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Results indicate that the gap between the optimal value and the proposed method followed the same trend as for smaller problem sizes.
Scatter plot between the optimal value of the weight associated to the visual stream in the audio-visual classifier and the performance of the corresponding visual stream in lipreading experiments.
Even when the error in IBO for BER optimization goes from 0.55 dB for SNR d =10 to 1.73 dB for SNR d =30 dB, the BER difference between the optimal value and the theoretical bounds is not very large since BER curves are rather flat around the optimum.
Specifically, the columns of Tables 2 5 evidence the average, the maximum, and the minimum of: the solution time, the gap (i.e., the difference between the optimal value found and the value of linear relaxation at the root node of the search tree, divided by the optimal value), and the number of nodes expanded in each group of instances belonging to a given dataset.
The established relationship between the optimal value of q and related model parameters, which is also shown in Figure 4, is given by (10) q ¯ = 0. 4570 n + 0. 8567.
Water enters mathematical programming models as an input constraint, such that its marginal value is found by relaxing the water constraint by adding a unit to the water available for production and calculating the difference between the optimal value before and after relaxing the constraint.
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In the above mentioned ratio, the nominator represents the difference between cx* (the optimal value of model (2)) and the cost of the ideal point, i.e., cx I.
The trade-off between the optimal values of Z1 and Z2 shows a reverse relation, which is similar to the result observed in the previous example.
In this table, column Δ opt/|G| displays the ratio between the optimal values, represented by Δ opt(G 1,G 2), and |G|.
Usually, there is a so-called duality gap between the optimal values of primal problem ( P ) and its Lagrange dual problem ( D ).
The degree of relation [Γ(x i, xj)] denotes the relationship between the potential causes and the optimal value of the decision factors and is expressed as Eq. (5).
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between the maximum value
between the optimal lag
between the optimal control
between the optimal threshold
between the optimal scheme
between the optimal policy
between the optimal choice
between the optimal sum-secrecy-rate
between the optimal resource
between the optimal block
between the optimal assignment
between the optimal a-out-of-b
between the optimal mesenchymal
between the optimal order
between the optimal power
between the optimal weight
between the optimal throughput
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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