Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

Big GABA II: Water-referenced edited MR spectroscopy at 25 research sites

Accurate and reliable quantification of brain metabolites measured in vivo using 1H magnetic resonance spectroscopy (MRS) is a topic of continued interest. Aside from differences in the basic approach to quantification, the quantification of metabolite data acquired at different sites and on different platforms poses an additional methodological challenge. In this study, spectrally edited γ-aminobutyric acid (GABA) MRS data were analyzed and GABA levels were quantified relative to an internal tissue water reference. Data from 284 volunteers scanned across 25 research sites were collected using GABA+ (GABA + co-edited macromolecules (MM)) and MM-suppressed GABA editing. The unsuppressed water signal from the volume of interest was acquired for concentration referencing. Whole-brain T1-weighted structural images were acquired and segmented to determine gray matter, white matter and cerebrospinal fluid voxel tissue fractions. Water-referenced GABA measurements were fully corrected for tissue-dependent signal relaxation and water visibility effects. The cohort-wide coefficient of variation was 17% for the GABA + data and 29% for the MM-suppressed GABA data. The mean within-site coefficient of variation was 10% for the GABA + data and 19% for the MM-suppressed GABA data. Vendor differences contributed 53% to the total variance in the GABA + data, while the remaining variance was attributed to site- (11%) and participant-level (36%) effects. For the MM-suppressed data, 54% of the variance was attributed to site differences, while the remaining 46% was attributed to participant differences. Results from an exploratory analysis suggested that the vendor differences were related to the unsuppressed water signal acquisition. Discounting the observed vendor-specific effects, water-referenced GABA measurements exhibit similar levels of variance to creatine-referenced GABA measurements. It is concluded that quantification using internal tissue water referencing is a viable and reliable method for the quantification of in vivo GABA levels

Feint Lines: Notes on the Creation of a Skateboard Choreography

Magnetic fields on a range of scales play a large role in the ecosystems of galaxies, both in the galactic disk and in the extended layers of gas away from the plane. Observing magnetic field strength, structure and orientation is complex, and necessarily indirect. Observational data of magnetic fields in the halo of the Milky Way are scarce, and non-conclusive about the large-scale structure of the field. In external galaxies, various large-scale configurations of magnetic fields are measured, but many uncertainties about exact configurations and their origin remain. There is a strong interaction between magnetic fields and other components in the interstellar medium such as ionized and neutral gas and cosmic rays. The energy densities of these components are comparable on large scales, indicating that magnetic fields are not passive tracers but that magnetic field feedback on the other interstellar medium components needs to be taken into account.Comment: 13 pages, 7 figures. Accepted in Space Science Review

Updated Nucleosynthesis Constraints on Unstable Relic Particles

We revisit the upper limits on the abundance of unstable massive relic particles provided by the success of Big-Bang Nucleosynthesis calculations. We use the cosmic microwave background data to constrain the baryon-to-photon ratio, and incorporate an extensively updated compilation of cross sections into a new calculation of the network of reactions induced by electromagnetic showers that create and destroy the light elements deuterium, he3, he4, li6 and li7. We derive analytic approximations that complement and check the full numerical calculations. Considerations of the abundances of he4 and li6 exclude exceptional regions of parameter space that would otherwise have been permitted by deuterium alone. We illustrate our results by applying them to massive gravitinos. If they weigh ~100 GeV, their primordial abundance should have been below about 10^{-13} of the total entropy. This would imply an upper limit on the reheating temperature of a few times 10^7 GeV, which could be a potential difficulty for some models of inflation. We discuss possible ways of evading this problem.Comment: 40 pages LaTeX, 18 eps figure

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM

Megalencephalic Leukoencephalopathy with Subcortical Cysts: A Third Confirmed Case with Literature Review

Megalencephalic leukoencephalopathy with subcortical cysts (MLC) causes early-onset, slowly progressive central nervous system white matter disease, macrocephaly, and later cognitive and motor decline. We describe brain structure in a patient with MLC and proven MLC1 mutations. A male, normal at birth, had macrocephaly at 6 months followed by developmental delay. Magnetic resonance imaging showed extensive signal abnormality in cerebral white matter and subcortical progressive cystic changes in the bilateral temporal and right frontal areas. Biopsy of frontal gyrus at age 15 months showed normal gray matter. The subcortical white matter was pale due to prominent fine uniform 2- to 4-mu-thick vacuoles with a few interspersed myelinated axons and rare microglia. The vacuoles had a single-, double-, or, rarely, triple-unit membrane (resembling myelin) and contained occasional organelles but no intermediate filaments. Both normal myelinated and thinly myelinated axons were observed. The outer and occasionally the inner layers of myelin surrounding intact axons formed blebs that may represent a source for vacuoles. Genetic analysis identified 2 heterozygous mutations of intron 3 (c.322-1 G>A) and intron 7 (c.597+1G>A), the 1st leading to deletion of amino acids 60 to 89 and the 2nd to deletion of amino acids 194 to 199. Fine uniform vacuolation of white matter with wide separation of myelinated axons is the hallmark of MLC in early childhoo

Creatine Transporter Deficiency in Two Brothers with Autism Spectrum Disorder

Creatine transporter deficiency (CTD) is a treatable, X-linked, inborn error of metabolism. Two brothers with autism spectrum disorder were diagnosed with CTD at the ages of 17 and 12 years. Both were found to have a previously reported hemizygous p.408delF (c.1216_1218delTTC) deletion mutation. Both patients were given creatine monohydrate, L-arginine, L-glycine and S-adenosylmethionine, which partially improved the behavioral problems. Serum creatinine levels, creatine peak at brain MR spectroscopy or creatine/creatinine ratio in urine should be evaluated to identify CTD in children with autistic behavior and language disorders