Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians

We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials are analyzed and the subtle differences, in the singularity structures of their quantum momentum functions, are pointed out. The role of the PT symmetry in the complex domain is also illustrated.Comment: 11 page

Disruption of a structurally important extracellular element in the Glycine Receptor leads to decreased synaptic integration and signaling resulting in Severe Startle Disease

Functional impairments or trafficking defects of inhibitory glycine receptors (GlyRs) have been linked to human hyperekplexia/startle disease and autism spectrum disorders. We found that a lack of synaptic integration of GlyRs, together with disrupted receptor function, is responsible for a lethal startle phenotype in a novel spontaneous mouse mutant shaky, caused by a missense mutation, Q177K, located in the extracellular β8–β9 loop of the GlyR α1 subunit. Recently, structural data provided evidence that the flexibility of the β8–β9 loop is crucial for conformational transitions during opening and closing of the ion channel and represents a novel allosteric binding site in Cys-loop receptors. We identified the underlying neuropathological mechanisms in male and female shaky mice through a combination of protein biochemistry, immunocytochemistry, and both in vivo and in vitro electrophysiology. Increased expression of the mutant GlyR α1Q177K subunit in vivo was not sufficient to compensate for a decrease in synaptic integration of α1Q177Kβ GlyRs. The remaining synaptic heteromeric α1Q177Kβ GlyRs had decreased current amplitudes with significantly faster decay times. This functional disruption reveals an important role for the GlyR α1 subunit β8–β9 loop in initiating rearrangements within the extracellular–transmembrane GlyR interface and that this structural element is vital for inhibitory GlyR function, signaling, and synaptic clustering

Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering

We report the first measurement of the parity-violating asymmetry A_PV in the elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060 (stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur

Multifrequency observation of the optically violent variable quasar 3C 446

Extensive optical and radio monitoring data and seven multifrequency spectra were obtained of the violently variable quasar 3C 446. The monitoring data suggest a correlation between the radio and optical outbursts, with the optical flare preceding the radio activity by 400-600 days. A difference in the statistical behavior of the optical and radio variability indicates that considerable processing occurs to the optical emitting plasma before it becomes radio emitting plasma. Within the radio band, outbursts proceed from high to low frequencies. An outburst in 1983 showed greater and more rapid variation in the optical than in the near-IR region. The 10-100 μm fluxes did not follow the higher frequency variation, suggesting a time delay between these spectral domains. During another time, the X-ray emission varied on a time scale of days and more rapidly than the UV or optical emission. On a time scale of weeks-months, the X-ray fluxes are well correlated with the UV-IR fluxes but not with the radio fluxes. The multifrequency data show that the flat radio spectrum turns over at 3-10 x 10^(11) Hz and the continuum steepens with frequency; ɑ(IR) = 1.1, ɑ(opt-UV) = -2 to -3. The X-ray emission lies an order of magnitude above an extrapolation of the optical-UV spectrum and has a harder spectrum. The power is primarily concentrated in the submillimeter and infrared region. When the source is faint, a blue bump may be present. The flux in the Lycx line is proportional to the UV continuum flux density when the source is bright but is independent of the continuum level when the source is faint. The data suggest that the X-rays are produced by the inverse Compton process from an emitting region (10^(16) cm) smaller than but related to the synchrotron emitting UV-IR region. The characteristic size of the emitting region increases with decreasing frequency from 10^(16) (X-ray region) to 1-3 x 10^(17) cm (far IR-submillimeter region) to 10^(19)-10^(20) cm (radio region). Plasma conditions are best constrained at the frequency when the source becomes transparent, the far IR-submillimeter band, where B ≈ 3-100 G, n ≈ 40-100 cm^(-3); and the Doppler boosting factor δ ≈ 1-5

Internal‐Rotation in Hydrogen Peroxide: The Far‐Infrared Spectrum and the Determination of the Hindering Potential

The torsional oscillation between the two OH groups of the hydrogen peroxide molecule is investigated through a study of the far‐infrared absorption spectrum of the molecule. A 1‐m‐focal‐length vacuum grating monochromator was used to scan the region from 15 to 700 cm−1 with an average resolution of 0.3 cm−1. The observed spectrum contains seven perpendicular‐type bands of which only the Q branches are resolved. The centers of the seven bands are at 11.43, 116.51, 198.57, 242.76, 370.70, 521.68, and 557.84 cm−1. These bands result from transitions between different states of the internal rotation and their identification makes it possible to construct the internal‐rotation energy level scheme through the first five excited states. Relative to the torsional ground state, these levels occur at 11.43, 254.2, 370.7, 569.3, and 775.9 cm−1.A theory of internal rotation in the hydrogen peroxide molecule is developed for use in the analysis of the far‐infrared spectra. In this theory, the Hamiltonian is constructed assuming all structural distances and angles fixed except the dihedral angle x defining the relative position of the two OH bars. By the use of a contact transformation the Hamiltonian is put in the form H (asymmetric top)+H(internal rotation) where the interaction between the internal and over‐all rotations arises through the x dependence of the inertial parameters of H(asymmetric top). It is assumed that the relative position of the two OH bars is governed by a potential‐energy function of the form V(x) = V1cosx+V2cos2x+V3cos3xV(x)=V1cosx+V2cos2x+V3cos3x. The internal‐rotation wave equation [αpx2+V(x)]M(x) = EM(x)[αpx2+V(x)]M(x)=EM(x) is solved numerically by an electronic‐computer and the potential function parameters V1=993 cm−1, V2=636 cm−1, and V3=44 cm−1 are chosen to fit the internal‐rotation energy‐level scheme. The trans and cis potential barrier heights are 386 and 2460 cm−1, respectively, and the potential‐function minima are located 111.5° from the cis configuration. Diagonalization of the matrix of the complete Hamiltonian to second order by the use of perturbation theory is sufficient to account for the observed Q‐branch shapes in the far infrared region.Two microwave frequencies observed by Massey and Bianco at 22 054.5 and 27 639.6 Mc/sec are identified from their Stark effects as the first excited‐state transitions J, K, n, τ=8, 6, 1, 1→7, 5, 1, 3 and J, K, n, τ=8, 5, 1, 3→9, 6, 1, 1, respectively, where the internal‐rotation quantum number n=1 denotes the first excited torsional state and where τ denotes trans symmetric (τ=1 and 2) or antisymmetric (τ=3 and 4) states. The form of the dipole moment operator is assumed to be μ0 cos(x/2) and μ0 is found to be 3.15 D in agreement with the value obtained from the torsional ground‐state transitions.Two J=0 microwave series observed by Massey, Beard, and Jen in a mixed sample of the deuterated species D2O2 and HOOD give confirmation of the potential function determined from the H2O2 analysis. The K=4→5 series is identified as the D2O2 first excited torsional state transition n=1→1, τ=4→2. The K=0→1 series is identified as the HOOD torsional ground‐state transition n=0→0, τ=4→2. Only very small changes in the trans barrier height are necessary to fit the constant terms of these series exactly. These changes, which are expected to arise from vibration‐internal rotation interactions, show a reasonable progression from H2O2 to D2O2: V (trans, HOOH) = 386 cm−1, V (trans, HOOD) = 381 cm−1 and V (trans, DOOD) = 378 cm−1.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71115/2/JCPSA6-42-6-1931-1.pd

Splitting hairs : dietary niche breadth modelling using stable isotope analysis of a sequentially grown tissue

AbstractStable isotope data from durable, sequentially grown tissues (e.g. hair, claw, and baleen) is commonly used for modelling dietary niche breadth. The use of tissues grown over multiple months to years, however, has the potential to complicate isotopic niche breadth modelling, as time-averaged stable isotope signals from whole tissues may obscure information available from chronologically resolved stable isotope signals in serially sectioned tissues.We determined if whole samples of brown bear guard hair produced different isotopic niche breadth estimates than those produced from subsampled, serially sectioned samples of the same tissue from the same set of individuals. We sampled guard hair from brown bears (Ursus arctos) in four regions of Alaska with disparate biogeographies and dietary resource availability. Whole hair and serially sectioned hair samples were used to produce paired isotopic dietary niche breadth estimates for each region in the SIBER Bayesian model framework in R.Isotopic data from serially sectioned hair consistently produced larger estimates of isotopic dietary niche breadth than isotope data from whole hair samples. Serial sampling captures finer-scale changes in diet and when cumulatively used to estimate isotopic niche breadth, the serially sampled isotope data more fully captures dietary variability and true isotopic niche breadth.Abstract Stable isotope data from durable, sequentially grown tissues (e.g. hair, claw, and baleen) is commonly used for modelling dietary niche breadth. The use of tissues grown over multiple months to years, however, has the potential to complicate isotopic niche breadth modelling, as time-averaged stable isotope signals from whole tissues may obscure information available from chronologically resolved stable isotope signals in serially sectioned tissues. We determined if whole samples of brown bear guard hair produced different isotopic niche breadth estimates than those produced from subsampled, serially sectioned samples of the same tissue from the same set of individuals. We sampled guard hair from brown bears (Ursus arctos) in four regions of Alaska with disparate biogeographies and dietary resource availability. Whole hair and serially sectioned hair samples were used to produce paired isotopic dietary niche breadth estimates for each region in the SIBER Bayesian model framework in R. Isotopic data from serially sectioned hair consistently produced larger estimates of isotopic dietary niche breadth than isotope data from whole hair samples. Serial sampling captures finer-scale changes in diet and when cumulatively used to estimate isotopic niche breadth, the serially sampled isotope data more fully captures dietary variability and true isotopic niche breadth

Intersectionality and Compromise: Enacting Government Policies in the Caribbean

The Caribbean as a region managed the education delivery response to COVID-19 through policy that emphasised a holistic government approach. Though each State maintains its sovereign right, throughout the various phases of the COVID-19 pandemic, locally governed Ministries of Education (Carrington, 1993) created guidance for what and how education was to continue in this region. This approach produced unique ways of continuing primary and secondary school education in the region. It also inevitably had unintended outcomes that many other regions experienced but few could quantify and qualify as to its impact on education as we knew it. Some of the unintended outcomes included how ministerial mandates were translated into actionable activities by teachers, parents and students given the challenges to financial, technological, and teaching resources. This chapter uses the pandemic as the landscape within which the stories of a variety of stakeholders (i.e., teachers, principals, parents) from the pre-tertiary sectors, in select countries outline points of intersectionality and compromise. This thus illustrates how solutions were formalised and actioned, as well as drawing on similarities and differences to extrapolate into a regional and international view