Extending the Ehresmann-Schein-Nambooripad Theorem

We extend the `join-premorphisms' part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (1991) for the `morphisms' part. However, it is so-called `meet-premorphisms' which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.Comment: 23 pages; final section on Szendrei expansions removed; further reordering of materia

Transverse self-fields within an electron bunch moving in an arc of a circle

As a consequence of motions driven by external forces, self-fields (which are different from the static case) originate within an electron bunch. In the case of magnetic external forces acting on an ultrarelativistic beam, the longitudinal self-interactions are responsible for CSR (Coherent Synchrotron Radiation)-related phenomena, which have been studied extensively. On the other hand, transverse self-interactions are present too. At the time being, existing theoretical analysis of transverse self-forces deal with the case of a bunch moving along a circular orbit only, without considering the situation of a bending magnet with a finite length. In this paper we propose an electrodynamical analysis of transverse self-fields which originate, at the position of a test particle, from an ultrarelativistic electron bunch moving in an arc of a circle. The problem will be first addressed within a two-particle system. We then extend our consideration to a line bunch with a stepped density distribution, a situation which can be easily generalized to the case of an arbitrary density distribution. Our approach turns out to be also useful in order to get a better insight in the physics involved in the case of simple circular motion and in order to address the well known issue of the partial compensation of transverse self-force.Comment: 23 pages, 14 figure

Advances in development of new tools for the study of phosphohistidine

Protein phosphorylation is an important post-translational modification that is an integral part of cellular function. The O-phosphorylated amino-acid residues, such as phosphoserine (pSer), phosphothreonine (pThr) and phosphotyrosine (pTyr), have dominated the literature while the acid labile N-linked phosphorylated amino acids, such as phosphohistidine (pHis), have largely been historically overlooked because of the acidic conditions routinely used in amino-acid detection and analysis. This review highlights some misinterpretations that have arisen in the existing literature, pinpoints outstanding questions and potential future directions to clarify the role of pHis in mammalian signalling systems. Particular emphasis is placed on pHis isomerization and the hybrid functionality for both pHis and pTyr of the proposed τ-pHis analogue bearing the triazole residue

Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger equation. It is shown that behaviour essentially depends on transition probability, and on dimensionless parameter which is a ratio of characteristic frequencies for low energy non-linear in-well oscillations and inter wells tunnelling. For the potential describing a finite motion (double-well) one has always a regular behaviour. For the small value of the parameter there is well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However for the large value of the parameter no oscillations at all for the survival probability, and there is almost an exponential decay with the characteristic time determined by Fermi golden rule. In this case one may not restrict oneself to only resonance pair levels. The number of perturbed by tunnelling levels grows proportionally to the value of this parameter (by other words instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermediate values of the parameter one has a crossover between both limiting cases, namely the exponential decay with subsequent long period recurrent behaviour.Comment: 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev.

Finite temperature mobility of a particle coupled to a fermion environment

We study numerically the finite temperature and frequency mobility of a particle coupled by a local interaction to a system of spinless fermions in one dimension. We find that when the model is integrable (particle mass equal to the mass of fermions) the static mobility diverges. Further, an enhanced mobility is observed over a finite parameter range away from the integrable point. We present a novel analysis of the finite temperature static mobility based on a random matrix theory description of the many-body Hamiltonian.Comment: 11 pages (RevTeX), 5 Postscript files, compressed using uufile

Signatures of photon and axion-like particle mixing in the gamma-ray burst jet

Photons couple to Axion-Like Particles (ALPs) or more generally to any pseudo Nambu-Goldstone boson in the presence of an external electromagnetic field. Mixing between photons and ALPs in the strong magnetic field of a Gamma-Ray Burst (GRB) jet during the prompt emission phase can leave observable imprints on the gamma-ray polarization and spectrum. Mixing in the intergalactic medium is not expected to modify these signatures for ALP mass > 10^(-14) eV and/or for < nG magnetic field. We show that the depletion of photons due to conversion to ALPs changes the linear degree of polarization from the values predicted by the synchrotron model of gamma ray emission. We also show that when the magnetic field orientation in the propagation region is perpendicular to the field orientation in the production region, the observed synchrotron spectrum becomes steeper than the theoretical prediction and as detected in a sizable fraction of GRB sample. Detection of the correlated polarization and spectral signatures from these steep-spectrum GRBs by gamma-ray polarimeters can be a very powerful probe to discover ALPs. Measurement of gamma-ray polarization from GRBs in general, with high statistics, can also be useful to search for ALPs.Comment: 17 pages, 3 figures. Accepted for publication in JCAP with minor change

Confronting hybrid inflation in supergravity with CMB data

$F$-term GUT inflation coupled to N=1 Supergravity is confronted with CMB data. Corrections to the string mass-per-unit-length away from the Bogomolny limit are taken into account. We find that a superpotential coupling 10^{-7}/\mcN \lesssim \kappa \lesssim 10^{-2}/\mcN, with \mcN the dimension of the Higgs-representation, is still compatible with the data. The parameter space is enlarged in warm inflation, as well as in the curvaton and inhomogeneous reheat scenario. $F$-strings formed at the end of $P$-term inflation are also considered. Because these strings satisfy the Bogomolny bound the bounds are stronger: the gauge coupling is constrained to the range $10^{-7} < g <10^{-4}$.Comment: 36 pages, 15 figure

A Mathematical Model of Liver Cell Aggregation In Vitro

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

31P NMR spectroscopy demonstrates large amounts of phosphohistidine in mammalian cells

Protein phosphorylation plays a key role in many cellular processes but there is presently no accurate information or reliable procedure to determine the relative abundance of many phosphoamino acids in cells. At pH ≤ 8, phosphohistidine is unstable compared to the extensively studied phosphoserine, phosphothreonine and phosphotyrosine. This study reports the absolute quantitative analysis of histidine phosphorylation of proteins from a human bronchial epithelial cell (16HBE14o-) lysate using 31P NMR spectroscopic analysis. The method was designed to minimize loss of the phosphohistidine phosphoryl group. Phosphohistidine was determined on average to be approximately one third as abundant as phosphoserine and phosphothreonine combined (and thus roughly 20 times more abundant than phosphotyrosine). The amount of phosphohistidine, and phosphoserine/phosphothreonine per gram of protein from a cell lysate was determined to be 23 μmol/g and 68 μmol/g respectively. The amount of phosphohistidine, and phosphoserine/phosphothreonine per cell was determined to be 1.8 fmol/cell, and 5.8 fmol/cell respectively. After tryptic digest of proteins from the16HBE14o- cell lysate, the phosphohistidine signal was abolished and increasing phosphoserine/phosphothreonine signal was observed, which has implications for mass spectrometry investigations. The 31P NMR spectroscopic analysis not only highlights the abundance of phosphohistidine, which likely reflects its importance in mammalian cells, but also provides a way of measuring and comparing levels of phosphorylated amino acids in cells

A Gravitational Aharonov-Bohm Effect, and its Connection to Parametric Oscillators and Gravitational Radiation

A thought experiment is proposed to demonstrate the existence of a gravitational, vector Aharonov-Bohm effect. A connection is made between the gravitational, vector Aharonov-Bohm effect and the principle of local gauge invariance for nonrelativistic quantum matter interacting with weak gravitational fields. The compensating vector fields that are necessitated by this local gauge principle are shown to be incorporated by the DeWitt minimal coupling rule. The nonrelativistic Hamiltonian for weak, time-independent fields interacting with quantum matter is then extended to time-dependent fields, and applied to problem of the interaction of radiation with macroscopically coherent quantum systems, including the problem of gravitational radiation interacting with superconductors. But first we examine the interaction of EM radiation with superconductors in a parametric oscillator consisting of a superconducting wire placed at the center of a high Q superconducting cavity driven by pump microwaves. We find that the threshold for parametric oscillation for EM microwave generation is much lower for the separated configuration than the unseparated one, which then leads to an observable dynamical Casimir effect. We speculate that a separated parametric oscillator for generating coherent GR microwaves could also be built.Comment: 25 pages, 5 figures, YA80 conference (Chapman University, 2012