Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Brane-world creation and black holes

An inflating brane world can be created from ``nothing'' together with its anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap m=(3/2)H, where H is the Hubble rate. We consider the analogue of the Nariai solution and argue that it describes the pair production of ``black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing or the production of AdS black holes in the vicinity of a pre-existing inflating brane world. The Lorentzian evolution of the brane world after creation is briefly discussed. An additional ``integration constant'' in the Friedmann equation-accompanying a term which dilutes like radiation-describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. In general, this could be a 5-dimensional black hole or a ``parallel'' brane world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the AdS/CFT correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

Carleson Measures and Logvinenko-Sereda sets on compact manifolds

Given a compact Riemannian manifold $M$ of dimension $m \geq 2$, we study the space of functions of $L^2(M)$generated by eigenfunctions ofeigenvalues less than $L \geq 1$ associated to the Laplace-Beltrami operator on $M$. On these spaces we give a characterization of the Carleson measures and the Logvinenko-Sereda sets.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

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.

Tenseness of Riemannian flows

We show that any transversally complete Riemannian foliation &em&F&/em& of dimension one on any possibly non-compact manifold M is tense; namely, (M,&em&F&/em&) admits a Riemannian metric such that the mean curvature form of &em&F&/em& is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize some well known results including Masa's characterization of tautness.

A bi-dimensional genome scan for prolificacy traits in pigs shows the existence of multiple epistatic QTL

Background: Prolificacy is the most important trait influencing the reproductive efficiency of pig production systems. The low heritability and sex-limited expression of prolificacy have hindered to some extent the improvement of this trait through artificial selection. Moreover, the relative contributions of additive, dominant and epistatic QTL to the genetic variance of pig prolificacy remain to be defined. In this work, we have undertaken this issue by performing one-dimensional and bi-dimensional genome scans for number of piglets born alive (NBA) and total number of piglets born (TNB) in a three generation Iberian by Meishan F2 intercross. Results: The one-dimensional genome scan for NBA and TNB revealed the existence of two genome-wide highly significant QTL located on SSC13 (P < 0.001) and SSC17 (P < 0.01) with effects on both traits. This relative paucity of significant results contrasted very strongly with the wide array of highly significant epistatic QTL that emerged in the bi-dimensional genome-wide scan analysis. As much as 18 epistatic QTL were found for NBA (four at P < 0.01 and five at P < 0.05) and TNB (three at P < 0.01 and six at P < 0.05), respectively. These epistatic QTL were distributed in multiple genomic regions, which covered 13 of the 18 pig autosomes, and they had small individual effects that ranged between 3 to 4% of the phenotypic variance. Different patterns of interactions (a × a, a × d, d × a and d × d) were found amongst the epistatic QTL pairs identified in the current work.Conclusions: The complex inheritance of prolificacy traits in pigs has been evidenced by identifying multiple additive (SSC13 and SSC17), dominant and epistatic QTL in an Iberian × Meishan F2 intercross. Our results demonstrate that a significant fraction of the phenotypic variance of swine prolificacy traits can be attributed to first-order gene-by-gene interactions emphasizing that the phenotypic effects of alleles might be strongly modulated by the genetic background where they segregate.

Multislice CT for assessing in-stent dimensions after left main coronary artery stenting: a comparison with three dimensional intravascular ultrasound

Objective: To evaluate the agreement between multislice CT (MSCT) and intravascular ultrasound (IVUS) to assess the in-stent lumen diameters and lumen areas of left main coronary artery (LMCA) stents. Design: Prospective, observational single centre study. Setting: A single tertiary referral centre. Patients: Consecutive patients with LMCA stenting excluding patients with atrial fibrillation and chronic renal failure. Interventions: MSCT and IVUS imaging at 912 months follow-up were performed for all patients. Main outcome measures: Agreement between MSCT and IVUS minimum luminal area (MLA) and minimum luminal diameter (MLD). A receiver operating characteristic (ROC) curve was plotted to find the MSCT cut-off point to diagnose binary restenosis equivalent to 6 mm2 by IVUS. Results: 52 patients were analysed. PassingBablok regression analysis obtained a β coefficient of 0.786 (0.586 to 1.071) for MLA and 1.250 (0.936 to 1.667) for MLD, ruling out proportional bias. The α coefficient was −3.588 (−8.686 to −0.178) for MLA and −1.713 (−3.583 to −0.257) for MLD, indicating an underestimation trend of MSCT. The ROC curve identified an MLA ≤4.7 mm2 as the best threshold to assess in-stent restenosis by MSCT. Conclusions: Agreement between MSCT and IVUS to assess in-stent MLA and MLD for LMCA stenting is good. An MLA of 4.7 mm2 by MSCT is the best threshold to assess binary restenosis. MSCT imaging can be considered in selected patients to assess LMCA in-stent restenosis

Psychometric properties and dimensional structure of the Spanish version of the Coping Responses Inventory - Adult Form

One of the goals of psychological assessment focuses on the adaptation of its instruments to different populations. The objective of this study is to establish the psychometric properties and dimensional structure of the Spanish version of the Coping Responses Inventory- Adult Form (CRI-Adult, Moos, 1993). The following criteria were analyzed: a) descriptive statistics; b) internal consistency reliability (Cronbach"s alpha, and intercorrelations between scales); c) test-retest reliability (4-week interval); d) dimensionality of CRI-Adult (exploratory factor analysis); e) construct validity (confirmatory factor analysis); f) convergent criterion validity (correlations between CRI-Adult and Coping Strategies Indicator, CSI, Amirkhan, 1990), and g) predictive criterion validity (correlations between CRI-Adult, and SCL-90-R, Derogatis, 1983). The results, obtained with 800 adults from Barcelona and surrounding area (334 men and 466 women, aged between 18 to 76 years) indicate that the Spanish version of CRIAdult has satisfactory psychometric properties that allow using this test with guarantee.

Multislice CT for assessing in-stent dimensions after left main coronary artery stenting: a comparison with three dimensional intravascular ultrasound

Objective: To evaluate the agreement between multislice CT (MSCT) and intravascular ultrasound (IVUS) to assess the in-stent lumen diameters and lumen areas of left main coronary artery (LMCA) stents. Design: Prospective, observational single centre study. Setting: A single tertiary referral centre. Patients: Consecutive patients with LMCA stenting excluding patients with atrial fibrillation and chronic renal failure. Interventions: MSCT and IVUS imaging at 9-12 months follow-up were performed for all patients. Main outcome measures: Agreement between MSCT and IVUS minimum luminal area (MLA) and minimum luminal diameter (MLD). A receiver operating characteristic (ROC) curve was plotted to find the MSCT cut-off point to diagnose binary restenosis equivalent to 6 mm2 by IVUS. Results: 52 patients were analysed. Passing-Bablok regression analysis obtained a β coefficient of 0.786 (0.586 to 1.071) for MLA and 1.250 (0.936 to 1.667) for MLD, ruling out proportional bias. The α coefficient was −3.588 (−8.686 to −0.178) for MLA and −1.713 (−3.583 to −0.257) for MLD, indicating an underestimation trend of MSCT. The ROC curve identified an MLA ≤4.7 mm2 as the best threshold to assess in-stent restenosis by MSCT. Conclusions: Agreement between MSCT and IVUS to assess in-stent MLA and MLD for LMCA stenting is good. An MLA of 4.7 mm2 by MSCT is the best threshold to assess binary restenosis. MSCT imaging can be considered in selected patients to assess LMCA in-stent restenosis