Limit Theorems For Quantum Walks Associated with Hadamard Matrices

We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given

Regularity and stability of electrostatic solutions in Kaluza-Klein theory

We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Besides black holes and wormholes, a new class of geodesically complete solutions is identified. A monopole perturbation is carried out, enabling us to prove analytically the stability of a large class of solutions, including all black holes and neutral solutions.Comment: 2 pages, "mprocl.sty" with LATEX 2.09, contribution to the 9th Marcel Grossmann meeting (MG9), Rome, July 200

Electrostatic solutions in Kaluza-Klein theory: geometry and stability

We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Both charged and neutral cases are considered. The analysis of the solutions, through their geometrical properties, reveals the existence of black holes, wormholes and naked singularities. A new class of regular solutions is identified. A monopole perturbation study of all these solutions is carried out, enabling us to prove analytically the stability of large classes of solutions. In particular, the black hole solutions are stable, while for the regular solutions the stability analysis leads to an eigenvalue problem.Comment: Latex file, 21 page

Bounds on the force between black holes

We treat the problem of N interacting, axisymmetric black holes and obtain two relations among physical parameters of the system including the force between the black holes. The first relation involves the total mass, the angular momenta, the distances and the forces between the black holes. The second one relates the angular momentum and area of each black hole with the forces acting on it.Comment: 13 pages, no figure

The Distance of the First Overtone RR Lyrae Variables in the MACHO LMC Database: A New Method to Correct for the Effects of Crowding

Previous studies have indicated that many of the RR Lyrae variables in the LMC have properties similar to the ones in the Galactic globular cluster M3. Assuming that the M3 RR Lyrae variables follow the same relationships among period, temperature, amplitude and Fourier phase parameter phi31 as their LMC counterparts, we have used the M3 phi31-logP relation to identify the M3-like unevolved first overtone RR Lyrae variables in 16 fields near the LMC bar. The temperatures of these variables were calculated from the M3 logP-logTe relation so that the extinction could be derived for each star separately. Since blended stars have lower amplitudes for a given period, the period amplitude relation should be a useful tool for identifying which stars are affected by crowding. We find that the low amplitude stars are brighter. We remove them from the sample and derive an LMC distance modulus 18.49+/-0.11.Comment: 30 pages, 7 figures, accepted for publication in the Astronomical Journa

Generalized Massive Gravity and Galilean Conformal Algebra in two dimensions

Galilean conformal algebra (GCA) in two dimensions arises as contraction of two copies of the centrally extended Virasoro algebra ($t\rightarrow t, x\rightarrow\epsilon x$ with $\epsilon\rightarrow 0$). The central charges of GCA can be expressed in term of Virasoro central charges. For finite and non-zero GCA central charges, the Virasoro central charges must behave as asymmetric form $O(1)\pm O(\frac{1}{\epsilon})$. We propose that, the bulk description for 2d GCA with asymmetric central charges is given by general massive gravity (GMG) in three dimensions. It can be seen that, if the gravitational Chern-Simons coupling $\frac{1}{\mu}$ behaves as of order O($\frac{1}{\epsilon}$) or ($\mu\rightarrow\epsilon\mu$), the central charges of GMG have the above $\epsilon$ dependence. So, in non-relativistic scaling limit $\mu\rightarrow\epsilon\mu$, we calculated GCA parameters and finite entropy in term of gravity parameters mass and angular momentum of GMG.Comment: 9 page

Metabolomic profiling of macrophages determines the discrete metabolomic signature and metabolomic interactome triggered by polarising immune stimuli

Priming and activating immune stimuli have profound effects on macrophages, however, studies generally evaluate stimuli in isolation rather than in combination. In this study we have investigated the effects of pro-inflammatory and anti-inflammatory stimuli either alone or in combination on macrophage metabolism. These stimuli include host factors such as IFNγ and ovalbumin-immunoglobulin immune complexes, or pathogen factors such as LPS. Untargeted LC-MS based metabolomics provided an in-depth profile of the macrophage metabolome, and revealed specific changes in metabolite abundance upon either individual stimuli or combined stimuli. Here, by factoring in an interaction term in the linear model, we define the metabolome interactome. This approach allowed us to determine whether stimuli interact in a synergistic or antagonistic manner. In conclusion this study demonstrates a robust approach to interrogate immune-metabolism, especially systems that model host-pathogen interactions

Inelastic Collapse of Three Particles

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.Comment: 6 pages, figures on request, accepted by PR

Relevance of histamine and tryptase concentrations in nasal secretions after nasal challenges with phosphate buffered saline and allergen

In this prospective study, a quantitative determination of histamine and tryptase in nasal secretions after nasal phosphate buffered saline (PBS) and allergen challenge was performed in 18 atopic patients who were compared with ten non-allergic healthy volunteers. The aim of the study was to determine the normal and pathological concentrations of these important mediators in nasal secretions. The second objective was to test the relevance of these two mast cell secreted mediators after nasal challenge. Results showed that the concentrations of tryptase in almost all samples were under the minimal detection limit (< 0.5 μU/g) and only a sigrtificant increase of tryptase (median, 28 μU/g) occurred immediately after nasal allergen challenge in the patient group. Histamine concentration significantly increased after every nasal PBS challenge (median, 69 ng/g after first PBS challenge and 165 ng/g after second PBS challenge) in the control group, as well as in the patient group after both PBS (median, 69 ng/g) and allergen (median, 214 ng/g) challenge. On the other hand, a rapid onset of sneezing and increase in nasal airway resistance was experienced only in the patient group after nasal allergen challenge, but did not occur after PBS challenge even though the histamine concentrations significantly increased in both groups. This study suggests that tryptase is a more preferable marker than histamine in quantitative monitoring of mast cell activation especially during the early phase nasal allergic reaction