Reflexivity of the translation-dilation algebras on L^2(R)

The hyperbolic algebra A_h, studied recently by Katavolos and Power, is the weak star closed operator algebra on L^2(R) generated by H^\infty(R), as multiplication operators, and by the dilation operators V_t, t \geq 0, given by V_t f(x) = e^{t/2} f(e^t x). We show that A_h is a reflexive operator algebra and that the four dimensional manifold Lat A_h (with the natural topology) is the reflexive hull of a natural two dimensional subspace.Comment: 10 pages, no figures To appear in the International Journal of Mathematic

Quantification of Plasma and Urine Thymidine and 2'-Deoxyuridine by LC-MS/MS for the Pharmacodynamic Evaluation of Erythrocyte Encapsulated Thymidine Phosphorylase in Patients with Mitochondrial Neurogastrointestinal Encephalomyopathy.

Mitochondrial neurogastrointestinal encephalomyopathy (MNGIE) is an ultra-rare disorder caused by mutations in TYMP, leading to a deficiency in thymidine phosphorylase and a subsequent systemic accumulation of thymidine and 2'-deoxyuridine. Erythrocyte-encapsulated thymidine phosphorylase (EE-TP) is under clinical development as an enzyme replacement therapy for MNGIE. Bioanalytical methods were developed according to regulatory guidelines for the quantification of thymidine and 2'-deoxyuridine in plasma and urine using liquid chromatography-tandem mass spectrometry (LC-MS/MS) for supporting the pharmacodynamic evaluation of EE-TP. Samples were deproteinized with 5% perchloric acid (v/v) and the supernatants analyzed using a Hypercarb column (30 × 2.1 mm, 3 µm), with mobile phases of 0.1% formic acid in methanol and 0.1% formic acid in deionized water. Detection was conducted using an ion-spray interface running in positive mode. Isotopically labelled thymidine and 2'-deoxyuridine were used as internal standards. Calibration curves for both metabolites showed linearity (r > 0.99) in the concentration ranges of 10-10,000 ng/mL for plasma, and 1-50 µg/mL for urine, with method analytical performances within the acceptable criteria for quality control samples. The plasma method was successfully applied to the diagnosis of two patients with MNGIE and the quantification of plasma metabolites in three patients treated with EE-TP

Personalised trails and learner profiling within e-learning environments

This deliverable focuses on personalisation and personalised trails. We begin by introducing and defining the concepts of personalisation and personalised trails. Personalisation requires that a user profile be stored, and so we assess currently available standard profile schemas and discuss the requirements for a profile to support personalised learning. We then review techniques for providing personalisation and some systems that implement these techniques, and discuss some of the issues around evaluating personalisation systems. We look especially at the use of learning and cognitive styles to support personalised learning, and also consider personalisation in the field of mobile learning, which has a slightly different take on the subject, and in commercially available systems, where personalisation support is found to currently be only at quite a low level. We conclude with a summary of the lessons to be learned from our review of personalisation and personalised trails

A Two-Player Game of Life

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.Comment: 7 pages, 3 figure

Collaborative trails in e-learning environments

This deliverable focuses on collaboration within groups of learners, and hence collaborative trails. We begin by reviewing the theoretical background to collaborative learning and looking at the kinds of support that computers can give to groups of learners working collaboratively, and then look more deeply at some of the issues in designing environments to support collaborative learning trails and at tools and techniques, including collaborative filtering, that can be used for analysing collaborative trails. We then review the state-of-the-art in supporting collaborative learning in three different areas – experimental academic systems, systems using mobile technology (which are also generally academic), and commercially available systems. The final part of the deliverable presents three scenarios that show where technology that supports groups working collaboratively and producing collaborative trails may be heading in the near future

Sampling properties of directed networks

For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN-component(s) of directed networks, a description of the effects of BFS sampling on other topological properties are all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven different complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure, as well as the number and structure of strongly connected components in sampled networks. In addition, at low sampling coverage (i.e. less than 40%), the values of average degree, variance of out-degree, degree auto-correlation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks, and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.Comment: 21 pages, 11 figure

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in [arXiv:math/0701645]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Efficient Representation of Multidimensional Data over Hierarchical Domains

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-46049-9_19[Abstract] We consider the problem of representing multidimensional data where the domain of each dimension is organized hierarchically, and the queries require summary information at a different node in the hierarchy of each dimension. This is the typical case of OLAP databases. A basic approach is to represent each hierarchy as a one-dimensional line and recast the queries as multidimensional range queries. This approach can be implemented compactly by generalizing to more dimensions the k2k2 -treap, a compact representation of two-dimensional points that allows for efficient summarization queries along generic ranges. Instead, we propose a more flexible generalization, which instead of a generic quadtree-like partition of the space, follows the domain hierarchies across each dimension to organize the partitioning. The resulting structure is much more efficient than a generic multidimensional structure, since queries are resolved by aggregating much fewer nodes of the tree.Ministerio de Economía, Industria y Competitividad; TIN2013-46238-C4-3-RMinisterio de Economía, Industria y Competitividad; IDI-20141259Ministerio de Economía, Industria y Competitividad; ITC-20151305Ministerio de Economía y Competitividad; ITC-20151247Xunta de Galicia; GRC2013/053Chile.Fondo Nacional de Desarrollo Científico y Tecnológico; 1-140796COST. IC130

Personalised trails and learner profiling in an e-learning environment

This deliverable focuses on personalisation and personalised trails. We begin by introducing and defining the concepts of personalisation and personalised trails. Personalisation requires that a user profile be stored, and so we assess currently available standard profile schemas and discuss the requirements for a profile to support personalised learning. We then review techniques for providing personalisation and some systems that implement these techniques, and discuss some of the issues around evaluating personalisation systems. We look especially at the use of learning and cognitive styles to support personalised learning, and also consider personalisation in the field of mobile learning, which has a slightly different take on the subject, and in commercially available systems, where personalisation support is found to currently be only at quite a low level. We conclude with a summary of the lessons to be learned from our review of personalisation and personalised trails