A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

How Do Aggregate Fluctuations Depend on the Network Structure of the Economy?

[spa] En este artículo, analizamos la volatilidad agregada de una economía estilizada donde los agentes estann conectados en redes. Si hay relaciones estratégicas entre las acciones de los agentes, choques idiosincráticos pueden generar fluctuaciones agregadas. Demonstramos que la volatilidad agregada depende de la estructura de redes de la economía de dos maneras. Por un lado, si hay más conexiones en la economía en su conjunto, la volatilidad agregada es más baja. Por otro lado, si las conexiones están más concentradas, la volatilidad agregada es más alta. Presentamos una aplicación de nuestras predicciones teóricas que utiliza datos de EEUU de conexiones intrasectoriales y de diversificación de las empresas.

How Do Aggregate Fluctuations Depend on the Network Structure of the Economy?

[spa] En este artículo, analizamos la volatilidad agregada de una economía estilizada donde los agentes estann conectados en redes. Si hay relaciones estratégicas entre las acciones de los agentes, choques idiosincráticos pueden generar fluctuaciones agregadas. Demonstramos que la volatilidad agregada depende de la estructura de redes de la economía de dos maneras. Por un lado, si hay más conexiones en la economía en su conjunto, la volatilidad agregada es más baja. Por otro lado, si las conexiones están más concentradas, la volatilidad agregada es más alta. Presentamos una aplicación de nuestras predicciones teóricas que utiliza datos de EEUU de conexiones intrasectoriales y de diversificación de las empresas.

Reliable computation of robust response tori on the verge of breakdown

We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.

Endoscopic epiglottopexy using Lichtenberger's needle carrier to avoid breakdown of repair.

Severe type III laryngomalacia LM is represented by a retroflexed epiglottis that touches the posterior pharyngeal wall and obstructs the laryngeal inlet. Endoscopic epiglottopexy is advised in such cases wherein pexy sutures are passed between the epiglottis and base of tongue. Using conventional needle carriers, it is difficult to pass such sutures that go deep enough into the tongue base. Such a pexy is prone to a break down. We describe a novel technique of placing these glossoepiglottic sutures using the Lichtenberger's needle carrier. We used this technique in three patients with excellent results and report no complications. We propose to use this technique in cases of epiglottic prolapse seen in severe LM and certain hypotonic conditions.

Aggregate material formulated with MSWI bottom ash and APC fly ash for use as secondary building material

The main goal of this paper is to obtain a granular material formulated with Municipal Solid Waste Incinerarion (MSWI) bottom ash (BA) and air pollution control (APC) ash to be used as secondary building material. Previously, an optimum concrete mixture using both MSWI residues as aggregates was formulated. A compromise between the environmental behaviour and the economy of the process was considered. Unconfined compressive strength and abrasion resistance values were measured in order to evaluate the mechanical properties. From these results, the granular mixture was not suited for certain applications owing to the high BA/APC content and low cement percentages used to reduce the costs of the final product. Nevertheless, the leaching test performed showed that the concentrations of all heavy metals were below the limits established by the current Catalan legislation for their reutilization. Therefore, the material studied might be mainly used in embankments, where high mechanical properties are not needed and environmental safety is assured.

Quality in work and aggregate productivity

We explore the relationship between quality in work and aggregate productivity in regions and sectors. Using recent Spanish aggregate data for the period 2001-2006, we find that quality in work may be an important factor to explain productivity levels in sectors and regions. We use two alternatives definitions of quality in work: one from survey data and the other from a social indicators approach. We also use two different measurements of labour productivity to test the robustness of our results. The estimates are run using a simultaneous equation model for our panel of data, and find important differences between high tech and low tech sectors: a positive relationship between quality in work and productivity in the former case, and a negative relationship in the latter. Consequently, on the one hand we see that quality in work is not only an objective per se, but may also be a production factor able to increase the wealth of regions; on the other hand, at the aggregate level, we may also find that high productivity levels coincide with lower quality in work conditions.

Factors affecting foster care breakdown in Spain

La ruptura del acogimiento familiar se ha definido como aquella situación en la que alguna de las partes implicadas causa una terminación de la intervención antes de haber alcanzado los objetivos establecidos en el plan de caso. Este trabajo presenta un estudio llevado a cabo en una muestra española de 318 casos cerrados de niños que fueron acogidos en familia ajena y extensa. Los datos se obtuvieron a través de la revisión exhaustiva de los expedientes de protección y acogimiento, complementada conentrevistas a los técnicos encargados de cada caso. La tasa de ruptura del conjunto de la muestra fue de 26,1%, si bien fuesignificativamente diferente en familia extensa (19,7%) que en familia ajena (31,2%). Los resultados de este estudio indican que las variables relacionadas con la ruptura dependen de la modalidad del acogimiento, en familia ajena o extensa. En el primer caso destacamos las variables relacionadas con las características del niño, especialmente los problemas de conducta y escolares, con especial relevancia en el grupo de 9-12 años, y el haber estado en acogimiento residencial previamente. En cambio, en extensaresulta más importante la problemática en los padres (prisión, salud mental) y el tener una medida de tutela. También el hecho de que se realice el acogimiento tras pasar por hogares de acogida resulta trascendental. Finalmente, la disponibilidad de recursos económicos e incluso los estudios de los acogedores parecen ser variables relacionadas con la ruptura de la acogida

Soil CO2 emission as related to incorporation of sugarcane crop residues and aggregate breaking after rotary tiller

Soil tillage is a process that accelerates soil organic matter decomposition transferring carbon to atmosphere, mainly in the CO2 form. In this study, the effect of rotary tillage on soil CO2 emission was investigated, including the presence of crop residues on the surface.Emissions were evaluated during 15 days after tillage in 3 plots: 1) non-tilled and without crop residues on soil surface (NTwo), 2) rotary tiller without the presence of crop residues on soil surface (RTwo), and 3) rotary tiller with the presence of crop residues in soil surface (RTw). Emissions from the RTw plot were higher than the other plots, (0.777 g CO2 m-2 h-1), with the lowest emissions recorded in the NTwo plot (0.414 g CO2 m-2 h-1). Total emission indicates that the difference of C-CO2 emitted to atmosphere corresponds to 3% of the total additional carbon in the crop residues in the RTw plot compared to RTwo. The increase in the RTwo emission in comparison to NTwo was followed by changes in the aggregate size distribution, especially those with average diameter lower than 2 mm. The increase in emission from the RTw plot in relation to RTwo was related to a decrease in crop residue mass on the surface, and its higher fragmentation and incorporation in soil. When the linear correlation between soil CO2 emission, and soil temperature and soil moisture is considered, only the RTw treatment showed significant correlation (p<0.05) with soil moisture.

Time sequence of changes in the responsiveness of glycogen breakdown to adrenergic agonists in perfused liver of rats with insulin-induced hypoglycemia

The time-course changes of the responsiveness of glycogen breakdown to a- and ß-adrenergic agonists during insulin-induced hypoglycemia (IIH) were investigated. Blood glucose levels were decreased prior to the alteration in the hepatic responsiveness to adrenergic agonists. The activation of hepatic glucose production and glycogenolysis by phenylephrine (2 µM) and isoproterenol (20 µM) was decreased in IIH. The changes in the responsiveness of glycogen catabolism were first observed for isoproterenol and later for phenylephrine. Hepatic ß-adrenergic receptors showed a higher degree of adrenergic desensitization than did a-receptors. Liver glycogen synthase activity, glycogen content and the catabolic effect of dibutyryl cyclic AMP (the ß-receptor second messenger) were not affected by IIH.

Early myelin breakdown following sural nerve crush: a freeze-fracture study

In this study we describe the early changes of the myelin sheath following surgical nerve crush. We used the freeze-fracture technique to better evaluate myelin alterations during an early stage of Wallerian degeneration. Rat sural nerves were experimentally crushed and animals were sacrificed by transcardiac perfusion 30 h after surgery. Segments of the nerves were processed for routine transmission electron microscopy and freeze-fracture techniques. Our results show that 30 h after the lesion there was asynchrony in the pattern of Wallerian degeneration, with different nerve fibers exhibiting variable degrees of axon disruption. This was observed by both techniques. Careful examination of several replicas revealed early changes in myelin membranes represented by vacuolization and splitting of consecutive lamellae, rearrangement of intramembranous particles and disappearance of paranodal transverse bands associated or not with retraction of paranodal myelin terminal loops from the axolemma. These alterations are compatible with a direct injury to the myelin sheath following nerve crush. The results are discussed in terms of a similar mechanism underlying both axon and myelin breakdown.

Responsiveness of glycogen breakdown to cyclic AMP in perfused liver from rats with insulin-induced hypoglycemia

The responsiveness of glycogen breakdown to cAMP was investigated in isolated perfused liver from male Wistar fed rats (200-220 g) with insulin-induced hypoglycemia. The activation of glycogenolysis by 3 µM cAMP was decreased (P<0.05) in livers from rats with hypoglycemia induced by the administration of insulin or during the direct infusion of insulin into the isolated liver. The direct effect of insulin on glycogen catabolism promoted by 3 µM cAMP occurred as early as 3 min after starting insulin infusion. In contrast, the cAMP agonists resistant to phosphodiesterases, 8Br-cAMP and 6MB-cAMP, used at the same concentration as cAMP, i.e., 3 µM, did not modify the effect of insulin. The data suggest that the decreased hepatic responsiveness of glycogen breakdown during insulin-induced hypoglycemia is a direct effect of insulin decreasing the intracellular levels of cAMP.

A Test of New Aggregate Damand Curvature Properties.

In This Paper We Present and Implement an Econometric Test of Both Negative Semi-Definiteness of the Matrix of Compensated Price Effects and of the Negative Quasi-Definiteness of the Matrix of Uncompensated Price Effects. This Test Allows Us to Evaluate Two Alternative Characterizations of Aggregate Demand Systems: the First, That They Behave Like Individual Demand Fuctions, and the Second, That They Respect the Properties Implied by the Assumptions Proposed by Hidebrand (1983) Or Grandmont (1984).