175 loci that influence regional surface area and 10 that influence regional thickness. Loci that affect regional surface area cluster near genes involved in the Wnt signaling pathway, which is known to influence areal identity. We observed significant positive genetic correlations and evidence of bidirectional causation of total surface area with both general cognitive functioning and educational attainment. We found additional positive genetic correlations between total surface area and Parkinson’s disease but did not find evidence of causation. Negative genetic correlations were evident between total surface area and insomnia, attention deficit hyperactivity disorder, depressive symptoms, major depressive disorder, and neuroticism. CONCLUSION This large-scale collaborative work enhances our understanding of the genetic architecture of the human cerebral cortex and its regional patterning. The highly polygenic architecture of the cortex suggests that distinct genes are involved in the development of specific cortical areas. Moreover, we find evidence that brain structure is a key phenotype along the causal pathway that leads from genetic variation to differences in general cognitive function