Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Dynamic remodelling of synapses can occur in the absence of the parent cell body

<p>Abstract</p> <p>Background</p> <p>Retraction of nerve terminals is a characteristic feature of development, injury and insult and may herald many neurodegenerative diseases. Although morphological events have been well characterized, we know relatively little about the nature of the underlying cellular machinery. Evidence suggests a strong local component in determining which neuronal branches and synapses are lost, but a greater understanding of this basic neurological process is required. Here we test the hypothesis that nerve terminals are semi-autonomous and able to rapidly respond to local stimuli in the absence of communication with their parent cell body.</p> <p>Results</p> <p>We used an isolated preparation consisting of distal peripheral nerve stumps, associated nerve terminals and post-synaptic muscle fibres, maintained in-vitro for up to 3 hrs. In this system synapses are intact but the presynaptic nerve terminal is disconnected from its cell soma. In control preparations synapses were stable for extended periods and did not undergo Wallerian degneration. In contrast, addition of purines triggers rapid changes at synapses. Using fluorescence and electron microscopy we observe ultrastructural and gross morphological events consistent with nerve terminal retraction. We find no evidence of Wallerian or Wallerian-like degeneration in these preparations. Pharmacological experiments implicate pre-synaptic P2X7 receptor subunits as key mediators of these events.</p> <p>Conclusion</p> <p>The data presented suggest; first that isolated nerve terminals are able to regulate connectivity independent of signals from the cell body, second that synapses exist in a dynamic state, poised to shift from stability to loss by activating intrinsic mechanisms and molecules, and third that local purines acting at purinergic receptors can trigger these events. A role for ATP receptors in this is not surprising since they are frequently activated during cellular injury, when adenosine tri-phosphate is released from damaged cells. Local control demands that the elements necessary to drive retraction are constitutively present. We hypothesize that pre-existing scaffolds of molecular motors and cytoskeletal proteins could provide the dynamism required to drive such structural changes in nerve terminals in the absence of the cell body.</p

Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles

We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.Comment: 8 pages, no figure

‘It would be okay if they came through the proper channels’: community perceptions and attitudes toward asylum seekers in Australia

Australia\u27s humanitarian programme contributes to UNHCR\u27s global resettlement programme and enhances Australia\u27s international humanitarian reputation. However, as the recent tragedy on Christmas Island has shown, the arrival of asylum seekers by boat continues to stimulate debate, discussion and reaction from the Australian public and the Australian media. In this study, we used a mixed methods community survey to understand community perceptions and attitudes relating to asylum seekers. We found that while personal contact with asylum seekers was important when forming opinions about this group of immigrants, for the majority of respondents, attitudes and opinions towards asylum seekers were more influenced by the interplay between traditional Australian values and norms, the way that these norms appeared to be threatened by asylum seekers, and the way that these threats were reinforced both in media and political rhetoric

Cortical cells are altered by factors including bone morphogenetic protein released from a placental barrier model under altered oxygenation

Episodes of hypoxia and hypoxia/reoxygenation during foetal development have been associated with increased risk of neurodevelopmental conditions presenting in later life. The mechanism for this is not understood; however, several authors have suggested that the placenta plays an important role. Previously we found both placentas from a maternal hypoxia model and pre-eclamptic placentas from patients release factors lead to a loss of dendrite complexity in rodent neurons. Here to further explore the nature and origin of these secretions we exposed a simple in vitro model of the placental barrier, consisting of a barrier of human cytotrophoblasts, to hypoxia or hypoxia/reoxygenation. We then exposed cortical cultures from embryonic rat brains to the conditioned media (CM) from below these exposed barriers and examined changes in cell morphology, number, and receptor presentation. The barriers released factors that reduced dendrite and astrocyte process lengths, decreased GABAB1 staining, and increased astrocyte number. The changes in astrocytes required the presence of neurons and were prevented by inhibition of the SMAD pathway and by neutralising Bone Morphogenetic Proteins (BMPs) 2/4. Barriers exposed to hypoxia/reoxygenation also released factors that reduced dendrite lengths but increased GABAB1 staining. Both oxygen changes caused barriers to release factors that decreased GluN1, GABAAα1 staining and increased GluN3a staining. We find that hypoxia in particular will elicit the release of factors that increase astrocyte number and decrease process length as well as causing changes in the intensity of glutamate and GABA receptor staining. There is some evidence that BMPs are released and contribute to these changes

Lamin A/C dysregulation contributes to cardiac pathology in a mouse model of severe spinal muscular atrophy

Cardiac pathology is emerging as a prominent systemic feature of spinal muscular atrophy (SMA), but little is known about the underlying molecular pathways. Using quantitative proteomics analysis, we demonstrate widespread molecular defects in heart tissue from the Taiwanese mouse model of severe SMA. We identify increased levels of lamin A/C as a robust molecular phenotype in the heart of SMA mice and show that lamin A/C dysregulation is also apparent in SMA patient fibroblast cells and other tissues from SMA mice. Lamin A/C expression was regulated in vitro by knockdown of the E1 ubiquitination factor ubiquitin-like modifier activating enzyme 1, a key downstream mediator of SMN-dependent disease pathways, converging on β-catenin signaling. Increased levels of lamin A are known to increase the rigidity of nuclei, inevitably disrupting contractile activity in cardiomyocytes. The increased lamin A/C levels in the hearts of SMA mice therefore provide a likely mechanism explaining morphological and functional cardiac defects, leading to blood pooling. Therapeutic strategies directed at lamin A/C may therefore offer a new approach to target cardiac pathology in SMA

ExoMol Molecular linelists -- XXXIII. The spectrum of Titanium Oxide

Accurate line lists are crucial for correctly modelling a variety of astrophysical phenomena, including stellar photospheres and the atmospheres of extra-solar planets. This paper presents a new line database Toto for the main isotopologues of titanium oxide (TiO): $^{46}$Ti$^{16}$O, $^{47}$Ti$^{16}$O, $^{48}$Ti$^{16}$O, $^{49}$Ti$^{16}$O and $^{50}$Ti$^{16}$O. The TiO line list contains transitions with wave-numbers up to 30,000 cm$^{-1}$ ie long-wards of 0.33 $\mu$m. The Toto line list includes all dipole-allowed transitions between 13 low-lying electronic states (X $^3\Delta$, a $^1\Delta$, d $^1\Sigma^+$, E $^3\Pi$, A $^3\Phi$ B $^3\Pi$, C $^3\Delta$, b $^1\Pi$, c $^1\Phi$, f $^1\Delta$, e $^1\Sigma^+$). Ab initio potential energy curves (PECs) are computed at the icMRCI level and combined with spin-orbit and other coupling curves. These PECs and couplings are iteratively refined to match known empirical energy levels. Accurate line intensities are generated using ab initio dipole moment curves. The Toto line lists are appropriate for temperatures below 5000 K and contain 30 million transitions for TiO; it is made available in electronic form via the CDS data centre and via www.exomol.com. Tests of the line lists show greatly improved agreement with observed spectra for objects such as M-dwarfs GJ876 and GL581