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Fig. 2 Derivation of threshold values regarding states of preservation (A C; [6]) related to system stress (FFH regulation [33]).

The calculation of the power increase is detailed in Appendix 2: derivation of Δ P in Algorithm 2. Next, it computes a benefit value b k that indicates how beneficial it is to increase the power for link k in terms of bit/sec/Hz/mW, i.e., what is the gain of the increased SINR in capacity for that link.

Additional file 2 Derivation of Equation   1.

Additional file 2: Derivation of the full conditional likelihood function.

(PDF 1894 kb) Additional file 2 Derivation for steady state rate equation.

The steps in the analyses were as follows: 1) analysis of item dimensionality; 2) derivation of item parameters and option characteristic curves (OCCs); 3) analysis of item fit; and 4) analysis of differential item functioning.

During treatment, power was increased in this frequency range independent of EEG location (Treatment: F1,7 = 16.2, p =.005; Derivation: F2,14 = 2.5, p >.1; Treatment X Derivation: F2,14 = 0.6, p >.4; 2-way rANOVA with factors Treatment and Derivation).

Vigilance states were visually scored from the records of the C3-A2 derivation for consecutive 20-s epochs according to standard criteria (Rechtschaffen and Kales 1968).

A 3-way rANOVA with the factors Treatment, Derivation and Non-REM sleep period revealed significant main effects (Treatment: F1,7 = 10.4, p <.02; Derivation: F2,14 = 7.5, p <.02; Non-REM sleep period: F2,14 = 45.3, p <.001), as well as a significant Derivation X Non-REM sleep period interaction (F4,28 = 4.5, p <.03).

A 2-way rANOVA with the factors Treatment and Derivation on log-transformed averaged power values in the 2.0 3.25 Hz, 8.5 10.25 Hz and 11.5 13.0 Hz bands revealed significant main effects (Treatment: minimum F1,7 = 9.7, p <.02; Derivation: minimum F2,14 = 5.6, p <.02), yet no Treatment X Derivation interactions.

We assume a 70% follow-up rate (30% attrition) and as such, we anticipate including T1D Derivation (n=128), T1D Validation (n=128) and a T2D Derivation (n=84) and T2D Validation (n=84) sets.