Perfect Prismatoids and the Conjecture Concerning Face Numbers of Centrally Symmetric Polytopes by M. A. Kozachok

“…In this paper we introduce and study a class of centrally symmetric polytopes – perfect prismatoids – and some its properties related to the famous conjecture concerning face numbers of centrally symmetric polytopes are proved. …”
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Some 0/1 polytopes need exponential size extended formulations by Rothvoss, Thomas

“…We prove that there are 0/1 polytopes P⊆R[superscript n] that do not admit a compact LP formulation. …”
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Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs by Kalman, Tamas, Postnikov, Alexander

“…Let G be a connected bipartite graph with colour classes E and V and root polytope Q. Regarding the hypergraph H=(V,E) induced by G, we prove that the interior polynomial of H is equivalent to the Ehrhart polynomial of Q, which in turn is equivalent to the h-vector of any triangulation of Q. …”
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Foundations of space-time finite element methods: Polytopes, interpolation, and integration by Frontin, Cory V, Walters, Gage S, Witherden, Freddie D, Lee, Carl W, Williams, David M, Darmofal, David L

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Polytopes, generating functions, and new statistics related to descents and inversions in permutations by Chebikin, Denis

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Combinatorics of colored factorizations, flow polytopes and of matrices over finite fields by Morales, Alejandro Henry

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Computing bounds on network capacity regions as a polytope reconstruction problem by Kim, Anthony, Medard, Muriel

“…We show that the network routing capacity region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the region. …”
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Asymmetric constraints with polytopic sets in MPC with application to coupled tanks system by Kouvaritakis, B, Cannon, M, Karas, A, Rohal-Ilkiv, B, Belavy, C

“…The paper embeds these results into an MPC law based on a dual mode prediction strategy and proposes algorithms for the systematic design of the polytopic terminal sets. The efficacy of the results is illustrated through application to a coupled tanks system. …”

Geometric combinatorics and computational molecular biology: Branching polytopes for RNA sequences by Harrington, H, Drellich, E, Gainer-Dewar, A, He, Q, Heitsch, C, Poznanovic, S

“…Techniques from geometric combinatorics, including polytopes and their normal fans, have been used previously to give parametric analyses of simple models for DNA sequence alignment and RNA branching configurations. …”

On the quadrature of multivariate highly oscillatory integrals over non-polytope domains by Olver, S

“…Unlike existing methods, we do not require the knowledge of moments, which enables us to derive an approximation when the oscillator is complicated, and when the domain is neither a simplex nor a polytope. The accuracy of this method improves as the frequency of oscillations increases. …”

On bounded partition dimension of different families of convex polytopes with pendant edges by Khali, Adnan, Said Husain, Sh. K, Nadeem, Muhammad Faisal

“…In this paper, we studied partition dimension of the some families of convex polytopes with pendant edge such as RPn , Dpn and Qpn and proved that these graphs have bounded partition dimension.…”

Pembinaan isipadu persempadanan orientasi diskrit politop dinamik menggunakan API XNA / by Nur Saadah Mohd. Shapri, Universiti Teknologi Malaysia. Fakulti Sains Komputer dan Sistem Maklumat 1352, Universiti Teknologi Malaysia. Pusat Pengurusan Penyelidikan 520

Subjects: “…Polytopes…”

Improved strategies of the Equality Set Projection (ESP) algorithm for computing polytope projection by B. Pei, B. Pei, W. Xu, Y. Li

“…<p>​​​​​​​This paper proposes an optimization method for the Equality Set Projection algorithm to compute the orthogonal projection of polytopes. However, its computational burden significantly increases for the case of dual degeneracy, which limits the application of the algorithm. …”
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Characteristics of Complexity: Clique Number of a Polytope Graph and Rectangle Covering Number by A. N. Maksimenko

“…Bondarenko found that the clique number of the graph of a polytope in many cases corresponds to the actual complexity of the optimization problem on the vertices of the polytope. …”
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Core Index of Perfect Matching Polytope for a 2-Connected Cubic Graph by Wang Xiumei, Lin Yixun

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Construction of Fullerenes and Pogorelov Polytopes with 5-, 6- and one 7-Gonal Face by Nikolai Erokhovets

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Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties by Khalid A. Alattas, Ardashir Mohammadzadeh, Saleh Mobayen, Hala M. Abo-Dief, Abdullah K. Alanazi, Mai The Vu, Arthur Chang

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Imputing Phylogenetic Trees Using Tropical Polytopes over the Space of Phylogenetic Trees by Ruriko Yoshida

“…In our approach, we consider a tropical polytope, a convex hull with respect to the tropical metric closest to the data points. …”
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Switched Polytopic Controller Applied on a Positive Reconfigurable Power Electronic Converter by Martín-A. Rodríguez-Licea, Francisco-J. Perez-Pinal, Alejandro-I. Barranco-Gutiérrez, Jose-C. Nuñez-Perez

“…In order to overcome these challenges, this paper proposes a kind of switched polytopic controller (SPC) suitable to stabilize an RPEC. …”
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On the Stability of a class of Polytopes of third order square matrices and stability radius by Efrén Vázquez Silva

“…In this work we investigate the stability properties of a convex symmetric timeinvariant third order matrix's polytope depending on a real positive parameter $r$. …”
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