A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a suitable tool for nonabelian, 2-dimensional, local-to-global problems. The methods are analogous to those developed by Brown and Higgins for similar theorems for other higher homotopy groupoids. An integral part of the proof is a detailed discussion of commutative cubes in a double category with connections, and a proof of the key result that any composition of commutative cubes is commutative. These results have recently been generalised to all dimensions by Philip Higgins.Comment: 19 pages, uses picte

Electronic doctoral theses in the UK: a sector-wide survey into policies, practice and barriers to Open Access

Sharing knowledge and research outputs is critical to the progress of science and human development, and a central tenet of academia. The Internet itself is a product of the academic community, and opening access to that community’s most important body of research, doctoral theses, is both a logical and an inevitable development. Progress toward open access to electronic theses has been slow in the UK. Much has been written on the perceived barriers and practical/infrastructural considerations that might explain this, but a comprehensive picture of that progress, and obstacles to it, was lacking. In 2010, a survey of policy and practice in UK HEIs was conducted by UCL (University College London) Library Services (commissioned by the Joint Information Systems Committee, JISC) to address this very issue. Incorporating inputs from 144 institutions currently awarding doctoral degrees, the work provides the first clear and detailed picture of the status of open access to doctoral research in the UK. The mission of the UK Council for Graduate Education (UKCGE) is to promote and support the interests of graduate education, and this it does through dissemination of best practice and intelligence on emergent trends; helping to shape policy and practice for the benefit of the UK HEI sector. This report contributes to that mission by bringing to the membership’s attention the results of this important work by UCL Library Services; a collaboration between UKCGE and the authors of the original work, it sets out the policies and practices that emerged from the survey and also considers what has been learned about the perceived barriers to the implementation of open access to electronic theses. The 2010 survey has enabled, for the first time, a differentiation to be made between barriers that are “real” and those which are unfounded and/or yet to be properly validated. At the same time, the work highlights the progress made in certain critical areas, as well as those that require our greater attention. A positive picture emerges for the UK on the adoption of the electronic thesis, with the majority of HEIs surveyed expected to be providing open access to their theses in five years’ time. A more detailed picture also emerges regarding the primary reasons for requests to restrict access to theses, some of which, notably, apply only to electronic (not print) theses. This has necessarily given rise to new policy developments. There is positive evidence also of collaboration among HEIs to provide an efficient and robust service for accessing electronic theses; pooling their resources and expertise either in the development of their institutional repositories or in operating a joint service. The key driver of open access to electronic theses is the opportunity for UK HEIs to “showcase” their research outputs to the widest possible audience and enhance their impact. There are no reliable means as yet to measure this impact, but there are encouraging early indications that electronic doctoral theses attract significant attention when made openly accessible. Open access to electronic theses may therefore indeed accelerate the sharing of knowledge and the progress of scientific discovery and human development

Algorithm based comparison between the integral method and harmonic analysis of the timing jitter of diode-based and solid-state pulsed laser sources

AbstractA comparison between two methods of timing jitter calculation is presented. The integral method utilizes spectral area of the single side-band (SSB) phase noise spectrum to calculate root mean square (rms) timing jitter. In contrast the harmonic analysis exploits the uppermost noise power in high harmonics to retrieve timing fluctuation. The results obtained show that a consistent timing jitter of 1.2ps is found by the integral method and harmonic analysis in gain-switched laser diodes with an external cavity scheme. A comparison of the two approaches in noise measurement of a diode-pumped Yb:KY(WO4)2 passively mode-locked laser is also shown in which both techniques give 2ps rms timing jitter

On arithmetic and asymptotic properties of up-down numbers

Let $\sigma=(\sigma_1,..., \sigma_N)$, where $\sigma_i =\pm 1$, and let $C(\sigma)$ denote the number of permutations $\pi$ of $1,2,..., N+1,$ whose up-down signature $\mathrm{sign}(\pi(i+1)-\pi(i))=\sigma_i$, for $i=1,...,N$. We prove that the set of all up-down numbers $C(\sigma)$ can be expressed by a single universal polynomial $\Phi$, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that $\Phi$ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers $C(\sigma)$, for fixed $N$. We prove a concise upper-bound for $C(\sigma)$, which describes the asymptotic behaviour of the up-down function $C(\sigma)$ in the limit $C(\sigma) \ll (N+1)!$.Comment: Recommended for publication in Discrete Mathematics subject to revision