fenchel duality theoremnetwork performance analysismin-plus algebraNetwork calculus has successfully been deployed to derive deterministic performance bounds in packet-switching networks. Recently, the deployment of the conjugate convex or concave transforms has been proposed as dual approach to this calculus...
The relationship between structure and function is fundamental in complex systems1,2,3, and important efforts have been invested in developing network models to better understand it. In particular, models of dynamics on networks4,5,6,7have been proposed to assess the influence of network structure...
What is complex analysis in mathematics? What is a field in abstract algebra? What is Rolle's Theorem and how do you find "c"? What is Kahler manifold? What is the topological dimension of Cantor set? What is spectral theorem and why is it useful?
We establish this difference in Theorem 3 of this paper. To overcome this drawback, contrary to the RDEA formulation in the literature, the starting point of the RDEA formulation in this paper is rather a robust fractional DEA (RFDEA) based on the budget uncertainty set of Bertsimas & Sim ...
We present an improvement of a recent duality theorem and a new result which stresses the fact that the strong duality, without assumptions on the interior of the ordering cone, is related to the normal cone.This is a preview of subscription content, log in via an institution to check access...
even in the case\(p=\frac{1}{2}\)where we a priori need one bit per possible edge to fully reconstructG. Consequently, the knowledge ofXreduces uncertainty aboutG(i.e.,H(G∣X) ≤ H(G), see ref.82, Theorem 2.6.5), and therefore allows for its reconstruction;I (X; G...
Now, we turn to the physical properties of the lifted MERA state that are distinct from the MERA. The MERA has polynomially decaying correlation functions; this behaviour is one of the reasons that the MERA is viewed as a good tensor network to approximate critical theories. In contrast, the...
It is similar to that in the case of a1 > a2 where the dual feasible spaces are also three subsets of R× Rn: (20) Hence, on the dual feasible spaces, the canonical dual problem () can be formulated as (21) Theorem 1 (perfect duality theorem). Suppose that vector is a stationa...
Understanding symmetries of VOAs with all the technical details is important for our construction, so in section 3.2 we recount the classic story about lifts from the underlying lattice, Kac's theorem for finite order automorphisms of Lie algebras, and a (computer-implementable) way to compute ...
In recent work (Lohmann et al. in J Math Pures Appl, 2022, https://doi.org/10.1016/j.matpur.2022.05.021 , Theorem 1.3.4) we have shown the equivalence of t