Local Conjugations of Groups and Applications to Number Fields

This dissertation studies pairs of subgroups H, H\u27 of a finite group G together with a bijective map Φ H −\u3e H\u27 that is a local conjugation, meaning that each element h in H is conjugate in G to its image Φ(h). The map Φ is not required to take products to products. The motivation for studying such pairs comes from a paper of F. Gassmann in 1926, in which he formulated an equivalent but different-sounding condition now known as Gassmann’s condition. There are now at least ten equivalent reformulations of Gassmann’s condition, of which local conjugation is perhaps the most elementary. The utility of studying local conjugation is that it raises natural questions. For example, if we do additionally require that the map Φ preserve products (that is, if it is required that Φ be an isomorphism as well as a local conjugation), does it follow that Φ is a global conjugation? An example showing the answer is no is given in this dissertation. Many applications of local conjugacy have been discovered. In number theory, the groups H, H\u27, G appear as Galois groups of field extensions of the field of algebraic number field k, and H, H\u27 are locally conjugate in G if and only if the fixed fields K, K\u27 of H, H\u27 have identical Dedekind zeta functions. In 1985, Sunada looked at H, H\u27, G as groups of deck isometrices of coverings of Riemann surfaces and showed that when H, H\u27 are locally conjugate but not conjugate in G then the corresponding Riemann surfaces are isospectral but non-isometric. And more recently, locally conjugate subgroups of a finite group G have been used to produce pairs of nonisomorphic graphs with identical Ihara zeta functions. All of this motivated the study of local conjugacy in this dissertation. Among other things, yet another reformulation, called cycle number equivalence, was discovered, which gives as a corollary a new proof of a theorem of Stuart and Perlis

Rayleigh-Lidar Determinations of the Vertical Wavelength of Mesospheric Gravity Wave

Atmospheric structures have been observed in the Rayleigh lidar data acquired between 1993 and 2004 at Utah State University (USU). The observations pertain to the density and temperature in the mesosphere between 45 and 90 km altitude. The structures referred to arise from monochromatic Atmospheric Gravity Waves (AGWs). Previous analysis of these data have searched for and found a spectrum with a peak in the vertical wavelength 12–16 km. It has been suggested by other researchers using other types of data that there may be another peak in the spectrum at shorter wavelengths. For this study the lidar data were re- analyzed to search for such waves. To do this, the altitude resolution was reduced from 3 km to 600 m. This enabled the shortest wavelength AGW that can be examined to be reduced from 6 km to ~1.2 km, thereby significantly extending the spectrum investigated. Two additional peaks in the spectrum were found at 1.25–1.75 and 3.0–4.0 km

Evolution of chemosensory tissues and cells across ecologically diverse Drosophilids

Chemosensory tissues exhibit significant between-species variability, yet the evolution of gene expression and cell types underlying this diversity remain poorly understood. To address these questions, we conducted transcriptomic analyses of five chemosensory tissues from six Drosophila species and integrated the findings with single-cell datasets. While stabilizing selection predominantly shapes chemosensory transcriptomes, thousands of genes in each tissue have evolved expression differences. Genes that have changed expression in one tissue have often changed in multiple other tissues but at different past epochs and are more likely to be cell type-specific than unchanged genes. Notably, chemosensory-related genes have undergone widespread expression changes, with numerous species-specific gains/losses including novel chemoreceptors expression patterns. Sex differences are also pervasive, including a D. melanogaster-specific excess of male-biased expression in sensory and muscle cells in its forelegs. Together, our analyses provide new insights for understanding evolutionary changes in chemosensory tissues at both global and individual gene levels

Chiral emergence in multistep hierarchical assembly of achiral conjugated polymers

Intimately connected to the rule of life, chirality remains a long-time fascination in biology, chemistry, physics and materials science. Chiral structures, e.g., nucleic acid and cholesteric phase developed from chiral molecules are common in nature and synthetic soft materials. While it was recently discovered that achiral but bent core mesogens can also form chiral helices, the assembly of chiral microstructures from achiral polymers has rarely been explored. Here, we reveal chiral emergence from achiral conjugated polymers for the first time, in which hierarchical helical structures are developed through a multistep assembly pathway. Upon increasing concentration beyond a threshold volume fraction, pre-aggregated polymer nanofibers form lyotropic liquid crystalline (LC) mesophases with complex, chiral morphologies. Combining imaging, X-ray and spectroscopy techniques with molecular simulations, we demonstrate that this structural evolution arises from torsional polymer molecules which induce multiscale helical assembly, progressing from nano- to micron scale helical structures as the solution concentration increases. This study unveils a previously unknown complex state of matter for conjugated polymers that can pave way to a new field of chiral (opto)electronics. We anticipate that hierarchical chiral helical structures can profoundly impact how conjugated polymers interact with light, transport charges, and transduce signals from biomolecular interactions and even give rise to properties unimagined before.Comment: 47 pages, 7 figure

Occipital Condyle Fracture – A Diagnosis Requiring High Suspicion

Traumatic injury causing occipital condyle fractures (OCF) are very rare. They are of critical clinical importance owing toimportant anatomical structures that need considerations of the occiput-atlantoaxial joint complex. Early diagnosis is of paramount importance since there may be associated lower cranial nerve palsies along with cervical spinal instability. Sometimes, this can be a diagnostic challenge in acute stage because of the inability to diagnose this injury with plain radiographs. To avoid this, high index of suspicion and relevant investigation of the craniocervical junction is indicated. Hence it helps in early recognition and diagnosis of OCF thus preventing possible neurological impairment. Here, we report a case of a 58 -year-old male who presented with complaints of neck pain and headache following physical assault

Modification of the nanostructure of lignocellulose cell walls via a non-enzymatic lignocellulose deconstruction system in brown rot wood-decay fungi

Abstract Wood decayed by brown rot fungi and wood treated with the chelator-mediated Fenton (CMF) reaction, either alone or together with a cellulose enzyme cocktail, was analyzed by small angle neutron scattering (SANS), sum frequency generation (SFG) spectroscopy, Fourier transform infrared (FTIR) analysis, X-ray diffraction (XRD), atomic force microscopy (AFM), and transmission electron microscopy (TEM). Results showed that the CMF mechanism mimicked brown rot fungal attack for both holocellulose and lignin components of the wood. Crystalline cellulose and lignin were both depolymerized by the CMF reaction. Porosity of the softwood cell wall did not increase during CMF treatment, enzymes secreted by the fungi did not penetrate the decayed wood. The enzymes in the cellulose cocktail also did not appear to alter the effects of the CMF-treated wood relative to enhancing cell wall deconstruction. This suggests a rethinking of current brown rot decay models and supports a model where monomeric sugars and oligosaccharides diffuse from the softwood cell walls during non-enzymatic action. In this regard, the CMF mechanism should not be thought of as a “pretreatment” used to permit enzymatic penetration into softwood cell walls, but instead it enhances polysaccharide components diffusing to fungal enzymes located in wood cell lumen environments during decay. SANS and other data are consistent with a model for repolymerization and aggregation of at least some portion of the lignin within the cell wall, and this is supported by AFM and TEM data. The data suggest that new approaches for conversion of wood substrates to platform chemicals in biorefineries could be achieved using the CMF mechanism with >75% solubilization of lignocellulose, but that a more selective suite of enzymes and other downstream treatments may be required to work when using CMF deconstruction technology. Strategies to enhance polysaccharide release from lignocellulose substrates for enhanced enzymatic action and fermentation of the released fraction would also aid in the efficient recovery of the more uniform modified lignin fraction that the CMF reaction generates to enhance biorefinery profitability

The K2-HERMES Survey: Age and Metallicity of the Thick Disc

Asteroseismology is a promising tool to study Galactic structure and evolution because it can probe the ages of stars. Earlier attempts comparing seismic data from the {\it Kepler} satellite with predictions from Galaxy models found that the models predicted more low-mass stars compared to the observed distribution of masses. It was unclear if the mismatch was due to inaccuracies in the Galactic models, or the unknown aspects of the selection function of the stars. Using new data from the K2 mission, which has a well-defined selection function, we find that an old metal-poor thick disc, as used in previous Galactic models, is incompatible with the asteroseismic information. We show that spectroscopic measurements of [Fe/H] and [$\alpha$/Fe] elemental abundances from the GALAH survey indicate a mean metallicity of $\log (Z/Z_{\odot})=-0.16$ for the thick disc. Here $Z$ is the effective solar-scaled metallicity, which is a function of [Fe/H] and [$\alpha$/Fe]. With the revised disc metallicities, for the first time, the theoretically predicted distribution of seismic masses show excellent agreement with the observed distribution of masses. This provides an indirect verification of the asteroseismic mass scaling relation is good to within five percent. Using an importance-sampling framework that takes the selection function into account, we fit a population synthesis model of the Galaxy to the observed seismic and spectroscopic data. Assuming the asteroseismic scaling relations are correct, we estimate the mean age of the thick disc to be about 10 Gyr, in agreement with the traditional idea of an old $\alpha$-enhanced thick disc.Comment: 21 pages, submitted to MNRA

Self-medication and non-doctor prescription practices in Pokhara valley, Western Nepal: a questionnaire-based study

BACKGROUND: Self-medication and non-doctor prescribing of drugs is common in developing countries. Complementary and alternative medications, especially herbs, are also commonly used. There are few studies on the use of these medications in Pokhara Valley, Western Nepal. METHODS: Previously briefed seventh semester medical students, using a semi-structured questionnaire, carried out the study on 142 respondents. Demographic information and information on drugs used for self-medication or prescribed by a non-allopathic doctor were collected. RESULTS: Seventy-six respondents (54%) were aged between 20 to 39 years. The majority of the respondents (72 %) stayed within 30 minutes walking distance of a health post/medical store. 59% of these respondents had taken some form of self-medication in the 6-month period preceding the study. The common reasons given for self-medication were mild illness, previous experience of treating a similar illness, and non-availability of health personnel. 70% of respondents were prescribed allopathic drugs by a non-allopathic doctor. The compounder and health assistant were common sources of medicines. Paracetamol and antimicrobials were the drugs most commonly prescribed. A significantly higher proportion of young (<40 years) male respondents had used self-medication than other groups. CONCLUSIONS: Self-medication and non-doctor prescribing are common in the Pokhara valley. In addition to allopathic drugs, herbal remedies were also commonly used for self-medication. Drugs, especially antimicrobials, were not taken for the proper duration. Education to help patients decide on the appropriateness of self-medication is required

Galaxy And Mass Assembly (GAMA): M-star-R-e relations of z=0 bulges, discs and spheroids

We perform automated bulge + disc decomposition on a sample of ~7500 galaxies from the Galaxy And Mass Assembly (GAMA) survey in the redshift range of 0.002<z<0.06 using SIGMA, a wrapper around GALFIT3. To achieve robust profile measurements we use a novel approach of repeatedly fitting the galaxies, varying the input parameters to sample a large fraction of the input parameter space. Using this method we reduce the catastrophic failure rate significantly and verify the confidence in the fit independently of \chi^2 Additionally, using the median of the final fitting values and the 16^{th}$ and 84^{th} percentile produces more realistic error estimates than those provided by GALFIT, which are known to be underestimated. We use the results of our decompositions to analyse the stellar mass - half-light radius relations of bulges, discs and spheroids. We further investigate the association of components with a parent disc or elliptical relation to provide definite z=0 disc and spheroid M-star-R-e} relations. We conclude by comparing our local disc and spheroid M-star-R-e} to simulated data from EAGLE and high redshift data from CANDELS-UDS. We show the potential of using the mass-size relation to study galaxy evolution in both cases but caution that for a fair comparison all data sets need to be processed and analysed in the same manner

Galaxy And Mass Assembly: the evolution of the cosmic spectral energy distribution from z = 1 to z = 0

We present the evolution of the cosmic spectral energy distribution (CSED) from z = 1 to 0. Our CSEDs originate from stacking individual spectral energy distribution (SED) fits based on panchromatic photometry from the Galaxy And Mass Assembly (GAMA) and COSMOS data sets in 10 redshift intervals with completeness corrections applied. Below z = 0.45, we have credible SED fits from 100 nm to 1 mm. Due to the relatively low sensitivity of the far-infrared data, our far-infrared CSEDs contain a mix of predicted and measured fluxes above z = 0.45. Our results include appropriate errors to highlight the impact of these corrections. We show that the bolometric energy output of the Universe has declined by a factor of roughly 4 – from 5.1 ± 1.0 at z ∼ 1 to 1.3 ± 0.3 × 1035 h70 W Mpc−3 at the current epoch. We show that this decrease is robust to cosmic sample variance, the SED modelling and other various types of error. Our CSEDs are also consistent with an increase in the mean age of stellar populations. We also show that dust attenuation has decreased over the same period, with the photon escape fraction at 150 nm increasing from 16 ± 3 at z ∼ 1 to 24 ± 5 per cent at the current epoch, equivalent to a decrease in AFUV of 0.4 mag. Our CSEDs account for 68 ± 12 and 61 ± 13 per cent of the cosmic optical and infrared backgrounds, respectively, as defined from integrated galaxy counts and are consistent with previous estimates of the cosmic infrared background with redshift