[J.sup.opt] = [s.summation over (k=

[J.sup.opt] = [s.summation over (k=1)][[alpha].sub.k][[phi].sub.k] + [t.summation over (k=1)][[beta].sub.k][[phi].sub.k] + [u.summation over (k=1)][[gamma].sub.k][[phi].sub.k] (4)

Here, the vectors [[phi].sub.k], [[phi].sub.k], and [[psi].sub.k] represent the vertices, rays, and linealities, respectively. Additionally, s, t, and u represent the upper boundaries of the sum functions indicating the number of vertices, rays, and linealities, respectively. Furthermore, [[alpha].sub.k], [[beta].sub.k], and [[gamma].sub.k] represent the weighting coefficient that satisfy the following constraints: [[summation].sup.s.sub.k=1] [[alpha].sub.k] = 1, [[alpha].sub.k] [greater than or equal to] 0, [[beta].sub.k] [greater than or equal to] 0, and [[gamma].sub.k] can take any value. In words, vertices can be summed by a convex combination, rays can be summed as a conical combination, and linealities can be summed as a linear combination.

This Minkowski sum alters (Equation (5)) once we split each reversible reaction into two irreversible reactions, because linealities do not exist anymore.

[J.sup.opt] = [s.summation over (k=1)[[alpha].sub.k][[phi].sub.k] + [t.summation over (k=1)][[beta].sub.k][[phi].sub.k] (5)

Each split reversible reaction fulfills all conditions for a ray, thus many more rays are found when we split each reversible reaction. Each of these additional rays is also an EFM and an extreme pathway which are considered irrelevant because they only reformulate reversibility [32, 40].

CoPE-FBA subnetworks and F-modules

Hasil (Bahasa Indonesia) 1:

[J.sup.opt] = [s.summation atas (k = 1)] [.sub.k [alpha]] [[phi].sub.k] + [t.summation atas (k = 1)] [.sub.k [beta]] [[phi].sub.k] + [u.summation atas (k = 1)] [[gamma].sub.k] [[phi].sub.k] (4)Di sini, vektor [[phi].sub.k], [.sub.k [phi]], dan [[psi].sub.k] mewakili simpul, sinar, dan linealities, masing-masing. Selain itu, s, t, dan Anda mewakili batas-batas atas jumlah fungsi menunjukkan jumlah simpul, sinar, dan linealities, masing-masing. Selain itu, [[alpha].sub.k], [.sub.k [beta]], dan mewakili [[gamma].sub.k] koefisien bobot yang memuaskan kendala berikut: [[penjumlahan].sup.s.sub.k = 1] [[alpha].sub.k] = 1, [[alpha].sub.k] [lebih besar dari atau sama dengan] 0, [[beta].sub.k] [lebih besar dari atau sama dengan] 0, dan [[gamma].sub.k] dapat mengambil nilai apapun. Dalam kata-kata, simpul dapat disimpulkan oleh kombinasi cembung, sinar dapat disimpulkan sebagai kombinasi kerucut, dan linealities dapat disimpulkan sebagai kombinasi linear.Jumlah Minkowski ini mengubah (persamaan (5)) setelah kita membagi setiap reaksi reversible menjadi dua reaksi ireversibel, karena linealities tidak ada lagi.[J.sup.opt] = [s.summation atas (k = 1) [[alpha].sub.k] [.sub.k [phi]] + [t.summation atas (k = 1)] [.sub.k [beta]] [[phi].sub.k] (5)Reaksi reversible split setiap memenuhi semua kondisi untuk sinar, sehingga lebih banyak sinar ditemukan ketika kita membagi setiap reaksi reversibel. Setiap dari sinar ini tambahan ini juga EFM dan jalur ekstrim yang dianggap tidak relevan karena mereka hanya merevisi reversibility [32, 40].Mengatasi-FBA Subnetwork dan F-modul