In order to exclude a possible trivial explanation that MG-132 might directly interfere with DNA-PK activity, lysates of PC-3 cells were incubated with MG-132 and studied for p53 phosphorylation.
Thus, in the paper, we significantly reduce the dictionary column size n by excluding the trivial template, while restricting the sparsity k to a relatively low value, e.g., k=10 in our experiments.
Therefore, excluding this trivial case, E ( u ) has no minimizer in W 1, 2.
In particular, when c 3 = 0, excluding the trivial solutions for (24), we are able to write the solution (25) for α 1 = 3 ( − 1 + e 2 + ( e 2 − 1 ) 2 + 4 e 3 − 4 e 1 ) and α 2 = − 6.
The assumption that each of the twelve parameters α i, β i, γ i, A i, B i and C i for i ∈ { 1, 2 } can be zero or positive and the inequalities in hypotheses (2) imply that for i = 1 there are 2 3 − 1 = 7 ways to choose the numerator of the first member of system (1) excluding the trivial case α 1 = β 1 = γ 1 = 0. Similarly, there are seven ways to choose the denominator.
As described in [6], excluding the trivial operations like reordering, the following signal processing tasks need to be performed at the transceiver: Transformation of the data signal of each subcarrier into the frequency domain Filtering in the frequency domain Transformation of the signal into the time domain.
HO-2 protein levels were not up-regulated in HO-1−/− mice, therefore excluding this trivial compensatory mechanism.
CHD was defined as the presence of right-sided valvular regurgitation or stenosis (excluding both trivial or mild findings [ 23]) plus morphologic changes including thickening, shortening, retraction, hypomobility or incomplete coaptation of the affected valves [ 2, 4].
Notice that a random set is intrinsically different from a true negative set: while negative and positive sets should be logically distinct, positive and random sets may overlap regardless of the size of the sets (excluding the trivial scenario of empty positive/random sets).
We use the Euclidean distances between α-carbons to construct a distance matrix D. Using a threshold of 8 Å to define "contact," and excluding trivial contacts (defined as those between residues that are separated by fewer than two intervening residues in the sequence), we convert D to a Boolean contact matrix C, where 1 represents "contact" and 0 represents "no contact".
