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.

Determinació de la ubicació estructural dels ions Yb3+ i Nb3+ en Yb:RTP, Nb:RTP i (Nb,Yb):RTP

Estudi elaborat a partir d’una estada al Stony Brook University al juliol del 2006. El RbTiOPO4 (RTP) monocristal•lí és un material d' òptica no lineal molt rellevant i utilitzat en la tecnologia làser actual, químicament molt estable i amb unes propietats físiques molt destacades, entre elles destaquen els alts coeficients electro-òptics i l'alt llindar de dany òptic que presenta. En els últims anys s’està utilitzant tecnològicament en aplicacions d'òptica no lineal en general i electro-òptiques en particular. En alguns casos ja ha substituït, millorant prestacions, a materials tals com el KTP o el LNB(1). Dopant RTP amb ions lantànids (Ln3+) (2-4), el material es converteix en un material làser auto-doblador de freqüència, combinant les seves propietats no lineals amb les de matriu làser. El RTP genera radiació de segon harmònic (SHG) a partir d’un feix fonamental amb longituds d’ona inferiors a 990 nm, que és el límit que presenta el KTP.La determinació de la ubicació estructural i l’estudi de l'entorn local del ions actius làser és de fonamental importància per a la correcta interpretació de les propietats espectroscòpiques d’aquest material. Mesures de difracció de neutrons sobre mostra de pols cristal•lí mostren que els ions Nb5+ i Ln3+ només substitueixin posicions de Ti4+ (8-9). Estudis molt recents d'EPR (electron paramagnetic resonance) semblen indicar que quan la concentració d'ió Ln3+ es baixa, aquest ió presenta la tendència a substituir l'ió alcalí present a l'estructura (10).Després dels resultats obtinguts en el present treball a partir de la tècnica EXAFS a la instal•lació sincrotò del Brookhaven National Laboratory/State University of New York (Stony Brook) es pot concloure definitivament que els ions Nb s’ubiquen en la posició Ti (1) i que els ions Yb3+ es distribueixen paritariament en les dues posicions del Ti (1 i 2). Aquests resultats aporten una valuosa informació per a la correcta interpretació dels espectres, tant d’absorció com d’emissió, del material i per la avaluació dels paràmetres del seu comportament durant l'acció làser.

High-resolution magnetic resonance imaging quantitatively detects individual pancreatic islets.

OBJECTIVE-We studied whether manganese-enhanced high-field magnetic resonance (MR) imaging (MEHFMRI) could quantitatively detect individual islets in situ and in vivo and evaluate changes in a model of experimental diabetes.RESEARCH DESIGN AND METHODS-Whole pancreata from untreated (n = 3), MnCl(2) and glucose-injected mice (n = 6), and mice injected with either streptozotocin (STZ; n = 4) or citrate buffer (n = 4) were imaged ex vivo for unambiguous evaluation of islets. Exteriorized pancreata of MnCl(2) and glucose-injected mice (n = 6) were imaged in vivo to directly visualize the gland and minimize movements. In all cases, MR images were acquired in a 14.1 Testa scanner and correlated with the corresponding (immuno)histological sections.RESULTS-In ex vivo experiments, MEHFMRI distinguished different pancreatic tissues and evaluated the relative abundance of islets in the pancreata of normoglycemic mice. MEHFMRI also detected a significant decrease in the numerical and volume density of islets in STZ-injected mice. However, in the latter measurements the loss of beta-cells was undervalued under the conditions tested. The experiments on the externalized pancreata confirmed that MEHFMRI could visualize native individual islets in living, anesthetized mice.CONCLUSIONS-Data show that MEHFMRI quantitatively visualizes individual islets in the intact mouse pancreas, both ex vivo and in vivo. Diabetes 60:2853-2860, 2011

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

Quantification of aortic flow by phase-contrast magnetic resonance in patients with bicuspid aortic valve.

AIMS: Bicuspid aortic valve (BAV) causes complex flow patterns in the ascending aorta (AAo), which may compromise the accuracy of flow measurement by phase-contrast magnetic resonance (PC-MR). Therefore, we aimed to assess and compare the accuracy of forward flow measurement in the AAo, where complex flow is more dominant in BAV patients, with flow quantification in the left ventricular outflow tract (LVOT) and the aortic valve orifice (AV), where complex flow is less important, in BAV patients and controls. METHODS AND RESULTS: Flow was measured by PC-MR in 22 BAV patients and 20 controls at the following positions: (i) LVOT, (ii) AV, and (iii) AAo, and compared with the left ventricular stroke volume (LVSV). The correlation between the LVSV and the forward flow in the LVOT, the AV, and the AAo was good in BAV patients (r = 0.97/0.96/0.93; P < 0.01) and controls (r = 0.96/0.93/0.93; P < 0.01). However, in relation with the LVSV, the forward flow in the AAo was mildly underestimated in controls and much more in BAV patients [median (inter-quartile range): 9% (4%/15%) vs. 22% (8%/30%); P < 0.01]. This was not the case in the LVOT and the AV. The severity of flow underestimation in the AAo was associated with flow eccentricity. CONCLUSION: Flow measurement in the AAo leads to an underestimation of the forward flow in BAV patients. Measurement in the LVOT or the AV, where complex flow is less prominent, is an alternative means for quantifying the systolic forward flow in BAV patients.

Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging.

The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100,000 degrees of freedom. Marching Cubes and Phong's incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear elastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.

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.

Which prior knowledge? Quantification of in vivo brain 13C MR spectra following 13C glucose infusion using AMARES.

The recent developments in high magnetic field 13C magnetic resonance spectroscopy with improved localization and shimming techniques have led to important gains in sensitivity and spectral resolution of 13C in vivo spectra in the rodent brain, enabling the separation of several 13C isotopomers of glutamate and glutamine. In this context, the assumptions used in spectral quantification might have a significant impact on the determination of the 13C concentrations and the related metabolic fluxes. In this study, the time domain spectral quantification algorithm AMARES (advanced method for accurate, robust and efficient spectral fitting) was applied to 13 C magnetic resonance spectroscopy spectra acquired in the rat brain at 9.4 T, following infusion of [1,6-(13)C2 ] glucose. Using both Monte Carlo simulations and in vivo data, the goal of this work was: (1) to validate the quantification of in vivo 13C isotopomers using AMARES; (2) to assess the impact of the prior knowledge on the quantification of in vivo 13C isotopomers using AMARES; (3) to compare AMARES and LCModel (linear combination of model spectra) for the quantification of in vivo 13C spectra. AMARES led to accurate and reliable 13C spectral quantification similar to those obtained using LCModel, when the frequency shifts, J-coupling constants and phase patterns of the different 13C isotopomers were included as prior knowledge in the analysis.

Coronary magnetic resonance angiography for assessment of the stent lumen: a phantom study.

PURPOSE: To evaluate the feasibility of visualizing the stent lumen using coronary magnetic resonance angiography in vitro. MATERIAL AND METHODS: Nineteen different coronary stents were implanted in plastic tubes with an inner diameter of 3 mm. The tubes were positioned in a plastic container filled with gel and included in a closed flow circuit (constant flow 18 cm/sec). The magnetic resonance images were obtained with a dual inversion fast spin-echo sequence. For intraluminal stent imaging, subtraction images were calculated from scans with and without flow. Subsequently, intraluminal signal properties were objectively assessed and compared. RESULTS: As a function of the stent type, various degrees of in-stent signal attenuation were observed. Tantalum stents demonstrated minimal intraluminal signal attenuation. For nitinol stents, the stent lumen could be identified, but the intraluminal signal was markedly reduced. Steel stents resulted in the most pronounced intraluminal signal voids. CONCLUSIONS: With the present technique, radiofrequency penetration into the stents is strongly influenced by the stent material. Thesefindings may have important implicationsforfuture stent design and stent imaging strategies.

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.