Conjugacy in Baumslag's group, generic case complexity, and division in power circuits

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} = y in G. The conjugacy problem is more difficult than the word problem, in general. We investigate the complexity of the conjugacy problem for two prominent groups: the Baumslag-Solitar group BS(1,2) and the Baumslag(-Gersten) group G(1,2). The conjugacy problem in BS(1,2) is TC^0-complete. To the best of our knowledge BS(1,2) is the first natural infinite non-commutative group where such a precise and low complexity is shown. The Baumslag group G(1,2) is an HNN-extension of BS(1,2). We show that the conjugacy problem is decidable (which has been known before); but our results go far beyond decidability. In particular, we are able to show that conjugacy in G(1,2) can be solved in polynomial time in a strongly generic setting. This means that essentially for all inputs conjugacy in G(1,2) can be decided efficiently. In contrast, we show that under a plausible assumption the average case complexity of the same problem is non-elementary. Moreover, we provide a lower bound for the conjugacy problem in G(1,2) by reducing the division problem in power circuits to the conjugacy problem in G(1,2). The complexity of the division problem in power circuits is an open and interesting problem in integer arithmetic.Comment: Section 5 added: We show that an HNN extension G = < H, b | bab^-1 = {\phi}(a), a \in A > has a non-amenable Schreier graph with respect to the base group H if and only if A \neq H \neq

Why Does Steady-State Magnetic Reconnection Have A Maximum Local Rate Of Order 0.1?

Simulations suggest collisionless steady-state magnetic reconnection of Harris-type current sheets proceeds with a rate of order 0.1, independent of dissipation mechanism. We argue this long-standing puzzle is a result of constraints at the magnetohydrodynamic (MHD) scale. We perform a scaling analysis of the reconnection rate as a function of the opening angle made by the upstream magnetic fields, finding a maximum reconnection rate close to 0.2. The predictions compare favorably to particle-in-cell simulations of relativistic electron-positron and non-relativistic electron-proton reconnection. The fact that simulated reconnection rates are close to the predicted maximum suggests reconnection proceeds near the most efficient state allowed at the MHD-scale. The rate near the maximum is relatively insensitive to the opening angle, potentially explaining why reconnection has a similar fast rate in differing models

The Diffusion Region in Collisionless Magnetic Reconnection

A review of present understanding of the dissipation region in magnetic reconnection is presented. The review focuses on results of the thermal inertia-based dissipation mechanism but alternative mechanisms are mentioned as well. For the former process, a combination of analytical theory and numerical modeling is presented. Furthermore, a new relation between the electric field expressions for anti-parallel and guide field reconnection is developed

Searches for Giant Pulses from Extragalactic Pulsars

We discuss the giant-pulse phenomenon exhibited by pulsars and the distances to which giant pulses might be detected from extragalactic pulsars. We describe the conditions under which a single-pulse search is more sensitive than a standard periodicity search. We find that, for certain pulse-amplitude distribution power laws and time series lengths, single-pulse searches can be superior. We present the results of searches toward several extragalactic targets, including M33, the LMC (PSR B0540-69) and several other galaxies. While we have not conclusively detected giant pulses from any of these targets, these searches illustrate the methodology of, issues related to and difficulties in these types of searches.Comment: Accepted by Ap

On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.Comment: 23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged

Mid Infrared Properties of Low Metallicity Blue Compact Dwarf Galaxies From Spitzer/IRS

We present a {\em Spitzer}-based mid-infrared study of a large sample of Blue Compact Dwarf galaxies (BCD) using the Infrared Spectrograph (IRS), including the first mid-IR spectrum of IZw18, the archetype for the BCD class and among the most metal poor galaxies known. We show the spectra of Polycyclic Aromatic Hydrocarbon (PAH) emission in low-metallicity environment. We find that the equivalent widths (EW) of PAHs at 6.2, 7.7, 8.6 and 11.2 $\mu$m are generally weaker in BCDs than in typical starburst galaxies and that the fine structure line ratio, [NeIII]/[NeII], has a weak anti-correlation with the PAH EW. A much stronger anti-correlation is shown between the PAH EW and the product of the [NeIII]/[NeII] ratio and the UV luminosity density divided by the metallicity. We conclude that PAH EW in metal-poor high-excitation environments is determined by a combination of PAH formation and destruction effects.Comment: 41 pages, 14 figure

New Insights into Dissipation in the Electron Layer During Magnetic Reconnection

Detailed comparisons are reported between laboratory observations of electron-scale dissipation layers near a reconnecting X-line and direct two-dimensional full-particle simulations. Many experimental features of the electron layers, such as insensitivity to the ion mass, are reproduced by the simulations; the layer thickness, however, is about 3-5 times larger than the predictions. Consequently, the leading candidate 2D mechanism based on collisionless electron nongyrotropic pressure is insufficient to explain the observed reconnection rates. These results suggest that, in addition to the residual collisions, 3D effects play an important role in electron-scale dissipation during fast reconnection.Comment: 17 pages, 4 figure

The Seyfert-Starburst Connection in X-rays. II. Results and Implications

We present the results of X-ray imaging and spectroscopic analysis of a sample of Seyfert 2 galaxies that contain starbursts, based on their optical and UV characteristics. These composite galaxies exhibit extended, soft, thermal X-ray emission, which we attribute to their starburst components. Comparing their X-ray and far-infrared properties with ordinary Seyfert and starburst galaxies, we identify the spectral characteristics of their various intrinsic emission sources. The observed far-infrared emission of the composite galaxies may be associated almost exclusively with star formation, rather than the active nucleus. The ratio of the hard X-ray luminosity to the far-infrared and [O III] 5007 luminosity distinguishes most of these composite galaxies from ``pure'' Seyfert 2 galaxies, while their total observed hard X-ray luminosity distinguishes them from ``pure'' starbursts. The hard nuclear X-ray source is generally heavily absorbed (N_H > 10^{23} cm^{-2}) in the composite galaxies. Based on these results, we suggest that the interstellar medium of the nuclear starburst is a significant source of absorption. The majority of the sample are located in groups or are interacting with other galaxies, which may trigger the starburst or allow rapid mass infall to the central black hole, or both. We conclude that starbursts are energetically important in a significant fraction of active galaxies, and starbursts and active galactic nuclei may be part of a common evolutionary sequence.Comment: 16 pages including 8 figures and 5 tables; to appear in the ApJ, Mar. 10, 200

Widespread expression of erythropoietin receptor in brain and its induction by injury

Erythropoietin (EPO) exerts potent neuroprotective, neuroregenerative and procognitive functions. However, unequivocal demonstration of erythropoietin receptor (EPOR) expression in brain cells has remained difficult since previously available anti-EPOR antibodies (EPOR-AB) were unspecific. We report here a new, highly specific, polyclonal rabbit EPOR-AB directed against different epitopes in the cytoplasmic tail of human and murine EPOR and its characterization by mass spectrometric analysis of immuno-precipitated endogenous EPOR, Western blotting, immunostaining and flow cytometry. Among others, we applied genetic strategies including overexpression, Lentivirus-mediated conditional knockout of EpoR and tagged proteins, both on cultured cells and tissue sections, as well as intracortical implantation of EPOR-transduced cells to verify specificity. We show examples of EPOR expression in neurons, oligodendroglia, astrocytes and microglia. Employing this new EPOR-AB with double-labeling strategies, we demonstrate membrane expression of EPOR as well as its localization in intracellular compartments such as the Golgi apparatus. Moreover, we show injury-induced expression of EPOR. In mice, a stereotactically applied stab wound to the motor cortex leads to distinct EpoR expression by reactive GFAP-expressing cells in the lesion vicinity. In a patient suffering from epilepsy, neurons and oligodendrocytes of the hippocampus strongly express EPOR. To conclude, this new analytical tool will allow neuroscientists to pinpoint EPOR expression in cells of the nervous system and to better understand its role in healthy conditions, including brain development, as well as under pathological circumstances, such as upregulation upon distress and injury