Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page

Intrinsic Shapes of Elliptical Galaxies

Tests for the intrinsic shape of the luminosity distribution in elliptical galaxies are discussed, with an emphasis on the uncertainties. Recent determinations of the ellipticity frequency function imply a paucity of nearly spherical galaxies, and may be inconsistent with the oblate hypothesis. Statistical tests based on the correlation of surface brightness, isophotal twisting, and minor axis rotation with ellipticity have so far not provided strong evidence in favor of the nearly oblate or nearly prolate hypothesis, but are at least qualitatively consistent with triaxiality. The possibility that the observed deviations of elliptical galaxy isophotes form ellipses are due to projection effects is evaluated. Dynamical instabilities may explain the absence of elliptical galaxies flatter than about E6, and my also play a role in the lack of nearly-spherical galaxies

Dynamics of Multiple Trafficking Behaviors of Individual Synaptic Vesicles Revealed by Quantum-Dot Based Presynaptic Probe

Although quantum dots (QDs) have provided invaluable information regarding the diffusive behaviors of postsynaptic receptors, their application in presynaptic terminals has been rather limited. In addition, the diffraction-limited nature of the presynaptic bouton has hampered detailed analyses of the behaviors of synaptic vesicles (SVs) at synapses. Here, we created a quantum-dot based presynaptic probe and characterized the dynamic behaviors of individual SVs. As previously reported, the SVs exhibited multiple exchanges between neighboring boutons. Actin disruption induced a dramatic decrease in the diffusive behaviors of SVs at synapses while microtubule disruption only reduced extrasynaptic mobility. Glycine-induced synaptic potentiation produced significant increases in synaptic and inter-boutonal trafficking of SVs, which were NMDA receptor- and actin-dependent while NMDA-induced synaptic depression decreased the mobility of the SVs at synapses. Together, our results show that sPH-AP-QD revealed previously unobserved trafficking properties of SVs around synapses, and the dynamic modulation of SV mobility could regulate presynaptic efficacy during synaptic activity

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

The Effects of NMDA Subunit Composition on Calcium Influx and Spike Timing-Dependent Plasticity in Striatal Medium Spiny Neurons

Calcium through NMDA receptors (NMDARs) is necessary for the long-term potentiation (LTP) of synaptic strength; however, NMDARs differ in several properties that can influence the amount of calcium influx into the spine. These properties, such as sensitivity to magnesium block and conductance decay kinetics, change the receptor's response to spike timing dependent plasticity (STDP) protocols, and thereby shape synaptic integration and information processing. This study investigates the role of GluN2 subunit differences on spine calcium concentration during several STDP protocols in a model of a striatal medium spiny projection neuron (MSPN). The multi-compartment, multi-channel model exhibits firing frequency, spike width, and latency to first spike similar to current clamp data from mouse dorsal striatum MSPN. We find that NMDAR-mediated calcium is dependent on GluN2 subunit type, action potential timing, duration of somatic depolarization, and number of action potentials. Furthermore, the model demonstrates that in MSPNs, GluN2A and GluN2B control which STDP intervals allow for substantial calcium elevation in spines. The model predicts that blocking GluN2B subunits would modulate the range of intervals that cause long term potentiation. We confirmed this prediction experimentally, demonstrating that blocking GluN2B in the striatum, narrows the range of STDP intervals that cause long term potentiation. This ability of the GluN2 subunit to modulate the shape of the STDP curve could underlie the role that GluN2 subunits play in learning and development

Caveolin-1 overexpression is an early event in the progression of papillary carcinoma of the thyroid

Caveolin-1 is a major structural component of caveolae, which are plasma membrane microdomains implicated in the regulation of intracellular signalling pathways. Previous in vitro and in vivo studies on the function of caveolin-1 in carcinoma showed controversial results, indicating that the physiological role of caveolin-1 varies according to the origin of carcinoma. In this study, we investigated caveolin-1 expression in thyroid neoplasms by means of immunohistochemistry using a rabbit polyclonal antibody against caveolin-1. Normal follicular cells did not express caveolin-1. In papillary carcinoma, caveolin-1 expression was observed in high incidence, and especially in microcancer (less than 1.0 cm in diameter), caveolin-1 was positive in all cases except one. In undifferentiated (anaplastic) carcinoma, its incidence was significantly reduced. On the other hand, all cases of follicular carcinoma and adenoma were classified as negative for caveolin-1. These results suggest that caveolin-1 may play a role predominantly in the early phase of papillary carcinoma, whereas it has little influence on follicular tumours