Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Phylogeny of the kinetoplastida: taxonomic problems and insights into the evolution of parasitism

To further investigate phylogeny of kinetoplastid protozoa, the sequences of small subunit (18S) ribosomal RNA of nine bodonid isolates and ten isolates of insect trypanosomatids have been determined. The root of the kinetoplastid tree was attached to the branch of Bodo designis and/or Cruzella marina. The suborder Trypanosomatina appeared as a monophyletic group, while the suborder Bodonina was paraphyletic. Among bodonid lineages, parasitic organisms were intermingled with free-living ones, implying multiple transitions to parasitism and supporting the `vertebrate-first hypothesis'. The tree indicated that the genera Cryptobia and Bodo are artificial taxa. Separation of fish cryptobias and Trypanoplasma borreli as different genera was not supported. In trypanosomatids, the genera Leptomonas and Blastocrithidia were polyphyletic, similar to the genera Herpetomonas and Crithidia and in contrast to the monophyletic genera Trypanosoma and Phytomonas. This analysis has shown that the morphological classification of kinetoplastids does not in general reflect their genetic affinities and needs a revision.

Morphological and molecular description of Blastocrithidia cyrtomeni sp. nov. (Kinetoplastea: Trypanosomatidae) associated with Cyrtomenus bergi Froeschner (Hemiptera: Cydnidae) from Colombia

A new trypanosomatid species, Blastocrithidia cyrtomeni, is herein described using morphological and molecular data. It was found parasitising the alimentary tract of the insect host Cyrtomenus bergi, a polyphagous pest. The morphology of B. cyrtomeni was investigated using light and transmission microscopy and molecular phylogeny was inferred from the sequences of spliced leader RNA (SL rRNA) - 5S rRNA gene repeats and the 18S small subunit (SSU) rRNA gene. Epimastigotes of variable size with straphanger cysts adhering to the middle of the flagellum were observed in the intestinal tract, hemolymph and Malpighian tubules. Kinetoplasts were always observed anterior to the nucleus. The ultrastructure of longitudinal sections of epimastigotes showed the flagellum arising laterally from a relatively shallow flagellar pocket near the kinetoplast. SL RNA and 5S rRNA gene repeats were positive in all cases, producing a 0.8-kb band. The amplicons were 797-803 bp long with > 98.5% identity, indicating that they originated from the same organism. According to the sequence analysis of the SL-5S rRNA gene repeats and the 18S SSU rRNA gene, B. cyrtomeni is different from all other known species or isolates of Trypanosomatidae. Both analyses indicate that among known species, it is most closely related to Blastocrithidia triatomae.

Epidemiologic study of low back pain in 1398 Swiss conscripts between 1985 and 1992.

The two objectives of this study, based on a sample of 1398 Swiss army conscripts born in 1966 who participated in a first study in 1985, were to measure the prevalence of low back pain (LBP) at age 26 years and its incidence between 19 and 26 years and to analyze the relationship between LBP and occupational, nonoccupational, or physical risk factors. The lifetime prevalence of LBP at age 26 was 69.1% and the incidence of LBP between 19 and 26, 44.7%. A history of LBP or a pathological physical examination result at age 19 did not predict the prevalence or the incidence at age 26. Standing, twisting, vibration, and heavy work were significantly associated with chronic LBP and/or the 1-year prevalence of LBP at age 26 (P<0.05). The evolution of sport and leisure-time activities from age 19 to 26 did not differ between people with or without LBP. The ergonomic organization of the workplace should represent a major element of future strategies to prevent LBP.

Epidemiologic study of low back pain in 1398 Swiss conscripts between 1985 and 1992.

The two objectives of this study, based on a sample of 1398 Swiss army conscripts born in 1966 who participated in a first study in 1985, were to measure the prevalence of low back pain (LBP) at age 26 years and its incidence between 19 and 26 years and to analyze the relationship between LBP and occupational, nonoccupational, or physical risk factors. The lifetime prevalence of LBP at age 26 was 69.1% and the incidence of LBP between 19 and 26, 44.7%. A history of LBP or a pathological physical examination result at age 19 did not predict the prevalence or the incidence at age 26. Standing, twisting, vibration, and heavy work were significantly associated with chronic LBP and/or the 1-year prevalence of LBP at age 26 (P < 0.05). The evolution of sport and leisure-time activities from age 19 to 26 did not differ between people with or without LBP. The ergonomic organization of the workplace should represent a major element of future strategies to prevent LBP.

Altered high-energy phosphate metabolism predicts contractile dysfunction and subsequent ventricular remodeling in pressure-overload hypertrophy mice.

To study the role of early energetic abnormalities in the subsequent development of heart failure, we performed serial in vivo combined magnetic resonance imaging (MRI) and (31)P magnetic resonance spectroscopy (MRS) studies in mice that underwent pressure-overload following transverse aorta constriction (TAC). After 3 wk of TAC, a significant increase in left ventricular (LV) mass (74 +/- 4 vs. 140 +/- 26 mg, control vs. TAC, respectively; P < 0.000005), size [end-diastolic volume (EDV): 48 +/- 3 vs. 61 +/- 8 microl; P < 0.005], and contractile dysfunction [ejection fraction (EF): 62 +/- 4 vs. 38 +/- 10%; P < 0.000005] was observed, as well as depressed cardiac energetics (PCr/ATP: 2.0 +/- 0.1 vs. 1.3 +/- 0.4, P < 0.0005) measured by combined MRI/MRS. After an additional 3 wk, LV mass (140 +/- 26 vs. 167 +/- 36 mg; P < 0.01) and cavity size (EDV: 61 +/- 8 vs. 76 +/- 8 microl; P < 0.001) increased further, but there was no additional decline in PCr/ATP or EF. Cardiac PCr/ATP correlated inversely with end-systolic volume and directly with EF at 6 wk but not at 3 wk, suggesting a role of sustained energetic abnormalities in evolving chamber dysfunction and remodeling. Indeed, reduced cardiac PCr/ATP observed at 3 wk strongly correlated with changes in EDV that developed over the ensuing 3 wk. These data suggest that abnormal energetics due to pressure overload predict subsequent LV remodeling and dysfunction.

Source spaces and perturbations for cluster complexes

Dans ce travail, nous définissons des objets composés de disques complexes marqués reliés entre eux par des segments de droite munis d’une longueur. Nous construisons deux séries d’espaces de module de ces objets appelés clus- ters, une qui sera dite non symétrique, la version ⊗, et l’autre qui est dite symétrique, la version •. Cette construction permet des choix de perturba- tions pour deux versions correspondantes des trajectoires de Floer introduites par Cornea et Lalonde ([CL]). Ces choix devraient fournir une nouvelle option pour la description géométrique des structures A∞ et L∞ obstruées étudiées par Fukaya, Oh, Ohta et Ono ([FOOO2],[FOOO]) et Cho ([Cho]). Dans le cas où L ⊂ (M, ω) est une sous-variété lagrangienne Pin± mono- tone avec nombre de Maslov ≥ 2, nous définissons une structure d’algèbre A∞ sur les points critiques d’une fonction de Morse générique sur L. Cette struc- ture est présentée comme une extension du complexe des perles de Oh ([Oh]) muni de son produit quantique, plus récemment étudié par Biran et Cornea ([BC]). Plus généralement, nous décrivons une version géométrique d’une catégorie de Fukaya avec seul objet L qui se veut alternative à la description (relative) hamiltonienne de Seidel ([Sei]). Nous vérifions la fonctorialité de notre construction en définissant des espaces de module de clusters occultés qui servent d’espaces sources pour des morphismes de comparaison.

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.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.

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

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.

3D printing and its applications

Eine zunehmende Anzahl von Artikeln in Publikumszeitschriften und Journalen rückt die direkte Herstellung von Bauteilen und Figuren immer mehr in das Bewusstsein einer breiten Öffentlichkeit. Leider ergibt sich nur selten ein einigermaßen vollständiges Bild davon, wie und in welchen Lebensbereichen diese Techniken unseren Alltag verändern werden. Das liegt auch daran, dass die meisten Artikel sehr technisch geprägt sind und sich nur punktuell auf Beispiele stützen. Dieser Beitrag geht von den Bedürfnissen der Menschen aus, wie sie z.B. in der Maslow’schen Bedürfnispyramide strukturiert dargestellt sind und unterstreicht dadurch, dass 3D Printing (oder Additive Manufacturing resp. Rapid Prototyping) bereits alle Lebensbereiche erfasst hat und im Begriff ist, viele davon zu revolutionieren.

3D Drucken und die Anwendungen

Eine zunehmende Anzahl von Artikeln in Publikumszeitschriften und Journalen rückt die direkte Herstellung von Bauteilen und Figuren immer mehr in das Bewusstsein einer breiten Öffentlichkeit. Leider ergibt sich nur selten ein einigermaßen vollständiges Bild davon, wie und in welchen Lebensbereichen diese Techniken unseren Alltag verändern werden. Das liegt auch daran, dass die meisten Artikel sehr technisch geprägt sind und sich nur punktuell auf Beispiele stützen. Dieser Beitrag geht von den Bedürfnissen der Menschen aus, wie sie z.B. in der Maslow’schen Bedürfnispyramide strukturiert dargestellt sind und unterstreicht dadurch, dass 3D Printing (oder Additive Manufacturing resp. Rapid Prototyping) bereits alle Lebensbereiche erfasst hat und im Begriff ist, viele davon zu revolutionieren.

Evolution of RNA editing in trypanosome mitochondria

Two different RNA editing systems have been described in the kinetoplast-mitochondrion of trypanosomatid protists. The first involves the precise insertion and deletion of U residues mostly within the coding regions of maxicircle-encoded mRNAs to produce open reading frames. This editing is mediated by short overlapping complementary guide RNAs encoded in both the maxicircle and the minicircle molecules and involves a series of enzymatic cleavage-ligation steps. The second editing system is a C34 to U34 modification in the anticodon of the imported tRNATrp, thereby permitting the decoding of the UGA stop codon as tryptophan. U-insertion editing probably originated in an ancestor of the kinetoplastid lineage and appears to have evolved in some cases by the replacement of the original pan-edited cryptogene with a partially edited cDNA. The driving force for the evolutionary fixation of these retroposition events was postulated to be the stochastic loss of entire minicircle sequence classes and their encoded guide RNAs upon segregation of the single kinetoplast DNA network into daughter cells at cell division. A large plasticity in the relative abundance of minicircle sequence classes has been observed during cell culture in the laboratory. Computer simulations provide theoretical evidence for this plasticity if a random distribution and segregation model of minicircles is assumed. The possible evolutionary relationship of the C to U and U-insertion editing systems is discussed.