2,220 research outputs found
Unravelling the Dodecahedral Spaces
The hyperbolic dodecahedral space of Weber and Seifert has a natural
non-positively curved cubulation obtained by subdividing the dodecahedron into
cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular
cover with the property that the canonical hypersurfaces made up of the
mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover
in which the associated cubulation is special. We also describe the natural
cubulation and covers of the spherical dodecahedral space (aka Poincar\'e
homology sphere).Comment: 15 pages + 6 pages appendix, 7 figures, 4 table
Randomised controlled trial of homoeopathy versus placebo in perennial allergic rhinitis with overview of four trial series
OBJECTIVE: To test the hypothesis that homoeopathy is a placebo by examining its effect in patients with allergic rhinitis and so contest the evidence from three previous trials in this series.
Design: Randomised, double blind, placebo controlled, parallel group, multicentre study.
SETTING: Four general practices and a hospital ear, nose, and throat outpatient department.
PARTICIPANTS: 51 patients with perennial allergic rhinitis. Intervention: Random assignment to an oral 30c homoeopathic preparation of principal inhalant allergen or to placebo.
MAIN OUTCOME MEASURES: Changes from baseline in nasal inspiratory peak flow and symptom visual analogue scale score over third and fourth weeks after randomisation.
RESULTS: Fifty patients completed the study. The homoeopathy group had a significant objective improvement in nasal airflow compared with the placebo group (mean difference 19.8 l/min, 95% confidence interval 10.4 to 29.1, P=0.0001). Both groups reported improvement in symptoms, with patients taking homoeopathy reporting more improvement in all but one of the centres, which had more patients with aggravations. On average no significant difference between the groups was seen on visual analogue scale scores. Initial aggravations of rhinitis symptoms were more common with homoeopathy than placebo (7 (30%) v 2 (7%), P=0.04). Addition of these results to those of three previous trials (n=253) showed a mean symptom reduction on visual analogue scores of 28% (10.9 mm) for homoeopathy compared with 3% (1.1 mm) for placebo (95% confidence interval 4.2 to 15.4, P=0.0007).
CONCLUSION: The objective results reinforce earlier evidence that homoeopathic dilutions differ from placebo
Extension of Pack Method for Compressive Tests
The pack method for determining compressive stress-strain graphs described in NACA Report No. 649 has been modified to extend it's application to thinner gages and stronger materials. The principal modifications consisted in the provision of additional support against instability cementing the specimens of the pack together with fused shellac and the provision of special clamps to hold the specimens together while the test is in progress. The shellac was found to increase the buckling load of the pack without any appreciable effect on the compressive stress-strain graph of the material. The extended pack method described in this note has made possible the application of stresses in excess of 220 kips per square inch to sheet material having a thickness of only 0.02 inch
Finiteness properties of cubulated groups
We give a generalized and self-contained account of Haglund-Paulin's
wallspaces and Sageev's construction of the CAT(0) cube complex dual to a
wallspace. We examine criteria on a wallspace leading to finiteness properties
of its dual cube complex. Our discussion is aimed at readers wishing to apply
these methods to produce actions of groups on cube complexes and understand
their nature. We develop the wallspace ideas in a level of generality that
facilitates their application.
Our main result describes the structure of dual cube complexes arising from
relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex
codimension-1 subgroups of a group G that is hyperbolic relative to
P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual
CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact
when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual
CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved
results in Sections 7 and 8. Several theorem numbers have changed from the
previous versio
Measuring visual cortical oxygenation in diabetes using functional near-infrared spectroscopy
Aims: Diabetes mellitus affects about 6% of the world’s population, and the chronic complications of the disease may result in macro- and micro-vascular changes. The purpose of the current study was to shed light on visual cortical oxygenation in diabetic individuals. We then aimed to compare the haemodynamic response (HDR) to visual stimulation with glycaemic control, given the likelihood of diabetic individuals suffering from such macro- and micro-vascular insult.
Methodology: Thirty participants took part in this explorative study, fifteen of whom had diabetes and fifteen of whom were non-diabetic controls. The HDR, measured as concentrations of oxyhaemoglobin [HbO] and deoxyhaemoglobin [HbR], to visual stimulation was recorded over the primary visual cortex (V1) using a dual-channel oximeter. The stimulus comprised a pattern-reversal checkerboard presented in a block design. Participants’ mean glycated haemoglobin (HbA1c) level (±SD) was 7.2±0.6% in the diabetic group and 5.5±0.4% in the non-diabetic group. Raw haemodynamic data were normalised to baseline, and the last 15 s of data from each ‘stimulus on’ and ‘stimulus off’ condition were averaged over seven duty cycles for each participant.
Results: There were statistically significant differences in ∆[HbO] and ∆[HbR] to visual stimulation between diabetic and non-diabetic groups (p<0.05). In the diabetic group, individuals with type 1 diabetes displayed an increased [HbO] (p<0.01) and decreased [HbR] (p<0.05) compared to their type 2 counterparts. There was also a linear relationship between both ∆[HbO] and ∆[HbR] as a function of HbA1c level (p<0.0005).
Conclusions: Our findings suggest that fNIRS can be used as a quantitative measure of cortical oxygenation in diabetes. Diabetic individuals have a larger HDR to visual stimulation compared to non-diabetic individuals. This increase in ∆[HbO] and decrease in ∆[HbR] appears to be correlated with HbA1c level
High visibility two photon interference of frequency time entangled photons generated in a quasi phase matched AlGaAs waveguide
We demonstrate experimentally the frequency time entanglement of photon pairs
produced in a CW pumped quasi phased matched AlGaAs superlattice waveguide. A
visibility of 96.0+-0.7% without background subtraction has been achieved,
which corresponds the violation of Bell inequality by 52 standard deviations
Dynamical Mass Generation in a Finite-Temperature Abelian Gauge Theory
We write down the gap equation for the fermion self-energy in a
finite-temperature abelian gauge theory in three dimensions. The instantaneous
approximation is relaxed, momentum-dependent fermion and photon self-energies
are considered, and the corresponding Schwinger-Dyson equation is solved
numerically. The relation between the zero-momentum and zero-temperature
fermion self-energy and the critical temperature T_c, above which there is no
dynamical mass generation, is then studied. We also investigate the effect
which the number of fermion flavours N_f has on the results, and we give the
phase diagram of the theory with respect to T and N_f.Comment: 20 LaTeX pages, 4 postscript figures in a single file, version to
appear in Physical Review
Dynamical Symmetry Breaking With a Fourth Generation
Adding a fourth generation to the Standard Model and assuming it to be valid
up to some cutoff \Lambda, we show that electroweak symmetry is broken by
radiative corrections due to the fourth generation. The effects of the fourth
generation are isolated using a Lagrangian with a genuine scalar without
self-interactions at the classical level. For masses of the fourth generation
consistent with electroweak precision data (including the B \rightarrow K \pi\
CP asymmetries) we obtain a Higgs mass of the order of a few hundreds GeV and a
cutoff \Lambda\ around 1-2 TeV. We study the reliability of the perturbative
treatment used to obtain these results taking into account the running of the
Yukawa couplings of the fourth quark generation with the aid of the
Renormalization Group (RG) equations, finding similar allowed values for the
Higgs mass but a slightly lower cut-off due to the breaking of the perturbative
regime. Such low cut-off means that the effects of new physics needed to
describe electroweak interactions at energy above \Lambda\ should be measurable
at the LHC. We use the minimal supersymmetric extension of the standard model
with four generations as an explicit example of models realizing the dynamical
electroweak symmetry breaking by radiative corrections and containing new
physics. Here, the cutoff is replaced by the masses of the squarks and
electroweak symmetry breaking by radiative corrections requires the squark
masses to be of the order of 1 TeV.Comment: 20 pages, 7 figures. New section adde
Derivative Expansion and the Effective Action for the Abelian Chern-Simons Theory at Higher Orders
We study systematically the higher order corrections to the parity violating
part of the effective action for the Abelian Chern-Simons theory in 2+1
dimensions, using the method of derivative expansion. We explicitly calculate
the parity violating parts of the quadratic, cubic and the quartic terms (in
fields) of the effective action. We show that each of these actions can be
summed, in principle, to all orders in the derivatives. However, such a
structure is complicated and not very useful. On the other hand, at every order
in the powers of the derivatives, we show that the effective action can also be
summed to all orders in the fields. The resulting actions can be expressed in
terms of the leading order effective action in the static limit. We prove gauge
invariance, both large and small of the resulting effective actions. Various
other features of the theory are also brought out.Comment: 36 page
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