Median smoothing

Table 3.5 A sequential process illustration of moving average and median smoothing.

Comparison of moving average (MA) and running median smoothing (RMS)... 

Each type of smoothing function removes different features in the data and often a combination of several approaches is recommended especially for real world problems. Dealing with outliers is an important issue sometimes these points are due to measurement errors. Many processes take time to deviate from the expected value, and a sudden glitch in the system unlikely to be a real effect. Often a combination of filters is recommend, for example a five point median smoothing followed by a three point Hanning window. These methods are very easy to implement computationally and it is possible to view the results of different filters simultaneously. 

Calculate three and five point median smoothing functions (denoted by 3 and 5 ) on the data (to do this, replace each point by the median of a span of N points), and plot die resultant graphs. 

Re-smoodi die three point median smoothed data by a furdier diree point median smoothing function (denoted by 33 ) and dien further by a Hanning window of die form Xj = 0.25a, + 0.5a-, + 0.25.v,+ (denoted by 33H ), plotting bodi graphs as appropriate. 

Moving Medians Smoothing n An alternate term for running medians smoothing. 

Input mapping methods can be divided into univariate, multivariate, and probabalistic methods. Univariate methods analyze the inputs by extracting the relationship between the measurements. These methods include various types of single-scale and multiscale filtering such as exponential smoothing, wavelet thresholding, and median filtering. Multivariate methods analyze... 

Dopamine is an intermediate product in the biosynthesis of noradrenaline. Furthermore it is an active transmitter by itself in basal ganglia (caudate nucleus), the nucleus accumbens, the olfactory tubercle, the central nucleus of the amygdala, the median eminence and some areas in the frontal cortex. It is functionally important, for example in the extra-pyramidal system and the central regulation of emesis. In the periphery specific dopamine receptors (Di-receptors) can be found in the upper gastrointestinal tract, in which a reduction of motility is mediated, and on vascular smooth muscle cells of splanchnic and renal arteries. Beside its effect on specific D-receptors, dopamine activates, at higher concentrations, a- and -adrenoceptors as well. Since its clinical profile is different from adrenaline and noradrenaline there are particular indications for dopamine, like situations of circulatory shock with a reduced kidney perfusion. Dopamine can dose-dependently induce nausea, vomiting, tachyarrhythmia and peripheral vasoconstriction. Dopamine can worsen cardiac ischaemia. 

In order to supress unrealistic daily variation of the threshold, we smooth with an eleven points median function and with a four degrees polynomial function. All the filaments events when correponding to PV values higher then threshold are detected. 

Figure 6.3 Quantal effects. Typical set of data after administration of increasing doses of drug to a group of subjects and observation of minimum dose at which each subject responds. Data shown are for 100 subjects dose increased in 0.2 mg/kg of body weight increments. Mean (ji) (and median) dose is 3.0 mg/kg standard deviation (v) is 0.8 mg/kg. Results plotted as histogram (bar graph) showing number responding at each dose smooth curve is normal distribution function calculated for ji of 3.0 and v of 0.8.

The B score (Brideau et al., 2003) is a robust analog of the Z score after median polish it is more resistant to outliers and also more robust to row- and column-position related systematic errors (Table 14.1). The iterative median polish procedure followed by a smoothing algorithm over nearby plates is used to compute estimates for row and column (in addition to plate) effects that are subtracted from the measured value and then divided by the median absolute deviation (MAD) of the corrected measures to robustly standardize for the plate-to-plate variability of random noise. A similar approach uses a robust linear model to obtain robust estimates of row and column effects. After adjustment, the corrected measures are standardized by the scale estimate of the robust linear model fit to generate a Z statistic referred to as the R score (Wu, Liu, and Sui, 2008). In a related approach to detect and eliminate systematic position-dependent errors, the distribution of Z score-normalized data for each well position over a screening run or subset is fitted to a statistical model as a function of the plate the resulting trend is used to correct the data (Makarenkov et al., 2007). 

To measure pressure, an enlarged tracing of the record was made and a smooth median line drawn through the vibrations. The intersection of this median line with the rise line (not visible in Figure 5 because of low intensity) was taken as the detonation pressure. 

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