Fast and accurate evaluation of a generalized incomplete gamma function

We present a computational procedure to evaluate the integral ∫xy sp-1 e-μs ds, for 0 ≤ x 0, which generalizes the lower (x=0) and upper (y=+∞) incomplete gamma functions. To allow for large values of x, y, and p while avoiding under/overflow issues in the standard double precision floating point arithmetic, we use an explicit normalization that is much more efficient than the classical ratio with the complete gamma function. The generalized incomplete gamma function is estimated with continued fractions, integrations by parts, or, when x ≈ y, with the Romberg numerical integration algorithm. We show that the accuracy reached by our algorithm improves a recent state-of-the-art method by two orders of magnitude, and is essentially optimal considering the limitations imposed by the floating point arithmetic. Moreover, the admissible parameter range of our algorithm (0 ≤ p,x,y ≤ 1015) is much larger than competing algorithms and its robustness is assessed through massive usage in an image processing application

Bootstrapping Value at Risk (VaR) : Circular Block Bootstrap vs. Standard Bootstrap

Bootstrapping kann als eine Variation des historischen Simulationsansatzes eingesetzt werden, welche darauf abzielt, das Konfidenzintervall des Value at Risks (VaR) zu berechnen. Die ursprüngliche Bootstrap-Methode, eingeführt von Efron im Jahre 1977, zieht jeweils zufällig einzelne Tagesrenditen aus einem Sample. Das zufällige Ziehen einzelner Tage führt jedoch insbesondere bei Zeitreihen dazu, dass die zeitliche Struktur der Renditen ignoriert wird. Aus diesem Grund wird in der Literatur der Block Bootstrap vorgeschlagen. Diese Arbeit befasst sich mit dem Circular Block Bootstrap (CBB) nach Politis und Romano. Dabei werden zufällig ganze Blöcke, aus dem Sample gezogen, um die Eigenschaften der zeitlichen Struktur innerhalb der Blöcke aufrechtzuerhalten. Circular bedeutet, dass das Sample-Ende mit dem Sample-Anfang verbunden wird, um das Ziehen von unvollständigen Blöcken zu verhindern. Diese Arbeit untersucht, ob das Ziehen von Blöcken mit der CBB-Methode die Abhängigkeit innerhalb der Zeitreihe tatsächlich besser berücksichtigt und den VaR exakter schätzen kann. Somit wird in dieser Arbeit ein Vergleich zwischen dem CBB und der Bootstrap Historical Simulation (BHS) gemacht. Um diese Fragestellung zu beantworten, wird der 10-Tages-VaR auf den beiden Konfidenzniveaus 95 % und 85 % berechnet. Dieser wird anhand eines Portfolios, bestehend aus fünf Aktien (Logitech, Novartis, Swiss Re, LafargeHolcim und Nestle) über die Zeitspanne vom 04.01.2010 – 16.03.2021 mit dem Rolling-Window-Prinzip angewendet. Dabei werden die beiden Bootstrap-Methoden anhand der Kombinationen, bestehend aus den verschiedenen Sample-Grössen von 250, 500, 750 und 1000 Tagen mit je 1000, 2000 und 3000 Simulationen getestet. Um die beiden Modelle zu vergleichen, wird mit dem Anteilswert-Test eruiert, ob die Modelle korrekt spezifiziert sind und das Risiko exakt einschätzen. Weiter muss sichergestellt werden, dass die Exceptions keine zeitliche Struktur mehr aufweisen. Dafür wird die Zufälligkeit der Exceptions mit dem Runs-Test und die Autokorrelation mit dem Ljung-Box-Test quantifiziert. Die Durchführung der Simulationen und des Backtestings wird in Python implementiert. Die Resultate zeigen, dass die CBB-Methode das exaktere Modell ist und somit das Ziehen von Blöcken anstelle einzelner Tage zu einer Verbesserung der Schätzung des VaRs herbeiführt. Zusätzlich wird bewiesen, dass der CBB die zeitliche Struktur besser ausgleicht, indem die Exceptions zufällig auftreten und keine Autokorrelation aufweisen. Insbesondere bei den Sample-Grössen von 750 und 1000 Tagen kann die CBB-Methode das Risiko am besten einschätzen. Eine weitere Erkenntnis ist, dass die Anzahl Simulationen (1000, 2000 und 3000) bei beiden Methoden keinen signifikanten Einfluss auf die Ergebnisse hat. Davon kann abgeleitet werden, dass 2000 und 3000 Simulationen keinen grossen Mehrwert für die Resultate generieren

Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations

International audienceInterpreting the celebrated Rudin-Osher-Fatemi (ROF) model in a Bayesian framework has led to interesting new variants for Total Variation image denoising in the last decade. The Posterior Mean variant avoids the so-called staircasing artifact of the ROF model but is computationally very expensive. Another recent variant, called TV-ICE (for Iterated Conditional Expectation), delivers very similar images but uses a much faster fixed-point algorithm. In the present work, we consider the TV-ICE approach in the case of a Poisson noise model. We derive an explicit form of the recursion operator, and show linear convergence of the algorithm, as well as the absence of staircasing effect. We also provide a numerical algorithm that carefully handles precision and numerical overflow issues, and show experiments that illustrate the interest of this Poisson TV-ICE variant

Static and dynamic behaviour of a 3D periodic structure

This contribution deals with the assessment of static and dynamic behavior a 3D-periodic structure. Equivalent Young and shear moduli are evaluated respectively via a spring-network calculation performed on a representative volume element (RVE)of the structure and an energy approach. To assess the accuracy of the two methods, FE simulations are performed, and tensile experiments are conducted on specimens cut out from 3D-structure panels. Results show disagreement for stiffness values along y-direction. This is thought to be due to stiffness variation between RVE's due to boundary conditions. A new analytical/numerical approach is proposed taking into consideration the presence of different types of boundary conditions on RVE's. Static results are further used as an input for FE investigations of the dynamic behavior of the structure. Two models are proposed: a) homogeneous and b) laminated models. Vibration tests are performed on different specimens and fundamental frequencies are noted. Results for both models correlate well with experimental data. However, the homogeneous model is limited to low frequencies

Finitary Simulation of Infinitary β\beta-Reduction via Taylor Expansion, and Applications

Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation theorem relating the normal form of the Taylor expansion of a term to its B\"ohm tree. This led us to consider extending this formalism to the infinitary $\lambda$-calculus, since the $\Lambda_{\infty}^{001}$ version of this calculus has B\"ohm trees as normal forms and seems to be the ideal framework to reformulate the Commutation theorem. We give a (co-)inductive presentation of $\Lambda_{\infty}^{001}$. We define a Taylor expansion on this calculus, and state that the infinitary $\beta$-reduction can be simulated through this Taylor expansion. The target language is the usual resource calculus, and in particular the resource reduction remains finite, confluent and terminating. Finally, we state the generalised Commutation theorem and use our results to provide simple proofs of some normalisation and confluence properties in the infinitary $\lambda$-calculus

Restricting Zap70 Expression to CD4+CD8+ Thymocytes Reveals a T Cell Receptor–dependent Proofreading Mechanism Controlling the Completion of Positive Selection

Although T cell receptor (TCR) signals are essential for intrathymic T cell–positive selection, it remains controversial whether they only serve to initiate this process, or whether they are required throughout to promote thymocyte differentiation and survival. To address this issue, we have devised a novel approach to interfere with thymocyte TCR signaling in a developmental stage-specific manner in vivo. We have reconstituted mice deficient for Zap70, a tyrosine kinase required for TCR signaling and normally expressed throughout T cell development, with a Zap70 transgene driven by the adenosine deaminase (ADA) gene enhancer, which is active in CD4+CD8+ thymocytes but inactive in CD4+ or CD8+ single-positive (SP) thymocytes. In such mice, termination of Zap70 expression impaired TCR signal transduction and arrested thymocyte development after the initiation, but before the completion, of positive selection. Arrested thymocytes had terminated Rag gene expression and up-regulated TCR and Bcl-2 expression, but failed to differentiate into mature CD4 or CD8 SP thymocytes, to be rescued from death by neglect or to sustain interleukin 7Rα expression. These observations identify a TCR-dependent proofreading mechanism that verifies thymocyte TCR specificity and differentiation choices before the completion of positive selection

How Detergent Impacts Membrane Proteins: Atomic-Level Views of Mitochondrial Carriers in Dodecylphosphocholine.

Characterizing the structure of membrane proteins (MPs) generally requires extraction from their native environment, most commonly with detergents. Yet, the physicochemical properties of detergent micelles and lipid bilayers differ markedly and could alter the structural organization of MPs, albeit without general rules. Dodecylphosphocholine (DPC) is the most widely used detergent for MP structure determination by NMR, but the physiological relevance of several prominent structures has been questioned, though indirectly, by other biophysical techniques, e.g., functional/thermostability assay (TSA) and molecular dynamics (MD) simulations. Here, we resolve unambiguously this controversy by probing the functional relevance of three different mitochondrial carriers (MCs) in DPC at the atomic level, using an exhaustive set of solution-NMR experiments, complemented by functional/TSA and MD data. Our results provide atomic-level insight into the structure, substrate interaction and dynamics of the detergent-membrane protein complexes and demonstrates cogently that, while high-resolution NMR signals can be obtained for MCs in DPC, they systematically correspond to nonfunctional states

Axion Search by Laser-based Experiment OSQAR

International audienceLaser-based experimentOSQAR in CERN is aimed to the search of the axions by twomethods. The photon regeneration experiment is using two LHC dipole magnets of the length 14.3 m and magnetic field 9.5 T equipped with an optical barrier at the end of the first magnet. It looks as light shining through the wall. No excess of events above the background was detected at this arrangement. Nevertheless, this result extends the exclusion region for the axion mass. The second method wants to measure the ultra-fine Vacuum Magnetic Birefringence for the first time. An optical scheme with electro-optical modulator has been proposed, validated and subsequently improved. Cotton-Mouton constant for air was determined in this experiment setup

Cardiac tamponade related to a coronary injury by a pericardial calcification: an unusual complication

<p>Abstract</p> <p>Background</p> <p>Cardiac tamponade is a rare but severe complication of pericardial effusion with a poor prognosis. Prompt diagnosis using transthoracic echocardiography allows guiding initial therapeutic management. Although etiologies are numerous, cardiac tamponade is more often due to a hemopericardium. Rarely, a coronary injury may result in such a hemopericardium with cardiac tamponade. Coronary artery aneurysm are the main etiologies but blunt, open chest trauma or complication of endovascular procedures have also been described.</p> <p>Case presentation</p> <p>A 83-year-old hypertensive man presented for dizziness and hypotension. The patient had oliguria and mottled skin. Transthoracic echocardiography disclosed a circumferential pericardial effusion with a compressed right atrium, confirmed by contrast-enhanced thoracic CT scan. A pig-tail catheter allowed to withdraw 500 mL of blood, resulting in a transient improvement of hemodynamics. Rapidly, recurrent hypotension prompted a reoperation. An active bleeding was identified at the level of the retroventricular coronary artery. The pericardium was thickened with several "sharping" calcified plaques in the vicinity of the bleeding areas. On day 2, vasopressors were stopped and the patient was successfully extubated. Final diagnosis was a spontaneous cardiac tamponade secondary to a coronary artery injury attributed to a "sharping"calcified pericardial plaque.</p> <p>Conclusion</p> <p>Cardiac tamponade secondary to the development of a hemopericardium may develop as the result of a myocardial and coronary artery injury induced by a calcified pericardial plaque.</p