A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Regulation of peripheral classical and non-classical monocytes on infliximab treatment in patients with rheumatoid arthritis and ankylosing spondylitis.

OBJECTIVE To investigate the regulatory effect of tumour necrosis factor (TNF) blockade with infliximab on the distribution of peripheral blood monocyte subpopulations in patients with rheumatoid arthritis (RA) and ankylosing spondylitis (AS). METHODS Purified CD11b+CD14+ monocytes from 5 patients with RA and 5 AS were analysed ex vivo before and after infliximab treatment by flow cytometry for CD16, CD163, CD11b, C-C chemokine receptor type 2 (CCR2) and CXC chemokine receptor 4 (CXCR4) at baseline and at days 2, 14, 84 and 168 after the first infliximab administration. Serum levels of the stromal cell-derived factor (SDF)-1 and monocyte chemotactic peptide (MCP)-1 at different time points were measured in either patient group before and on infliximab treatment. RESULTS Anti-TNF treatment with infliximab led to a significant increase of circulating CD11b+ non-classical and a concomitantly decrease of CD11b+ classical monocytes, to a decline in SDF-1 levels and reduced expression of CCR2 and CXCR4 on non-classical monocyte subpopulation. CONCLUSIONS Our study shows, that TNFα blockade by infliximab resulted in a dichotomy of the regulation of classical and non-classical monocytes that might have substantial impact on inhibition of osteoclastogenesis and of subsequent juxta-articular bone destruction and systemic bone loss in RA and AS.

Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.

Chern-Simons theory on Seifert 3-manifolds

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds Σ by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of non-Abelian flat connections, reduces the complete partition function of the non-Abelian theory on M to a 2-dimensional Abelian theory on the orbifold Σ, which is easily evaluated.

Effect of short-wave (6-22 MHz) magnetic fields on sleep quality and melatonin cycle in humans: the Schwarzenburg shut-down study

This paper describes the results of a unique "natural experiment" of the operation and cessation of a broadcast transmitter with its short-wave electromagnetic fields (6-22 MHz) on sleep quality and melatonin cycle in a general human population sample. In 1998, 54 volunteers (21 men, 33 women) were followed for 1 week each before and after shut-down of the short-wave radio transmitter at Schwarzenburg (Switzerland). Salivary melatonin was sampled five times a day and total daily excretion and acrophase were estimated using complex cosinor analysis. Sleep quality was recorded daily using a visual analogue scale. Before shut down, self-rated sleep quality was reduced by 3.9 units (95% CI: 1.7-6.0) per mA/m increase in magnetic field exposure. The corresponding decrease in melatonin excretion was 10% (95% CI: -32 to 20%). After shutdown, sleep quality improved by 1.7 units (95% CI: 0.1-3.4) per mA/m decrease in magnetic field exposure. Melatonin excretion increased by 15% (95% CI: -3 to 36%) compared to baseline values suggesting a rebound effect. Stratified analyses showed an exposure effect on melatonin excretion in poor sleepers (26% increase; 95% CI: 8-47%) but not in good sleepers. Change in sleep quality and melatonin excretion was related to the extent of magnetic field reduction after the transmitter's shut down in poor but not good sleepers. However, blinding of exposure was not possible in this observational study and this may have affected the outcome measurements in a direct or indirect (psychological) way.

An insulin infusion advisory system for type 1 diabetes patients based on non-linear model predictive control methods

In this paper, an Insulin Infusion Advisory System (IIAS) for Type 1 diabetes patients, which use insulin pumps for the Continuous Subcutaneous Insulin Infusion (CSII) is presented. The purpose of the system is to estimate the appropriate insulin infusion rates. The system is based on a Non-Linear Model Predictive Controller (NMPC) which uses a hybrid model. The model comprises a Compartmental Model (CM), which simulates the absorption of the glucose to the blood due to meal intakes, and a Neural Network (NN), which simulates the glucose-insulin kinetics. The NN is a Recurrent NN (RNN) trained with the Real Time Recurrent Learning (RTRL) algorithm. The output of the model consists of short term glucose predictions and provides input to the NMPC, in order for the latter to estimate the optimum insulin infusion rates. For the development and the evaluation of the IIAS, data generated from a Mathematical Model (MM) of a Type 1 diabetes patient have been used. The proposed control strategy is evaluated at multiple meal disturbances, various noise levels and additional time delays. The results indicate that the implemented IIAS is capable of handling multiple meals, which correspond to realistic meal profiles, large noise levels and time delays.

Effect of electromagnetic fields on highly diluted remedies measured by ultraviolet spectroscopy

Purpose: In homeopathy or anthroposophically extended medicine high dilutions are used. They showed significant differences in ultraviolet light (UV) transmission between controls and different dilution levels. Exposing such dilutions to physical factors such as UV light or elevated temperature (37�C) yielded significantly different UV transmissions values compared to unexposed dilutions. The aim was to test whether electromagnetic fields (EMF) of a mobile phone affect the UV absorbance of dilutions of Atropa belladonna (Ab) and quartz. Methods: Commercially available dilutions of Ab 4x, 6x, 12x, 15x, 30x and of quartz 6x, 12x, 15x, 30x were investigated. On 5 days, 4 samples of each dilution were exposed to the EMF by a mobile phone at 900MHz (GSM) with an output power of 2W for 3 h. Control samples were kept in a separate room. UV-absorbance of the samples in the range from 190 to 340 nm was measured in randomized order. The average absorbance from 200 to 340 nm and from 200 to 240 nm was compared between exposed and unexposed samples by a dependent t-test. Results: Between unexposed and exposed dilutions of Ab and quartz no significant differences were detected, except for quartz 12x over the range from 200 to 340 nm. Conclusion: Exposure of high dilutions of Ab and quartz to GSM EMF of a mobile phone did not alter UV absorbance of these dilutions.

Influence of quantized massive matter fields on the Casimir effect

Charged massive matter fields of spin-0 and spin- 1/2 are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed. Read More: http://www.worldscientific.com/doi/10.1142/S0217732315500996