IGBP1 protein, human

In order to investigate cross-frequency interactions we have developed a tool calculating coherence between a low frequency signal and the time-course of the power at higher frequencies. Let the signal {X_t} be represented by the time series X₁, X₂, …, X_N. First, the time-course of power S₁(f₂), S₂(f₂), …, S_N(f₂) was estimated for frequency f₂ by applying a sliding tapered time-window followed by a Fourier transformation:
Here where is the sampling frequency. The function is a Hanning taper K data points-long equaling the length of the sliding time window. The length of the time-window decreased with frequency: where M denoted the numbers of cycles per time window. We chose to use M = 7 cycles (for the intracranial data we used M = 6 cycles). Next, the coherency Coh(f₁,f₂) was estimated between signal {X_t} and the estimate of the time-course of power{S_t(f₂)} for a given frequency f₁. The coherency was calculated with respect to the two time series divided into M segments being L = 2048 data points long (for the intracranial data we used L = 1024 due to the lower sampling frequency): where
The coherence was the absolute value of the coherency . The phase difference between the signal at f₁ and the power at f₂ is given by the angle of the coherency . In this case refer to a 2048 points Hanning window and ^* to the complex conjugate. This allowed us to characterize the phase-to-power cross-frequency interaction with respect to f₁ and f₂ sensor by sensor. To assess reliability of the estimated coherence, a statistical analysis was performed by randomly shifting the time course of signal {X_t} (at least 3001 points) with respect to the estimated power {S_t(f₂)} and recalculating the coherence for the channel with the most pronounced effect (based on visual inspection). Repeating this 200 times yielded a distribution of coherence values. Further, a maximum coherence value between the alpha band and any of the frequencies between 2 and 100 Hz has been identified in every randomization. The proportion of the randomization coherence values above the coherence value to be tested corresponded to the p-value.
In order to assess phase relationship between alpha and gamma power, we bandpass-filtered the MEG data +/−4 Hz of the alpha peak frequency determined from the power spectra in each subject with acausal FFT filter. Next, 0.6 s of unfiltered epochs of data phase aligned to the alpha cycles were extracted. This was done by identifying the peaks of the alpha cycles in the bandpass-filtered data. Time-frequency representations (TFRs) of power were calculated for each segment using Fourier transforms calculated for short sliding time windows. Power estimates were averaged across trials. We applied a Hanning taper to an adaptive time window of 6 cycles for each frequency between 2–150 Hz (ΔT = 6/f). This analysis was done using the FieldTrip toolbox (http://www.ru.nl/neuroimaging/fieldtrip).

Moisture, crude protein, and crude lipid in the whole fish body were analyzed by AOAC (1995). Moisture was measured by drying samples at 110°C to a constant weight. Crude protein was measured based on the Kjeldahl method, and crude lipid was measured by the Soxhlet extraction method (FOSS, Soxtec 2050).
The freeze dryer (ALPHA 1–4 LD freeze dryer, Kleist, Germany) was used to dry the raw materials and experimental diets to a constant weight at –50°C. The automatic amino acid analyzer (L-8900, Hitachi) was used to determine the amino acid profiles of freeze-dried samples after acid hydrolysis (6 N HCl at 110°C for 24 h).

Plant samples were collected for laboratory analyses in individual experimental plots. Five consecutive stalks (which were cut with a sharp knife above the soil) were taken completely randomly in five places. The samples were put in a plastic bag, labelled immediately upon arrival from the field. The tillers were incubated in the laboratory storage at 5 °C and 90% RH. After 3 days the samples were cut and well mixed. A representative from each sample was frozen and stored at least at −20 °C in a freezer (Whirpool AFG 6402 E-B, Benton Harbor, MI, USA). For laboratory analyses the frozen material was freeze-dried (Alpha model 1–4 LSC, Martin Christ, Osterode, Germany). The materials were lyophilized to permanent weight with a moisture content <2%. Dried wheats were also milled to obtain a fine powder (particle size 0.3–0.5 mm mesh) using an Ultra-Centrifuge Retsch mill ZM 100 (Retsch, Germany). The ground samples were stored in the dark in air-tight bags in desiccators.