Ince's limits for confluent and double-confluent Heun equations

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable $z$, while the other is given by a series of modified Bessel functions and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when $z_{0}$ tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schr\"odinger equation for inverse fourth and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk

Changing minds? Not in Congress!

This paper shows a variety of evidence that members of Congress are ideologically consistent. Based upon the roll call voting record, once elected to Congress, members adopt a consistent ideological position and maintain it over time. There may be changing minds, but they are not in Congress. Copyright Springer Science+Business Media, LLC 2007Congress, NOMINATE, Optimal Classification,

Paleo-Yardangs -- Wind-Scoured Desert Landforms at the Permo-Triassic Unconformity

In Canyonlands National Park, south-east Utah, at least 29 partly exhumed, aligned sandstone ridges trending generally N20-degrees-W occur at the upper unconformable surface of the Lower Permian (Leonardian) White Rim Sandstone. The ridges are at least 1.5 km long, 250 m wide and have up to 14 m of vertical relief (mean of 9 m). A thin lag of coarse sandstone that contains wind-ripple laminae and granule ripples directly overlies the ridges. Angular blocks of sandstone within the lag and sand-filled fissures immediately below the lag, within the ridges, attest to early cementation of the ridge-forming material. SE-dipping aeolian cross-strata within the White Rim Sandstone and within the lag closely parallel the ridge trend. The ridges are interpreted as wind-sculpted desert landforms (yardangs) that developed on the lithified upper surface of the White Rim Sandstone during an extended period of hyperaridity towards the end of the Permian

All in the timing: Considering time at multiple stages of group research

The role of time in measuring group and team temporality constitutes more than a methodological issue—it is a theoretical question. That is, if group interaction is theorized as processual and processes occur through time, then research on team temporality, as well as a range of other issues, must grapple with the methodological implications of our theories. This article contributes to ingroup's aim to advance theory and methods for understanding groups by exploring methodological approaches that allow us to capture a variety of team processes over time. Three case studies address the practical issues involved with employing various types of time-sensitive data collection, time-dependent coding, and time-based analysis, including their advantages and disadvantages. Together, the authors describe diverse field and analytical methods useful for interrogating theoretical assumptions about time in groups. Doing so expands the notion of group temporality to consider the role of both epochal and fungible times at multiple stages of group research