Spectral flow and iteration of closed semi-Riemannian geodesics

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Nouveaux paramètres d'exploration de la fonction plaquettaire en clinique : thrombose tardive, profilage micro-membranaire et détection de sous-populations cellulaires

Les plaquettes sanguines sont les principaux acteurs de l’hémostase primaire et de la thrombose, deux éléments majeurs de la physiopathologie vasculaire. Plusieurs médicaments régulent les fonctions plaquettaires mais peu de tests sont validés pour suivre leur efficacité en fonction de l’évolution clinique des patients. Mon doctorat a eu pour but de développer de nouvelles approches d’évaluation de la fonction plaquettaire. Deux essais cliniques réalisés sur des patients atteints de syndrome coronarien stable ont constitué la première partie de mon doctorat. La première étude met en évidence la nécessité d'une standardisation des tests biologiques pour la détection de patients répondant moins au clopidogrel, un inhibiteur du récepteur plaquettaire de l'ADP P2Y12. L’étude suivante montre le potentiel thérapeutique, chez ces patients, de l’inhibition conjointe de P2Y12 et du second récepteur plaquettaire de l'ADP P2Y1, sur la fonction plaquettaire. De plus, le suivi en temps réel par vidéomiscroscopie a permis de distinguer des effets précoces et tardifs des antiplaquettaires sur la formation du thrombus en chambre de perfusion. La seconde partie de mon doctorat concerne les microdomaines membranaires de type « lipid rafts » qui tiennent une place fondamentale dans les fonctions cellulaires et plaquettaires. Ainsi plusieurs récepteurs dépendent de ces microdomaines, régulant la fonction plaquettaire et les effets des médicaments antiplaquettaires. Cependant, les techniques d’étude de ces microdomaines sont complexes et peu adaptées aux études cliniques. Profitant de nouvelles sondes fluorescentes sensibles au niveau d’ordre liquide membranaire (OLM), nous avons développé une méthode de mesure de l’OLM par cytométrie de flux spectrale. Grâce à cette approche, nous avons montré que l’activation plaquettaire diminue l’OLM alors qu’il est augmenté chez des patients traités par un inhibiteur de la synthèse du cholestérol ou par le clopidogrel. Nous avons également mis en évidence, en condition de forces de cisaillement élevées correspondant à celles retrouvées au niveau de sténoses artérielles, une sous-population plaquettaire présentant un OLM plus bas. Le passage dans le domaine clinique de ces approches fondamentales qui privilégient l’étude dynamique des plaquettes pourrait permettre d’améliorer le diagnostique et le suivi de traitement de pathologies cardiovasculaires.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Comparison of different lattice definitions of the topological charge

We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the HermitianWilson- Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.

Evaluation of flow regimes in a semi-cylindrical spouted bed through statistical, mutual information, spectral and Hurst`s analysis

Hydrodynamic studies were conducted in a semi-cylindrical spouted bed column of diameter 150 mm, height 1000 mm, conical base included angle of 60 degrees and inlet orifice diameter 25 mm. Pressure transducers at several axial positions were used to obtain pressure fluctuation time series with 1.2 and 2.4 mm glass beads at U/U-ms from 0.3 to 1.6, and static bed depths from 150 to 600 mm. The conditions covered several flow regimes (fixed bed, incipient spouting, stable spouting, pulsating spouting, slugging, bubble spouting and fluidization). Images of the system dynamics were also acquired through the transparent walls with a digital camera. The data were analyzed via statistical, mutual information theory, spectral and Hurst`s Rescaled Range methods to assess the potential of these methods to characterize the spouting quality. The results indicate that these methods have potential for monitoring spouted bed operation.

Spectral waveform analysis of intranodal arterial blood flow in abnormally large superficial lymph nodes in dogs

Objective-To evaluate pulsed-wave Doppler spectral parameters as a method for distinguishing between neoplastic and inflammatory peripheral lymphadenopathy in dogs. Sample Population-40 superficial lymph nodes from 33 dogs with peripheral lymphadenopathy. Procedures-3 Doppler spectral tracings were recorded from each node. Spectral Doppler analysis including assessment of the resistive index, peak systolic velocity-to-end diastolic velocity (S:D) ratio, diastolic notch velocity-to-peak systolic velocity (N:S) ratio, and end diastolic velocity-to-diastolic notch velocity ratio was performed for each tracing. Several calculation methods were used to determine the Doppler indices for each lymph node. After the ultrasonographic examination, fine needle aspirates or excisional biopsy specimens of the examined lymph nodes were obtained, and lymphadenopathy was classified as either inflammatory or neoplastic (lymphomatous or metastatic) via cytologic or histologic examination. Results of Doppler analysis were compared with cytologic or histopathologic findings. Results-The Doppler index with the highest diagnostic accuracy was the S:D ratio calculated from the first recorded tracing; a cutoff value of 3.22 yielded sensitivity of 91%, specificity of 100%, and negative predictive value of 89% for detection of neoplasia. Overall diagnostic accuracy was 95%. At a sensitivity of 100%, the most accurate index was the N:S ratio calculated from the first recorded tracing; a cutoff value of 0.45 yielded specificity of 67%, positive predictive value of 81%, and overall diagnostic accuracy of 86.5%. Conclusions and Clinical Relevance-Results suggested that noninvasive Doppler spectral analysis may be useful in the diagnosis of neoplastic versus inflammatory peripheral lymphadenopathy in dogs.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

A Spectral Analysis of LDA Turbulent Flow Measurements in a Ship Air Wake

Helicopters are one of the most important tactical elements in maritime operations. The necessity for an improvement in the conditions in which the landing and take-off operations are carried out leads to the study of the flow that separates from the ship?s superstructure over the flight deck. To investigate this flow a series of wind tunnel experiments have been performed by testing a sub-scale model of a generic frigate. Measurements of the flow?s velocity have been taken by means of Laser Doppler Anemometry (LDA) in five points that simulate the last path of the landing trajectory. The data obtained in these experiments is manipulated in a frequency analysis where the corresponding spectra are calculated. Onboard measurements from an actual full scale frigate are analyzed and compared with the wind tunnel results. Conclusions obtained consist of a series of illustrative values of turbulent energy frequency ranges which can be valuable for any study in this field. The comparison shows a clear similarity between both experiments, reasserting the wind tunnel measurements and its reliability.

Cadmium telluride nanocrystals as luminescent sensitizers in flow analysis

A fully automated multipumping flow system (MPFS) using water-soluble CdTe quantum dots (QD) as sensitizers is proposed for the chemiluminometric determination of the anti-diabetic drugs gliclazide and glipizide in pharmaceutical formulations. The nanocrystals acted as enhancers of the weak CL emission produced upon oxidation of sulphite by Ce(IV) in acidic medium, thus improving sensitivity and expanding the dynamical analytical concentration range. By interacting with the QD, the two analytes prevented their sensitizing effect yielding a chemiluminescence quenching of the Ce(IV)-SO(3)(2-)CdTe QD system. The pulsed flow inherent to MPFS assured a fast and efficient mixing of all solutions inside the flow cell, circumventing the need for a reaction coil and facilitating the monitoring of the short-lived generated chemiluminescent species. QD crystal size, concentration and spectral region for measurement were investigated. (C) 2011 Elsevier B.V. All rights reserved.

Floquet stability analysis of the flow around an oscillating cylinder

This investigative work is concerned with the flow around a circular cylinder submitted to forced transverse oscillations. The goal is to investigate how the transition to turbulence is initiated in the wake for cases with different Reynolds numbers (Re) and displacement amplitudes (A). For each Re the motion frequency is kept constant, close to the Strouhal number of the flow around a fixed cylinder at the same Re. Stability analysis of two-dimensional periodic flows around a forced-oscillating cylinder is carried out with respect to three-dimensional infinitesimal perturbations. The procedure consists of performing a Floquet type analysis of time-periodic base flows, computed using the spectral/hp element method. With the results of the Floquet calculations, considerations regarding the stability of the system are drawn, and the form of the instability at its onset is obtained. The critical Reynolds number is observed to change with the amplitude of oscillation. With respect to instabilities, unstable modes with the same symmetry as mode A of a fixed cylinder are observed; however, they present different wavelengths. Also, the instabilities observed for the oscillating cylinder are distinctively stronger in the braid shear layers. Other unstable modes similar to mode B are found. Quasi-periodic modes are observed in the 2S wake, and subharmonic mode occurrences are reported in P + S wakes. (C) 2009 Elsevier Ltd. All rights reserved.

The Effect of Valsartan versus Non-RAAS Treatment on Autoregulation of Cerebral Blood Flow.

Background: Cerebral autoregulation (CA) is a protective mechanism which maintains the steadiness of the cerebral blood flow (CBF) through a broad range of systemic blood pressure (BP). Acute hypertension has been shown to reduce the cerebrovascular adaptation to BP variations. However, it is still unknown whether CA is impaired in chronic hypertension. This study evaluated whether a strict control of BP affects the CA in patients with chronic hypertension, and compared a valsartan-based regimen to a regimen not inhibiting the renin-angiotensin-aldosterone system (non-RAAS). Methods: Eighty untreated patients with isolated systolic hypertension were randomized to valsartan 320 mg or to a non-RAAS regimen during 6 months. The medication was upgraded to obtain BP <140/90 mm Hg. Continuous recordings of arterial BP and CBF velocity (transcranial Doppler) were performed during periods of 5 minutes, at rest, and at different levels of alveolar CO(2) pressure provided by respiratory maneuvers. The dominant frequency of CBF oscillations was determined for each patient. Dynamic CA was measured as the mean phase shift between BP and CBF by cross-spectral analysis in the medium frequency and in the dominant CBF frequency. Results: Mean ambulatory 24-hour BP fell from 144/87 to 127/79 mm Hg in the valsartan group and from 144/87 to 134/81 mm Hg in the non-RAAS group (p = 0.13). Both groups had a similar reduction in the central BP and in the carotido-femoral pulse wave velocity. The average phase shift between BP fluctuations and CBF response at rest was normal at randomization (1.82 ± 0.08 s), which is considered a preserved autoregulation and increased to 1.91 ± 0.12 s at the end of study (p = 0.45). The comparison of both treatments showed no significant difference (-0.01 ± 0.17 s vs. 0.16 ± 0.16 s, p = 0.45) for valsartan versus non-RAAS groups. The plasmatic level of glycosylated hemoglobin decreased in the valsartan arm compared to the non-RAAS arm (-0.23 ± 0.06 vs. -0.08 ± 0.07%, p = 0.07). Conclusions: In elderly hypertensive men with isolated chronic systolic hypertension, CA seems efficient at baseline and is not significantly affected by 6 months of BP-lowering treatment. This suggests that the preventive effects of BP medication against stroke are not mediated through a restoration of the CA.