Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Estimating Phillips Curves in Turbulent Times using the ECB’s Survey of Professional Forecasters

This paper uses forecasts from the European Central Bank's Survey of Professional Forecasters to investigate the relationship between inflation and inflation expectations in the euro area. We use theoretical structures based on the New Keynesian and Neoclassical Phillips curves to inform our empirical work. Given the relatively short data span of the Survey of Professional Forecasters and the need to control for many explanatory variables, we use dynamic model averaging in order to ensure a parsimonious econometric speci cation. We use both regression-based and VAR-based methods. We find no support for the backward looking behavior embedded in the Neo-classical Phillips curve. Much more support is found for the forward looking behavior of the New Keynesian Phillips curve, but most of this support is found after the beginning of the financial crisis.

Estimating United States Phillips Curves With Expectations Consistent With The Statistical Process Of Inflation

‘Modern’ Phillips curve theories predict inflation is an integrated, or near integrated, process. However, inflation appears bounded above and below in developed economies and so cannot be ‘truly’ integrated and more likely stationary around a shifting mean. If agents believe inflation is integrated as in the ‘modern’ theories then they are making systematic errors concerning the statistical process of inflation. An alternative theory of the Phillips curve is developed that is consistent with the ‘true’ statistical process of inflation. It is demonstrated that United States inflation data is consistent with the alternative theory but not with the existing ‘modern’ theories.

Poor and Sick: Estimating the relationship between Household Income and Health

This study evaluates the effect of the individual‘s household income on their health at the later stages of working life. A structural equation model is utilised in order to derive a composite and continuous index of the latent health status from qualitative health status indicators. The endogenous relationship between health status and household income status is taken into account by using IV estimators. The findings reveal a significant effect of individual household income on health before and after endogeneity is taken into account and after a host of other factors which is known to influence health, including hereditary factors and the individual‘s locus of control. Importantly, it is also shown that the childhood socioeconomic position of the individual has long lasting effects on health as it appears to play a significant role in determining health during the later stages of working life.

Estimating the Price of ROCs

The UK government introduced the Renewable Obligation (RO), a system of tradable quotas, to encourage the installation of renewable electricity capacity. Each unit of generation from renewables created a renewable obligation certificate (ROC). Electricity generators must either; earn ROCs through their own production, purchase ROCs in the market or pay the buy-out price to comply with the quota set by the RO. A unique aspect of this regulation is that all entities holding ROCs receive a share of the buy-out fund (the sum of all compliance purchases using the buy-out price). This set-up ensures that the difference between the market price for ROCs and the buy-out price should equal the expected share of the buy-out fund, as regulated entities arbitrage these two compliance options. The expected share of the buy-out fund depends on whether enough renewable generation is available to meet the quota. This analysis tests whether variables associated with renewable generation or electricity demand are correlated with, and thus can help predict, the price of ROCs.

A Multiple Break Panel Approach to Estimating United States Phillips Curves

Phillips curves are often estimated without due attention being paid to the underlying time series properties of the data. In particular, the consequences of inflation having discrete breaks in mean have not been studied adequately. We show by means of simulations and a detailed empirical example based on United States data that not taking account of breaks may lead to biased, and therefore spurious, estimates of Phillips curves. We suggest a method to account for the breaks in mean inflation and obtain meaningful and unbiased estimates of the short- and long-run Phillips curves in the United States.

Estimating the Impact on Efficiency of the Adoption of a Voluntary Environmental Standard: An Empirical Study of the Global Copper Mining Industry

This paper uses data on the world's copper mining industry to measure the impact on efficiency of the adoption of the ISO 14001 environmental standard. Anecdotal and case study literature suggests that firms are motivated to adopt this standard so as to achieve greater efficiency through changes in operating procedures and processes. Using plant level panel data from 1992-2007 on most of the world's industrial copper mines, the study uses stochastic frontier methods to investigate the effects of ISO adoption. The variety of models used in this study find that adoption either tends to improve efficiency or has no impact on efficiency, but no evidence is found that ISO adoption decreases efficiency.

Validity of impedance-based equations for the prediction of total body water as measured by deuterium dilution in African women.

BACKGROUND: Little information is available on the validity of simple and indirect body-composition methods in non-Western populations. Equations for predicting body composition are population-specific, and body composition differs between blacks and whites. OBJECTIVE: We tested the hypothesis that the validity of equations for predicting total body water (TBW) from bioelectrical impedance analysis measurements is likely to depend on the racial background of the group from which the equations were derived. DESIGN: The hypothesis was tested by comparing, in 36 African women, TBW values measured by deuterium dilution with those predicted by 23 equations developed in white, African American, or African subjects. These cross-validations in our African sample were also compared, whenever possible, with results from other studies in black subjects. RESULTS: Errors in predicting TBW showed acceptable values (1.3-1.9 kg) in all cases, whereas a large range of bias (0.2-6.1 kg) was observed independently of the ethnic origin of the sample from which the equations were derived. Three equations (2 from whites and 1 from blacks) showed nonsignificant bias and could be used in Africans. In all other cases, we observed either an overestimation or underestimation of TBW with variable bias values, regardless of racial background, yielding no clear trend for validity as a function of ethnic origin. CONCLUSIONS: The findings of this cross-validation study emphasize the need for further fundamental research to explore the causes of the poor validity of TBW prediction equations across populations rather than the need to develop new prediction equations for use in Africa.

Estimating patterns of leaf herbivory along an altitudinal transect in NE Queensland rainforests: might global warming increase leaf herbivory in tropical rainforests?

Climate change has been taking place at unprecedented rates over the past decades. These fast alterations caused by human activities are leading to a global warming of the planet. Warmer temperatures are going to have important effects on vegetation and especially on tropical forests. Insects as well will be affected by climate change. This study tested the hypothesis that higher temperatures lead to a higher insect pressure on vegetation. Visual estimations of leaf damage were recorded and used to assess the extent of herbivory in nine 0.1ha plots along an altitudinal gradient, and therefore a temperature gradient. These estimations were made at both a community level and a species level, on 2 target species. Leaf toughness tests were performed on samples from the target species from each plot. Results showed a strong evidence of increasing insect damage along increasing temperature, with no significant effect from the leaf toughness.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Stable stationary states of non-local interaction equations

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

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.

A peripheral dose calculation model for estimating second cancer risk after breast radiotherapy

AbstractBreast cancer is one of the most common cancers affecting one in eight women during their lives. Survival rates have increased steadily thanks to early diagnosis with mammography screening and more efficient treatment strategies. Post-operative radiation therapy is a standard of care in the management of breast cancer and has been shown to reduce efficiently both local recurrence rate and breast cancer mortality. Radiation therapy is however associated with some late effects for long-term survivors. Radiation-induced secondary cancer is a relatively rare but severe late effect of radiation therapy. Currently, radiotherapy plans are essentially optimized to maximize tumor control and minimize late deterministic effects (tissue reactions) that are mainly associated with high doses (» 1 Gy). With improved cure rates and new radiation therapy technologies, it is also important to evaluate and minimize secondary cancer risks for different treatment techniques. This is a particularly challenging task due to the large uncertainties in the dose-response relationship.In contrast with late deterministic effects, secondary cancers may be associated with much lower doses and therefore out-of-field doses (also called peripheral doses) that are typically inferior to 1 Gy need to be determined accurately. Out-of-field doses result from patient scatter and head scatter from the treatment unit. These doses are particularly challenging to compute and we characterized it by Monte Carlo (MC) calculation. A detailed MC model of the Siemens Primus linear accelerator has been thoroughly validated with measurements. We investigated the accuracy of such a model for retrospective dosimetry in epidemiological studies on secondary cancers. Considering that patients in such large studies could be treated on a variety of machines, we assessed the uncertainty in reconstructed peripheral dose due to the variability of peripheral dose among various linac geometries. For large open fields (> 10x10 cm2), the uncertainty would be less than 50%, but for small fields and wedged fields the uncertainty in reconstructed dose could rise up to a factor of 10. It was concluded that such a model could be used for conventional treatments using large open fields only.The MC model of the Siemens Primus linac was then used to compare out-of-field doses for different treatment techniques in a female whole-body CT-based phantom. Current techniques such as conformai wedged-based radiotherapy and hybrid IMRT were investigated and compared to older two-dimensional radiotherapy techniques. MC doses were also compared to those of a commercial Treatment Planning System (TPS). While the TPS is routinely used to determine the dose to the contralateral breast and the ipsilateral lung which are mostly out of the treatment fields, we have shown that these doses may be highly inaccurate depending on the treatment technique investigated. MC shows that hybrid IMRT is dosimetrically similar to three-dimensional wedge-based radiotherapy within the field, but offers substantially reduced doses to out-of-field healthy organs.Finally, many different approaches to risk estimations extracted from the literature were applied to the calculated MC dose distribution. Absolute risks varied substantially as did the ratio of risk between two treatment techniques, reflecting the large uncertainties involved with current risk models. Despite all these uncertainties, the hybrid IMRT investigated resulted in systematically lower cancer risks than any of the other treatment techniques. More epidemiological studies with accurate dosimetry are required in the future to construct robust risk models. In the meantime, any treatment strategy that reduces out-of-field doses to healthy organs should be investigated. Electron radiotherapy might offer interesting possibilities with this regard.RésuméLe cancer du sein affecte une femme sur huit au cours de sa vie. Grâce au dépistage précoce et à des thérapies de plus en plus efficaces, le taux de guérison a augmenté au cours du temps. La radiothérapie postopératoire joue un rôle important dans le traitement du cancer du sein en réduisant le taux de récidive et la mortalité. Malheureusement, la radiothérapie peut aussi induire des toxicités tardives chez les patients guéris. En particulier, les cancers secondaires radio-induits sont une complication rare mais sévère de la radiothérapie. En routine clinique, les plans de radiothérapie sont essentiellement optimisées pour un contrôle local le plus élevé possible tout en minimisant les réactions tissulaires tardives qui sont essentiellement associées avec des hautes doses (» 1 Gy). Toutefois, avec l'introduction de différentes nouvelles techniques et avec l'augmentation des taux de survie, il devient impératif d'évaluer et de minimiser les risques de cancer secondaire pour différentes techniques de traitement. Une telle évaluation du risque est une tâche ardue étant donné les nombreuses incertitudes liées à la relation dose-risque.Contrairement aux effets tissulaires, les cancers secondaires peuvent aussi être induits par des basses doses dans des organes qui se trouvent hors des champs d'irradiation. Ces organes reçoivent des doses périphériques typiquement inférieures à 1 Gy qui résultent du diffusé du patient et du diffusé de l'accélérateur. Ces doses sont difficiles à calculer précisément, mais les algorithmes Monte Carlo (MC) permettent de les estimer avec une bonne précision. Un modèle MC détaillé de l'accélérateur Primus de Siemens a été élaboré et validé avec des mesures. La précision de ce modèle a également été déterminée pour la reconstruction de dose en épidémiologie. Si on considère que les patients inclus dans de larges cohortes sont traités sur une variété de machines, l'incertitude dans la reconstruction de dose périphérique a été étudiée en fonction de la variabilité de la dose périphérique pour différents types d'accélérateurs. Pour de grands champs (> 10x10 cm ), l'incertitude est inférieure à 50%, mais pour de petits champs et des champs filtrés, l'incertitude de la dose peut monter jusqu'à un facteur 10. En conclusion, un tel modèle ne peut être utilisé que pour les traitements conventionnels utilisant des grands champs.Le modèle MC de l'accélérateur Primus a été utilisé ensuite pour déterminer la dose périphérique pour différentes techniques dans un fantôme corps entier basé sur des coupes CT d'une patiente. Les techniques actuelles utilisant des champs filtrés ou encore l'IMRT hybride ont été étudiées et comparées par rapport aux techniques plus anciennes. Les doses calculées par MC ont été comparées à celles obtenues d'un logiciel de planification commercial (TPS). Alors que le TPS est utilisé en routine pour déterminer la dose au sein contralatéral et au poumon ipsilatéral qui sont principalement hors des faisceaux, nous avons montré que ces doses peuvent être plus ou moins précises selon la technTque étudiée. Les calculs MC montrent que la technique IMRT est dosimétriquement équivalente à celle basée sur des champs filtrés à l'intérieur des champs de traitement, mais offre une réduction importante de la dose aux organes périphériques.Finalement différents modèles de risque ont été étudiés sur la base des distributions de dose calculées par MC. Les risques absolus et le rapport des risques entre deux techniques de traitement varient grandement, ce qui reflète les grandes incertitudes liées aux différents modèles de risque. Malgré ces incertitudes, on a pu montrer que la technique IMRT offrait une réduction du risque systématique par rapport aux autres techniques. En attendant des données épidémiologiques supplémentaires sur la relation dose-risque, toute technique offrant une réduction des doses périphériques aux organes sains mérite d'être étudiée. La radiothérapie avec des électrons offre à ce titre des possibilités intéressantes.