Low dimensional cohomology of general conformal algebras gcNgc_N

We compute the low dimensional cohomologies $\tilde H^q(gc_N,C)$, H^q(gc_N,\C) of the infinite rank general Lie conformal algebras $gc_N$ with trivial coefficients for $q\le3, N=1$ or $q\le2, N\ge2$. We also prove that the cohomology of $gc_N$ with coefficients in its natural module is trivial, i.e., H^*(gc_N,\C[\ptl]^N)=0; thus partially solve an open problem of Bakalov-Kac-Voronov in [{\it Comm. Math. Phys.,} {\bf200} (1999), 561-598].Comment: 18 page

Determination of the position maximum for electron Compton scattering in electron microscopy

We study electron Compton scattering with an electron microscope by means of a Castaing-Henry filter. In the electron-spectroscopic-diffraction mode the positions of the Compton maxima in the diffraction plane are determined. We find a nearly constant shift of this position with respect to the value given by E=q2/2. The intensity of Compton-scattered electrons does not peak at the scattering angle predicted by the binary collision mode. The energy dispersion of the Compton profile is well described by E=q2/2

Cooperative Data Exchange based on MDS Codes

The cooperative data exchange problem is studied for the fully connected network. In this problem, each node initially only possesses a subset of the $K$ packets making up the file. Nodes make broadcast transmissions that are received by all other nodes. The goal is for each node to recover the full file. In this paper, we present a polynomial-time deterministic algorithm to compute the optimal (i.e., minimal) number of required broadcast transmissions and to determine the precise transmissions to be made by the nodes. A particular feature of our approach is that {\it each} of the $K-d$ transmissions is a linear combination of {\it exactly} $d+1$ packets, and we show how to optimally choose the value of $d.$ We also show how the coefficients of these linear combinations can be chosen by leveraging a connection to Maximum Distance Separable (MDS) codes. Moreover, we show that our method can be used to solve cooperative data exchange problems with weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur

Making it Rich and Personal: crafting an institutional personal learning environment

Many of the communities interested in learning and teaching technologies within higher education now accept the view that a conception of personal learning environments provides a the most realistic and workable perspective of learners’ interactions with and use of technology. This view may not be reflected in the behaviour of those parts of a university which normally purchase and deploy technology infrastructure. These departments or services are slow to change because they are typically, and understandably, risk-averse; the more so, because the consequences of expensive decisions about infrastructure will stay with the organisation for many years. Furthermore across the broader (less technically or educationally informed) academic community, the awareness of and familiarity with technologies in support of learning may be varied. In this context, work to innovate the learning environment will require considerable team effort and collective commitment. This paper presents a case study account of institutional processes harnessed to establish a universal personal learning environment fit for the 21st century. The challenges encountered were consequential of our working definition of a learning environment, which went beyond simple implementation. In our experience the requirements became summarised as “its more than a system, it’s a mindset”. As well as deploying technology ‘fit for purpose’ we were seeking to create an environment that could play an integral and catalytic part in the university’s role of enabling transformative education. Our ambitions and aspirations were derived from evidence in the literature. We also drew on evidence of recent and current performance in the university; gauged by institutional benchmarking and an extensive student survey. The paper presents and analyses this qualitative and quantitative data. We provide an account and analysis of our progress to achieve change, the methods we used, problems encountered and the decisions we made on the way

Quantum communication in the presence of a horizon

Based on homodyne detection, we discuss how the presence of an event horizon affects quantum communication between an inertial partner, Alice, and a uniformly accelerated partner, Rob. We show that there exists a low frequency cutoff for Rob's homodyne detector that maximizes the signal to noise ratio and it approximately corresponds to the Unruh frequency. In addition, the low frequency cutoff which minimizes the conditional variance between Alice's input state and Rob's output state is also approximately equal to the Unruh frequency. Thus the Unruh frequency provides a natural low frequency cutoff in order to optimize quantum communication of both classical and quantum information between Alice and Rob.Comment: 7 pages, 6 figure