Asymptotic enumeration of 2-covers and line graphs

In this paper we find asymptotic enumerations for the number of line graphs on $n$-labelled vertices and for different types of related combinatorial objects called 2-covers. We find that the number of 2-covers, $s_n$, and proper 2-covers, $t_n$, on $[n]$ both have asymptotic growth $$s_n\sim t_n\sim B_{2n}2^{-n}\exp(-\frac12\log(2n/\log n))= B_{2n}2^{-n}\sqrt{\frac{\log n}{2n}},$$ where $B_{2n}$ is the $2n$th Bell number, while the number of restricted 2-covers, $u_n$, restricted, proper 2-covers on $[n]$, $v_n$, and line graphs $l_n$, all have growth $$u_n\sim v_n\sim l_n\sim B_{2n}2^{-n}n^{-1/2}\exp(-[\frac12\log(2n/\log n)]^2).$$ In our proofs we use probabilistic arguments for the unrestricted types of 2-covers and and generating function methods for the restricted types of 2-covers and line graphs

Asymptotics for incidence matrix classes

We define {\em incidence matrices} to be zero-one matrices with no zero rows or columns. A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or identification by permutation of rows/columns are imposed. We find asymptotics and relationships for the number of matrices with $n$ ones in these classes as $n\to\infty$.Comment: updated and slightly expanded versio

Perineal resuturing versus expectant management following vaginal delivery complicated by a dehisced wound (PREVIEW): A pilot and feasibility randomised controlled trial

Objective: To establish the feasibility of conducting a definitive randomised controlled trial (RCT) comparing the effectiveness of resuturing versus expectant management for dehisced perineal wounds. Design: A multicentre pilot and feasibility RCT. Setting Ten UK maternity units from July 2011 to July 2013. Population: Eligible women with a dehisced perineal wound within 2 weeks of childbirth. Methods: The interventions were resuturing or expectancy. Randomisation was via web or telephone, stratified by participating centre. Blinding was not possible due to the nature of the interventions. Analysis was by intention-to-treat. Outcome: The primary outcome measure was wound healing at 6-8 weeks. Results: The study revealed a number of feasibility issues, particularly strong patient and clinician preference for treatment options at recruiting centres and the timing of the primary outcome measure. Thirty-four women were randomised (17 in each arm). Data from 33 women were analysed on an intention-to-treat analysis to obtain preliminary estimates of effect size. There was a difference in wound healing at 2 weeks favouring resuturing (OR 20.00, 95% CI 2.04 to 196.37, p=0.004). However, by 6-8 weeks all but one wound in both groups had healed. Conclusions: PREVIEW revealed a number of feasibility issues, which impacted on recruitment rate. These will have to be taken into account in the design of any future definitive study. In this feasibility study, resuturing was associated with quicker wound healing and women reported higher satisfaction rates with the outcome at 3 months

Asymptotic enumeration of incidence matrices

We discuss the problem of counting {\em incidence matrices}, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with $n$ ones as $n\to\infty$. We also give refined results for the asymptotic number of $i\times j$ incidence matrices with $n$ ones.Comment: jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda

Searching for the Kuhnian moment : the Black-Scholes-Merton formula and the evolution of modern finance theory

The Black-Scholes-Merton formula has been put to widespread use by options traders because it provides a means of calculating the theoretically 'correct' price of stock options. Traders can therefore see whether the market price of stock options undervalues or overvalues them compared with their hypothetical Black-Scholes-Merton price, before choosing to buy or sell options accordingly. As a consequence of this close relationship between options pricing theory and options pricing practice, a strong performativity loop was activated, whereby market prices quickly converged on the hypothetical Black-Scholes-Merton prices following the dissemination of the formula. The theory has therefore had significant real-world effects, but how should we characterize the initial instinct to derive the theory from a philosophy of science perspective? The two books under review suggest that a Kuhnian reading of the advancement of scientific knowledge might well be the most appropriate. But, on closer inspection, it becomes clear that the publication of the Black-Scholes-Merton formula should not be seen as a Kuhnian moment with paradigm-shaping attributes. It is shown that, at most, the formula acts as an important exemplar which, via its use in the training of options pricing theorists and options pricing practitioners, reinforces the entrenchment of finance theory within the orthodox economics worldview

GW4 Bridging the Gap

Bridging the Gap identified that realising the full benefits of Arts and Humanities research collaborations requires deeper consideration of research relationships as processes rather than just a means to an end. A processual approach demonstrates the potential role of Arts and Humanities research collaborations within a dynamic regional creative and cultural ecosystem can achieve a number of successes

Analysis of Mice Lacking DNaseI Hypersensitive Sites at the 5′ End of the IgH Locus

The 5′ end of the IgH locus contains a cluster of DNaseI hypersensitive sites, one of which (HS1) was shown to be pro-B cell specific and to contain binding sites for the transcription factors PU.1, E2A, and Pax5. These data as well as the location of the hypersensitive sites at the 5′ border of the IgH locus suggested a possible regulatory function for these elements with respect to the IgH locus. To test this notion, we generated mice carrying targeted deletions of either the pro-B cell specific site HS1 or the whole cluster of DNaseI hypersensitive sites. Lymphocytes carrying these deletions appear to undergo normal development, and mutant B cells do not exhibit any obvious defects in V(D)J recombination, allelic exclusion, or class switch recombination. We conclude that deletion of these DNaseI hypersensitive sites does not have an obvious impact on the IgH locus or B cell development

Q-switch-pumped supercontinuum for ultra-high resolution optical coherence tomography

In this Letter, we investigate the possibility of using a commercially availabl