For p i, i = 1, 2, ⋯, n, introduce a latent variable Z i where for hypothesis testing (1), we have (2) { Z i = 0 if H 0 : no GxG for the i th test (Pattern 1, Pr (P ≤ p ) = p ) Z i = 1 i f H a : GxG for the i th test (Pattern 2, Pr (P ≤ p ) > p ), for p ∈ (0, 1 ).
When using this smoothing approach, for each GAM component, the smooth function is reduced to a linear combination of B-splines f i = B i α i, where for each i = 1,…, p, B i is the B-splines matrix of N × m dimension (N number of observations and m number of knots).
The model that we adopt is a joint probability model for the outcome y i and profile X i, where for each individual, independent of every other, (1) p (Y i, X i | Θ ) = ∑ c = 1 ∞ ψ c p (Y i | Θ c, Θ 0 ) p (X i | Θ c, Θ 0 ).
Put differently, with a1, a2, …, a K denoting the vertices of the simplex S K−1 representing a dataset X found in step I, any of its accessions x can be expressed as x = ∑ i = 1 K λ i a i, where, for all 1 ≤ i ≤ K, the quantity λ i ≥ 0 is the genetic contribution of founder a i to x and ∑ i = 1 K λ i = 1.
If there are n i at-risk periods for patient i, then the complete information for patient i can be represented by n i triplets (Y i 11, Y i 12, Δ i 1 ),..., (Y i n i 1, Y i n i 2, Δ i n i ) where, for the jth triplet, Y ij 1 is the start of the jth at-risk period, Y ij 2 is the end of the jth at-risk period, Δ ij is the censoring indicator and Y i 11 = 0.
Given a disjoint pair I and J of { 1, 2, …, m }, we can consider a quasi-ordered set ( R m, ≼ I ( m ) ) that depends on I, where, for any x, y ∈ R m, x ≼ I ( m ) y if and only if x ( k ) ≤ y ( k ) for k ∈ I and y ( k ) ≤ x ( k ) for k ∈ J. Then we have the following interesting existence.
Consider a Lie algebra ( L, ) over a field k with a well-ordered linear basis X = { x i | i ∈ I } and multiplication table S = { [ x i x j ] = [ | x i x j | ] | i > j, i, j ∈ I }, where for every i, j ∈ I we write [ | x i x j | ] = Σ t α i j t x t with α i j t ∈ k.
The percentage GC content of each calculated bin (GC i, where i stands for individual bins) was computed for GC normalization.
In case of packet transmission failure due to fading or collisions, source node after sensing for DIFS duration backs off for a random duration that is uniformly distributed over the contention window interval [0, CW i ], where for the i th retransmission attempt CW i = 2 i CWmin and CW i ∈ [CWmin, CWmax].
The concept (1) BUA was described as that for each exon c i from C it is possible to find a best assembly ended with c i, i.e., g u (c i ) = < c1',... c i >, where for all other assembly g' ended with c i, P(g u (c i ))> = P(g').
The center effects are modeled by γ0 i where γ01 = 0 for identifiability constraint.
