Polynomial Adjustment Research Articles

Third Order Polynomial Bundle Adjustment For Optical Calibration Refinement

We propose a refinement and validity region expansion process of a 3rd order polynomial calibration based on bundle adjustment. The present methodology can be expanded to any model as long as the mapping is a smooth function. Both methods are tested with a tomographic Particle Tracking Velocimetry measurement whose results are compared in terms of the smoothness and length of the retrieved tracks. The refinement method shows a significant improvement in both the associated PDFs. Similarly, the expansion shows a corresponding behaviour to the original calibration even though a higher degree of smoothness of the tracks is achieved.

Evaluation of biophysical alterations in the epithelial and endothelial layer of patients with Bullous Keratopathy

The cornea is a fundamental ocular tissue for the sense of sight. Thanks to it, the refraction of two-thirds of light manages to participate in the visual process and protect against mechanical damage. Because it is transparent, avascular, and innervated, the cornea comprises five main layers: Epithelium, Bowman's layer, stroma, Descemet's membrane, and endothelium. Each layer plays a key role in the functionality and maintenance of ocular tissue, providing unique ultrastructural and biomechanical properties. Bullous Keratopathy (BK) is an endothelial dysfunction that leads to corneal edema, loss of visual acuity, epithelial blisters, and severe pain, among other symptoms. The corneal layers are subject to changes in their biophysical properties promoted by Keratopathy. In this context, the Atomic Force Microscopy (AFM) technique in air was used to investigate the anterior epithelial surface and the posterior endothelial surface, healthy and with BK, using a triangular silicone tip with a nominal spring constant of 0.4 N/m. Six human corneas (n = 6) samples were used for each analyzed group. Roughness data, calculated by third-order polynomial adjustment, adhesion, and Young's modulus, were obtained to serve as a comparison and identification of morphological and biomechanical changes possibly associated with the pathology, such as craters and in the epithelial layer and exposure of a fibrotic layer due to loss of the endothelial cell wall. Endothelial cell membrane area and volume data were calculated, obtaining a relevant comparison between the control and patient. Such results may provide new data on the physical properties of the ocular tissue to understand the physiology of the cornea when it has pathology.

Analysis of the general uncertainty propagation and calculation of the systematic uncertainty of the Neumann equation of state for surface free energy determination

The determination of the surface free energy (γSV) of solid materials provides information to explain and understand a wide variety of phenomena in surface science. One of the most widely used methods to determine the value of γSV is the Neumann equation of state (EQS), whose application requires the values of the contact angle (θ) and the surface tension of a probe liquid (γLV). Both parameters are determined experimentally, and their values may be subject to considerable uncertainty. In the present work, the uncertainties of the EQS are analyzed by means of the Taylor series method, using a polynomial adjustment to the EQS previously reported. This analysis allowed us to determine the effects of the θ and γLV uncertainties on γSV values. The γSV of polyoxymethylene (POM) and polytetrafluoroethylene (PTFE) was calculated using the EQS from four probe liquids and taking into account the propagation of the θ and γLV uncertainties. Generally, the comparison of the γSV values calculated from the different probe fluids revealed significant differences. As a solution to this inconsistency in the EQS method, we proposed taking into account a systematic standard uncertainty associated with the method equal to 1.3 mJ/m2. This allowed the differences between the γSV values for the different probe liquids to be non-significant and therefore the method to be consistent.

Measurement of Ultrasound Propagation Velocity in Liquids Using an FPGA Module

The design and development of an ultrasonic device for the measurement of ultrasonic propagation velocity in liquids based on Field Programmable Gate Array (FPGA) architecture is described. The device was implemented using a DE0-Nano-SoC Development Kit FPGA development module, a 2x16 LCD Display, a 2-channel quadrature output optical encoder with push button, two ultrasonic transducers and an external module for interfacing with the transducers containing the circuits corresponding to the transmitter, receiver and amplifier. For the development, the Altera Integrated Development Environment (IDE) software called Quartus II was used, which allows the logical design and supports different HDL hardware description languages, such as Verilog and VHLD. Although the device was calibrated to measure the acoustic velocity of water in the range of 35°C to 40°C, due to its design characteristics it is feasible to extend its application to measure acoustic velocity in different liquids, delimiting the operation intervals. The device acquires 100 readings per second, calculates the average with polynomial adjustment and displays the value of the ultrasonic propagation velocity in the fluid with a resolution of 0.01 [m/s] with a refresh rate of one second.

Non-Destructive Post-Harvest Tomato Mass Estimation Model Based on Its Area via Computer Vision and Error Minimization Approaches

Tomato commercialization in Mexican and Latin-American markets is economically affected by three main physical aspects of the fruit: ripening time, size, and mass. Digital image processing combined with mathematical models and machine learning approaches allows the development of prediction models to minimize fruit waste, among other applications. Particularly crossed validation, linear and non-linear adjustment by quadratic mean least error approximation, and digital image processing are used to obtain a post-harvest mass loss estimation model based upon the fruit’s area. A database for fruit characterization of 97,200 images and mass (kg) and area (cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) measurement entries over a continuous post-harvest timeline of 54 days was considered in the methodology. Results from the linear (polynomial) adjustment model presented an efficiency of 94.65%, while the non-linear (exponential and potential) adjustment models gave in their turn efficiencies of 99.21 and 99.82%, respectively. It was concluded that the best mass loss estimation model was the potential adjustment one, with an approximation error of just 0.18% between actual and estimated data.

Improving resistance training prescription through the load-velocity relationship in breast cancer survivors: The case of the leg-press exercise

ABSTRACT The aims of this study were: (i) to analyse the load-velocity relationship in the bilateral leg-press exercise in female breast cancer survivors, (ii) to assess whether mean velocity (MV) or peak velocity (PV) show stronger relationship with the relative load, and (iii) to examine whether linear (LA) or polynomic (PA) adjustment predict the velocities associated with each %1RM with greater precision. Twenty-two female breast cancer survivors (age: 50.2 ± 10.8 years, weight: 69.6 ± 15.2 kg, height: 160.51 ± 5.25 cm) completed an incremental load test until 1RM in the bilateral leg-press exercise. The MV and the PV of the concentric phase were measured in each repetition using a linear velocity transducer, and were analysed by regression models using LA and PA. A very close relationship of MV (R 2 = 0.924; p < 0.0001; SEE = 0.08m.s−1 by LA, and R² = 0.952; p < 0.0001; SEE = 0.063 m.s−1 by PA) and PV (R² = 0.928; p < 0.0001; SEE = 0.119 m.s−1 by LA and R² = 0.941; p < 0.0001; SEE = 0.108 m.s−1 by PA) with %1RM were observed. The MV of 1RM was 0.24 ± 0.03 m·s−1, whereas the PV at 1RM was 0.60 ± 0.10 m.s−1. A comprehensive analysis of the bilateral leg-press load-velocity relationship in breast cancer survivors is presented. The results suggest that MV is the most recommendable velocity variable to prescribe the relative load during resistance training, and that the PA presents better accuracy to predict velocities associated with each %1RM, although LA is sufficiently valid to use this model as an alternative to the quadratic model. The implications for resistance training in breast cancer are discussed.

Procedure for the quantification of the degradation index of Photovoltaic Generators

A procedure is presented for the quantification of the degradation index of Photovoltaic Generators, based on the quantification of the operational losses inherent in the system, which allows maintaining the nominal operating conditions and by the warranty terms of the photovoltaic generator. A photovoltaic generator connected to the network with a nominal power of 7.5 kWp, installed in the Solar Energy Research Center of Santiago de Cuba, is used to evaluate and validate the procedure. The starting point is the mathematical model of the photovoltaic generator, then the operational losses of the photovoltaic generator are quantified and the mathematical model is adjusted to real conditions, through a polynomial adjustment. The results obtained show that the photovoltaic generator presents deviations in terms of the nominal power generation, because the operational losses are 7% with respect to the values ​​given by the manufacturer.

Fault Diagnostic Methodology for Grid-Connected Photovoltaic Systems

This research focuses on the design of a fault diagnosis methodology to contribute to the improvement of efficiency, maintainability and availability indicators of Grid-Connected Photovoltaic Systems. To achieve this, we start from the study of the mathematical model of the photovoltaic generator, then, a procedure is performed to quantify the operational losses of the photovoltaic generator and adjust the mathematical model of this to the real conditions of the system, through a polynomial adjustment. A real system of nominal power 7.5 kWp installed in the Solar Energy Research Center of the province of Santiago de Cuba is used to evaluate the proposed methodology. Based on the results obtained, the proposed approach is validated to demonstrate that it successfully supervises the system. The methodology was able to detect and identify 100% of the simulated failures and the tests carried out had a maximum false alarm rate of 0.22%, evidencing its capacity.

Geometric Accuracy Assessment of Deimos-2 Panchromatic Stereo Pairs: Sensor Orientation and Digital Surface Model Production.

Accurate elevation data, which can be extracted from very high-resolution (VHR) satellite images, are vital for many engineering and land planning applications. In this way, the main goal of this work is to evaluate the capabilities of VHR Deimos-2 panchromatic stereo pairs to obtain digital surface models (DSM) over different land covers (bare soil, urban and agricultural greenhouse areas). As a step prior to extracting the DSM, different orientation models based on refined rational polynomial coefficients (RPC) and a variable number of very accurate ground control points (GCPs) were tested. The best sensor orientation model for Deimos-2 L1B satellite images was the RPC model refined by a first-order polynomial adjustment (RPC1) supported on 12 accurate and evenly spatially distributed GCPs. Regarding the Deimos-2 based DSM, its completeness and vertical accuracy were compared with those obtained from a WorldView-2 panchromatic stereo pair by using exactly the same methodology and semiglobal matching (SGM) algorithm. The Deimos-2 showed worse completeness values (about 6% worse) and vertical accuracy results (RMSEZ 42.4% worse) than those computed from WorldView-2 imagery over the three land covers tested, although only urban areas yielded statistically significant differences (p < 0.05).

Construction and calibration of Time Domain Reflectometry probes for assessing soil humidity in distropheric red latosol

Among the indirect methods of assessing soil moisture, Time Domain Reflectometry (TDR) stands out, which uses the soil dielectric constant to provide volumetric moisture efficiently, quickly and non-destructively. Despite a practical and precise method, TDR has a high cost due to the probes and its Data Logger. In view of this, the present work aims to build and calibrate TDR probes to assess moisture in a Dystrophic Red Latosol. The present work was carried out in the experimental area of the hydraulics laboratory of the Federal University of Grande Dourados (UFGD), located in Dourados-MS, at latitude 22⁰ 12 'south, longitude 54⁰ 59' west and altitude of 434 meters. Each probe built consisted of 3 stainless steel rods (Ø = 3 mm; L = 230 mm) RG 98 cable with 90% mesh and 50 ohm impedance, 4.7 pF ceramic capacitor and BNC connector. The construction procedures followed the following steps: 1- Making the cable, 2- Preparing the rods, 3- Welding the rods to the wires, 4 -Operating test and 5 - finishing phase. After construction, they were calibrated with the characteristic soil of the Region, proceeding with the Probe Reading in two depths (10 and 30 cm) and simultaneous collection of deformed soil samples to determine the moisture based on mass in Laboratory. Subsequently, calibrations with cubic polynomial adjustment were performed. The results showed adjustments with high determination coefficients, and the probes developed showed satisfactory performances.

Leaf gas exchange and chlorophyll index in guava fertirrigated with bovine biofertilizer and nitrogen

The objective of this work was to evaluate the influence of fertirrigation with nitrogen and liquid bovine biofertilizer on gas exchange and leaf chlorophyll index of 'paluma' guava (Psidium guajava L.). The experimental design was randomized blocks with treatments distributed in a factorial arrangement (2 × 4) referring to mineral fertilizing with N (50% and 100% of N recommended) and biofertilizer concentrations (0, 2.5, 5.0 and 7.5% of the fertirrigated volume). Variables evaluated were chlorophyll a (Chl a), chlorophyll b (Chl b), total chlorophyll indexes (Chltotal), internal CO2 concentration (Ci), stomatal conductance (gs), transpiration (E), net photosynthesis (A), instant carboxylation efficiency (iCE) and water use efficiency (WUE). The biofertilizer significantly affected Chl a, Chl b, Chltotal, A, gs and E, with quadratic polynomial adjustment of the results. However, there was no effect of N fertilization and interaction between the factors. Maximum index of Chltotal was 32.31 obtained with the estimated dose of 3.8% of the biofertilizer; while A, gs and E presented maximum responses of 19.09 µmol of CO2 m-2 s-1, 0.28 mol of H2O m-2 s-1 and 4.93 mmol of H2O m-2 s-1, with estimated doses of 3.6%, 3.6%, and 3.7%, respectively. Generally, liquid bovine biofertilizer applied via fertirrigation affects positively the photosynthetic responses in 'paluma' guava, however, with decreasing effects for doses above 3.8%.

Drawn out of the shadows: Surveying secretive forest species with camera trap distance sampling

Abstract With animal species disappearing at unprecedented rates, we need an efficient monitoring method providing reliable estimates of population density and abundance, critical for the assessment of population status and trend. We deployed 160 camera traps (CTs) systematically over 743 locations covering 17,127 km2 of evergreen lowland rainforest of Salonga National Park, block South, Democratic Republic of the Congo. We evaluated the applicability of CT distance sampling (CTDS) to species different in size and behaviour. To improve precision of estimates, we evaluated two methods estimating species' availability (‘A’) for detection by CTs. We recorded 16,700 video clips, revealing 43 different animal taxa. We estimated densities of 14 species differing in physical, behavioural and ecological traits, and extracted species‐specific availability from available video footage using two methods (a) ‘ACa’ (Cappelle et al. [2019] Am. J. Primatol., 81, e22962) and (b) ‘ARo’ (Rowcliffe et al. [2014] Methods Ecol. Evol. 5, 1170). With sample sizes being large enough, we found minor differences between ACa and ARo in estimated densities. In contrast, low detectability and reactivity to the camera were main sources of bias. CTDS proved efficient for estimating density of homogenously rather than patchily distributed species. Synthesis and applications. Our application of camera trap distance sampling (CTDS) to a diverse vertebrate community demonstrates the enormous potential of this methodology for surveys of terrestrial wildlife, allowing rapid assessments of species' status and trends that can translate into effective conservation strategies. By providing the first estimates of understudied species such as the Congo peafowl, the giant ground pangolin and the cusimanses, CTDS may be used as a tool to revise these species' conservation status in the IUCN Red List of Threatened Species. Based on the constraints we encountered, we identify improvements to the current application, enhancing the general applicability of this method.

Fuzzy system applied to a hydraulic turbine efficiency curve fitting

This paper reports the results of different fuzzy-based approaches applied to the fitting of a hydraulic turbine efficiency curve. This kind of curve is granted by the turbine manufacturer as a three-dimensional dataset that needs to be properly fitted in order to provide the turbine efficiency for any values of net head and water discharge in the relevant space and, therefore, guarantee an as realistic as possible representation of the hydroelectric power plant’s machines. The clustering algorithm Fuzzy C-Means and the ANFIS and Extreme Learning ANFIS architectures were widely tested and compared to the conventional polynomial adjustment. Since the studied curve is nonlinear, researches involving any kind of nonlinear curve fitting can benefit from this work’s information.

Inertial Sensors Embedded in Smartphones as a Tool for Fatigue Assessment Based on Acceleration in Survivors of Breast Cancer.

Cancer-related fatigue is a symptom commonly reported in survivors of breast cancer and is the most variable symptom. Besides questionnaires like PIPER to assess cancer-related fatigue, there is a need to objectively measure fatigue. The aim of this study was to assess the physiological dimension of fatigue based on acceleration during a 30-second maximal sit-to-stand test. This was a cross-sectional study. Linear acceleration from a smartphone placed on the sternum was recorded in 70 survivors of breast cancer. Fourth-degree polynomial adjustment from the acceleration signal to the vertical and anterior-posterior axis was calculated. The fatigue temporal cut-off point was detected as a change in the curve slope of the first maximum point of acceleration. Women were aged 51.8 (8.9) years with a body mass index of 25.4 (5.1) Kg/m2. They performed 23.6 (6.57) number of repetitions. The mean fatigue cut-off point from the total sample was 10.2 (3.1) seconds. Further research should employ time-prolonged tests to study acceleration behavior beyond 30seconds as well as include a physiological criterion that justifies the nonlinear saturation of the acceleration-based criterion. This study assessed fatigue through a low-cost and easy-to-use methodology during a functional and widely used test such as 30-second maximal sit-to-stand. This would allow clinicians to assess fatigue in a short-effort exercise to individualize exercise prescription dose, measure changes during intervention, and track fatigue objectively throughout survivorship.

Higher-order normal approximation approach for highly reliable system assessment

In this study, the issue of system reliability assessment (SRA) based on component failure data is considered. In industrial statistics, the delta method has become a popular approach for confidence interval approximation. However, for high reliability systems, usually the assessment is confronted with very limited component sample size, variant multi-parameter lifetime models, and complex system structure. Along with strict requirement on assessment accuracy and computational efficiency, existing approaches barely work under these circumstances. In this article, a normal approximation approach is proposed for determining the lower confidence limit of system reliability using components’ time-to-failure data. The polynomial adjustment method is adopted to construct higher-order approximate confidence limit. The main contribution of this work is constructing an integrated methodology for SRA. Specifically, a reliability-based Winterbottom-extended Cornish-Fisher (R-WCF) expansion method for log-location-scale family is elaborated. The proposed methodology exceeds the efficient limitation of Cramer Rao’s theory. Numerical studies are conducted to illustrate the effectiveness of the proposed approach, and results show that the R-WCF approach is more efficient than the delta method for highly reliable system assessment, especially with ultra-small sample size. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transactions.

Optimal load for the muscle power profile of prone bench pull in Brazilian Jiu-Jitsu athletes

No studies were observed optimal intensity loads for the muscle power performance during prone bench pull exercise in Brazilian Jiu-Jitsu athletes (BJJ) and this exercise is more similar with grip technics. To identify the optimal intensity for the muscle power performance variables during PBP exercise in BJJ athletes. Fifteen athletes (25.5 ± 4.9 years; 65.6 ± 12.2 kg; 177.5 ± 4.7 cm) performed PBP at 30, 40, 50 and 60% of one repetition maximum (1RM) in a random order. The mean power (MP), mean velocity (MV), mean propulsive power (MPP) and mean propulsive velocity (MPV) were determined by measuring the barbell displacement by a linear encoder. In all power performance variables, higher power output was observed at 40 and 50% 1RM when compared to 30 and 60% 1RM (MP: F = 29.07; p 0.001). Additionally, it was observed higher MPP at 50% 1RM when compared to 40% 1RM (F = 55.23; p < 0.001). The polynomial adjustment indicated that the optimal intensity load for producing highest power performance ranged from 45 to 50% 1RM (R 2 = 0.938–0.989) across all variables. The loads between 45 and 50% 1RM produced the optimal muscle power performance during PBP exercise in BJJ athletes.

A Log-Density Estimation Methodology Applicable to Massive Bivariate Data

First, it is shown that a univariate bona fide density approximation can be obtained by assuming that the derivative of the logarithm of the density function under consideration is expressible as a rational function or a polynomial. Then, the density function of a bivariate continuous random vector is approximated by standardizing it and applying a polynomial adjustment to the product of the density approximants of the marginal distributions. As well, it is explained that this approach can easily be extended to the estimation of density functions. For illustrative purposes, the proposed methodology is applied to several datasets. Since this technique is solely based on sample moments, it readily lends itself to the modeling of large datasets.

Improving georeferencing accuracy of Very High Resolution satellite imagery using freely available ancillary data at global coverage

ABSTRACTWhile impressive direct geolocation accuracies better than 5.0 m CE90 (90% of circular error) can be achieved from the last DigitalGlobe’s Very High Resolution (VHR) satellites (i.e. GeoEye-1 and WorldView-1/2/3/4), it is insufficient for many precise geodetic applications. For these sensors, the best horizontal geopositioning accuracies (around 0.55 m CE90) can be attained by using third-order 3D rational functions with vendor’s rational polynomial coefficients data refined by a zero-order polynomial adjustment obtained from a small number of very accurate ground control points (GCPs). However, these high-quality GCPs are not always available. In this work, two different approaches for improving the initial direct geolocation accuracy of VHR satellite imagery are proposed. Both of them are based on the extraction of three-dimensional GCPs from freely available ancillary data at global coverage such as multi-temporal information of Google Earth and the Shuttle Radar Topography Mission 30 m digital elevation model. The application of these approaches on WorldView-2 and GeoEye-1 stereo pairs over two different study sites proved to improve the horizontal direct geolocation accuracy values around of 75%.

Global Polynomial Kernel Hazard Estimation

&lt;p&gt;This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically reduces bias with unchanged variance. A simulation study investigates the finite-sample properties of GPA. The method is tested on local constant and local linear estimators. From the simulation experiment we conclude that the global estimator improves the goodness-of-fit. An especially encouraging result is that the bias-correction works well for small samples, where traditional bias reduction methods have a tendency to fail.&lt;/p&gt;

Crecimiento fetal en el recién nacido peruano

OBJETIVO: Obtener curvas de crecimiento intrauterino propias de un grupo seleccionado de recién nacidos peruanos. DISEÑO: Estudio descriptivo, transversal. LUGAR: Hospitales del Ministerio de Salud del Perú. PARTICIPANTES:Recién nacidos. INTERVENCIONES: Enrolamiento prospectivo de recién nacidos vivos sucesivos. Se estandarizó las técnicas de pesaje y medición del recién nacido, de acuerdo al Centro Latinoamericano de Perinatología (CLAP-OPS/OMS); el diagnóstico de la edad gestacional fue por fecha de última menstruación; se excluyó la patología materna y fetal que alterara el crecimiento fetal; se descartó tabaquismo y desnutrición materna. Se utilizó media, desviación estándar, percentiles 10, 50 y 90 de peso, talla y perímetro cefálico. Las curvas fueron dibujadas y alisadas utilizando ajuste polinomial de tercer orden en programa Excel. PRINCIPALES MEDIDAS DE RESULTADOS: Curvas de crecimiento intrauterino, según peso, talla y perímetro cefálico. RESULTADOS: En el ‘2005, en 29 hospitales del Ministerio de Salud motivo del estudio nacieron 99 439 recién nacidos, 50 568 cumplieron condiciones de selección (50,8%), con los que se elaboró curvas de crecimiento fetal entre las 24 y 43 semanas de gestación. Las semanas 39 y 40 de gestación fueron las más representativas (55,8%), con un promedio de peso de 3 295 g + 407 g y 3 400 + 421 g, respectivamente (percentiles 10, 50 y 90 fueron: 2 750, 3 275, 3 810 g y 2 875, 3 385, 3 930 g, respectivamente). La talla promedio de nacimiento fue 49,7 cm + 2,3 y 50,1 cm + 2,3, respectivamente, y el perímetro cefálico, 343 mm + 16 y 345 mm + 16, respectivamente. CONCLUSIONES: Se presenta una familia de curvas de crecimiento fetal, según peso, talla y perímetro cefálico, en un grupo seleccionado de recién nacidos peruanos.