Estatística aplicada à química: dez dúvidas comuns

Ten common doubts of chemistry students and professionals about their statistical applications are discussed. The use of the N-1 denominator instead of N is described for the standard deviation. The statistical meaning of the denominators of the root mean square error of calibration (RMSEC) and root mean square error of validation (RMSEV) are given for researchers using multivariate calibration methods. The reason why scientists and engineers use the average instead of the median is explained. Several problematic aspects about regression and correlation are treated. The popular use of triplicate experiments in teaching and research laboratories is seen to have its origin in statistical confidence intervals. Nonparametric statistics and bootstrapping methods round out the discussion.

Aplicação de técnicas multivariadas e inteligência artificial na análise de espectros de infravermelho para determinação de matéria orgânica em amostras de solos

In this paper studies based on Multilayer Perception Artificial Neural Network and Least Square Support Vector Machine (LS-SVM) techniques are applied to determine of the concentration of Soil Organic Matter (SOM). Performances of the techniques are compared. SOM concentrations and spectral data from Mid-Infrared are used as input parameters for both techniques. Multivariate regressions were performed for a set of 1117 spectra of soil samples, with concentrations ranging from 2 to 400 g kg-1. The LS-SVM resulted in a Root Mean Square Error of Prediction of 3.26 g kg-1 that is comparable to the deviation of the Walkley-Black method (2.80 g kg-1).

PREDICTING THE BOILING POINT OF PCDD/Fs BY THE QSPR METHOD BASED ON THE MOLECULAR DISTANCE-EDGE VECTOR INDEX

The quantitative structure property relationship (QSPR) for the boiling point (Tb) of polychlorinated dibenzo-p-dioxins and polychlorinated dibenzofurans (PCDD/Fs) was investigated. The molecular distance-edge vector (MDEV) index was used as the structural descriptor. The quantitative relationship between the MDEV index and Tb was modeled by using multivariate linear regression (MLR) and artificial neural network (ANN), respectively. Leave-one-out cross validation and external validation were carried out to assess the prediction performance of the models developed. For the MLR method, the prediction root mean square relative error (RMSRE) of leave-one-out cross validation and external validation was 1.77 and 1.23, respectively. For the ANN method, the prediction RMSRE of leave-one-out cross validation and external validation was 1.65 and 1.16, respectively. A quantitative relationship between the MDEV index and Tb of PCDD/Fs was demonstrated. Both MLR and ANN are practicable for modeling this relationship. The MLR model and ANN model developed can be used to predict the Tb of PCDD/Fs. Thus, the Tb of each PCDD/F was predicted by the developed models.

Comparison between hydrographically conditioned digital elevation models in the morphometric charaterization of watersheds

The aim of this study was to compare the hydrographically conditioned digital elevation models (HCDEMs) generated from data of VNIR (Visible Near Infrared) sensor of ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer), of SRTM (Shuttle Radar Topography Mission) and topographical maps from IBGE in a scale of 1:50,000, processed in the Geographical Information System (GIS), aiming the morphometric characterization of watersheds. It was taken as basis the Sub-basin of São Bartolomeu River, obtaining morphometric characteristics from HCDEMs. Root Mean Square Error (RMSE) and cross validation were the statistics indexes used to evaluate the quality of HCDEMs. The percentage differences in the morphometric parameters obtained from these three different data sets were less than 10%, except for the mean slope (21%). In general, it was observed a good agreement between HCDEMs generated from remote sensing data and IBGE maps. The result of HCDEM ASTER was slightly higher than that from HCDEM SRTM. The HCDEM ASTER was more accurate than the HCDEM SRTM in basins with high altitudes and rugged terrain, by presenting frequency altimetry nearest to HCDEM IBGE, considered standard in this study.

Evaluation of thermorregulatory capacity of dairy buffaloes using infrared thermography

ABSTRACT The objective of this study was to evaluate the thermoregulatory response of dairy buffaloes in pre-milking and post-milking. To identify animal thermoregulatory capacity, skin surface temperatures were taken by an infrared thermometer (SST), a thermographic camera (MTBP) as well as respiratory rate records (RR). Black Globe and Humidity Index (BGHI), radiating thermal load (RTL) and enthalpy (H) were used to characterize the thermal environment. Artificial Neural Networks analyzed those indices as well as animal physiological data, using a single layer trained with the least mean square (LMS) algorithm. The results indicated that pre-milking and post-milking environments reached BGHI, RR, SST and MTBP values above thermal neutrality zone for buffaloes. In addition, limits of surface skin temperatures were mostly influenced by changing ambient conditions to the detriment of respiratory rates. It follows that buffaloes are sensitive to environmental changes and their skin temperatures are the best indicators of thermal comfort in relation to respiratory rate.

Fibrinonecrotic enteritis of piglets in a commercial farm: a postmortem study of the prevalence and the role of lesion associated agents Isospora suis and Clostridium perfringens

The objectives were to determine the prevalence of fibrinonecrotic enteritis (FNE) on a farrow-to-finish farm of 1,000 sows, to categorize the pathological changes, and to to investigate the lesion associated agents Isospora suis and Clostridium perfringens. Causes of preweaning mortality (PWM) were classified into 8 categories including FNE. Obtained data were evaluated for statistical significance by adjusted Chi-square analysis. Samples of FNE were taken for complementary studies including a PCR technique for genotyping toxin genes of Clostridium perfringens from gut samples fixed in 10% neutral formalin. From 3,153 piglets examined, less than 1% was classified as FNE. FNE prevalence increased progressively from the first to the third week, the last differing statistically from the others. Eighty percent of gut samples with FNE lesions were positive to Isospora suis, when examined by PCR from 9 severe FNE lesions detected 7 positive samples only for a toxin gene, characteristic of C. perfringens type-A.

Estimation of aircraft aerodynamic derivatives using Extended Kalman Filter

Design of flight control laws, verification of performance predictions, and the implementation of flight simulations are tasks that require a mathematical model of the aircraft dynamics. The dynamical models are characterized by coefficients (aerodynamic derivatives) whose values must be determined from flight tests. This work outlines the use of the Extended Kalman Filter (EKF) in obtaining the aerodynamic derivatives of an aircraft. The EKF shows several advantages over the more traditional least-square method (LS). Among these the most important are: there are no restrictions on linearity or in the form which the parameters appears in the mathematical model describing the system, and it is not required that these parameters be time invariant. The EKF uses the statistical properties of the process and the observation noise, to produce estimates based on the mean square error of the estimates themselves. Differently, the LS minimizes a cost function based on the plant output behavior. Results for the estimation of some longitudinal aerodynamic derivatives from simulated data are presented.

Time course of changes in heart rate and blood pressure variability in streptozotocin-induced diabetic rats treated with insulin

Autonomic neuropathy is a frequent complication of diabetes associated with higher morbidity and mortality in symptomatic patients, possibly because it affects autonomic regulation of the sinus node, reducing heart rate (HR) variability which predisposes to fatal arrhythmias. We evaluated the time course of arterial pressure and HR and indirectly of autonomic function (by evaluation of mean arterial pressure (MAP) variability) in rats (164.5 ± 1.7 g) 7, 14, 30 and 120 days after streptozotocin (STZ) injection, treated with insulin, using measurements of arterial pressure, HR and MAP variability. HR variability was evaluated by the standard deviation of RR intervals (SDNN) and root mean square of successive difference of RR intervals (RMSSD). MAP variability was evaluated by the standard deviation of the mean of MAP and by 4 indices (P1, P2, P3 and MN) derived from the three-dimensional return map constructed by plotting MAPn x [(MAPn+1) - (MAPn)] x density. The indices represent the maximum concentration of points (P1), the longitudinal axis (P2), and the transversal axis (P3) and MN represents P1 x P2 x P3 x 10-3. STZ induced increased urinary glucose in diabetic (D) rats compared to controls (C). Seven days after STZ, diabetes reduced resting HR from 380.6 ± 12.9 to 319.2 ± 19.8 bpm, increased HR variability, as demonstrated by increased SDNN, from 11.77 ± 1.67 to 19.87 ± 2.60 ms, did not change MAP, and reduced P1 from 61.0 ± 5.3 to 51.5 ± 1.8 arbitrary units (AU), P2 from 41.3 ± 0.3 to 29.0 ± 1.8 AU, and MN from 171.1 ± 30.2 to 77.2 ± 9.6 AU of MAP. These indices, as well as HR and MAP, were similar for D and C animals 14, 30 and 120 days after STZ. Seven-day rats showed a negative correlation of urinary glucose with resting HR (r = -0.76, P = 0.03) as well as with the MN index (r = -0.83, P = 0.01). We conclude that rats with short-term diabetes mellitus induced by STZ presented modified autonomic control of HR and MAP which was reversible. The metabolic control may influence these results, suggesting that insulin treatment and a better metabolic control in this model may modify arterial pressure, HR and MAP variability

Fractures of the proximal femur: correlation with vitamin D receptor gene polymorphism

Fractures are the feared consequences of osteoporosis and fractures of the proximal femur (FPF) are those that involve the highest morbidity and mortality. Thus far, evaluation of bone mineral density (BMD) is the best way to determine the risk of fracture. Genetic inheritance, in turn, is one of the major determinants of BMD. A correlation between different genotypes of the vitamin D receptor (VDR) and BMD has been recently reported. On this basis, we decided to determine the importance of the determination of VDR genotype in the presence of an osteoporotic FPF in a Brazilian population. We studied three groups: group I consisted of 73 elderly subjects older than 65 years (78.5 ± 7.2 years) hospitalized for nonpathological FPF; group II consisted of 50 individuals older than 65 years (72.9 ± 5.2 years) without FPF and group III consisted of 98 young normal Brazilian individuals aged 32.6 ± 6.6 years (mean ± SD). Analysis of VDR gene polymorphism by restriction fragment length polymorphism (RFLP) was performed by PCR amplification followed by BsmI digestion of DNA isolated from peripheral leukocytes. The genotype distribution in group I was 20.5% BB, 42.5% Bb and 37% bb and did not differ significantly from the values obtained for group II (16% BB, 36% Bb and 48% bb) or for group III (10.2% BB, 47.6% Bb and 41.8% bb). No differences in genotype distribution were observed between sexes or between the young and elderly groups. We conclude that determination of VDR polymorphism is of no practical use for the prediction of FPF. Other nongenetic factors probably start to affect bone mass, the risk to fall and consequently the occurrence of osteoporotic fractures with advancing age.

Evaluation of electromyographic activity and heart rate responses to isometric exercise. The role played by muscular mass and type

The purpose of the present study was to examine the relationship between the electromyographic (EMG) activity and heart rate (HR) responses induced by isometric exercise performed by knee extension (KE) and flexion (KF) in men. Fifteen healthy male subjects, 21 ± 1.3 years (mean ± SD), were submitted to KE and KF isometric exercise tests at 100% of maximal voluntary contraction (MVC). The exercises were performed with one leg (right or left) and with two legs simultaneously, for 10 s in the sitting position with the hip and knee flexed at 90o. EMG activity (root mean square values) and HR (beats/min) were recorded simultaneously both at rest and throughout the sustained contraction. The HR responses to isometric exercise in KE and KF were similar when performed with one and two legs. However, the HR increase was always significantly higher in KE than KF (P<0.05), whereas the EMG activity was higher in KE than in KF (P<0.05), regardless of the muscle mass (one or two legs) involved in the effort. The correlation coefficients between HR response and the EMG activity during KE (r = 0.33, P>0.05) and KF (r = 0.15, P>0.05) contractions were not significant. These results suggest that the predominant mechanism responsible for the larger increase in HR response to KE as compared to KF in our study could be dependent on qualitative and quantitative differences in the fiber type composition found in each muscle group. This mechanism seems to demand a higher activation of motor units with a corresponding increase in central command to the cardiovascular centers that modulate HR control.

Heart rate variability under resting conditions in postmenopausal and young women

The aim of the present study was to compare the modulation of heart rate in a group of postmenopausal women to that of a group of young women under resting conditions on the basis of R-R interval variability. Ten healthy postmenopausal women (mean ± SD, 58.3 ± 6.8 years) and 10 healthy young women (mean ± SD, 21.6 ± 0.82 years) were submitted to a control resting electrocardiogram (ECG) in the supine and sitting positions over a period of 6 min. The ECG was obtained from a one-channel heart monitor at the CM5 lead and processed and stored using an analog to digital converter connected to a microcomputer. R-R intervals were calculated on a beat-to-beat basis from the ECG recording in real time using a signal-processing software. Heart rate variability (HRV) was expressed as standard deviation (RMSM) and mean square root (RMSSD). In the supine position, the postmenopausal group showed significantly lower (P<0.05) median values of RMSM (34.9) and RMSSD (22.32) than the young group (RMSM: 62.11 and RMSSD: 49.1). The same occurred in the sitting position (RMSM: 33.0 and RMSSD: 18.9 compared to RMSM: 57.6 and RMSSD: 42.8 for the young group). These results indicate a decrease in parasympathetic modulation in postmenopausal women compared to young women which was possibly due both to the influence of age and hormonal factors. Thus, time domain HRV proved to be a noninvasive and sensitive method for the identification of changes in autonomic modulation of the sinus node in postmenopausal women.

Effect of the acupoints ST-36 (Zusanli) and SP-6 (Sanyinjiao) on intestinal myoelectric activity of Wistar rats

Despite its ancient use as a therapeutic tool to treat several ailments, acupuncture still faces the challenge of scrutiny by Western science both in terms of its efficacy and in terms of the characterization of its effects and mechanisms of actions underlying these effects. We investigated under well-controlled and carefully characterized conditions the influence of electrical stimulation of acupuncture points ST-36 (Zusanli) and SP-6 (Sanyinjiao) on the myoelectric activity of the small intestine of 38 adult male Wistar rats. Electrical recordings obtained by means of four electrodes chronically implanted in the small intestine were used to assess the effects of acupuncture (electroacupuncture stimulation set at 2 Hz, intermittent stimulation, 1 V, for 30 min). Immobilization of the animals was associated with a consistent decrease (-8 ± 7%) in the myoelectric activity of the small intestine as measured by means of the root mean square. Conversely, acupuncture was able to significantly increase (overshoot) this activity compared to baseline (+44 ± 7%). In contrast, immobilized animals subjected to sham acupuncture had only modest (nonsignificant) increases in myoelectric activity (+9 ± 6%). Using carefully controlled conditions we confirmed previous noncontrolled studies on the ability of acupuncture to alter intestinal motility. The characterization of the topographic and temporal profiles of the effects observed here represents a basis for future dissection of the physiological and pharmacological systems underlying these effects.

Measuring higher order optical aberrations of the human eye: techniques and applications

In the present paper we discuss the development of "wave-front", an instrument for determining the lower and higher optical aberrations of the human eye. We also discuss the advantages that such instrumentation and techniques might bring to the ophthalmology professional of the 21st century. By shining a small light spot on the retina of subjects and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberrations (astigmatism, myopia, hyperopia) and higher order aberrations (coma, spherical aberration, etc.). We have measured artificial eyes with calibrated ametropia ranging from +5 to -5 D, with and without 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS) sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes. The HS sensor sends information to a computer software for decomposition of wave-front aberrations into a set of Zernike polynomials. These polynomials have special mathematical properties and are more suitable in this case than the traditional Seidel polynomials. We have demonstrated that this technique is more precise than conventional autorefraction, with a root mean square error (RMSE) of less than 0.1 µm for a 4-mm diameter pupil. In terms of dioptric power this represents an RMSE error of less than 0.04 D and 5º for the axis. This precision is sufficient for customized corneal ablations, among other applications.

Functional changes of human quadriceps muscle injured by eccentric exercise

The present study evaluated functional changes of quadriceps muscle after injury induced by eccentric exercise. Maximal isometric torque of quadriceps and the surface electromyography (root mean square, RMS, and median frequency, MDF) of the vastus medialis oblique (VMO) and vastus lateralis (VL) muscles were examined before, immediately after and during the first 7 days after injury. Serum creatine kinase (CK) levels and magnetic resonance imaging (MRI) were used to identify muscle injury. The subject was used as her own control and percent refers to pre-injury data. Experiments were carried out with a sedentary 23-year-old female. Injury was induced by 4 bouts of 15 maximal isokinetic eccentric contractions (angular velocity of 5º/s; range of motion from 40º to 110º of knee flexion). The isometric torque of the quadriceps (knee at 90º flexion) decreased 52% immediately after eccentric exercise and recovered on the 5th day. The highest reduction of RMS occurred on the 2nd day after injury in both VL (63%) and VMO (66%) and only VL recovered to the pre-injury level on the 7th day. Immediately after injury, the MDF decreased by 5 and 3% (VMO and VL, respectively) and recovered one day later. Serum CK levels increased by 109% on the 2nd day and were still increased by 32% on the 7th day. MRI showed large areas of injury especially in the deep region of quadriceps. In conclusion, eccentric exercise decreased the isometric torque and electromyographic signals of quadriceps muscle, which were recovered in one week, despite the muscle regeneration signals.

Relationship between cardiovascular dysfunction and hyperglycemia in streptozotocin-induced diabetes in rats

Streptozotocin (STZ)-induced diabetes in rats is characterized by cardiovascular dysfunction beginning 5 days after STZ injection, which may reflect functional or structural autonomic nervous system damage. We investigated cardiovascular and autonomic function, in rats weighing 166 ± 4 g, 5-7, 14, 30, 45, and 90 days after STZ injection (N = 24, 33, 27, 14, and 13, respectively). Arterial pressure (AP), mean AP (MAP) variability (standard deviation of the mean of MAP, SDMMAP), heart rate (HR), HR variability (standard deviation of the normal pulse intervals, SDNN), and root mean square of successive difference of pulse intervals (RMSSD) were measured. STZ induced increased glycemia in diabetic rats vs control rats. Diabetes reduced resting HR from 363 ± 12 to 332 ± 5 bpm (P < 0.05) 5 to 7 days after STZ and reduced MAP from 121 ± 2 to 104 ± 5 mmHg (P = 0.007) 14 days after STZ. HR and MAP variability were lower in diabetic vs control rats 30-45 days after STZ injection (RMSSD decreased from 5.6 ± 0.9 to 3.4 ± 0.4 ms, P = 0.04 and SDMMAP from 6.6 ± 0.6 to 4.2 ± 0.6 mmHg, P = 0.005). Glycemia was negatively correlated with resting AP and HR (r = -0.41 and -0.40, P < 0.001) and with SDNN and SDMMAP indices (r = -0.34 and -0.49, P < 0.01). Even though STZ-diabetic rats presented bradycardia and hypotension early in the course of diabetes, their autonomic function was reduced only 30-45 days after STZ injection and these changes were negatively correlated with plasma glucose, suggesting a metabolic origin.