To do this, a commonly used approach consists to calculate the Choquet integral directly from the values provided by the decision maker for the interaction indices I 2 ( A ), and by using the expression of C v given by Grabisch in [28]: C v ( z ) = ∑ i, j ∈ N | I ij > 0 ( z i ∧ z j ) I ij + ∑ i, j ∈ N | I ij < 0 ( z i ∨ z j ) | I ij | + ∑ i ∈ N z i ϕ i − 1 2 ∑ j ≠ i I ij, (1).
The volume of the ion exchanger in mass unit of the membrane has been estimated as ϵ m / − ϵ m m / ρ b, and the porosity of the HZD layer ϵ ¯ was calculated using the expression: ϵ ¯ = V micr / − V micr ρ b mπ ϵ m / − ϵ m. (6).
We estimate the optical properties of the blood-free kidney with the expression µ′s = (1− ϕv) µ′s,ev, where ϕv ≈0.07 is the average vascular volume fraction determined from our vascular corrosion casts; the value of the reduced scattering coefficient of the bulk extravascular tissue, µ′s,ev, is estimated using the expression µ′s,ev = µ′s − ϕv µ′s,v/(1− ϕv)≈4.3cm−1.
Fitting the observed beta-diversity using the expressions obtained from eq. (1) when v'i = v' and d'i = d' yields v' = 2.2 ·10−5 and d' = 3.82 ·10−5, corresponding to the modelled beta-diversity curves indicated by solid lines in Figure 3.
Similarly, for a general reversible reaction, we used the expression form: (3) r = g v f ∏ i A i m i − v b ∏ j B j m j, where v f and v b were determined as follows: (4) v f = βv and v b = β − 1 v, if v > 0, (5) v f = β − 1 v and v b = βv, if v < 0, where β is a parameter that relates the rate of the forward and backward reactions to the overall flux at the reference condition.
@whitehouse just used the expression "FTW".
The data Quality Control was performed using the Affymetrix Expression Console v 1.1 (Affymetrix, Santa Clara, CA, USA) software to check whether all parameters met the quality specifications.
Therefore, the average distance in the overlapped area will be defined using the following expression: D o v = ∑ ( i, j ) ∈ I A B A p j ⋅ | a i j - b i j | ∑ ( i, j ) ∈ I A B A p j = ∑ ( i, j ) ∈ I A B j ⋅ | a i j - b i j | ∑ ( i, j ) ∈ I A B j (11).
Apoptosis was evaluated by measuring Annexin-V expression using the Annexin-V FITC kit (Becton Dickenson, Oxford, UK).
Following staining of the microarray, the fluorescent images were detected in a GeneChip® Scanner 3000 and expression data were extracted using the GeneChip Command Console Software AGCCC) v 2.0 (Affymetrix).
