Extrapolation theory for the real interpolation method

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega

An automatic methodology for obtaining optimum shape factors for the radial point interpolation method

In this letter, a methodology is proposed for automatically (and locally) obtaining the shape factor c for the Gaussian basis functions, for each support domain, in order to increase numerical precision and mainly to avoid matrix inversion impossibilities. The concept of calibration function is introduced, which is used for obtaining c. The methodology developed was applied for a 2-D numerical experiment, which results are compared to analytical solution. This comparison revels that the results associated to the developed methodology are very close to the analytical solution for the entire bandwidth of the excitation pulse. The proposed methodology is called in this work Local Shape Factor Calibration Method (LSFCM).

Model reduction for nonlinear aerodynamics and aeroelasticity using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by
a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted
by proper orthogonal decomposition (POD). The aeroelastic reduce order
model (ROM) is completed by introducing a nonlinear mapping function
between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using
a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil
and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit
cycle oscillations (LCO), which the model is able to predict. For all cases
tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow
field with sufficient accuracy at a fraction of the cost of full order CFD
model.

Model reduction for nonlinear aeroelasticity using the Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of computational fluid dynamic (CFD) code for fast nonlinear aerodynamic modeling. First, a nonlinear function is identified on selected interpolation points defined by discrete empirical interpolation method (DEIM). The flow field is then reconstructed by a least square approximation of flow modes extracted by proper orthogonal decomposition (POD). The proposed model is applied in the prediction of limit cycle oscillation for a plunge/pitch airfoil and a delta wing with linear structural model, results are validate against a time accurate CFD-FEM code. The results show the model is able to replicate the aerodynamic forces and flow fields with sufficient accuracy while requiring a fraction of CFD cost.

Ground truth determination for segmentation of tomographic volumes using interpolation

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Interpolation methods for stochastic processes spaces

In this paper the scales of classes of stochastic processes are introduced. New interpolation theorems and boundedness of some transforms of stochastic processes are proved. Interpolation method for generously-monotonous rocesses is entered. Conditions and statements of interpolation theorems concern he xed stochastic process, which diers from the classical results.

A new method for evaluating regional air quality forecasts

A Kriging interpolation method is combined with an object-based evaluation measure to assess the ability of the UK Met Office's dispersion and weather prediction models to predict the evolution of a plume of tracer as it was transported across Europe. The object-based evaluation method, SAL, considers aspects of the Structure, Amplitude and Location of the pollutant field. The SAL method is able to quantify errors in the predicted size and shape of the pollutant plume, through the structure component, the over- or under-prediction of the pollutant concentrations, through the amplitude component, and the position of the pollutant plume, through the location component. The quantitative results of the SAL evaluation are similar for both models and close to a subjective visual inspection of the predictions. A negative structure component for both models, throughout the entire 60 hour plume dispersion simulation, indicates that the modelled plumes are too small and/or too peaked compared to the observed plume at all times. The amplitude component for both models is strongly positive at the start of the simulation, indicating that surface concentrations are over-predicted by both models for the first 24 hours, but modelled concentrations are within a factor of 2 of the observations at later times. Finally, for both models, the location component is small for the first 48 hours after the start of the tracer release, indicating that the modelled plumes are situated close to the observed plume early on in the simulation, but this plume location error grows at later times. The SAL methodology has also been used to identify differences in the transport of pollution in the dispersion and weather prediction models. The convection scheme in the weather prediction model is found to transport more pollution vertically out of the boundary layer into the free troposphere than the dispersion model convection scheme resulting in lower pollutant concentrations near the surface and hence a better forecast for this case study.

Precipitation isoscape of high reliefs: interpolation scheme designed and tested for monthly resolved precipitation oxygen isotope records of an Alpine domain

Stable oxygen isotope composition of atmospheric precipitation (δ18Op) was scrutinized from 39 stations distributed over Switzerland and its border zone. Monthly amount-weighted δ18Op values averaged over the 1995–2000 period showed the expected strong linear altitude dependence (−0.15 to −0.22‰ per 100 m) only during the summer season (May–September). Steeper gradients (~ −0.56 to −0.60‰ per 100 m) were observed for winter months over a low elevation belt, while hardly any altitudinal difference was seen for high elevation stations. This dichotomous pattern could be explained by the characteristically shallower vertical atmospheric mixing height during winter season and provides empirical evidence for recently simulated effects of stratified atmospheric flow on orographic precipitation isotopic ratios. This helps explain "anomalous" deflected altitudinal water isotope profiles reported from many other high relief regions. Grids and isotope distribution maps of the monthly δ18Op have been calculated over the study region for 1995–1996. The adopted interpolation method took into account both the variable mixing heights and the seasonal difference in the isotopic lapse rate and combined them with residual kriging. The presented data set allows a point estimation of δ18Op with monthly resolution. According to the test calculations executed on subsets, this biannual data set can be extended back to 1992 with maintained fidelity and, with a reduced station subset, even back to 1983 at the expense of faded reliability of the derived δ18Op estimates, mainly in the eastern part of Switzerland. Before 1983, reliable results can only be expected for the Swiss Plateau since important stations representing eastern and south-western Switzerland were not yet in operation.

A web processing service for validating interpolation

An interoperable web processing service (WPS) for the automatic interpolation of environmental data has been developed in the frame of the INTAMAP project. In order to assess the performance of the interpolation method implemented, a validation WPS has also been developed. This validation WPS can be used to perform leave one out and K-fold cross validation: a full dataset is submitted and a range of validation statistics and diagnostic plots (e.g. histograms, variogram of residuals, mean errors) is received in return. This paper presents the architecture of the validation WPS and a case study is used to briefly illustrate its use in practice. We conclude with a discussion on the current limitations of the system and make proposals for further developments.

Desenvolvimento e análise de uma rede neural artificial para estimativa da erosividade da chuva para o Estado de São Paulo

O conhecimento do valor da erosividade da chuva (R) de determinada localidade é fundamental para a estimativa das perdas de solo feitas a partir da Equação Universal de Perdas de Solo, sendo, portanto, de grande importância no planejamento conservacionista. A fim de obter estimativas do valor de R para localidades onde este é desconhecido, desenvolveu-se uma rede neural artificial (RNA) e analisou-se a acurácia desta com o método de interpolação "Inverso de uma Potência da Distância" (ID). Comparando a RNA desenvolvida com o método de interpolação ID, verificou-se que a primeira apresentou menor erro relativo médio na estimativa de R e melhor índice de confiança, classificado como "Ótimo", podendo, portanto, ser utilizada no planejamento de uso, manejo e conservação do solo no Estado de São Paulo.

Variabilidade espacial do estado nutricional do cafeeiro conilon utilizando índice DRIS

A combinação da agricultura de precisão e do Sistema Integrado de Recomendação Foliar (DRIS) possibilita monitorar espacialmente o balanço nutricional dos cafezais para fornecer recomendações de adubação mais equilibradas e mais ajustadas economicamente. O objetivo deste trabalho foi avaliar a variabilidade espacial do estado nutricional do cafeeiro conilon, utilizando o Índice de Balanço Nutricional (IBN) e sua relação com a produtividade. A produtividade das plantas em cada ponto amostral foi determinada e construiu-se o seu mapa considerando a variabilidade espacial; determinou-se o Índice de Equilíbrio Nutricional (IBN) das plantas em cada ponto amostral e construiu-se o seu mapa; e utilizou-se a análise de componentes principais (ACP) para estimar o IBN do cafeeiro por cokrigagem. Os dados do cafeeiro conilon foram coletados em fazenda experimental, no município de Cachoeiro de Itapemirim-ES. O IBN do cafeeiro e a sua produtividade foram analisados por meio de geoestatística, com base nos modelos e parâmetros dos semivariogramas, utilizando o método de interpolação krigagem ordinária para estimar valores para locais não amostrados. O índice de Balanço Nutricional da lavoura do cafeeiro conilon apresentou dependência espacial, porém não apresentou correlação linear e nem espacial com a produtividade. A lavoura em estudo se encontra em desequilíbrio nutricional, sendo que entre os macronutrientes, o Potássio foi o que apresentou maior desequilíbrio na área, entre os micronutrientes, o Zinco e o Ferro foram os que apresentaram menores concentrações nas folhas. A confecção dos mapas possibilitou a distinção de regiões com maior e menor desequilíbrio nutricional e produtividade, o que possibilita adotar o manejo de forma diferenciada e localizada. A análise multivariada baseada em componentes principais fornece componentes com alta correlação com as variáveis originais P, Ca, Zn , Cu, K e B. A cokrigagem utilizando as componentes principais permite estimar o IBN e a produtividade da área.

Validation of percutaneous puncture trajectory during renal access using 4D ultrasound reconstruction

Background: An accurate percutaneous puncture is essential for disintegration and removal of renal stones. Although this procedure has proven to be safe, some organs surrounding the renal target might be accidentally perforated. This work describes a new intraoperative framework where tracked surgical tools are superimposed within 4D ultrasound imaging for security assessment of the percutaneous puncture trajectory (PPT). Methods: A PPT is first generated from the skin puncture site towards an anatomical target, using the information retrieved by electromagnetic motion tracking sensors coupled to surgical tools. Then, 2D ultrasound images acquired with a tracked probe are used to reconstruct a 4D ultrasound around the PPT under GPU processing. Volume hole-filling was performed in different processing time intervals by a tri-linear interpolation method. At spaced time intervals, the volume of the anatomical structures was segmented to ascertain if any vital structure is in between PPT and might compromise the surgical success. To enhance the volume visualization of the reconstructed structures, different render transfer functions were used. Results: Real-time US volume reconstruction and rendering with more than 25 frames/s was only possible when rendering only three orthogonal slice views. When using the whole reconstructed volume one achieved 8-15 frames/s. 3 frames/s were reached when one introduce the segmentation and detection if some structure intersected the PPT. Conclusions: The proposed framework creates a virtual and intuitive platform that can be used to identify and validate a PPT to safely and accurately perform the puncture in percutaneous nephrolithotomy.

Avaliação do potencial eólico para geração de energia eléctrica

Trabalho Final de Mestrado para a obtenção do grau de Mestre em Engenharia Mecânica /Energia

Solució paral·lelitzada d'interpolació kriging amb ajust automatitzat del variograma

El principal objectiu d'aquest treball és proporcionar una metodologia per a reduir el temps de càlcul del mètode d'interpolació kriging sense pèrdua de la qualitat del model resultat. La solució adoptada ha estat la paral·lelització de l'algorisme mitjançant MPI sobre llenguatge C. Prèviament ha estat necessari automatitzar l'ajust del variograma que millor s'adapta a la distribució espacial de la variable d'estudi. Els resultats experimentals demostren la validesa de la solució implementada, en reduir de forma significativa els temps d'execució final de tot el procés.

Impact of reduced cerebral perfusion pressure on outcome after severe traumatic brain injury is dependent on brain tissue oxygen pressure

INTRODUCTION. Reduced cerebral perfusion pressure (CPP) may worsen secondary damage and outcome after severe traumatic brain injury (TBI), however the optimal management of CPP is still debated. STUDY HYPOTHESIS: We hypothesized that the impact of CPP on outcome is related to brain tissue oxygen tension (PbtO2) level and that reduced CPP may worsen TBI prognosis when it is associated with brain hypoxia. DESIGN. Retrospective analysis of prospective database. METHODS. We analyzed 103 patients with severe TBI who underwent continuous PbtO2 and CPP monitoring for an average of 5 days. For each patient, duration of reduced CPP (\60 mm Hg) and brain hypoxia (PbtO2\15 mm Hg for[30 min [1]) was calculated with linear interpolation method and the relationship between CPP and PbtO2 was analyzed with Pearson's linear correlation coefficient. Outcome at 30 days was assessed with the Glasgow Outcome Score (GOS), dichotomized as good (GOS 4-5) versus poor (GOS 1-3). Multivariable associations with outcome were analyzed with stepwise forward logistic regression. RESULTS. Reduced CPP (n=790 episodes; mean duration 10.2 ± 12.3 h) was observed in 75 (74%) patients and was frequently associated with brain hypoxia (46/75; 61%). Episodes where reduced CPP were associated with normal brain oxygen did not differ significantly between patients with poor versus those with good outcome (8.2 ± 8.3 vs. 6.5 ± 9.7 h; P=0.35). In contrast, time where reduced CPP occurred simultaneously with brain hypoxia was longer in patients with poor than in those with good outcome (3.3±7.4 vs. 0.8±2.3 h; P=0.02). Outcome was significantly worse in patients who had both reduced CPP and brain hypoxia (61% had GOS 1-3 vs. 17% in those with reduced CPP but no brain hypoxia; P\0.01). Patients in whom a positive CPP-PbtO2 correlation (r[0.3) was found also were more likely to have poor outcome (69 vs. 31% in patients with no CPP-PbtO2 correlation; P\0.01). Brain hypoxia was an independent risk factor of poor prognosis (odds ratio for favorable outcome of 0.89 [95% CI 0.79-1.00] per hour spent with a PbtO2\15 mm Hg; P=0.05, adjusted for CPP, age, GCS, Marshall CT and APACHE II). CONCLUSIONS. Low CPP may significantly worsen outcome after severe TBI when it is associated with brain tissue hypoxia. PbtO2-targeted management of CPP may optimize TBI therapy and improve outcome of head-injured patients.