On the evaluation of some three-body variational integrals

Stable recursive relations are presented for the numerical computation of the integrals $$\int d{\bf r}_1 d{\bf r}_2 r_1^{l-1} r_2^{m-1} r_{12}^{n-1} \exp{\{-\alpha r_1 -\beta r_2 -\gamma r_{12}\}}$$ ($l$, $m$ and $n$ integer, $\alpha$, $\beta$ and $\gamma$ real) when the indices $l$, $m$ or $n$ are negative. Useful formulas are given for particular values of the parameters $\alpha$, $\beta$ and $\gamma$.Comment: 12 pages, 1 figure (PS) and 3 tables. Old figures 2 and 3 replaced by Tables I and III. A further table added. Paper enlarged giving some tips on the convergence of quadrature

Self-avoiding fractional Brownian motion - The Edwards model

In this work we extend Varadhan's construction of the Edwards polymer model to the case of fractional Brownian motions in $\R^d$, for any dimension $d\geq 2$, with arbitrary Hurst parameters $H\leq 1/d$.Comment: 14 page

The HIF1A Functional Genetic Polymorphism at Locus +1772 Associates with Progression to Metastatic Prostate Cancer and Refractoriness to Hormonal Castration

The hypoxia inducible factor 1 alpha (HIF1a) is a key regulator of tumour cell response to hypoxia, orchestrating mechanisms known to be involved in cancer aggressiveness and metastatic behaviour. In this study we sought to evaluate the association of a functional genetic polymorphism in HIF1A with overall and metastatic prostate cancer (PCa) risk and with response to androgen deprivation therapy (ADT). The HIF1A +1772 C>T (rs11549465) polymorphism was genotyped, using DNA isolated from peripheral blood, in 1490 male subjects (754 with prostate cancer and 736 controls cancer-free) through Real-Time PCR. A nested group of cancer patients who were eligible for androgen deprivation therapy was followed up. Univariate and multivariate models were used to analyse the response to hormonal treatment and the risk for developing distant metastasis. Age-adjusted odds ratios were calculated to evaluate prostate cancer risk. Our results showed that patients under ADT carrying the HIF1A +1772 T-allele have increased risk for developing distant metastasis (OR, 2.0; 95%CI, 1.1-3.9) and an independent 6-fold increased risk for resistance to ADT after multivariate analysis (OR, 6.0; 95%CI, 2.2-16.8). This polymorphism was not associated with increased risk for being diagnosed with prostate cancer (OR, 0.9; 95%CI, 0.7-1.2). The HIF1A +1772 genetic polymorphism predicts a more aggressive prostate cancer behaviour, supporting the involvement of HIF1a in prostate cancer biological progression and ADT resistance. Molecular profiles using hypoxia markers may help predict clinically relevant prostate cancer and response to ADT

Current deformation in Central Afar and triple junction kinematics deduced from GPS and InSAR measurements

Kinematics of divergent boundaries and Rift-Rift-Rift junctions are classically studied using long-term geodetic observations. Since significant magma-related displacements are expected, short-term deformation provides important constraints on the crustal mechanisms involved both in active rifting and in transfer of extensional deformation between spreading axes. Using InSAR and GPS data, we analyse the surface deformation in the whole Central Afar region in detail, focusing on both the extensional deformation across the Quaternary magmato-tectonic rift segments, and on the zones of deformation transfer between active segments and spreading axes. The largest deformation occurs across the two recently activated Asal-Ghoubbet (AG) and Manda Hararo-Dabbahu (MH-D) magmato-tectonic segments with very high strain rates, whereas the other Quaternary active segments do not concentrate any large strain, suggesting that these rifts are either sealed during interdyking periods or not mature enough to remain a plate boundary. Outside of these segments, the GPS horizontal velocity field shows a regular gradient following a clockwise rotation of the displacements from the Southeast to the East of Afar, with respect to Nubia. Very few shallow creeping structures can be identified as well in the InSAR data. However, using these data together with the strain rate tensor and the rotations rates deduced from GPS baselines, the present-day strain field over Central Afar is consistent with the main tectonic structures, and therefore with the long-term deformation. We investigate the current kinematics of the triple junction included in our GPS data set by building simple block models. The deformation in Central Afar can be described by adding a central microblock evolving separately from the three surrounding plates. In this model, the northern block boundary corresponds to a deep EW-trending trans-tensional dislocation, locked from the surface to 10–13 km and joining at depth the active spreading axes of the Red Sea and the Aden Ridge, from AG to MH-D rift segments. Over the long-term, this plate configuration could explain the presence of the en-échelon magmatic basins and subrifts. However, the transient behaviour of the spreading axes implies that the deformation in Central Afar evolves depending on the availability of magma supply within the well-established segments

A New Paradigm for Large Earthquakes in Stable Continental Plate Interiors

Large earthquakes within stable continental regions (SCR) show that significant amounts of elastic strain can be released on geological structures far from plate boundary faults, where the vast majority of the Earth's seismic activity takes place. SCR earthquakes show spatial and temporal patterns that differ from those at plate boundaries and occur in regions where tectonic loading rates are negligible. However, in the absence of a more appropriate model, they are traditionally viewed as analogous to their plate boundary counterparts, occuring when the accrual of tectonic stress localized at long-lived active faults reaches failure threshold. Here we argue that SCR earthquakes are better explained by transient perturbations of local stress or fault strength that release elastic energy from a pre-stressed lithosphere. As a result, SCR earthquakes can occur in regions with no previous seismicity and no surface evidence for strain accumulation. They need not repeat, since the tectonic loading rate is close to zero. Therefore, concepts of recurrence time or fault slip rate do not apply. As a consequence, seismic hazard in SCRs is likely more spatially distributed than indicated by paleoearthquakes, current seismicity, or geodetic strain rates

Vehicle emissions and consumer information in car advertisements

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