Linear-Size Approximations to the Vietoris-Rips Filtration

The Vietoris-Rips filtration is a versatile tool in topological data analysis. It is a sequence of simplicial complexes built on a metric space to add topological structure to an otherwise disconnected set of points. It is widely used because it encodes useful information about the topology of the underlying metric space. This information is often extracted from its so-called persistence diagram. Unfortunately, this filtration is often too large to construct in full. We show how to construct an O(n)-size filtered simplicial complex on an $n$-point metric space such that its persistence diagram is a good approximation to that of the Vietoris-Rips filtration. This new filtration can be constructed in $O(n\log n)$ time. The constant factors in both the size and the running time depend only on the doubling dimension of the metric space and the desired tightness of the approximation. For the first time, this makes it computationally tractable to approximate the persistence diagram of the Vietoris-Rips filtration across all scales for large data sets. We describe two different sparse filtrations. The first is a zigzag filtration that removes points as the scale increases. The second is a (non-zigzag) filtration that yields the same persistence diagram. Both methods are based on a hierarchical net-tree and yield the same guarantees

Fixed-Field Alternating-Gradient Accelerators

These notes provide an overview of Fixed-Field Alternating-Gradient (FFAG) accelerators for medical applications. We begin with a review of the basic principles of this type of accelerator, including the scaling and non-scaling types, highlighting beam dynamics issues that are of relevance to hadron ac- celerators. The potential of FFAG accelerators in the field of hadron therapy is discussed in detail, including an overview of existing medical FFAG designs. The options for FFAG treatment gantries are also considered.Comment: Notes composed for the 2015 CERN Specialised Accelerator School on Medical Accelerators. Submitted to CERN Yellow Reports serie

Attitudes to Makaton in the ages on integration and inclusion

The Makaton Vocabulary was developed in the 1970’s and became, and has remained, one of most pervasive and influential pedagogical approaches for children with severe learning difficulties. This article looks at attitudes towards Makaton and compares findings from two studies, carried out in a sample of special schools in the south west of England during 1986 and 1995. Overall, the results suggest that attitudes towards the use of Makaton signs have become more positive. Makaton signs are now regarded, overall, as supporting and facilitating language development, and earlier concerns about stigmatisation have declined. There is some evidence to suggest that this latter change is influenced by changes in attitudes to British Sign Language. The 1986 study predicted that new technology would have a significant impact on attitudes to language and communication systems such as Makaton, but this prediction was not supported in the 2005 study. The article highlights also how different attitudes towards Makaton can exist within the same school, and how this situation can have a significant impact on the educational experiences and opportunities of children with severe learning difficulties. The article concludes that the apparent educational movements of integration or inclusion produce different attitudes towards Makaton and how it is used. However, although Makaton signing has become seen as a tool to create educational inclusion, the extent to which the system itself has actually changed is a contentious issu

No evidence for dust B-mode decorrelation in Planck data

Constraints on inflationary $B$-modes using Cosmic Microwave Background polarization data commonly rely on either template cleaning or cross-spectra between maps at different frequencies to disentangle galactic foregrounds from the cosmological signal. Assumptions about how the foregrounds scale with frequency are therefore crucial to interpreting the data. Recent results from the Planck satellite collaboration claim significant evidence for a decorrelation in the polarization signal of the spatial pattern of galactic dust between 353 GHz and 217 GHz. Such a decorrelation would suppress power in the cross spectrum between high frequency maps, where the dust is strong, and lower frequency maps, where the sensitivity to cosmological $B$-modes is strongest. Alternatively, it would leave residuals in lower frequency maps cleaned with a template derived from the higher frequency maps. If not accounted for, both situations would result in an underestimate of the dust contribution and thus an upward bias on measurements of the tensor-to-scalar ratio, $r$. In this paper we revisit this measurement and find that the no-decorrelation hypothesis cannot be excluded with the Planck data. There are three main reasons for this: i) there is significant noise bias in cross spectra between Planck data splits that needs to be accounted for; ii) there is strong evidence for unknown instrumental systematics whose amplitude we estimate using alternative Planck data splits; iii) there are significant correlations between measurements in different sky patches that need to be taken into account when assessing the statistical significance. Between $\ell=55-90$ and over $72\%$ of the sky, the dust $BB$ correlation between 217 GHz and 353 GHz is $1.001^{+.004/.021}_{-.004/.000}$ ($68\%~stat./syst.$) and shows no significant trend with sky fraction.Comment: 16 pages, 13 figure

Comment on "Superfluid stability in the BEC-BCS crossover"

We point out an error in recent work by Pao, Wu, and Yip [Phys. Rev.B {\bf 73}, 132506 (2006)], that stems from their use of a necessary but not sufficient condition [positive compressibility (magnetic susceptibility) and superfluid stiffness] for the stability of the ground state of a polarized Fermi gas. As a result, for a range of detunings their proposed ground-state solution is a local maximum rather than a minimum of the ground state energy, which thereby invalidates their proposed phase diagram for resonantly interacting fermions under an imposed population difference.Comment: 4 pages, 2 figures. Version in PR

Technical Barriers to Trade in the European Union: Importance for the Accession Countries. CEPS Working Document No. 144, April 2000

With trade in industrial products between the EU and the CEECs now essentially free of tariff and non-tariff restrictions, the principal impact of accession to the EU on trade flows will be through access to the Single Market of the EU. A key element of this will be the removal of technical barriers to trade. In this paper we try and highlight the importance of technical barriers to trade between the EU and the various CEECs, distinguishing sectors according to the different approaches to the removal of these barriers in the EU: mutual recognition, detailed harmonisation (old approach) and minimum requirements (new approach). We utilise two sources of information on technical regulations: a sectoral classification from a previous study of the impact of the Single Market and our own detailed translation of EU product related directives into the relevant tariff codes. The analysis suggests that the importance of technical barriers varies considerably across the CEECs. The adjustment implications of access to the Single Market are likely to be greatest for those most advanced in their accession negotiations

Intrinsic resistivity and the SO(5) theory of high-temperature superconductors

The topological structure of the order parameter in Zhang's SO(5) theory of superconductivity allows for an unusual type of dissipation mechanism via which current-carrying states can decay. The resistivity due to this mechanism, which involves orientation rather than amplitude order-parameter fluctuations, is calculated for the case of a thin superconducting wire. The approach is a suitably modified version of that pioneered by Langer and Ambegaokar for conventional superconductors.Comment: 4 pages, including 1 figure (REVTEX); references added, minor corrections mad

Mass Media and Polarisation Processes in the Bounded Confidence Model of Opinion Dynamics

This paper presents a social simulation in which we add an additional layer of mass media communication to the social network \'bounded confidence\' model of Deffuant et al (2000). A population of agents on a lattice with continuous opinions and bounded confidence adjust their opinions on the basis of binary social network interactions between neighbours or communication with a fixed opinion. There are two mechanisms for interaction. \'Social interaction\' occurs between neighbours on a lattice and \'mass communication,\' adjusts opinions based on an agent interacting with a fixed opinion. Two new variables are added, polarisation: the degree to which two mass media opinions differ, and broadcast ratio: the number of social interactions for each mass media communication. Four dynamical regimes are observed, fragmented, double extreme convergence, a state of persistent opinion exchange leading to single extreme convergence and a disordered state. Double extreme convergence is found where agents are less willing to change opinion and mass media communications are common or where there is moderate willingness to change opinion and a high frequency of mass media communications. Single extreme convergence is found where there is moderate willingness to change opinion and a lower frequency of mass media communication. A period of persistent opinion exchange precedes single extreme convergence, it is characterized by the formation of two opposing groups of opinion separated by a gradient of opinion exchange. With even very low frequencies of mass media communications this results in a move to central opinions followed by a global drift to one extreme as one of the opposing groups of opinion dominates. A similar pattern of findings is observed for Neumann and Moore neighbourhoods.Opinion Dynamics, Mass Media, Polarisation, Extremists, Consensus