On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree

In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum: 40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative of the Legendre function of the first kind, $P_{\nu}(z)$, with respect to its degree $\nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{\nu}^{\pm m}(z)$, with respect to the degree $\nu$, for $m\in\mathbb{N}$. At first, we establish several contour-integral representations of $\partial P_{\nu}^{\pm m}(z)/\partial\nu$. They are then used to derive Rodrigues-type formulas for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ with $n\in\mathbb{N}$. Next, some closed-form expressions for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, $Q_{n}^{\pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}$, $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$ and $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}$, all with $m>n$, are evaluated in terms of $[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}$.Comment: LateX, 40 pages, 1 figure, extensive referencin

When fecundity does not equal fitness: evidence of an offspring quantity versus quality trade-off in pre-industrial humans

Maternal fitness should be maximized by the optimal division of reproductive investment between offspring number and offspring quality. While evidence for this is abundant in many taxa, there have been fewer tests in mammals, and in particular, humans. We used a dataset of humans spanning three generations from pre-industrial Finland to test how increases in maternal fecundity affect offspring quality and maternal fitness in contrasting socio-economic conditions. For ‘resource-poor’ landless families, but not ‘resource-rich’ landowning families, maternal fitness returns diminished with increased maternal fecundity. This was because the average offspring contribution to maternal fitness declined with increased maternal fecundity for landless but not landowning families. This decline was due to reduced offspring recruitment with increased maternal fecundity. However, in landowning families, recruited offspring fecundity increased with increased maternal fecundity. This suggests that despite decreased offspring recruitment, maternal fitness is not reduced in favourable socio-economic conditions due to an increase in subsequent offspring fecundity. These results provide evidence consistent with an offspring quantity–quality trade-off in the lifetime reproduction of humans from poor socio-economic conditions. The results also highlight the importance of measuring offspring quality across their whole lifespan to estimate reliably the fitness consequences of increased maternal fecundity

Is Cosmic Parity Violation Responsible for the Anomalies in the WMAP Data?

This research demonstrates that parity violation in general relativity can simultaneously explain the observed loss in power and alignment at a preferred axis ('Axis of Evil')in the low multipole moments of the WMAP data. This observational possibility also provides an experimental window for an inflationary leptogenesis mechanism arising from large-scale parity violation. A velocity dependent potential is induced from gravitational backreaction, which modifies the primordial scalar angular power spectrum of density perturbations in the CMB. This modification suppresses power of odd parity multipoles on large scales which can be associated with the scale of a massive right-handed neutrino.Comment: 5 pages, included new references, expanded on some calculation

MC decomposition and boride formation in a next generation polycrystalline Ni based superalloy during isothermal exposure at 900 °C

Detailed microstructural characterisation of phases present in a next generation polycrystalline Ni based superalloy after thermal exposure at 900 °C was carried out, focusing on carbides and borides. Metastable M5B3 precipitated after 32 h had a stoichiometry of (Cr0.7Mo0.2W0.1)5B3 with substitutions with Ni, Co, Nb and Ta. Fine M23C6 (a = 10.62 Å) was overgrown by metastable M5B3, as shown by rigorous TEM-SAD pattern investigation. The borides were eventually dominated by Mo rich M3B2, at the apparent expense of MC. Decomposition of MC was confirmed; it transformed sequentially to γ and then γ΄. The primary driving force for the MC decomposition was attributed to γ΄ precipitation, increasing its fraction to the thermodynamic equilibrium at 900 °C

Ramanujan and Extensions and Contractions of Continued Fractions

If a continued fraction $K_{n=1}^{\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\infty} a_{n}/b_{n}$ we mean a continued fraction $K_{n=1}^{\infty} c_{n}/d_{n}$ whose odd or even part is $K_{n=1}^{\infty} a_{n}/b_{n}$. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if $K_{n=1}^{\infty}a_{n}/b_{n}$ is the even part); (ii) Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart.Comment: 16 page

Damned if they do, damned if they don't: negotiating the tricky context of anti-social behaviour and keeping safe in disadvantaged urban neighbourhoods

Young people's relationship with anti-social behaviour (ASB) is complicated. While their behaviours are often stereotyped as anti-social (e.g. ‘hanging about’), they also experience ASB in their neighbourhood. In this study, we explore young people's own perspectives on ASB, comparing results from ‘go-along’ interviews and focus groups conducted in disadvantaged neighbourhoods in Glasgow, Scotland. This article discusses how young people's everyday experience of ASB was contextualised by social factors such as cultural stereotyping of marginalised groups, poor social connectivity and spatial marginalisation within their neighbourhood. Furthermore, we found that these social factors were mutually reinforcing and interacted in a way that appeared to leave young people in a ‘no-win’ situation regarding their association with ASB. Participation in ASB and attempts to avoid such involvement were seen to involve negative consequences: participation could entail violence and spatial restrictions linked to territoriality, but avoidance could lead to being ostracised from their peer group. Regardless of involvement, young people felt that adults stereotyped them as anti-social. Our findings therefore provide support for policies and interventions aimed at reducing ASB (perpetrated by residents of all ages); in part by better ensuring that young people have a clear incentive for avoiding such behaviours

Bathyal demersal fishes of the Charlie-Gibbs Fracture Zone region (49°–54°N) of the Mid-Atlantic Ridge : III. Results from remotely operated vehicle (ROV) video transects

Peer reviewedPublisher PD

Transformation of an uncertain video search pipeline to a sketch-based visual analytics loop

Traditional sketch-based image or video search systems rely on machine learning concepts as their core technology. However, in many applications, machine learning alone is impractical since videos may not be semantically annotated sufficiently, there may be a lack of suitable training data, and the search requirements of the user may frequently change for different tasks. In this work, we develop a visual analytics systems that overcomes the shortcomings of the traditional approach. We make use of a sketch-based interface to enable users to specify search requirement in a flexible manner without depending on semantic annotation. We employ active machine learning to train different analytical models for different types of search requirements. We use visualization to facilitate knowledge discovery at the different stages of visual analytics. This includes visualizing the parameter space of the trained model, visualizing the search space to support interactive browsing, visualizing candidature search results to support rapid interaction for active learning while minimizing watching videos, and visualizing aggregated information of the search results. We demonstrate the system for searching spatiotemporal attributes from sports video to identify key instances of the team and player performance. © 1995-2012 IEEE

The Geometry of D=11 Null Killing Spinors

We determine the necessary and sufficient conditions on the metric and the four-form for the most general bosonic supersymmetric configurations of D=11 supergravity which admit a null Killing spinor i.e. a Killing spinor which can be used to construct a null Killing vector. This class covers all supersymmetric time-dependent configurations and completes the classification of the most general supersymmetric configurations initiated in hep-th/0212008.Comment: 30 pages, typos corrected, reference added, new solution included in section 5.1; uses JHEP3.cl