Sensitivity analysis in optimized parametric curve fitting

Purpose – Curve fitting from unordered noisy point samples is needed for surface reconstruction in many applications -- In the literature, several approaches have been proposed to solve this problem -- However, previous works lack formal characterization of the curve fitting problem and assessment on the effect of several parameters (i.e. scalars that remain constant in the optimization problem), such as control points number (m), curve degree (b), knot vector composition (U), norm degree (k), and point sample size (r) on the optimized curve reconstruction measured by a penalty function (f) -- The paper aims to discuss these issues -- Design/methodology/approach - A numerical sensitivity analysis of the effect of m, b, k and r on f and a characterization of the fitting procedure from the mathematical viewpoint are performed -- Also, the spectral (frequency) analysis of the derivative of the angle of the fitted curve with respect to u as a means to detect spurious curls and peaks is explored -- Findings - It is more effective to find optimum values for m than k or b in order to obtain good results because the topological faithfulness of the resulting curve strongly depends on m -- Furthermore, when an exaggerate number of control points is used the resulting curve presents spurious curls and peaks -- The authors were able to detect the presence of such spurious features with spectral analysis -- Also, the authors found that the method for curve fitting is robust to significant decimation of the point sample -- Research limitations/implications - The authors have addressed important voids of previous works in this field -- The authors determined, among the curve fitting parameters m, b and k, which of them influenced the most the results and how -- Also, the authors performed a characterization of the curve fitting problem from the optimization perspective -- And finally, the authors devised a method to detect spurious features in the fitting curve -- Practical implications – This paper provides a methodology to select the important tuning parameters in a formal manner -- Originality/value - Up to the best of the knowledge, no previous work has been conducted in the formal mathematical evaluation of the sensitivity of the goodness of the curve fit with respect to different possible tuning parameters (curve degree, number of control points, norm degree, etc.)

Fault detection with Conditional Gaussian Network

International audience

Euclidean Distance Between Haar Orthogonal and Gaussian Matrices

In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix (Formula presented.). If (Formula presented.) denotes the vector formed by the first m-coordinates of the ith row of (Formula presented.) and (Formula presented.), our main result shows that the Euclidean norm of (Formula presented.) converges exponentially fast to (Formula presented.), up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm (Formula presented.) and we find a coupling that improves by a factor (Formula presented.) the recently proved best known upper bound on (Formula presented.). Our main result also has applications in Quantum Information Theory.

Breaking the curve with candels: a Bayesian approach to reveal the non-universality of the dust-attenuation law at high redshift

Dust attenuation affects nearly all observational aspects of galaxy evolution, yet very little is known about the form of the dust-attenuation law in the distant universe. Here, we model the spectral energy distributions of galaxies at z ~ 1.5–3 from CANDELS with rest-frame UV to near-IR imaging under different assumptions about the dust law, and compare the amount of inferred attenuated light with the observed infrared (IR) luminosities. Some individual galaxies show strong Bayesian evidence in preference of one dust law over another, and this preference agrees with their observed location on the plane of infrared excess (IRX, L_TIR/L_UV) and UV slope (β). We generalize the shape of the dust law with an empirical model, A_ λ,σ =E(B-V)k_ λ (λ / λ v)^ σ where k_λ is the dust law of Calzetti et al., and show that there exists a correlation between the color excess E(B-V) and tilt δ with δ =(0.62±0.05)log(E(B-V))+(0.26±0.02). Galaxies with high color excess have a shallower, starburst-like law, and those with low color excess have a steeper, SMC-like law. Surprisingly, the galaxies in our sample show no correlation between the shape of the dust law and stellar mass, star formation rate, or β. The change in the dust law with color excess is consistent with a model where attenuation is caused by scattering, a mixed star–dust geometry, and/or trends with stellar population age, metallicity, and dust grain size. This rest-frame UV-to-near-IR method shows potential to constrain the dust law at even higher redshifts (z>3).

Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.

Modellazione assistita di curve di probabilità (POD) per il rilevamento di difetti strutturali mediante fibre ottiche

I sensori a fibre ottiche rappresentano una delle tecnologie più promettenti per il monitoraggio di varie strutture ingegneristiche. Tali sensori, dopo che sono stati incollati su differenti tipologie di strutture grazie a un dispositivo optoelettronico, restituiscono il profilo di deformazione del materiale ospite. Tuttavia, risulta piuttosto complicato ottenere queste curve, in quanto sono necessari numerosi provini che richiedono spese onerose e molto tempo per i singoli esperimenti. In più, si deve tenere in considerazione che i provini non sono mai completamente identici e che l’operatore può commettere errori. In questo studio si genera un programma attraverso cui si simulano diversi andamenti di deformazione, cercando di riprodurre al meglio i vari casi sperimentali. Infine, utilizzando un codice già esistente, si ricavano le curve di probabilità di rilevamento del danno in funzione della lunghezza di cricca. Una volta creato il codice, si modificano alcuni parametri, in particolare si alterano lo shear lag e alcune caratteristiche meccaniche della fibra ottica, ovvero il raggio e il modulo di Young, per vedere l’influenza che hanno sulle curve di probabilità. I risultati hanno dimostrato che lo shear lag della fibra ottica deve essere il più possibile alto e di conseguenza il raggio e il modulo di Young della fibra devono essere bassi, in quanto quest’ultimi si trovano a denominatore della formula usata per calcolare lo shear lag.

Analisi di curve di luce del pianeta XO-2b tramite la tecnica della variazione dei tempi di transito.

La ricerca di esopianeti è un ambito astrofisico in continua evoluzione. Nuovi metodi vengono proposti con l’obiettivo di individuare pianeti con una varietà di caratteristiche sempre più ampia, per poter definire al meglio la storia di formazione ed evoluzione dei sistemi planetari. Un metodo recente in grado di caratterizzare pianeti di piccola massa è lo studio della variazione del tempo di transito (TTV), basato sulla modulazione del periodo orbitale di un pianeta noto causata dalla perturbazione di un corpo aggiuntivo. In questo lavoro proponiamo l’analisi delle curve di luce del pianeta XO-2Nb al fine di individuare TTV. Questo sistema è di particolare rilevanza poiché ospitato dalla prima stella binaria wide in cui entrambe le componenti presentano un proprio sistema planetario. Tra le due stelle solo XO-2N presenta un pianeta transitante, requisito per l’applicazione del metodo proposto. L’analisi dei dati è stata svolta utilizzando il metodo della fotometria differenziale di apertura, normalizzando la curva di luce del target ad altre due stelle di riferimento presenti nel campo di vista dello strumento. I risultati ottenuti evidenziano l’assenza di variazioni di periodo orbitale per XO-2Nb e sono consistenti con un’effemeride lineare. La nuova effemeride calcolata risulta tre volte più precisa rispetto al più recente studio in letteratura, e permetterà di predire futuri transiti con una precisione migliore di un minuto fino al 2035. Abbiamo stabilito un limite superiore all’ampiezza del TTV permessa dai nostri dati, ricavando il valore massimo della massa di un eventuale pianeta perturbatore, pari a 0.15 masse terrestri. Abbiamo ricavato in maniera indipendente i parametri fisici ed orbitali di XO-2Nb, confermando e raffinando i valori presenti in letteratura. I risultati ottenuti suggeriscono che, in determinati casi, l’analisi fotometrica eseguita utilizzando telescopi medio-piccoli da terra può essere competitiva con i più avanzati telescopi spaziali.

Mechanisms Predisposing Penile Fracture And Long-term Outcomes On Erectile And Voiding Functions.

Purpose. To determine the mechanisms predisposing penile fracture as well as the rate of long-term penile deformity and erectile and voiding functions. Methods. All fractures were repaired on an emergency basis via subcoronal incision and absorbable suture with simultaneous repair of eventual urethral lesion. Patients' status before fracture and voiding and erectile functions at long term were assessed by periodic follow-up and phone call. Detailed history included cause, symptoms, and single-question self-report of erectile and voiding functions. Results. Among the 44 suspicious cases, 42 (95.4%) were confirmed, mean age was 34.5 years (range: 18-60), mean follow-up 59.3 months (range 9-155). Half presented the classical triad of audible crack, detumescence, and pain. Heterosexual intercourse was the most common cause (28 patients, 66.7%), followed by penile manipulation (6 patients, 14.3%), and homosexual intercourse (4 patients, 9.5%). Woman on top was the most common heterosexual position (n = 14, 50%), followed by doggy style (n = 8, 28.6%). Four patients (9.5%) maintained the cause unclear. Six (14.3%) patients had urethral injury and two (4.8%) had erectile dysfunction, treated by penile prosthesis and PDE-5i. No patient showed urethral fistula, voiding deterioration, penile nodule/curve or pain. Conclusions. Woman on top was the potentially riskiest sexual position (50%). Immediate surgical treatment warrants long-term very low morbidity.

Advancing Bag-of-visual-words Representations For Lesion Classification In Retinal Images.

Diabetic Retinopathy (DR) is a complication of diabetes that can lead to blindness if not readily discovered. Automated screening algorithms have the potential to improve identification of patients who need further medical attention. However, the identification of lesions must be accurate to be useful for clinical application. The bag-of-visual-words (BoVW) algorithm employs a maximum-margin classifier in a flexible framework that is able to detect the most common DR-related lesions such as microaneurysms, cotton-wool spots and hard exudates. BoVW allows to bypass the need for pre- and post-processing of the retinographic images, as well as the need of specific ad hoc techniques for identification of each type of lesion. An extensive evaluation of the BoVW model, using three large retinograph datasets (DR1, DR2 and Messidor) with different resolution and collected by different healthcare personnel, was performed. The results demonstrate that the BoVW classification approach can identify different lesions within an image without having to utilize different algorithms for each lesion reducing processing time and providing a more flexible diagnostic system. Our BoVW scheme is based on sparse low-level feature detection with a Speeded-Up Robust Features (SURF) local descriptor, and mid-level features based on semi-soft coding with max pooling. The best BoVW representation for retinal image classification was an area under the receiver operating characteristic curve (AUC-ROC) of 97.8% (exudates) and 93.5% (red lesions), applying a cross-dataset validation protocol. To assess the accuracy for detecting cases that require referral within one year, the sparse extraction technique associated with semi-soft coding and max pooling obtained an AUC of 94.2 ± 2.0%, outperforming current methods. Those results indicate that, for retinal image classification tasks in clinical practice, BoVW is equal and, in some instances, surpasses results obtained using dense detection (widely believed to be the best choice in many vision problems) for the low-level descriptors.

A Highly Improved Method For Sensitive Determination Of Amitriptyline In Pharmaceutical Formulations Using An Unmodified Carbon Nanotube Electrode In The Presence Of Sulfuric Acid.

The present paper describes a novel, simple and reliable differential pulse voltammetric method for determining amitriptyline (AMT) in pharmaceutical formulations. It has been described for many authors that this antidepressant is electrochemically inactive at carbon electrodes. However, the procedure proposed herein consisted in electrochemically oxidizing AMT at an unmodified carbon nanotube paste electrode in the presence of 0.1 mol L(-1) sulfuric acid used as electrolyte. At such concentration, the acid facilitated the AMT electroxidation through one-electron transfer at 1.33 V vs. Ag/AgCl, as observed by the augmentation of peak current. Concerning optimized conditions (modulation time 5 ms, scan rate 90 mV s(-1), and pulse amplitude 120 mV) a linear calibration curve was constructed in the range of 0.0-30.0 μmol L(-1), with a correlation coefficient of 0.9991 and a limit of detection of 1.61 μmol L(-1). The procedure was successfully validated for intra- and inter-day precision and accuracy. Moreover, its feasibility was assessed through analysis of commercial pharmaceutical formulations and it has been compared to the UV-vis spectrophotometric method used as standard analytical technique recommended by the Brazilian Pharmacopoeia.

Neck Circumference As A New Anthropometric Indicator For Prediction Of Insulin Resistance And Components Of Metabolic Syndrome In Adolescents: Brazilian Metabolic Syndrome Study.

To evaluate the correlation between neck circumference and insulin resistance and components of metabolic syndrome in adolescents with different adiposity levels and pubertal stages, as well as to determine the usefulness of neck circumference to predict insulin resistance in adolescents. Cross-sectional study with 388 adolescents of both genders from ten to 19 years old. The adolescents underwent anthropometric and body composition assessment, including neck and waist circumferences, and biochemical evaluation. The pubertal stage was obtained by self-assessment, and the blood pressure, by auscultation. Insulin resistance was evaluated by the Homeostasis Model Assessment-Insulin Resistance. The correlation between two variables was evaluated by partial correlation coefficient adjusted for the percentage of body fat and pubertal stage. The performance of neck circumference to identify insulin resistance was tested by Receiver Operating Characteristic Curve. After the adjustment for percentage body fat and pubertal stage, neck circumference correlated with waist circumference, blood pressure, triglycerides and markers of insulin resistance in both genders. The results showed that the neck circumference is a useful tool for the detection of insulin resistance and changes in the indicators of metabolic syndrome in adolescents. The easiness of application and low cost of this measure may allow its use in Public Health services.

Biochemical, Anthropometric And Body Composition Indicators As Predictors Of Hepatic Steatosis In Obese Adolescents.

To describe the prevalence of hepatic steatosis and to assess the performance of biochemical, anthropometric and body composition indicators for hepatic steatosis in obese teenagers. Cross-sectional study including 79 adolecents aged from ten to 18 years old. Hepatic steatosis was diagnosed by abdominal ultrasound in case of moderate or intense hepatorenal contrast and/or a difference in the histogram ≥7 on the right kidney cortex. The insulin resistance was determined by the Homeostasis Model Assessment-Insulin Resistance (HOMA-IR) index for values >3.16. Anthropometric and body composition indicators consisted of body mass index, body fat percentage, abdominal circumference and subcutaneous fat. Fasting glycemia and insulin, lipid profile and hepatic enzymes, such as aspartate aminotransferase, alanine aminotransferase, gamma-glutamyltransferase and alkaline phosphatase, were also evaluated. In order to assess the performance of these indicators in the diagnosis of hepatic steatosis in teenagers, a ROC curve analysis was applied. Hepatic steatosis was found in 20% of the patients and insulin resistance, in 29%. Gamma-glutamyltransferase and HOMA-IR were good indicators for predicting hepatic steatosis, with a cutoff of 1.06 times above the reference value for gamma-glutamyltransferase and 3.28 times for the HOMA-IR. The anthropometric indicators, the body fat percentage, the lipid profile, the glycemia and the aspartate aminotransferase did not present significant associations. Patients with high gamma-glutamyltransferase level and/or HOMA-IR should be submitted to abdominal ultrasound examination due to the increased chance of having hepatic steatosis.

Propylthiouracil Quantification In Human Plasma By High-performance Liquid Chromatography Coupled With Electrospray Tandem Mass Spectrometry: Application In A Bioequivalence Study.

A rapid, sensitive and specific method for quantifying propylthiouracil in human plasma using methylthiouracil as the internal standard (IS) is described. The analyte and the IS were extracted from plasma by liquid-liquid extraction using an organic solvent (ethyl acetate). The extracts were analyzed by high performance liquid chromatography coupled with electrospray tandem mass spectrometry (HPLC-MS/MS) in negative mode (ES-). Chromatography was performed using a Phenomenex Gemini C18 5μm analytical column (4.6mm×150mm i.d.) and a mobile phase consisting of methanol/water/acetonitrile (40/40/20, v/v/v)+0.1% of formic acid. For propylthiouracil and I.S., the optimized parameters of the declustering potential, collision energy and collision exit potential were -60 (V), -26 (eV) and -5 (V), respectively. The method had a chromatographic run time of 2.5min and a linear calibration curve over the range 20-5000ng/mL. The limit of quantification was 20ng/mL. The stability tests indicated no significant degradation. This HPLC-MS/MS procedure was used to assess the bioequivalence of two propylthiouracil 100mg tablet formulations in healthy volunteers of both sexes in fasted and fed state. The geometric mean and 90% confidence interval CI of Test/Reference percent ratios were, without and with food, respectively: 109.28% (103.63-115.25%) and 115.60% (109.03-122.58%) for Cmax, 103.31% (100.74-105.96%) and 103.40% (101.03-105.84) for AUClast. This method offers advantages over those previously reported, in terms of both a simple liquid-liquid extraction without clean-up procedures, as well as a faster run time (2.5min). The LOQ of 20ng/mL is well suited for pharmacokinetic studies. The assay performance results indicate that the method is precise and accurate enough for the routine determination of the propylthiouracil in human plasma. The test formulation with and without food was bioequivalent to reference formulation. Food administration increased the Tmax and decreased the bioavailability (Cmax and AUC).

Determination Of Flavanones In Orange Juices Obtained From Different Sources By Hplc/dad.

Flavanones (hesperidin, naringenin, naringin, and poncirin) in industrial, hand-squeezed orange juices and from fresh-in-squeeze machines orange juices were determined by HPLC/DAD analysis using a previously described liquid-liquid extraction method. Method validation including the accuracy was performed by using recovery tests. Samples (36) collected from different Brazilian locations and brands were analyzed. Concentrations were determined using an external standard curve. The limits of detection (LOD) and the limits of quantification (LOQ) calculated were 0.0037, 1.87, 0.0147, and 0.0066 mg 100 g(-1) and 0.0089, 7.84, 0.0302, and 0.0200 mg 100 g(-1) for naringin, hesperidin, poncirin, and naringenin, respectively. The results demonstrated that hesperidin was present at the highest concentration levels, especially in the industrial orange juices. Its average content and concentration range were 69.85 and 18.80-139.00 mg 100 g(-1). The other flavanones showed the lowest concentration levels. The average contents and concentration ranges found were 0.019, 0.01-0.30, and 0.12 and 0.1-0.17, 0.13, and 0.01-0.36 mg 100 g(-1), respectively. The results were also evaluated using the principal component analysis (PCA) multivariate analysis technique which showed that poncirin, naringenin, and naringin were the principal elements that contributed to the variability in the sample concentrations.

Waist-to-height Ratio Percentiles And Cutoffs For Obesity: A Cross-sectional Study In Brazilian Adolescents.

This study aimed to describe the distribution of waist-to-height ratio (WHtR) percentiles and cutoffs for obesity in Brazilian adolescents. A cross-sectional study including adolescents aged 10 to 15 years was conducted in the city of São Paulo, Brazil; anthropometric measurements (weight, height, and waist-circumference) were taken, and WHtRs were calculated and then divided into percentiles derived by using Least Median of Squares (LMS) regression. The receiver operating characteristic (ROC) curve was used in determining cutoffs for obesity (BMI ≥ 97th percentile) and Mann-Whitney and Kruskal-Wallis tests were used for comparing variables. The study included 8,019 adolescents from 43 schools, of whom 54.5% were female, and 74.8% attended public schools. Boys had higher mean WHtR than girls (0.45 ± 0.06 vs 0.44 ± 0.05; p=0.002) and higher WHtR at the 95th percentile (0.56 vs 0.54; p<0.05). The WHtR cutoffs according to the WHO criteria ranged from 0.467 to 0.506 and 0.463 to 0.496 among girls and boys respectively, with high sensitivity (82.8-95%) and specificity (84-95.5%). The WHtR was significantly associated with body adiposity measured by BMI. Its age-specific percentiles and cutoffs may be used as additional surrogate markers of central obesity and its co-morbidities.