1,390 research outputs found
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
Cholinergic innervation of human mesenteric lymphatic vessels
Background: The cholinergic neurotransmission within the human mesenteric lymphatic vessels has been poorly studied. Therefore, our aim is to analyse the cholinergic nerve fibres of lymphatic vessels using the traditional enzymatic techniques of staining, plus the biochemical modifications of acetylcholinesterase (AChE) activity.Materials and methods: Specimens obtained from human mesenteric lymphatic vessels were subjected to the following experimental procedures: 1) drawing, cutting and staining of tissues; 2) staining of total nerve fibres; 3) enzymatic staining of cholinergic nerve fibres; 4) homogenisation of tissues; 5) biochemical amount of proteins; 6) biochemical amount of AChE activity; 6) quantitative analysis of images; 7) statistical analysis of data.Results: The mesenteric lymphatic vessels show many AChE positive nerve fibres around their wall with an almost plexiform distribution. The incubation time was performed at 1 h (partial activity) and 6 h (total activity). Moreover, biochemical dosage of the same enzymatic activity confirms the results obtained with morphological methods.Conclusions: The homogenates of the studied tissues contain strong AChE activity. In our study, the lymphatic vessels appeared to contain few cholinergic nerve fibres. Therefore, it is expected that perivascular nerve stimulation stimulates cholinergic nerves innervating the mesenteric arteries to release the neurotransmitter AChE, which activates muscarinic or nicotinic receptors to modulate adrenergic neurotransmission. These results strongly suggest, that perivascular cholinergic nerves have little or no effect on the adrenergic nerve function in mesenteric arteries. The cholinergic nerves innervating mesenteric arteries do not mediate direct vascular responses.
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving
We derive efficient algorithms for coarse approximation of algebraic
hypersurfaces, useful for estimating the distance between an input polynomial
zero set and a given query point. Our methods work best on sparse polynomials
of high degree (in any number of variables) but are nevertheless completely
general. The underlying ideas, which we take the time to describe in an
elementary way, come from tropical geometry. We thus reduce a hard algebraic
problem to high-precision linear optimization, proving new upper and lower
complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding
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
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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
Search for Sub-TeV Gamma Rays Coincident with BATSE Gamma Ray Bursts
Project GRAND is a 100m x 100m air shower array of proportional wire chambers
(PWCs). There are 64 stations each with eight 1.29 m^2 PWC planes arranged in
four orthogonal pairs placed vertically above one another to geometrically
measure the angles of charged secondaries. A steel plate above the bottom pair
of PWCs differentiates muons (which pass undeflected through the steel) from
non-penetrating particles. FLUKA Monte Carlo studies show that a TeV gamma ray
striking the atmosphere at normal incidence produces 0.23 muons which reach
ground level where their angles and identities are measured. Thus,
paradoxically, secondary muons are used as a signature for gamma ray primaries.
The data are examined for possible angular and time coincidences with eight
gamma ray bursts (GRBs) detected by BATSE. Seven of the GRBs were selected
because of their good acceptance by GRAND and high BATSE Fluence. The eighth
GRB was added due to its possible coincident detection by Milagrito. For each
of the eight candidate GRBs, the number of excess counts during the BATSE T90
time interval and within plus or minus five degrees of BATSE's direction was
obtained. The highest statistical significance reported in this paper (2.7
sigma) is for the event that was predicted to be the most likely to be observed
(GRB 971110).Comment: To be presented at the XXVIII International Cosmic Ray Conference,
Tsukuba, Japa
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%
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