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Kramers-Kronig (KK) equations allow us to obtain the real or imaginary part of linear, causal and time constant functions, starting from the imaginary or real part respectively. They are normally applied on different practical applications as a control method. A common problem in measurements is the lack of data in a wide-range frequency, due to some of the inherent limitations of experiments or practical limitations of the used technology. Different solutions to this problem were proved, such as several methods for extrapolation, some of which based on piecewise polynomial fit or the approach based on the expected asymptotical behavior. In this work, we propose an approach based on the symmetric extrapolation method to generate data in missing frequency ranges, to minimize the estimated error of the KK equations. The results show that with data from impedance measurements of an electrode-electrolyte interface, the adjustment error of the transformed functions can be drastically reduced to below 1%.

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BACKGROUND: Linear analysis has classically provided powerful tools for understanding the behavior of neural populations, but the neuron responses to real-world stimulation are nonlinear under some conditions, and many neuronal components demonstrate strong nonlinear behavior. In spite of this, temporal and frequency dynamics of neural populations to sensory stimulation have been usually analyzed with linear approaches. NEW METHOD: In this paper, we propose the use of Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD), a data-driven template-free algorithm, plus the Hilbert transform as a suitable tool for analyzing population oscillatory dynamics in a multi-dimensional space with instantaneous frequency (IF) resolution. RESULTS: The proposed approach was able to extract oscillatory information of neurophysiological data of deep vibrissal nerve and visual cortex multiunit recordings that were not evidenced using linear approaches with fixed bases such as the Fourier analysis. COMPARISON WITH EXISTING METHODS: Texture discrimination analysis performance was increased when Noise-Assisted Multivariate Empirical Mode plus Hilbert transform was implemented, compared to linear techniques. Cortical oscillatory population activity was analyzed with precise time-frequency resolution. Similarly, NA-MEMD provided increased time-frequency resolution of cortical oscillatory population activity. CONCLUSIONS: Noise-Assisted Multivariate Empirical Mode Decomposition plus Hilbert transform is an improved method to analyze neuronal population oscillatory dynamics overcoming linear and stationary assumptions of classical methods.

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The development of a fully automated on-line monitoring and control system is very important in bioprocesses. One of the most important parameters in these processes is biomass. This review discusses different methods for biomass quantification. A general definition of biomass and biovolume are presented. Interesting concepts about active but not culturable cells considerations are included as well as concepts that must be taken into account when selecting biomass quantification technology. Chemical methods have had few applications in biomass measurement to date; however, bioluminescence can selectively enumerate viable cells. Photometric methods including fluorescence and scattered light measurements are presented. Reference methods including dry and wet weight, viable counts and direct counts are discussed, as well as the physical methods of flow cytometry, impedancimetric and dielectric techniques.

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The electromyographic study of the muscles involved in the complex movements of the shoulder, is usually one way to quantifying the static and dynamic joint's behavior. In particular, the deltoid medium EMG produced a phenomenon similar to a hysteresis cycle when its amplitude was plotted as a function of the lateral angular position during a static, step by step, sequential abduction-adduction of the arm. Such a cycle was consistently repeated in 16 subjects (12 males and 4 females). The paired Student t-test, after comparing the mean EMG values of the rectified wave for the same arm opening angle between abduction and adduction, produced a highly significant difference (alpha<0.001) in all subjects. In all likelihood, it manifests the participation of muscles other than the deltoid medium in the overall movement (as for example, the anterior and posterior deltoids), that is, they are collaborating muscles that are different in the opening or lifting of the arm from those involved in its closure or lowering. Thus, it is concluded that a quantifiable and significant deltoid medium EMG difference has been demonstrated when the muscle is either ready to abduction or ready to adduction. The effect is fully reproducible between 0 and 90 degrees of an arm in static position within the scapular plane.

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Muscle fibre conduction velocity is an important measurement in electrophysiology, both in the research laboratory and in clinical practice. It is usually measured by placing electrodes spaced at known distances and estimating the transit time of the action potential. The problem, common to all methods, is the estimation of this time delay. Several measurement procedures, in the time and frequency domains, have been proposed. Time-domain strategies usually require two acquisition channels, whereas some frequency-domain methods can be implemented using a single one. The method described operates in the time domain, making use of the autocorrelation function of the difference signal obtained from two needle electrodes and only one acquisition channel. Experimental results were obtained from the electromyogram of two biceps muscles (two adult male subjects, nine records each) under voluntary contraction, yielding an average of 3.58 m s(-1) (SD=0.04 m s(-1)) and 3.37m s(-1) (SD=0.03 m s(-1)), respectively. Several tests showed that the proposed method works properly with electromyogram records as short as 0.3 s.

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Classic impedance microbiology (CIM) is based on the measurement of the impedance components that appear between a pair of electrodes submerged in a cell containing inoculated broth. Either a bipolar or a tetrapolar technique can be applied, requiring about 1 x 10(3) to 3 x 10(7) cells/ml to produce detectable changes in the impedance curves. Theoretical analysis of the electrode-electrolyte interface during bacterial growth is lacking, with no generally accepted measuring standards. Besides, there is considerable disagreement. We separated out the interface and medium components using the frequency variation technique (FVT) and also analyzed the interface reactance-resistance diagram, both before and after bacterial growth. Medium resistance Rm, interface reactance Xi, and interface resistance Ri, were quantified as time functions growth curves, from the complex bipolar impedance seen between two electrodes. We took into account the electrical current density, the temperature and the associated circuitry, also explaining the theoretical and experimental bases that justify the proposed dissecting procedure. It was found that, within the working frequency range, Rm, Ri, and Xi percental growth curves are frequency-independent, i.e., neither Rm(f), nor Xi(f) nor Ri(f) changed their slopes before, during and after bacterial growth. Besides, no alpha-dispersion effect in Rm curves was detected. It is concluded that impedance microbiology could become a fertile area for interdisciplinary knowledge; its development might offer new avenues for basic and applied research.

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The impedancimetric method is a technique for the rapid evaluation of milk bacterial content and also of its subproducts. Several authors have made use of culture conductance changes during bacterial growth for quantitative and qualitative assessments of microbial growth. However, interface capacitance curves, Ci, have not been used. In this paper, we quantify bacteria in cow raw milk by following their growth as the above-mentioned capacitance change time course event. With it, bigger growth variations, shorter detection times and a better coefficient of correlation with the plate count method were obtained than those yielded by conductance curves. Calibration was performed by plotting initial known concentrations, IC (CFU/ml), as a function of the time detection theshold (TDT).

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An apparatus for the measurement of bacterial growth is described. The instrument applies alternate adequate sequential currents of two different frequencies through a pair of electrodes immersed in a cultured medium. It monitors, detects and quantifies the growth of micro-organisms based on the measurement of the impedance across the two electrodes and, simultaneously, it measures the variation in the medium turbidity. The medium conductivity and the interface electrode impedance changes can be extracted from the measured impedance. The variations in turbidity can be calibrated in absorbance or optical density units. Moreover, all these parameters are also proportional to bacterial proliferation. The computer-controlled apparatus processes and displays the parameters on a monitor showing bulk resistance, electrode impedance and turbidity changes as time course events. The equipment can detect aerobic or anaerobic micro-organisms and permits the operator simultaneously to assess impedance and turbidity, or it can produce each parameter as a separate event. Time growth curves of different micro-organisms are presented in the results.

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The measurement of a physiological event caused by a change in dimension, conductivity, or permittivity can be easily carried out by the impedance technique, requiring only the application of two or more electrodes, which are easy to apply. In some cases, the impedance is transformed into its resistive and reactive components, in others the total impedance is measured. In certain cases only a change in impedance, with or without separation into its components, contains enough information to be correlated to the physiological event. Recent measurements of physiological data by impedance techniques have reemphasized the value of the painless and harmless acquisition from human and animal subjects in such diverse domains as manned spacecraft, nutrition, and electrical impedance imaging. This part attempts to present all the numerous experiments performed on humans to estimate changes in volume, orientation, and distribution of fluids and tissues accompanying physiological activity. The main sections concern the respiratory system, the cardiovascular system, the brain, the total body impedance, muscle and skin impedance, and bacteriometry.

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We measured impedance in a cell containing culture broth inoculated with E. coli, before and during bacterial growth. The electrode interface impedance components (Ri, Xi) and the culture medium component Rm were separated by making use of the Warburg's model frequency dependent properties. Measurements were carried out at different frequencies (from 18 Hz to 18 kHz) with a constant current impedance bridge as growth proceeded. It was found that: Growth curves for Ri and Xi showed a similar temporal pattern within the frequency range of 18-100 Hz. Dispersion was not observed in Rm, meaning that the same growth response was obtained within the 18-18,000 Hz range. At low frequency, the resistive and capacitive reactive components, or Rb and Xb, respectively, were directly measured, where Rb = (2.Ri + Rm) and Xb = 2.Xi and, at high frequency (above 5 kHz), Rm was obtained (for Zi is negligible). Thus, Ri was easily discriminated from Rm by simple arithmetic: Ri = [Rb (low f) - Rb (high f)]/2. In four experiments, the maximum spread of Xi, Ri, and Rm was smaller than 5%, indicating good repeatability. There is potential new information in dissecting out the growth curve in three separate component curves.

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The digital impedance meter is a microprocessor-based instrument able to detect, quantify and identify micro-organisms. The equipment makes use of the bipolar technique of measuring the impedance modulus of six cells containing inoculated culture broth. It performs temperature compensation automatically. Growth curves are stored in memory as time course events and can be displayed on any suitable device.

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By means of the bipolar impedance technique, we detected bacterial growth in an inoculated broth as its time course absolute impedance. From it, the impedance change relative to sterile medium was obtained, calculating also its time derivative. The repeatability of the derivative curves (they overlapped within a band better than 3.3%) permitted the identification of a double-hump pattern which, in principle, could be accepted as an indicator of the type of bacteria (Escherichia coli). After six experimental series, the growth curves appeared as sensitive to the initial concentration of bacteria and to the culture time preceding inoculation; they were also dependent on the temperature and on the average basal impedance. Temperature showed a greater effect (one order of magnitude) on the lag-phase of the growth curve than on the stationary-phase. This effect occurs because the impedance growth curves tend to get away from the reference offered by the sterile medium. The best working conditions were obtained for an average basal impedance of 510 ohms under well controlled temperature conditions (variations smaller than or equal to 0.20 degrees C) with wire stainless steel electrodes vertically immersed in the culture broth. This impedance technique appears as inexpensive and easy to automatizing for large number of samples.

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