A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional generalisations display such symmetries as well, in spite of being perfectly ordered. We present first steps and results towards a general frame to investigate such systems, with emphasis on statistical properties that are helpful to understand and compare the diffraction images. An alternative substitution rule for the pinwheel tiling, with two different prototiles, permits the derivation of several combinatorial and spectral properties of this still somewhat enigmatic example. These results are compared with properties of the square lattice and its powder diffraction.Comment: 16 pages, 8 figure

Gaussian-random Ensembles of Pseudo-Hermitian Matrices

Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of pseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic Riemann-zeros (${1 \over 2}\pm i t_n)$ would rather correspond to some PT-symmetric (pseudo-Hermitian) Hamiltonian.Comment: Invited Talk Delivered in II International Workshop on `Pseudo-Hermitian Hanmiltonians in Physics' at Prague, June 14-16, 200

A propelling neutron star in the enigmatic Be-star γ\gamma~Cassiopeia

The enigmatic X-ray emission from the bright optical star, $\gamma$ Cassiopeia, is a long-standing problem. $\gamma$ Cas is known to be a binary system consisting of a Be-type star and a low-mass ($M\sim 1\,M_\odot$) companion of unknown nature orbiting in the Be-disk plane. Here we apply the quasi-spherical accretion theory onto a compact magnetized star and show that if the low-mass companion of $\gamma$ Cas is a fast spinning neutron star, the key observational signatures of $\gamma$ Cas are remarkably well reproduced. Direct accretion onto this fast rotating neutron star is impeded by the propeller mechanism. In this case, around the neutron star magnetosphere a hot shell is formed that emits thermal X-rays in qualitative and quantitative agreement with observed properties of the X-ray emission from $\gamma$ Cas. We suggest that $\gamma$ Cas and its analogs constitute a new subclass of Be-type X-ray binaries hosting rapidly rotating neutron stars formed in supernova explosions with small kicks. The subsequent evolutionary stage of $\gamma$ Cas and its analogs should be the X Per-type binaries comprising low-luminosity slowly rotating X-ray pulsars. The model explains the enigmatic X-ray emission from $\gamma$ Cas, and also establishes evolutionary connections between various types of rotating magnetized neutron stars in Be-binaries.Comment: 6 pages, accepted for publication in MNRA

Beneficial autoimmunity at body surfaces – immune surveillance and rapid type 2 immunity regulate tissue homeostasis and cancer

Epithelial cells line body surface tissues and provide a physicochemical barrier to the external environment. Frequent microbial and non-microbial challenges such as those imposed by mechanical disruption, injury or exposure to noxious environmental substances including chemicals, carcinogens, ultraviolet-irradiation or toxins cause activation of epithelial cells with release of cytokines and chemokines as well as alterations in the expression of cell surface ligands. Such display of epithelial stress is rapidly sensed by tissue resident immunocytes, which can directly interact with self-moieties on epithelial cells and initiate both local and systemic immune responses. Epithelial cells are thus key drivers of immune surveillance at body surface tissues. However, epithelial cells have a propensity to drive type 2 immunity (rather than type 1) upon non-invasive challenge or stress – a type of immunity whose regulation and function still remain enigmatic. Here we review the induction and possible role of type 2 immunity in epithelial tissues and propose that rapid immune surveillance and type 2 immunity are key regulators of tissue homeostasis and carcinogenesis

XSHOOTER spectroscopy of the enigmatic planetary nebula Lin49 in the Small Magellanic Cloud

We performed a detailed spectroscopic analysis of the fullerene C60-containing planetary nebula (PN) Lin49 in the Small Magellanic Cloud (SMC) using XSHOOTER at the European Southern Observatory Very Large Telescope and the Spitzer/Infrared Spectrograph instruments. We derived nebular abundances for nine elements. We used TLUSTY to derive photospheric parameters for the central star. Lin49 is C-rich and metal-deficient PN (Z ∼ 0.0006). The nebular abundances are in good agreement with asymptotic giant branch nucleosynthesis models for stars with initial mass 1.25 M⊙ and metallicity Z = 0.001. Using the TLUSTY synthetic spectrum of the central star to define the heating and ionizing source, we constructed the photoionization model with CLOUDY that matches the observed spectral energy distribution (SED) and the line fluxes in the UV to far-IR wavelength ranges simultaneously. We could not fit the ∼1–5 μm SED using a model with 0.005–0.1-μm-sized graphite grains and a constant hydrogen density shell owing to the prominent near-IR excess, while at other wavelengths the model fits the observed values reasonably well. We argue that the near-IR excess might indicate either (1) the presence of very small particles in the form of small carbon clusters, small graphite sheets, or fullerene precursors, or (2) the presence of a high-density structure surrounding the central star. We found that SMC C60 PNe show a near-IR excess component to lesser or greater degree. This suggests that these C60 PNe might maintain a structure nearby their central star

No entropy enigmas for N=4 dyons

We explain why multi-centered black hole configurations where at least one of the centers is a large black hole do not contribute to the indexed degeneracies in theories with N=4 supersymmetry. This is a consequence of the fact that such configurations, although supersymmetric, belong to long supermultiplets. As a result, there is no entropy enigma in N=4 theories, unlike in N=2 theories.Comment: 14 page