The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1

Effects of a dual inhibitor of angiotensin converting enzyme and neutral endopeptidase, MDL 100,240, on endocrine and renal functions in healthy volunteers.

OBJECTIVE: To investigate the endocrine and renal effects of the dual inhibitor of angiotensin converting enzyme and neutral endopeptidase, MDL 100,240. DESIGN: A randomized, placebo-controlled, crossover study was performed in 12 healthy volunteers. METHODS: MDL 100,240 was administered intravenously over 20 min at single doses of 6.25 and 25 mg in subjects with a sodium intake of 280 (n = 6) or 80 (n = 6) mmol/day. Measurements were taken of supine and standing blood pressure, plasma angiotensin converting enzyme activity, angiotensin II, atrial natriuretic peptide, urinary atrial natriuretic peptide and cyclic GMP excretion, effective renal plasma flow and the glomerular filtration rate as p-aminohippurate and inulin clearances, electrolytes and segmental tubular function by endogenous lithium clearance. RESULTS: Supine systolic blood pressure was consistently decreased by MDL 100,240, particularly after the high dose and during the low-salt intake. Diastolic blood pressure and heart rate did not change. Plasma angiotensin converting enzyme activity decreased rapidly and dose-dependently. In both the high- and the low-salt treatment groups, plasma angiotensin II levels fell and renin activity rose accordingly, while plasma atrial natriuretic peptide levels remained unchanged. In contrast, urinary atrial natriuretic peptide excretion increased dose-dependently under both diets, as did urinary cyclic GMP excretion. Effective renal plasma flow and the glomerular filtration rate did not change. The urinary flow rate increased markedly during the first 2 h following administration of either dose of MDL 100,240 (P < 0.001) and, similarly, sodium excretion tended to increase from 0 to 4 h after the dose (P = 0.07). Potassium excretion remained stable. Proximal and distal fractional sodium reabsorption were not significantly altered by the treatment. Uric acid excretion was increased. The safety and clinical tolerance of MDL 100,240 were good. CONCLUSIONS: The increased fall in blood pressure in normal volunteers together with the preservation of renal hemodynamics and the increased urinary volume, atrial natriuretic peptide and cyclic GMP excretion distinguish MDL 100,240 as a double-enzyme inhibitor from inhibitors of the angiotensin converting enzyme alone. The differences appear to be due, at least in part, to increased renal exposure to atrial natriuretic peptide following neutral endopeptidase blockade.

Liquid line of descent of a basanitic liquid at 1.5 GPa: Constraints for metasomatic vein formation

The metasomatism observed in the oceanic and continental lithosphere is generally interpreted to represent a continuous differentiation process forming anhydrous and hydrous veins plus a cryptic enrichment in the surrounding peridotite. In order to constrain the mechanisms of vein formation and potentially clarify the nature and origin of the initial metasomatic agent, we performed a series of high-pressure experiments simulating the liquid line of descent of a basanitic magma differentiating within continental or mature oceanic lithosphere. This series of experiments has been conducted in an end-loaded piston cylinder apparatus starting from an initial hydrous ne-normative basanite at 1.5 GPa and temperature varying between 1,250 and 980°C. Near-pure fractional crystallization process was achieved in a stepwise manner in 30°C temperature steps and starting compositions corresponding to the liquid composition of the previous, higher-temperature glass composition. Liquids evolve progressively from basanite to peralkaline, aluminum-rich compositions without significant SiO2 variation. The resulting cumulates are characterized by an anhydrous clinopyroxene + olivine assemblage at high temperature (1,250-1,160°C), while at lower temperature (1,130-980°C), hydrous cumulates with dominantly amphibole + minor clinopyroxene, spinel, ilmenite, titanomagnetite and apatite (1,130-980°C) are formed. This new data set supports the interpretation that anhydrous and hydrous metasomatic veins could be produced during continuous differentiation processes of primary, hydrous alkaline magmas at high pressure. However, the comparison between the cumulates generated by the fractional crystallization from an initial ne-normative liquid or from hy-normative initial compositions (hawaiite or picrobasalt) indicates that for all hydrous liquids, the different phases formed upon differentiation are mostly similar even though the proportions of hydrous versus anhydrous minerals could vary significantly. This suggests that the formation of amphibole-bearing metasomatic veins observed in the lithospheric mantle could be linked to the differentiation of initial liquids ranging from ne-normative to hy-normative in composition. The present study does not resolve the question whether the metasomatism observed in lithospheric mantle is a precursor or a consequence of alkaline magmatism; however, it confirms that the percolation and differentiation of a liquid produced by a low degree of partial melting of a source similar or slightly more enriched than depleted MORB mantle could generate hydrous metasomatic veins interpreted as a potential source for alkaline magmatism by various authors.

Association of CYP3A5 genotypes with blood pressure and renal function in African families.

OBJECTIVE: Renal cytochrome P450 3A5 (CYP3A5) activity has been associated with blood pressure and salt sensitivity in humans. We determined whether CYP3A5 polymorphisms are associated with ambulatory blood pressure (ABP) and with glomerular filtration rate (GFR) in African families. METHODS: Using a cross-sectional design, 375 individuals from 72 families, each with at least two hypertensive siblings, were recruited through a hypertension register in the Seychelles (Indian Ocean). We analyzed the association between the CYP3A5 alleles (*1, *3, *6 and *7) and ABP, GFR and renal sodium handling (fractional excretion of lithium), from pedigree data, allowing for other covariates and familial correlations. RESULTS: CYP3A5*1 carriers increased their daytime systolic and diastolic ABP with age (0.55 and 0.23 mmHg/year) more than non-carriers (0.21 and 0.04 mmHg/year). CYP3A5*1 had a significant main effect on daytime systolic/diastolic ABP [regression coefficient (SE): -29.6 (10.0)/-8.2 (4.1) mmHg, P = 0.003/0.045, respectively] and this effect was modified by age (CYP3A5*1 x age interactions, P = 0.017/0.018). For night-time ABP, the effect of CYP3A5*1 was modified by urinary sodium excretion, not by age. For renal function, CYP3A5*1 carriers had a 7.6(3.8) ml/min lower GFR (P = 0.045) than non-carriers. Proximal sodium reabsorption decreased with age in non-carriers, but not in CYP3A5*1 carriers (P for interaction = 0.02). CONCLUSIONS: These data demonstrate that CYP3A5 polymorphisms are associated with ambulatory BP, CYP3A5*1 carriers showing a higher age- and sodium- related increase in ABP than non-carriers. The age effect may be due, in part, to the action of CYP3A5 on renal sodium handling.

Magnetic resonance imaging determinants of intraindividual variability in the elderly: combined analysis of grey and white matter.

Elderly individuals display a rapid age-related increase in intraindividual variability (IIV) of their performances. This phenomenon could reflect subtle changes in frontal lobe integrity. However, structural studies in this field are still missing. To address this issue, we computed an IIV index for a simple reaction time (RT) task and performed magnetic resonance imaging (MRI) including voxel based morphometry (VBM) and the tract based spatial statistics (TBSS) analysis of diffusion tensor imaging (DTI) in 61 adults aged from 22 to 88 years. The age-related IIV increase was associated with decreased fractional anisotropy (FA) as well as increased radial (RD) and mean (MD) diffusion in the main white matter (WM) fiber tracts. In contrast, axial diffusion (AD) and grey matter (GM) densities did not show any significant correlation with IIV. In multivariate models, only FA has an age-independent effect on IIV. These results revealed that WM but not GM changes partly mediated the age-related increase of IIV. They also revealed that the association between WM and IIV could not be only attributed to the damage of frontal lobe circuits but concerned the majority of interhemispheric and intrahemispheric corticocortical connections.

Estrategies per la inversió tridimensional de dades magnetotel.lúriques:

Projecte de recerca elaborat a partir d’una estada a la Dublin Institute for Advanced Studies, Irlanda, entre setembre i desembre del 2009.En els últims anys s’ha realitzat un important avanç en la modelització tridimensional en magnetotel•lúrica (MT) gracies a l'augment d’algorismes d’inversió tridimensional disponibles. Aquests codis utilitzen diferents formulacions del problema (diferències finites, elements finits o equacions integrals), diverses orientacions del sistema de coordenades i, o bé en el conveni de signe, més o menys, en la dependència temporal. Tanmateix, les impedàncies resultants per a tots els valors d'aquests codis han de ser les mateixes una vegada que es converteixen a un conveni de signe comú i al mateix sistema de coordenades. Per comparar els resultats dels diferents codis hem dissenyat models diferents de resistivitats amb estructures tridimensional incrustades en un subsòl homogeni. Un requisit fonamental d’aquests models és que generin impedàncies amb valors importants en els elements de la diagonal, que no són menyspreables. A diferència dels casos del modelització de dades magnetotel.lúriques unidimensionals i bidimensionals, pel al cas tridimensional aquests elements de les diagonals del tensor d'impedància porten informació sobre l'estructura de la resistivitat. Un dels models de terreny s'utilitza per comparar els diferents algoritmes que és la base per posterior inversió dels diferents codis. Aquesta comparació va ser seguida de la inversió per recuperar el conjunt de dades d'una estructura coneguda.

Calderón-Zygmund kernels and rectifiability in the plane

Vegeu el resum a l'inici del document del fitxer adjunt.

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Diseño de la herramienta G.I.A. (Gestión Integral de Accesibilidad)

Con este PFC se ha pretendido desarrollar una herramienta que permita a organismos encargados de la gestión de la accesibilidad la realización de Planes Integrales de Accesibilidad de forma ágil e intuitiva, consiguiendo con ello mejorar la accesibilidad global dentro de un municipio y por consiguiente a los ciudadanos en general. De esta manera se dispondrá de información actualizada que reduzca las barreras arquitectónicas y mejore la accesibilidad universal de los espacios públicos.

Connectome alterations in schizophrenia

Introduction : DTI has proven to be an exquisite biomarker of tissue microstructure integrity. This technique has been successfully applied to schizophrenia in showing that fractional anisotropy (FA, a marker of white matter integrity) is diminished in several areas of the brain (Kyriakopoulos M et al (2008)). New ways of representing diffusion data emerged recently and achieved to create structural connectivity maps in healthy brains (Hagmann P et al. (2008)). These maps have the capacity to study alterations over the entire brain at the connection and network level. This is of high interest in complex disconnection diseases like schizophrenia. We report on the specific network alterations of schizophrenic patients. Methods : 13 patients with chronic schizophrenia were recruited from in-patient, day treatment, out-patient clinics. Comparison subjects were recruited and group-matched to patients on age, sex, handedness, and parental social economic-status. This study was approved by the local IRB and subjects had to give informed written consent. They were scanned with a 3T clinical MRI scanner. DTI and high-resolution anatomical T1w imaging were performed during the same session. The path from diffusion MRI to a multi-resolution structural connection matrices of the entire brain is a five steps process that was performed in a similar way as described in Hagmann P et al. (2008). (1) DTI and T1w MRI of the brain, (2) segmentation of white and gray matter, (3) white matter tractography, (4) segmentation of the cortex into 242 ROIs of equal surface area covering the entire cortex (Fig 1), (5) the connection network was constructed by measuring for each ROI to ROI connection the related average FA along the corresponding tract. Results : For every connection between 2 ROIs of the network we tested the hypothesis H0: "average FA along fiber pathway is larger or equal in patients than in controls". H0 was rejected for connections where average FA in a connection was significantly lower in patients than in controls. Threshold p-value was 0.01 corrected for multiple comparisons with false discovery rate. We identified consistently that temporal, occipito-temporal, precuneo-temporal as well as frontal inferior and precuneo-cingulate connections were altered (Fig 2: significant connections in yellow). This is in agreement with the known literature, which showed across several studies that FA is diminished in several areas of the brain. More precisely, abnormalities were reported in the prefrontal and temporal white matter and to some extent also in the parietal and occipital regions. The alterations reported in the literature specifically included the corpus callosum, the arcuate fasciculus and the cingulum bundle, which was the case here as well. In addition small world indexes are significantly reduced in patients (p<0.01) (Fig. 3). Conclusions : Using connectome mapping to characterize differences in structural connectivity between healthy and diseased subjects we were able to show widespread connectional alterations in schizophrenia patients and systematic small worldness decrease, which is a marker of network desorganization. More generally, we described a method that has the capacity to sensitively identify structure alterations in complex disconnection syndromes where lesions are widespread throughout the connectional network.

Protein synthesis in jejunum and liver of neonatal calves fed vitamin A and lactoferrin

Rates of protein synthesis (PS) and turnover are more rapid during the neonatal period than during any other stage of postnatal life. Vitamin A and lactoferrin (Lf) can stimulate PS in neonates. However, newborn calves are vitamin A deficient and have a low Lf status, but plasma vitamin A and Lf levels increase rapidly after ingestion of colostrum. Neonatal calves (n = 6 per group) were fed colostrum or a milk-based formula without or with vitamin A, Lf, or vitamin A plus Lf to study PS in the jejunum and liver. l-[(13)C]Valine was intravenously administered to determine isotopic enrichment of free (nonprotein-bound) Val (AP(Free)) in the protein precursor pool, atom percentage excess (APE) of protein-bound Val, fractional protein synthesis rate (FSR) in the jejunum and liver, and isotopic enrichment of Val in plasma (APE(Pla)) and in the CO(2) of exhaled air (APE(Ex)). The APE, AP(Free), and FSR in the jejunum and liver did not differ significantly among groups. The APE(Ex) increased, whereas APE(Pla) decreased over time, but there were no group differences. Correlations were calculated between FSR(Jej) and histomorphometrical and histochemical data of the jejunum, and between FSR(Liv) and blood metabolites. There were negative correlations between FSR(Liv) and plasma albumin concentrations and between FSR(Jej) and the ratio of villus height:crypt depth, and there was a positive correlation between FSR(Jej) and small intestinal cell proliferation in crypts. Hence, there were no effects of vitamin A and Lf and no interactions between vitamin A and Lf on intestinal and hepatic PS. However, FSR(Jej) was correlated with histomorphometrical traits of the jejunum and FSR(Liv) was correlated with plasma albumin concentrations.

Operator expansion: definition and molecular integral applications

Es defineix l'expansió general d'operadors com una combinació lineal de projectors i s'exposa la seva aplicació generalitzada al càlcul d'integrals moleculars. Com a exemple numèric, es fa l'aplicació al càlcul d'integrals de repulsió electrònica entre quatre funcions de tipus s centrades en punts diferents, i es mostren tant resultats del càlcul com la definició d'escalat respecte a un valor de referència, que facilitarà el procés d'optimització de l'expansió per uns paràmetres arbitraris. Es donen resultats ajustats al valor exacte