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

Integrative gene-metabolite network with implemented causality deciphers informational fluxes of sulphur stress response

The systematic accumulation of gene expression data, although revolutionary, is insufficient in itself for an understanding of system-level physiology. In the post-genomic era, the next cognitive step is linking genes to biological processes and assembling a mosaic of data into global models of biosystem function. A dynamic network of informational flows in Arabidopsis plants perturbed by sulphur depletion is presented here. With the use of an original protocol, the first blosystem response network was reconstructed from a time series of transcript and metabolite profiles, which, on the one hand, integrates complex metabolic and transcript data and, on the other hand, possesses a causal relationship. Using the informational fluxes within this reconstruction, it was possible to link system perturbation to response endpoints. Robustness and stress tolerance, as consequences of scale-free network topology, and hubs, as potential controllers of homeostasis maintenance, were revealed. Communication paths of propagating system excitement directed to physiological endpoints, such as anthocyanin accumulation and enforced root formation were dissected from the network. An auxin regulatory circuit involved in the control of a hypo-sulphur stress response was uncovered

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

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

Palaeomagnetic time and space constraints of the Early Cretaceous Rhenodanubian Flysch zone (Eastern Alps)

© The Authors 2017. The Rhenodanubian Flysch zone (RDF) is a Lower Cretaceous-lower Palaeocene turbidite succession extending for ~500 km from the Danube at Vienna to the Rhine Valley (Eastern Alps). It consists of calcareous and siliciclastic turbidite systems deposited in a trench abyssal plain. The age of deposition has been estimated through micropalaeontologic dating. However, palaeomagnetic studies constraining the age and the palaeolatitude of deposition of the RDF are still missing. Here, we present palaeomagnetic data from the Early Cretaceous Tristel and Rehbreingraben Formations of the RDF from two localities in the Bavarian Alps (Rehbrein Creek and Lainbach Valley, southern Germany), and from the stratigraphic equivalent of the Falknis Nappe (Liechtenstein). The quality of the palaeomagnetic signal has been assessed by either fold test (FT) or reversal test (RT). Sediments from the Falknis Nappe are characterized by a pervasive syntectonic magnetic overprint as tested by negative FT, and are thus excluded from the study. The sediments of the Rehbreingraben Formation at Rehbrein Creek, with positive RT, straddle magnetic polarity Chron M0r and the younger M'-1r' reverse event, with an age of ~127-123 Ma (late Barremian-early Aptian). At Lainbach Valley, no polarity reversals have been observed, but a positive FT gives confidence on the reliability of the data. The primary palaeomagnetic directions, after correction for inclination shallowing, allow to precisely constrain the depositional palaeolatitude of the Tristel and Rehbreingraben Formations around ~28°N. In a palaeogeographic reconstruction of the Alpine Tethys at the Barremian/Aptian boundary, the RDF is located on the western margin of the Briançonnais terrain, which was separated from the European continent by the narrow Valais Ocean

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