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

The effect of collisional enhancement of Balmer lines on the determination of the primordial helium abundance

This paper describes a new determination of the primordial helium abundance (Y_P), based on the abundance analysis of five metal-poor extragalactic HII regions. For three regions of the sample (SBS 0335-052, I Zw 18, and H29) we present tailored photoionization models based on improved calculations with respect to previous models. In particular, we use the photoionization models to study quantitatively the effect of collisional excitation of Balmer lines on the determination of the helium abundance (Y) in the individual regions. This effect is twofold: first, the intensities of the Balmer lines are enhanced with respect to the pure recombination value, mimicking a higher hydrogen abundance; second, the observed reddening is larger than the true extinction, due to the differential effect of collisions on different Balmer lines. In addition to these effects, our analysis takes into account the following features of HII regions: (i) the temperature structure, (ii) the density structure, (iii) the presence of neutral helium, (iv) the collisional excitation of the HeI lines, (v) the underlying absorption of the HeI lines, and (vi) the optical thickness of the HeI lines. The object that shows the highest increase in Y after the inclusion of collisional effects in the analysis is SBS 0335-052, whose helium abundance has been revised by Delta Y = +0.0107. The revised Y values for the five objects in our sample yield an increase of +0.0035 in Y_P, giving Y_P = 0.2391 +/- 0.0020.Comment: 59 pages, 8 figures. AAS Latex. Accepted for publication in the Astrophysical Journa

The Second INTEGRAL AGN Catalogue

The INTEGRAL mission provides a large data set for studying the hard X-ray properties of AGN and allows testing of the unified scheme for AGN. We present analysis of INTEGRAL IBIS/ISGRI, JEM-X, and OMC data for 199 AGN supposedly detected by INTEGRAL above 20 keV. The data analysed here allow a significant spectral extraction on 148 objects and an optical variability study of 57 AGN. The slopes of the hard X-ray spectra of Seyfert 1 and Seyfert~2 galaxies are found to be consistent within the uncertainties, whereas higher cut-off energies and lower luminosities are measured for the more absorbed / type 2 AGN. The intermediate Seyfert 1.5 objects exhibit hard X-ray spectra consistent with those of Seyfert 1. When applying a Compton reflection model, the underlying continua appear the same in Seyfert 1 and 2 with photon index 2, and the reflection strength is about R = 1, when assuming different inclination angles. A significant correlation is found between the hard X-ray and optical luminosity and the mass of the central black hole in the sense that the more luminous objects appear to be more massive. There is also a general trend toward the absorbed sources and type 2 AGN having lower Eddington ratios. The black holemass appears to form a fundamental plane together with the optical and X-ray luminosity of the form Lv being proportional to Lx^0.6 M^0.2, similar to that found between radio luminosity Lr, Lx, and M. The unified model for Seyfert galaxies seems to hold, showing in hard X-rays that the central engine is the same in Seyfert 1 and 2, but seen under different inclination angles and absorption. (Abridged)Comment: 26 pages, 16 figures, accepted for publication in A&A. Corrections by language editor included in version

Statistical properties of giant pulses from the Crab pulsar

We have studied the statistics of giant pulses from the Crab pulsar for the first time with particular reference to their widths. We have analyzed data collected during 3.5 hours of observations conducted with the Westerbork Synthesis Radio Telescope operated in a tied-array mode at a frequency of 1200 MHz. The PuMa pulsar backend provided voltage recording of X and Y linear polarization states in two conjugate 10 MHz bands. We restricted the time resolution to 4 microseconds to match the scattering on the interstellar inhomogeneities. In total about 18000 giant pulses (GP) were detected in full intensity with a threshold level of 6 sigma. Cumulative probability distributions (CPD) of giant pulse energies were analyzed for groups of GPs with different effective widths in the range 4 to 65 microseconds. The CPDs were found to manifest notable differences for the different GP width groups. The slope of a power-law fit to the high-energy portion of the CPDs evolves from -1.7 to -3.2 when going from the shortest to the longest GPs. There are breaks in the CPD power-law fits indicating flattening at low energies with indices varying from -1.0 to -1.9 for the short and long GPs respectively. The GPs with a stronger peak flux density were found to be of shorter duration. We compare our results with previously published data and discuss the importance of these peculiarities in the statistical properties of GPs for the heoretical understanding of the emission mechanism responsible for GP generation.Comment: 5 pages, 2 figures. Accepted by Astronomy and Astrophysic

Evaluating Matrix Circuits

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as polynomial identity testing for skew arithmetic circuits

Gigantism in unique biogenic magnetite at the Paleocene-Eocene Thermal Maximum

We report the discovery of exceptionally large biogenic magnetite crystals in clay-rich sediments spanning the Paleocene-Eocene Thermal Maximum (PETM) in a borehole at Ancora, New Jersey. Aside from previously-described abundant bacterial magnetofossils, electron microscopy reveals novel spearhead-like and spindle-like magnetite up to 4 μm long and hexaoctahedral prisms up to 1.4 μm long. Similar to magnetite produced by magnetotactic bacteria, these single-crystal particles exhibit chemical composition, lattice perfection, and oxygen isotopes consistent with an aquatic origin. Electron holography indicates single-domain magnetization despite their large crystal size. We suggest that the development of a thick suboxic zone with high iron bioavailability – a product of dramatic changes in weathering and sedimentation patterns driven by severe global warming – drove diversification of magnetite-forming organisms, likely including eukaryotes

Flux and field line conservation in 3--D nonideal MHD flows: Remarks about criteria for 3--D reconnection without magnetic neutral points

We make some remarks on reconnection in plasmas and want to present some calculations related to the problem of finding velocity fields which conserve magnetic flux or at least magnetic field lines. Hereby we start from views and definitions of ideal and non-ideal flows on one hand, and of reconnective and non-reconnective plasma dynamics on the other hand. Our considerations give additional insights into the discussion on violations of the frozen--in field concept which started recently with the papers by Baranov & Fahr (2003a; 2003b). We find a correlation between the nonidealness which is given by a generalized form of the Ohm's law and a general transporting velocity, which is field line conserving.Comment: 9 pages, 2 figures, submitted to Solar Physic

GRB 021219: the first Gamma-Ray Burst localized in real time with IBAS

On December 19, 2002, during the Performance and Verification Phase of INTEGRAL, a Gamma-Ray Burst (GRB) has been detected and localized in real time with the INTEGRAL Burst Alert System (IBAS). Here we present the results obtained with the IBIS and SPI instruments. The burst had a time profile with a single peak lasting about 6 s. The peak spectrum can be described by a single power law with photon index $\Gamma$=1.6$\pm$0.1 and flux $\sim$3.7 photons cm$^{-2}$ s$^{-1}$ (20 - 200 keV). The fluence in the same energy range is 9$\times10^{-7}$ erg cm$^{-2}$. Time resolved spectroscopy performed with IBIS/ISGRI shows a clear hard to soft evolution of the spectrum.Comment: 4 pages, 3 figures, latex, accepted for publication in A&A INTEGRAL special issu

Conducting rigorous research with subgroups of at-risk youth: lessons learned from a teen pregnancy prevention project in Alaska

In 2010, Alaska Department of Health and Social Services (DHSS) received federal funding to test an evidence-based teen pregnancy prevention program. The grant required a major modification to an existing program and a randomized control trial (RCT) to test its effectiveness. As the major modifications, Alaska used peer educators instead of adults to deliver the program to youth aged 1419 instead of the original curriculum intended age range of 1214. Cultural and approach adaptations were included as well. After 4 years of implementation and data collection, the sample was too small to provide statistically significant results. The lack of findings gave no information about the modification, nor any explanation of how the curriculum was received, or reasons for the small sample. This paper reports on a case study follow-up to the RCT to better understand outcome and implementation results. For this study, researchers reviewed project documents and interviewed peer educators, state and local staff, and evaluators. Three themes emerged from the data: (a) the professional growth of peer educators and development of peer education, (b) difficulties resulting from curriculum content, especially for subpopulations of sexually active youth, youth identified as lesbian, gay, bisexual, transgender, queer, intersex and/or asexual, pregnant, and parenting youth and (c) the appropriateness of an RCT with subpopulations of at-risk youth. Three recommendations emerged from the case study. First, including as many stakeholders as possible in the program and evaluation design phases is essential, and must be supported by appropriate funding streams and training. Second, there must be recognition of the multiple small subpopulations found in Alaska when adapting programs designed for a larger and more homogeneous population. Third, RCTs may not be appropriate for all population subgroups.Ye