Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

Tropical varieties for non-archimedean analytic spaces

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Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

Norm inequalities in multidimensional Lorentz spaces

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

MB-MDR: Model-Based Multifactor Dimensionality Reduction for detecting interactions in high-dimensional genomic data

L’anàlisi de l’efecte dels gens i els factors ambientals en el desenvolupament de malalties complexes és un gran repte estadístic i computacional. Entre les diverses metodologies de mineria de dades que s’han proposat per a l’anàlisi d’interaccions una de les més populars és el mètode Multifactor Dimensionality Reduction, MDR, (Ritchie i al. 2001). L’estratègia d’aquest mètode és reduir la dimensió multifactorial a u mitjançant l’agrupació dels diferents genotips en dos grups de risc: alt i baix. Tot i la seva utilitat demostrada, el mètode MDR té alguns inconvenients entre els quals l’agrupació excessiva de genotips pot fer que algunes interaccions importants no siguin detectades i que no permet ajustar per efectes principals ni per variables confusores. En aquest article il•lustrem les limitacions de l’estratègia MDR i d’altres aproximacions no paramètriques i demostrem la conveniència d’utilitzar metodologies parametriques per analitzar interaccions en estudis cas-control on es requereix l’ajust per variables confusores i per efectes principals. Proposem una nova metodologia, una versió paramètrica del mètode MDR, que anomenem Model-Based Multifactor Dimensionality Reduction (MB-MDR). La metodologia proposada té com a objectiu la identificació de genotips específics que estiguin associats a la malaltia i permet ajustar per efectes marginals i variables confusores. La nova metodologia s’il•lustra amb dades de l’Estudi Espanyol de Cancer de Bufeta.

3-T direct MR arthrography of the wrist: value of finger trap distraction to assess intrinsic ligament and triangular fibrocartilage complex tears.

PURPOSE: To determine the value of applying finger trap distraction during direct MR arthrography of the wrist to assess intrinsic ligament and triangular fibrocartilage complex (TFCC) tears. MATERIALS AND METHODS: Twenty consecutive patients were prospectively investigated by three-compartment wrist MR arthrography. Imaging was performed with 3-T scanners using a three-dimensional isotropic (0.4 mm) T1-weighted gradient-recalled echo sequence, with and without finger trap distraction (4 kg). In a blind and independent fashion, two musculoskeletal radiologists measured the width of the scapholunate (SL), lunotriquetral (LT) and ulna-TFC (UTFC) joint spaces. They evaluated the amount of contrast medium within these spaces using a four-point scale, and assessed SL, LT and TFCC tears, as well as the disruption of Gilula's carpal arcs. RESULTS: With finger trap distraction, both readers found a significant increase in width of the SL space (mean Δ = +0.1mm, p ≤ 0.040), and noticed more contrast medium therein (p ≤ 0.035). In contrast, the differences in width of the LT (mean Δ = +0.1 mm, p ≥ 0.057) and UTFC (mean Δ = 0mm, p ≥ 0.728) spaces, as well as the amount of contrast material within these spaces were not statistically significant (p = 0.607 and ≥ 0.157, respectively). Both readers detected more SL (Δ = +1, p = 0.157) and LT (Δ = +2, p = 0.223) tears, although statistical significance was not reached, and Gilula's carpal arcs were more frequently disrupted during finger trap distraction (Δ = +5, p = 0.025). CONCLUSION: The application of finger trap distraction during direct wrist MR arthrography may enhance both detection and characterisation of SL and LT ligament tears by widening the SL space and increasing the amount of contrast within the SL and LT joint spaces.

Influence of seasons and sampling strategy on assessment of bioaerosols in sewage treatment plants in Switzerland

An assessment of sewage workers' exposure to airborne cultivable bacteria, fungi and inhaled endotoxins was performed at 11 sewage treatment plants. We sampled the enclosed and unenclosed treatment areas in each plant and evaluated the influence of seasons (summer and winter) on bioaerosol levels. We also measured personal exposure to endotoxins of workers during special operation where a higher risk of bioaerosol inhalation was assumed. Results show that only fungi are present in significantly higher concentrations in summer than in winter (2331 +/- 858 versus 329 +/- 95 CFU m(-3)). We also found that there are significantly more bacteria in the enclosed area, near the particle grids for incoming water, than in the unenclosed area near the aeration basins (9455 +/- 2661 versus 2435 +/- 985 CFU m(-3) in summer and 11 081 +/- 2299 versus 2002 +/- 839 CFU m(-3) in winter). All bioaerosols were frequently above the recommended values of occupational exposure. Workers carrying out special tasks such as cleaning tanks were exposed to very high levels of endotoxins (up to 500 EU m(-3)) compared to routine work. The species composition and concentration of airborne Gram-negative bacteria were also studied. A broad spectrum of different species within the Pseudomonadaceae and the Enterobacteriaceae families were predominant in nearly all plants investigated. [Authors]

Renal transplantation following aorto-iliac reconstruction is a safe a strategy

Introduction: Renal transplantation is considered the treatment of choice for end-stage renal disease. However, the association of occlusive aorto-iliac disease and chronic renal failure is frequent and aorto-iliac reconstruction may be necessary prior to renal transplantation. This retrospective study reviews the results of this operative strategy.Material and Methods: Between January 2001 and June 2010, 309 patients underwent renal transplantation at our institution and 8 patients had prior aorto-iliac reconstruction using prosthetic material. There were 6 men and 2 women with a median age of 62 years (range 51-70). Five aorto-bifemoral and 2 aorto-bi-iliac bypasses were performed for stage II (n=5), stage IV (n=1) and aortic aneurysm (n=1). In one patient, iliac kissing stents and an ilio-femoral bypass were implanted. 4 cadaveric and 4 living donor renal transplantations were performed with an interval of 2 months to 10 years after revascularization.The results were analysed with respect of graft and patients survival. Differences between groups were tested by the log rank method.Results: No complications and no death occurred in the post-operative period. All bypasses remained patent during follow-up. The median time of post transplantation follow-up was 46 months for all patients and 27 months for patients with prior revascularization. In the revascularized group and control group, the graft and patient survival at 1 year were respectively 100%/96%, 100%/99% and at 5 years 86%/86%, 86%/94%, without significant differences between both groups.Discussion: Our results suggest that renal transplantation following prior aorto-iliac revascularisation with prosthetic material is safe and effective. Patients with end-stage renal disease and concomitant aorto-iliac disease should therefore be considered for renal transplantation. However, caution in the interpretation of the results is indicated due to the small sample size of our study.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Euclidean geometric invariant of framed knots in manifolds

We present an invariant of a three dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. An important feature of our work is that we are not using any nontrivial representation of the manifold fundamental group or knot group.

Which screening strategy using BMD measurements would be most cost effective for hip fracture prevention in elderly women? A decision analysis based on a Markov model.

INTRODUCTION: Hip fractures are responsible for excessive mortality, decreasing the 5-year survival rate by about 20%. From an economic perspective, they represent a major source of expense, with direct costs in hospitalization, rehabilitation, and institutionalization. The incidence rate sharply increases after the age of 70, but it can be reduced in women aged 70-80 years by therapeutic interventions. Recent analyses suggest that the most efficient strategy is to implement such interventions in women at the age of 70 years. As several guidelines recommend bone mineral density (BMD) screening of postmenopausal women with clinical risk factors, our objective was to assess the cost-effectiveness of two screening strategies applied to elderly women aged 70 years and older. METHODS: A cost-effectiveness analysis was performed using decision-tree analysis and a Markov model. Two alternative strategies, one measuring BMD of all women, and one measuring BMD only of those having at least one risk factor, were compared with the reference strategy "no screening". Cost-effectiveness ratios were measured as cost per year gained without hip fracture. Most probabilities were based on data observed in EPIDOS, SEMOF and OFELY cohorts. RESULTS: In this model, which is mostly based on observed data, the strategy "screen all" was more cost effective than "screen women at risk." For one woman screened at the age of 70 and followed for 10 years, the incremental (additional) cost-effectiveness ratio of these two strategies compared with the reference was 4,235 euros and 8,290 euros, respectively. CONCLUSION: The results of this model, under the assumptions described in the paper, suggest that in women aged 70-80 years, screening all women with dual-energy X-ray absorptiometry (DXA) would be more effective than no screening or screening only women with at least one risk factor. Cost-effectiveness studies based on decision-analysis trees maybe useful tools for helping decision makers, and further models based on different assumptions should be performed to improve the level of evidence on cost-effectiveness ratios of the usual screening strategies for osteoporosis.

Hopf bifurcation in higher dimensional differential systems via the averaging method

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