On rigid analytic uniformizations of Jacobians of Shimura curves

The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a proof of a conjecture formulated by M. Greenberg in hispaper on Stark-Heegner points and quaternionic Shimura curves, thus making Greenberg's construction of local points on elliptic curves over Q unconditional.

Equations of hyperelliptic Shimura curves

We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld’s nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet’s bimodules and the specialization of Heegner points, as introduced in [21]. As an application, we provide a list of equations of Shimura curves and quotients of them obtained by our algorithm that had been conjectured by Kurihara.

Nonpersistence of resonant caustics in perturbed elliptic billiards

Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics —the ones whose tangent trajectories are closed polygons— are destroyed under generic perturbations of the billiard table. We prove that none of the resonant elliptical caustics persists under a large class of explicit perturbations of the original ellipse. This result follows from a standard Melnikov argument and the analysis of the complex singularities of certain elliptic functions.

A new automated method versus continuous positive airway pressure method for measuring pressure-volume curves in patients with acute lung injury

Objective: To compare pressure–volume (P–V) curves obtained with the Galileo ventilator with those obtained with the CPAP method in patients with ALI or ARDS receiving mechanical ventilation. P–V curves were fitted to a sigmoidal equation with a mean R2 of 0.994 ± 0.003. Lower (LIP) and upper inflection (UIP), and deflation maximum curvature (PMC) points calculated from the fitted variables showed a good correlation between methods with high intraclass correlation coefficients. Bias and limits of agreement for LIP, UIP and PMC obtained with the two methods in the same patient were clinically acceptable.

Geometry and physics of catenanes applied to the study of DNA replication.

The concept of ideal geometric configurations was recently applied to the classification and characterization of various knots. Different knots in their ideal form (i.e., the one requiring the shortest length of a constant-diameter tube to form a given knot) were shown to have an overall compactness proportional to the time-averaged compactness of thermally agitated knotted polymers forming corresponding knots. This was useful for predicting the relative speed of electrophoretic migration of different DNA knots. Here we characterize the ideal geometric configurations of catenanes (called links by mathematicians), i.e., closed curves in space that are topologically linked to each other. We demonstrate that the ideal configurations of different catenanes show interrelations very similar to those observed in the ideal configurations of knots. By analyzing literature data on electrophoretic separations of the torus-type of DNA catenanes with increasing complexity, we observed that their electrophoretic migration is roughly proportional to the overall compactness of ideal representations of the corresponding catenanes. This correlation does not apply, however, to electrophoretic migration of certain replication intermediates, believed up to now to represent the simplest torus-type catenanes. We propose, therefore, that freshly replicated circular DNA molecules, in addition to forming regular catenanes, may also form hemicatenanes.

Biologic data of Macaca mulatta, Macaca fascicularis, and Saimiri sciureusused for research at the fiocruz primate center

Physiological parameters of laboratory animals used for biomedical research is crucial for following several experimental procedures. With the intent to establish baseline biologic parameters for non-human primates held in closed colonies, hematological and morphometric data of captive monkeys were determined. Data of clinically healthy rhesus macaques (Macaca mulatta), cynomolgus monkeys (Macaca fascicularis), and squirrel monkeys (Saimiri sciureus) were collected over a period of five years. Animals were separated according to sex and divided into five age groups. Hematological data were compared with those in the literature by Student's t test. Discrepancies with significance levels of 0.1, 1 or 5% were found in the hematological studies. Growth curves showed that the sexual dimorphism of rhesus monkeys appeared at an age of four years. In earlier ages, the differences between sexes could not be distinguished (p < 0.05). Sexual dimorphism in both squirrel monkeys and cynomolgus monkeys occurred at an age of about 32 months. Data presented in this paper could be useful for comparative studies using primates under similar conditions.

Paranasal sinuses in children: size evaluation of maxillary, sphenoid, and frontal sinuses by magnetic resonance imaging and proposal of volume index percentile curves.

Our objective was to establish the age-related 3D size of maxillary, sphenoid, and frontal sinuses. A total of 179 magnetic resonance imaging (MRI) of children under 17 years (76 females, 103 males) were included and sinuses were measured in the three axes. Maxillary sinuses measured at birth (mean+/-standard deviation) 7.3+/-2.7 mm length (or antero-posterior)/4.0+/-0.9 mm height (or cranio-caudal)/2.7+/-0.8 mm width (or transverse). At 16 years old, maxillary sinus measured 38.8+/-3.5 mm/36.3+/-6.2 mm/27.5+/-4.2 mm. Sphenoid sinus pneumatization starts in the third year of life after conversion from red to fatty marrow with mean values of 5.8+/-1.4 mm/8.0+/-2.3 mm/5.8+/-1.0 mm. Pneumatization progresses gradually to reach at 16 years 23.0+/-4.5 mm/22.6+/-5.8 mm/12.8+/-3.1 mm. Frontal sinuses present a wide variation in size and most of the time are not valuable with routine head MRI techniques. They are not aerated before the age of 6 years. Frontal sinuses dimensions at 16 years were 12.8+/-5.0 mm/21.9+/-8.4 mm/24.5+/-13.3 mm. A sinus volume index (SVI) of maxillary and sphenoid sinus was computed using a simplified ellipsoid volume formula, and a table with SVI according to age with percentile variations is proposed for easy clinical application. Percentile curves of maxillary and sphenoid sinuses are presented to provide a basis for objective determination of sinus size and volume during development. These data are applicable to other techniques such as conventional X-ray and CT scan.

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Closed rupture of the tibialis anterior tendon : a report of 2 cases

Closed rupture of the tibialis anterior tendon is a rare injury, and it usually affects individuals older than 50 years of age. This rare injury tends to occur spontaneously, and this often delays diagnosis and adequate treatment. Although direct surgical repair of the ruptured tibialis anterior tendon is generally considered the treatment of choice, nonanatomic repair, tendon lengthening, or tendon transfer might be necessary in cases where shortening of the muscle-tendon unit has taken place. In this report, we describe 2 cases that involved the surgical repair of closed ruptures of the tibialis anterior tendon. In the first case, direct repair was undertaken at approximately 6 months after the onset of symptoms, and in the second case repair of the tibialis anterior tendon required augmentation tenodesis with the extensor retinaculum. Level of Clinical Evidence: 4.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Closed and open grade I and II tibial shaft fractures treated by reamed intramedullary nailing

RESUME Objectif : Le but de cette étude est d'évaluer les résultats du traitement par enclouage centre-médullaire alésé des fractures diaphysaires du tibia aussi bien fermées que pour les fractures ouvertes de stade I et II selon Gustillo. Méthodes: Entre 1997 et 2000, 119 patients présentant une fracture diaphysaire du tibia ont été traités dans notre service par un enclouage centre-médullaire alésé. En postopératoire, 96 patients, soit 70 fractures fermées et 26 fractures ouvertes I et II selon Gustillo, ont été suivis cliniquement et radiologiquement pour une période de plus d'une année et demi. L'introduction du clou centro-médullaire a été faite selon la technique habituelle, soit transtendineuse ou paratendineusé rotulienne. Tous les clous ont été alésés jusqu'à 1,5 mm au-dessus du diamètre du clou. Les patients ayant une fracture isolée du tibia ont été immédiatement mobilisés en charge partielle pour une période de 6 semaines. Ceux qui avaient des lésions associées, notamment au niveau de la cheville épsilatérale, ont nécessité la mise en place d'un plâtre de Type Sarmiento. Résultats : Six patients (6,3%) ont développé un syndrome des loges après chirurgie. Quarante-huit cas (50%) ont nécessité une dynamisation du clou après une période moyenne de 12 semaines en raison d'un retard de consolidation. En général, 90,6% des fractures ont consolidé après 24 semaines postopératoires en moyenne, sans aucune différence significative entre les fractures fermées et les fractures ouvertes. Deux patients (2,1 %) présentant une fracture ouverte degré II ont développé une infection profonde ayant nécessité un traitement. Nous avons également observé 9,4% de cals vicieux minimes et sans conséquence clinique. Huit patients (8,3%) ont eu une brisure des vis de .verrouillage mais également sans conséquence clinique. Au dernier contrôle, 52% des patients, dont ('introduction du clou s'est faite en transtendineux ont des douleurs antérieures du genou contre 14% parmi ceux où l'introduction était paratendineuse. Conclusion : L'enclouage centre-médullaire reste le traitement de choix pour les fractures diaphysaires du tibia, qu'elles soient fermées ou ouvertes degré I ou II selon Gustillo.

Investigation into Randolph Public Library's Closed Session Violations, December 11, 2006

Investigative report produced by Iowa Citizens' Aide/Ombudsman

Hemoglobin curves during pregnancy before and after fortification of flours with iron

Objective: To assess the level of hemoglobin-Hb during pregnancy before and after fortification of flours with iron. Method: A cross-sectional study with data from 12,119 pregnant women attended at a public prenatal from five macro regions of Brazil. The sample was divided into two groups: Before-fortification (birth before June/2004) and After-fortification (last menstruation after June/2005). Hb curves were compared with national and international references. Polynomial regression models were built, with a significance level of 5%. Results: Although the higher levels of Hb in all gestational months after-fortification, the polynomial regression did not show the fortification effect (p=0.3). Curves in the two groups were above the references in the first trimester, with following decrease and stabilization at the end of pregnancy. Conclusion: Although the fortification effect was not confirmed, the study presents variation of Hb levels during pregnancy, which is important for assistencial practice and evaluation of public policies.