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First, the partial distortions M i for each frame in the video sequence have been calculated.
w = wm i k i × k i m i, for w = t P i + s i (3).
C and D based on M i, for i = 1, 2, and 3, are calculated, and the distances to target A are computed.
As explained in Section 4.1, the value of m i for node n i is determined from the relative values of Eresidual(i) and Ethreshold(i).
Lemma 8 Let { a m 1 }, { a m 2 }, …, { a m n }, { b m 1 }, { b m 2 }, …, { b m n } ⊂ [ 0, ∞ ) be 2n sequences of non-negative real numbers and suppose that there exist ψ, φ ∈ Ψ such that ψ ( a m + 1 i ) ≤ ( b m i ) for all i and all m, and ψ ( max 1 ≤ i ≤ n b m i ) ≤ ψ ( max 1 ≤ i ≤ n a m i ) for all m. Then { a m i } → 0 for all i. Proof Let c m = max 1 ≤ i ≤ n a m i for all m.
Then, having observed the magnitude data M i for each hypocenter's coordinates (x i, y i ) with i = 1,2,…, N, the current likelihood function of θ can be written by for M i > Mc.
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$$\end{documentt} B ' : = g ∈ G ∣ g, m ∈ I for all m ∈ B. Then, a formal concept is a pair (A, B) with A′ = B and B′ = A.
TH x broadcasts a request to {M i } for establishing a group key, after appending its identity, velocity, GPS, and the list of {M i } within a particular sequence, denoted as NList x to the request.
CytoSolve as shown in Fig. 2c uses a dynamic messaging approach to exchange data via message passing across the ensemble of models, { M i } (for i = 1 to D) to evaluate the integrated solution.
This Appendix provides the theoretical framework and the conditions upon which integrating an ensemble of molecular pathway models, { M i } (for i = 1 to D) yields the dynamically integrated solution O is possible.
On μ(N) we will consider the ordering induced by the product partial order on ℕ n ; that is, (m1,…, m n )≥(m′1,…, m′ n ) if and only if, m i ≥ m′ i for each i=1,…, n.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com