Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table

Quasi-discretization Of The Electron Continuum Emitted In Collisions Of 0.6 Mev U−¹ Au11+ With Noble Gases

We have measured relative doubly differential cross sections for electron emission in collisions of 0.6 MeV u−1 Au11+ projectile ions with He, Ne and Ar targets for laboratory electron-detection angles between 17\u27 and 80\u27 and electron energies from 100 eV to well above the classical binary encounter region. The authors observe that, independent of the target Zt, the electron spectra display three characteristic peak-line structures whose energies are nearly invariant with observation angle. These structures are attributed to the diffraction of quasi-free target electrons in the potential of the projectile. © 1992 IOP Publishing Ltd

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of 'source' species, which receive input signals. Signals are transmitted to all other species in the system (the 'target' species) with a specific delay and transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and recalled to build discrete dynamical models. By separating reaction time and concentration we can greatly simplify the model, circumventing typical problems of complex dynamical systems. The transfer function transformation can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant insight, while remaining an executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modules that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. We also found that overall interconnectedness depends on the magnitude of input, with high connectivity at low input and less connectivity at moderate to high input. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.Comment: 13 pages, 5 tables, 15 figure

Built-in and induced polarization across LaAlO3_3/SrTiO3_3 heterojunctions

Ionic crystals terminated at oppositely charged polar surfaces are inherently unstable and expected to undergo surface reconstructions to maintain electrostatic stability. Essentially, an electric field that arises between oppositely charged atomic planes gives rise to a built-in potential that diverges with thickness. In ultra thin film form however the polar crystals are expected to remain stable without necessitating surface reconstructions, yet the built-in potential has eluded observation. Here we present evidence of a built-in potential across polar \lao ~thin films grown on \sto ~substrates, a system well known for the electron gas that forms at the interface. By performing electron tunneling measurements between the electron gas and a metallic gate on \lao ~we measure a built-in electric field across \lao ~of 93 meV/\AA. Additionally, capacitance measurements reveal the presence of an induced dipole moment near the interface in \sto, illuminating a unique property of \sto ~substrates. We forsee use of the ionic built-in potential as an additional tuning parameter in both existing and novel device architectures, especially as atomic control of oxide interfaces gains widespread momentum.Comment: 6 pages, 4 figures. Submitted to Nature physics on May 1st, 201

Long-term outcomes of biological mesh repair following extra levator abdominoperineal excision of the rectum: an observational study of 100 patients

BackgroundCurrent evidence suggests that pelvic floor reconstruction following extralevator abdominoperineal excision of rectum (ELAPER) may reduce the risk of perineal herniation of intra-abdominal contents. Options for reconstruction include mesh and myocutaneous flaps, for which long-term follow-up data is lacking. The aim of this study was to evaluate the long-term outcomes of biological mesh (Surgisis®, Biodesign™) reconstruction following ELAPER.MethodsA retrospective review of all patients having ELAPER in a single institution between 2008 and 2018 was perfomed. Clinic letters were scrutinised for wound complications and all available cross sectional imaging was reviewed to identify evidence of perineal herniation (defined as presence of intra-abdominal content below a line between the coccyx and the lower margin of the pubic symphysis on sagittal view).ResultsOne hundred patients were identified (median age 66, IQR 59–72 years, 70% male). Median length of follow-up was 4.9 years (IQR 2.3–6.7 years). One, 2- and 5-year mortality rates were 3, 8 and 12%, respectively. Thirty three perineal wounds had not healed by 1 month, but no mesh was infected and no mesh needed to be removed. Only one patient developed a symptomatic perineal hernia requiring repair. On review of imaging a further 7 asymptomatic perineal hernias were detected. At 4 years the cumulative radiologically detected perineal hernia rate was 8%.ConclusionsThis study demonstrates that pelvic floor reconstruction using biological mesh following ELAPER is both safe and effective as a long-term solution, with low major complication rates. Symptomatic perineal herniation is rare following mesh reconstruction, but may develop sub clinically and be detectable on cross-sectional imaging

Interferometry of Direct Photons in Central 280Pb+208Pb Collisions at 158A GeV

Two-particle correlations of direct photons were measured in central 208Pb+208Pb collisions at 158 AGeV. The invariant interferometric radii were extracted for 100<K_T<300 MeV/c and compared to radii extracted from charged pion correlations. The yield of soft direct photons, K_T<300 MeV/c, was extracted from the correlation strength and compared to theoretical calculations.Comment: 5 pages, 4 figure

The human Origin Recognition Complex is essential for pre-RC assembly, mitosis and maintenance of nuclear structure

The Origin Recognition Complex (ORC) cooperates with CDC6, MCM2-7, and CDT1 to form pre- RC complexes at origins of DNA replication. Here we report tiling-sgRNA CRISPR screens that show that each subunit of ORC and CDC6 are essential in human cells. Using an auxin-inducible degradation system, stable cell lines were created that ablate ORC2 rapidly, revealing multiple cell division cycle phenotypes. The primary defect in the absence of ORC2 was cells encountering difficulty in initiating DNA replication or progressing through the cell division cycle due to reduced MCM2-7 loading onto chromatin in G1 phase. The nuclei of ORC2 deficient cells were also large, with decompacted heterochromatin. Some ORC2 deficient cells that completed DNA replication entered into, but never exited mitosis. ORC1 knockout cells also demonstrated extremely slow cell proliferation and abnormal cell and nuclear morphology. Thus, ORC proteins and CDC6 are indispensable for normal cellular proliferation and contribute to nuclear organization

Systematics of Inclusive Photon Production in 158 AGeV Pb Induced Reactions on Ni, Nb, and Pb Targets

The multiplicity of inclusive photons has been measured on an event-by-event basis for 158 AGeV Pb induced reactions on Ni, Nb, and Pb targets. The systematics of the pseudorapidity densities at midrapidity (rho_max) and the width of the pseudorapidity distributions have been studied for varying centralities for these collisions. A power law fit to the photon yield as a function of the number of participating nucleons gives a value of 1.13+-0.03 for the exponent. The mean transverse momentum, , of photons determined from the ratio of the measured electromagnetic transverse energy and photon multiplicity, remains almost constant with increasing rho_max. Results are compared with model predictions.Comment: 16 pages including 4 figure

Scaling of Particle and Transverse Energy Production in 208Pb+208Pb collisions at 158 A GeV

Transverse energy, charged particle pseudorapidity distributions and photon transverse momentum spectra have been studied as a function of the number of participants (N_{part}) and the number of binary nucleon-nucleon collisions (N_{coll}) in 158 A GeV Pb+Pb collisions over a wide impact parameter range. A scaling of the transverse energy pseudorapidity density at midrapidity as N_{part}^{1.08 \pm 0.06} and N_{coll}^{0.83 \pm 0.05} is observed. For the charged particle pseudorapidity density at midrapidity we find a scaling as N_{part}^{1.07 \pm 0.04} and N_{coll}^{0.82 \pm 0.03}. This faster than linear scaling with N_{part} indicates a violation of the naive Wounded Nucleon Model.Comment: 13 pages, 16 figures, submitted to European Physical Journal C (revised results for scaling exponents