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Estimation of I0 can be further reformulated in terms of testing the hypotheses β1= 0,…,βp="0.
The resulting model is formulated as a two-stage stochastic mixed-integer bilevel nonlinear program, which can be further reformulated into a tractable single-level stochastic mixed-integer linear program by applying KKT conditions and Glover's linearization method.
Substitute (30) into (18), the maximization problem of secrecy capacity can be further reformulated as begin{aligned} max_{{mathbf{w}}_{R}}quad &frac{{mathbf{w}}_{R}^{H}{widetilde{mathbf{G}}{mathbf{w}}_{R}}}{{mathbf{w}}_{R}^{H}{widetilde{mathbf{H}}{mathbf{w}}_{R}}} mathrm{s.t.} quad&|{mathbf{w}}_{R}|^{2}leq{P_{t}-P_{j}} end{aligned} (31).
According to the expression of the maximum Doppler frequency (4), the SNR state transition probabilities with the actual speed v1can be further reformulated as p k, k + 1 1 ≈ 2 Π Γ k + 1 m γ rd 0 v 1 f c c e − Γ k + 1 m γ rd 0 T s e − Γ k m γ rd 0 − e − Γ k + 1 m γ rd 0, (29).
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These constrained optimization problems are further reformulated to unconstrained optimization problems by a vector space approach.
The relaxed sub-problem for location and service allocation decisions is further reformulated into a second-order conic program.
Using the Kronecker product, the high-cost MUSIC function is further reformulated as an eigenvector-based optimization problem, and a new low-complexity cost function with spatial aliasing is derived.
To investigate whether the rMM model (with affinities in the millimolar range) could be further improved or not, we reformulated the ODE model as an SDE model.
The approach was further improved by reformulating the simulation formulas where the order in which the summation operations are executed is imposed.
(The rule was later invalidated by the courts, and is now being reformulated).
In our study non- or partial responders from step 1 were further randomised to a controlled study with a reformulated, intensified CBT or SSRI (+ CBT-support as defined).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com