Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Validity, reliability and responsiveness of the French language translation of the Western Ontario Shoulder Instability Index (WOSI).

BACKGROUND: The WOSI (Western Ontario Shoulder Instability Index) is a self-administered quality of life questionnaire designed to be used as a primary outcome measure in clinical trials on shoulder instability, as well as to measure the effect of an intervention on any particular patient. It is validated and is reliable and sensitive. As it is designed to measure subjective outcome, it is important that translation should be methodologically rigorous, as it is subject to both linguistic and cultural interpretation. OBJECTIVE: To produce a French language version of the WOSI that is culturally adapted to both European and North American French-speaking populations. MATERIALS AND METHODS: A validated protocol was used to create a French language WOSI questionnaire (WOSI-Fr) that would be culturally acceptable for both European and North American French-speaking populations. Reliability and responsiveness analyses were carried out, and the WOSI-Fr was compared to the F-QuickDASH-D/S (Disability of the Arm, Shoulder and Hand-French translation), and Walch-Duplay scores. RESULTS: A French language version of the WOSI (WOSI-Fr) was accepted by a multinational committee. The WOSI-Fr was then validated using a total of 144 native French-speaking subjects from Canada and Switzerland. Comparison of results on two WOSI-Fr questionnaires completed at a mean interval of 16 days showed that the WOSI-Fr had strong reliability, with a Pearson and interclass correlation of r=0.85 (P=0.01) and ICC=0.84 [95% CI=0.78-0.88]. Responsiveness, at a mean 378.9 days after surgical intervention, showed strong correlation with that of the F-QuickDASH-D/S, with r=0.67 (P<0.01). Moreover, a standardized response means analysis to calculate effect size for both the WOSI-Fr and the F-QuickDASH-D/S showed that the WOSI-Fr had a significantly greater ability to detect change (SRM 1.55 versus 0.87 for the WOSI-Fr and F-QuickDASH-D/S respectively, P<0.01). The WOSI-Fr showed fair correlation with the Walch-Duplay. DISCUSSION: A French-language translation of the WOSI questionnaire was created and validated for use in both Canadian and Swiss French-speaking populations. This questionnaire will facilitate outcome assessment in French-speaking settings, collaboration in multinational studies and comparison between studies performed in different countries. TYPE OF STUDY: Multicenter cohort study. LEVEL OF EVIDENCE: II.

A public-key cryptosystem based on second order linear sequences

Based on Lucas functions, an improved version of the Diffie-Hellman distribution key scheme and to the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions

Is the consumption-income ratio stationary? Evidence from linear and nonlinear panel unit root tests for OECD and non-OECD countries

This paper applies recently developed heterogeneous nonlinear and linear panel unit root tests that account for cross-sectional dependence to 24 OECD and 33 non-OECD countries’ consumption-income ratios over the period 1951–2003. We apply a recently developed methodology that facilitates the use of panel tests to identify which individual cross-sectional units are stationary and which are nonstationary. This extends evidence provided in the recent literature to consider both linear and nonlinear adjustment in panel unit root tests, to address the issue of cross-sectional dependence, and to substantially expand both time-series and cross sectional dimensions of the data analysed. We find that the majority (65%) of the series are nonstationary with slightly fewer OECD countries’ (61%) series exhibiting a unit root than non-OECD countries (68%).

A theoretical and practical study on linear reforms of dual taxes

We extend the linear reforms introduced by Pf¨ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act ‘35/2006’) introduced with respect to the previous tax.

Diagnostic et traitement de l'instabilité rotulienne [Diagnosis and treatment of patellar instability].

Patellar instability concerns mostly young and active patients. Because of the condition's multifactorial origin, knowledge about the risk factors of patella instability and the biomechanics of the femoropatellar joint are necessary to understand this disorder. Most of the patellar dislocations are spontaneously reduced. Only the patient's history, clinical examination and appropriate imaging lead to the correct diagnosis. If haemarthrosis is present, MRI is recommended to rule out concomitant injuries. A traumatic patellar dislocation without history of prior dislocation is treated conservatively. Surgical treatment is indicated in presence of intra-articular injury or for recurrent dislocations. The surgical procedure should correct the different factors of patella instability identified by preoperative analysis.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

Quasiconformal maps, analytic capacity, and non linear potentials

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

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

A robust genomic signature for the detection of colorectal cancer patients with microsatellite instability phenotype and high mutation frequency.

Microsatellite instability (MSI) occurs in 10-20% of colorectal tumours and is associated with good prognosis. Here we describe the development and validation of a genomic signature that identifies colorectal cancer patients with MSI caused by DNA mismatch repair deficiency with high accuracy. Microsatellite status for 276 stage II and III colorectal tumours has been determined. Full-genome expression data was used to identify genes that correlate with MSI status. A subset of these samples (n = 73) had sequencing data for 615 genes available. An MSI gene signature of 64 genes was developed and validated in two independent validation sets: the first consisting of frozen samples from 132 stage II patients; and the second consisting of FFPE samples from the PETACC-3 trial (n = 625). The 64-gene MSI signature identified MSI patients in the first validation set with a sensitivity of 90.3% and an overall accuracy of 84.8%, with an AUC of 0.942 (95% CI, 0.888-0.975). In the second validation, the signature also showed excellent performance, with a sensitivity 94.3% and an overall accuracy of 90.6%, with an AUC of 0.965 (95% CI, 0.943-0.988). Besides correct identification of MSI patients, the gene signature identified a group of MSI-like patients that were MSS by standard assessment but MSI by signature assessment. The MSI-signature could be linked to a deficient MMR phenotype, as both MSI and MSI-like patients showed a high mutation frequency (8.2% and 6.4% of 615 genes assayed, respectively) as compared to patients classified as MSS (1.6% mutation frequency). The MSI signature showed prognostic power in stage II patients (n = 215) with a hazard ratio of 0.252 (p = 0.0145). Patients with an MSI-like phenotype had also an improved survival when compared to MSS patients. The MSI signature was translated to a diagnostic microarray and technically and clinically validated in FFPE and frozen samples.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.