On Pythagoras' theorem for products of spectral triples

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and provide non-unital counter-examples inspired by K-homology.Comment: Paper slightly shortened to match the published version; Lett. Math. Phys. 201

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D_N which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP_q(l), for any l>1 and 0<q<1. They provide 0^+ dimensional equivariant even spectral triples. If l is odd and N=(l+1)/2, the spectral triple is real with KO-dimension 2l mod 8.Comment: 54 pages, no figures, dcpic, pdflate

Teaching mathematics for search using a tutorial style of delivery

Understanding of mathematics is needed to underpin the process of search, either explicitly with Exact Match (Boolean logic, adjacency) or implicitly with Best match natural language search. In this paper we outline some pedagogical challenges in teaching mathematics for information retrieval (IR) to postgraduate information science students. The aim is to take these challenges either found by experience or in the literature, to identify both theoretical and practical ideas in order to improve the delivery of the material and positively affect the learning of the target audience by using a tutorial style of teaching. Results show that there is evidence to support the notion that a more pro-active style of teaching using tutorials yield benefits both in terms of assessment results and student satisfaction

Metric Properties of the Fuzzy Sphere

The fuzzy sphere, as a quantum metric space, carries a sequence of metrics which we describe in detail. We show that the Bloch coherent states, with these spectral distances, form a sequence of metric spaces that converge to the round sphere in the high-spin limit.Comment: Slightly shortened version, no major changes, two new references, version to appear on Letters in Mathematical Physic

Prospects in Constraining the Dark Energy Potential

We generalize to non-flat geometries the formalism of Simon et al. (2005) to reconstruct the dark energy potential. This formalism makes use of quantities similar to the Horizon-flow parameters in inflation, can, in principle, be made non-parametric and is general enough to be applied outside the simple, single scalar field quintessence. Since presently available and forthcoming data do not allow a non-parametric and exact reconstruction of the potential, we consider a general parametric description in term of Chebyshev polynomials. We then consider present and future measurements of H(z), Baryon Acoustic Oscillations surveys and Supernovae type 1A surveys, and investigate their constraints on the dark energy potential. We find that, relaxing the flatness assumption increases the errors on the reconstructed dark energy evolution but does not open up significant degeneracies, provided that a modest prior on geometry is imposed. Direct measurements of H(z), such as those provided by BAO surveys, are crucially important to constrain the evolution of the dark energy potential and the dark energy equation of state, especially for non-trivial deviations from the standard LambdaCDM model.Comment: 22 pages, 7 figures. 2 references correcte

Real-time traffic event detection using Twitter data

Incident detection is an important component of intelligent transport systems and plays a key role in urban traffic management and provision of traveller information services. Due to its importance, a wide number of researchers have developed different algorithms for real-time incident detection. However, the main limitation of existing techniques is that they do not work well in conditions where random factors could influence traffic flows. Twitter is a valuable source of information as its users post events as they happen or shortly after. Therefore, Twitter data have been used to predict a wide variety of real-time outcomes. This paper aims to present a methodology for a real-time traffic event detection using Twitter. Tweets are obtained through the Twitter streaming application programming interface in real time with a geolocation filter. Then, the author used natural language processing techniques to process the tweets before they are fed into a text classification algorithm that identifies if it is traffic related or not. The authors implemented their methodology in the West Midlands region in the UK and obtained an overall accuracy of 92·86%

Forward Global Photometric Calibration of the Dark Energy Survey

Many scientific goals for the Dark Energy Survey (DES) require calibration of optical/NIR broadband $b = grizY$ photometry that is stable in time and uniform over the celestial sky to one percent or better. It is also necessary to limit to similar accuracy systematic uncertainty in the calibrated broadband magnitudes due to uncertainty in the spectrum of the source. Here we present a "Forward Global Calibration Method (FGCM)" for photometric calibration of the DES, and we present results of its application to the first three years of the survey (Y3A1). The FGCM combines data taken with auxiliary instrumentation at the observatory with data from the broad-band survey imaging itself and models of the instrument and atmosphere to estimate the spatial- and time-dependence of the passbands of individual DES survey exposures. "Standard" passbands are chosen that are typical of the passbands encountered during the survey. The passband of any individual observation is combined with an estimate of the source spectral shape to yield a magnitude $m_b^{\mathrm{std}}$ in the standard system. This "chromatic correction" to the standard system is necessary to achieve sub-percent calibrations. The FGCM achieves reproducible and stable photometric calibration of standard magnitudes $m_b^{\mathrm{std}}$ of stellar sources over the multi-year Y3A1 data sample with residual random calibration errors of $\sigma=5-6\,\mathrm{mmag}$ per exposure. The accuracy of the calibration is uniform across the $5000\,\mathrm{deg}^2$ DES footprint to within $\sigma=7\,\mathrm{mmag}$. The systematic uncertainties of magnitudes in the standard system due to the spectra of sources are less than $5\,\mathrm{mmag}$ for main sequence stars with $0.5<g-i<3.0$.Comment: 25 pages, submitted to A

Personal identity (de)formation among lifestyle travellers: A double-edged sword?

This article explores the personal identity work of lifestyle travellers – individuals for whom extended leisure travel is a preferred lifestyle that they return to repeatedly. Qualitative findings from in-depth semi-structured interviews with lifestyle travellers in northern India and southern Thailand are interpreted in light of theories on identity formation in late modernity that position identity as problematic. It is suggested that extended leisure travel can provide exposure to varied cultural praxes that may contribute to a sense of social saturation. Whilst a minority of the respondents embraced a saturation of personal identity in the subjective formation of a cosmopolitan cultural identity, several of the respondents were paradoxically left with more identity questions than answers as the result of their travels

NTT and NOT spectroscopy of SDSS-II supernovae

Context. The SDSS-II Supernova Survey, conducted between 2005 and 2007, was designed to detect a large number of Type Ia supernovae (SNe Ia) around z~0.2, the redshift "gap" between low-z and high-z SN searches. The survey has provided multi-band photometric lightcurves for variable targets, and SN candidates were scheduled for spectroscopic observations, primarily to provide SN classification and accurate redshifts. We present SN spectra obtained in 2006 and 2007 using the NTT and the NOT. Aims. We provide an atlas of SN spectra in the range z =0.03-0.32 that complements the well-sampled lightcurves from SDSS-II in the forthcoming three-year SDSS SN cosmology analysis. The sample can, for example, be used for spectral studies of SNe Ia, which are critical for understanding potential systematic effects when SNe are used to determine cosmological distances. Methods. The spectra were reduced in a uniform manner, and special care was taken in estimating the uncertainties for the different processing steps. Host-galaxy light was subtracted when possible and the SN type fitted using the SuperNova IDentification code (SNID). We also present comparisons between spectral and photometric dating using SALT lightcurve fits to the photometry from SDSS-II, as well as the global distribution of our sample in terms of the lightcurve parameters: stretch and colour. Results. We report new spectroscopic data from 141 SNe Ia, mainly between -9 and +15 days from lightcurve maximum, including a few cases of multi-epoch observations. This homogeneous, host-galaxy subtracted, SN Ia spectroscopic sample is among the largest such data sets and unique in its redshift interval. The sample includes two potential SN 1991T-like SNe (SN 2006on and SN 2007ni) and one potential SN 2002cx-like SN (SN 2007ie). In addition, the new compilation includes spectra from 23 confirmed Type II and 8 Type Ib/c SNe.Comment: Accepted for publication in A&