Pairs of geometric foliations of regular and singular surfaces

We examine some generic features of surfaces in the Euclidean 3-space $\mathbb{R}^3$ related to the Gauss map on the surface. We consider these features on smooth surfaces and on singular surfaces with a cross-cap singularity. We study some symmetries between two classical pairs of foliations defined on smooth surfaces in $\mathbb{R}^3$: the asymptotic curves and the characteristic curves (called harmonic mean curvature lines in \cite{garciasotomayorharmonic}). The asymptotic curves exist in hyperbolic regions of surfaces and have been well studied. The characteristic curves are in certain ways the analogy of the asymptotic curves in elliptic regions. In this thesis we extend this analogy. . We use We produce results on the characteristic curves mirroring those of Uribe-Vargas (\cite{uribevargas}) on the asymptotic curves. By considering cross-ratios of Legendrian lines in the manifold of contact elements to the surface we show that certain properties of the characteristic curves are invariant under projective transformations, and examine their behaviour at cusps of Gauss. We establish an analogy of the Beltrami-Enepper Theorem, which allows us to distinguish between the two characteristic foliations in a natural geometric way. We show that the local properties of characteristic curves may be used to prove certain global results concerning the elliptic regions of smooth surfaces. Motivated by the study of the asymptotic, principal and characteristic curves on surfaces in $\mathbb{R}^3$, we construct a natural one-to-one correspondence between the set of non-degenerate binary differential equations (BDEs) and linear involutions on the real projective line. We show that one may construct pairs of BDEs that have various symmetric properties using a single involution on $\mathbb{R}P^1$. We study the folded singularities of BDEs, and associate an affine invariant to such points. We show that one may associate a complex parameter to folded singularities that determines the relative positions of various curves of interest. We show that the BDEs asymptotic, characteristic, and principal curves are related to other quadratic forms on surfaces. These include the BDE that defines the lines of arithmetic mean curvature which are studied in \cite{garciasotomayorarith}, and the third fundamental form of the surface. We define a new pair of foliations of a surface which we label the minimal orthogonal spherical image (MOSI) curves which are the integral curves of those tangent directions to a surface that have orthogonal images under the Gauss map, and are inclined at an extremal angle. We establish the configurations of the MOSI curves in a neighbourhood of umbilic points, parabolic points and cusps of Gauss. We construct natural 1-parameter families of BDEs that interpolate between the BDEs we have studied, and establish relationships between these families. We exhibit the existence of a curve of points of zero torsion of the characteristic curves, and a curve of points where the tangent plane to the surface is the osculating plane of a characteristic curve. We determine the behaviour of these curves near cusps of Gauss and umbilic points. We study BDEs with coefficients that vanish simultaneously at an isolated point and with discriminant having an $A_2$-singularity at that point. We show that such BDEs can be grouped into three distinct types, and study the differences between these types in terms of their codimension and the linear parts of their coefficients. We establish the topological configurations of the solution curves in each case with codimension $\leq4$. We study the asymptotic and characteristic curves in the neighbourhood of a parabolic cross-cap, that is, on a singular surface with a cross-cap singularity with a parabolic set having a cusp singularity at the singular point. We obtain the topological configurations of these foliations both in the domain of a parametrisation of such a surface, and on the surface itself. We construct a natural one-parameter family of surfaces with cross-cap singularities in which the parabolic cross-cap is the transition from a hyperbolic cross-cap to an elliptic cross-cap. We study the bifurcations of the asymptotic and characteristic curves in this family

Evolution of realized Eltonian niches across Rajidae species

The notion that closely related species resemble each other in ecological niche space (i.e., phylogenetic dependence) has been a long-standing, contentious paradigm in evolutionary biology, the incidence of which is important for predicting the ecosystem-level effects of species loss. Despite being examined across a multitude of terrestrial taxa, many aspects of niche conservatism have yet to be explored in marine species, especially for characteristics related to resource use and trophic behavior (Eltonian niche characteristics, ENCs). We combined ENCs derived from stable isotope ratios at assemblage- and species-levels with phylogenetic comparative methods, to test the hypotheses that benthic marine fishes (1) exhibit similar assemblage-wide ENCs regardless of geographic location and (2) display phylogenetically dependent ENCs at the species level. We used a 12-species sub-set of the monophyletic group Rajidae sampled from three independent assemblages (Central California, Gulf of Alaska, and Northwest Atlantic), which span two ocean basins. Assemblage-level ENCs implied low trophic diversity and high evenness, suggesting that Rajidae assemblages may exhibit a well-defined trophic role, a trend consistent regardless of geographic location. At the species level, we found evidence for phylogenetic dependence of ENCs relating to trophic diversity (i.e., isotopic niche width; SEAc). Whether individuals can be considered functional equivalents across assemblages is hard to ascertain because we did not detect a significant phylogenetic signal for ENCs relating to trophic function (e.g., trophic position). Thus, additional, complimentary approaches are required to further examine the phylogenetic dependence of species functionality. Our approach illustrates the potential of stable isotope-derived niche characteristics to provide insight on macroecological processes occurring across evolutionary time, which could help predict how assemblages may respond to the effects of species loss

Intraoperative electrocochleographic characteristics of auditory neuropathy spectrum disorder in cochlear implant subjects

Auditory neuropathy spectrum disorder (ANSD) is characterized by an apparent discrepancy between measures of cochlear and neural function based on auditory brainstem response (ABR) testing. Clinical indicators of ANSD are a present cochlear microphonic (CM) with small or absent wave V. Many identified ANSD patients have speech impairment severe enough that cochlear implantation (CI) is indicated. To better understand the cochleae identified with ANSD that lead to a CI, we performed intraoperative round window electrocochleography (ECochG) to tone bursts in children (n = 167) and adults (n = 163). Magnitudes of the responses to tones of different frequencies were summed to measure the “total response” (ECochG-TR), a metric often dominated by hair cell activity, and auditory nerve activity was estimated visually from the compound action potential (CAP) and auditory nerve neurophonic (ANN) as a ranked “Nerve Score”. Subjects identified as ANSD (45 ears in children, 3 in adults) had higher values of ECochG-TR than adult and pediatric subjects also receiving CIs not identified as ANSD. However, nerve scores of the ANSD group were similar to the other cohorts, although dominated by the ANN to low frequencies more than in the non-ANSD groups. To high frequencies, the common morphology of ANSD cases was a large CM and summating potential, and small or absent CAP. Common morphologies in other groups were either only a CM, or a combination of CM and CAP. These results indicate that responses to high frequencies, derived primarily from hair cells, are the main source of the CM used to evaluate ANSD in the clinical setting. However, the clinical tests do not capture the wide range of neural activity seen to low frequency sounds

Coding culture: challenges and recommendations for comparative cultural databases

Considerable progress in explaining cultural evolutionary dynamics has been made by applying rigorous models from the natural sciences to historical and ethnographic information collected and accessed using novel digital platforms. Initial results have clarified several long-standing debates in cultural evolutionary studies, such as population origins, the role of religion in the evolution of complex societies and the factors that shape global patterns of language diversity. However, future progress requires recognition of the unique challenges posed by cultural data. To address these challenges, standards for data collection, organisation and analysis must be improved and widely adopted. Here, we describe some major challenges to progress in the construction of large comparative databases of cultural history, including recognising the critical role of theory, selecting appropriate units of analysis, data gathering and sampling strategies, winning expert buy-in, achieving reliability and reproducibility in coding, and ensuring interoperability and sustainability of the resulting databases. We conclude by proposing a set of practical guidelines to meet these challenges

De novo assembly of the dual transcriptomes of a polymorphic raptor species and its malarial parasite

Pauli M, Chakarov N, Rupp O, et al. De novo assembly of the dual transcriptomes of a polymorphic raptor species and its malarial parasite. BMC Genomics. 2015;16(1): 1038

Spectroscopy of Broad Line Blazars from 1LAC

We report on optical spectroscopy of 165 Flat Spectrum Radio Quasars (FSRQs) in the Fermi 1LAC sample, which have helped allow a nearly complete study of this population. Fermi FSRQ show significant evidence for non-thermal emission even in the optical; the degree depends on the gamma-ray hardness. They also have smaller virial estimates of hole mass than the optical quasar sample. This appears to be largely due to a preferred (axial) view of the gamma-ray FSRQ and non-isotropic (H/R ~ 0.4) distribution of broad-line velocities. Even after correction for this bias, the Fermi FSRQ show higher mean Eddington ratios than the optical population. A comparison of optical spectral properties with Owens Valley Radio Observatory radio flare activity shows no strong correlation.Comment: Accepted for publication in Ap

Cardiogoniometry compared to fractional flow reserve at identifying physiologically significant coronary stenosis: The Cardioflow Study

Cardiogoniometry (CGM) is method of 3-dimensional electrocardiographic assessment which has been shown to identify patients with angiographically defined, stable coronary artery disease (CAD). However, angiographic evidence of CAD, does not always correlate to physiologically significant disease. The aim of our study was to assess the ability of CGM to detect physiologically significant coronary stenosis defined by fractional flow reserve (FFR). In a tertiary cardiology centre, elective patients with single vessel CAD were enrolled into a prospective double blinded observational study. A baseline CGM recording was performed at rest. A second CGM recording was performed during the FFR procedure, at the time of adenosine induced maximal hyperaemia. A significant CGM result was defined as an automatically calculated ischaemia score < 0 and a significant FFR ratio was defined as < 0.80. Measures of diagnostic performance (including sensitivity and specificity) were calculated for CGM at rest and during maximal hyperaemia. Forty-five patients were included (aged 61.1 ± 11.0; 60.0% male), of which eighteen (40%) were found to have significant CAD when assessed by FFR. At rest, CGM yielded a sensitivity of 33.3% and specificity of 63.0%. At maximal hyperaemia the sensitivity and specificity of CGM was 71.4 and 50.0% respectively. The diagnostic performance of CGM to detect physiologically significant stable CAD is poor at rest. Although, the diagnostic performance of CGM improves substantially during maximal hyperaemia, it does not reach sufficient levels of accuracy to be used routinely in clinical practice

High Redshift LAEs and their Cosmic Evolution: Morphologies, SFR and AGN Activity from z~2 to 6

We studied a large sample of ∼ 4000 high redshift Lyman-alpha Emitters (LAEs) in order to determine their properties and infer how they might have evolved into the local Universe. This was done through the exploration of the SC4K survey (Sobral et al. 2018a) and making use of the Hubble Space Telescope (HST), Chandra X-ray Observatory (Chandra) and the Very Large Array (VLA). We find that SC4K LAEs are mostly (69 ± 4%) compact disky galaxies (average S ́ersic index, n = 1.9 ± 2.2) The average star formation rate SFRLyα of LAEs is ≈ 17 M⊙ yr−1 . We find that SFR increases with increasing stellar mass. We also observed a characteristic ‘peak’ in SFR at M ∼ 10^9.3 M⊙, at redshift z ∼ 2.5, and progressing to higher stellar masses at higher redshifts. We find a total of 303 X-ray or radio detected active galactic nuclei (AGN) within the SC4K catalogue. These AGN have a range of black hole accretion rates (BHARs) from ∼ 0.03 M⊙ yr−1 to ∼ 3.3 M⊙ yr−1. The AGN fraction increases with increasing Lyα luminosity and decreases with increasing redshift, peaking at z ∼ 3. LAEs found at z ∼ 2−6 with a stellar mass M ∼ 10^10 M⊙ and a SFR ∼ 5.4M⊙yr−1 are consistent with being progenitors of Milky Way-like galaxies progenitor. Additionally, we found that the majority of the SC4K LAEs consists of cluster-like progenitors that will go on to form the brightest cluster galaxies (BCGs) in the local Universe

Spectroscopy of the Largest Ever γ-Ray-selected BL Lac Sample

We report on spectroscopic observations covering most of the 475 BL Lacs in the second Fermi Large Area Telescope (LAT) catalog of active galactic nuclei (AGNs). Including archival measurements (correcting several erroneous literature values) we now have spectroscopic redshifts for 44% of the BL Lacs. We establish firm lower redshift limits via intervening absorption systems and statistical lower limits via searches for host galaxies for an additional 51% of the sample leaving only 5% of the BL Lacs unconstrained. The new redshifts raise the median spectroscopic z from 0.23 to 0.33 and include redshifts as large as z = 2.471. Spectroscopic redshift minima from intervening absorbers have z = 0.70, showing a substantial fraction at large z and arguing against strong negative evolution. We find that detected BL Lac hosts are bright ellipticals with black hole masses M_• ~ 10^(8.5) – 10^9, substantially larger than the mean of optical AGNs and LAT Flat Spectrum Radio Quasar samples. A slow increase in M_• with z may be due to selection bias. We find that the power-law dominance of the optical spectrum extends to extreme values, but this does not strongly correlate with the γ-ray properties, suggesting that strong beaming is the primary cause of the range in continuum dominance