On the polytope escape problem for continuous linear dynamical systems by Ouaknine, J, Sousa-Pinto, J, Worrell, J

“…The Polytope Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function f : R d → R d and a convex polytope P ⊆ R d , both with rational descriptions, whether there exists an initial point x0 in P such that the trajectory of the unique solution to the differential equation ( x˙(t) = f(x(t)) x(0) = x0 is entirely contained in P. …”

Tensor product model transformation in polytopic model-based control / by Baranyi, Peter, Yam, Y., Varlaki, Peter

Hypergraphs of Special Type and CUT Polytope Relaxations Properties Analysis by A. V. Nikolaev

“…The topic of the research is a relationship between a class of hypergraphs of a special type and properties of the points of the cut polytope relaxations $M_{n,k}$. It is established that for a sufficiently large $n$ in $M_{n,4}$ and $M_{n,5}$ polytopes, there are points which have no integer vertices in any expansion in a convex combination of $M_{n,3}$ vertices.…”
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Double Schubert polynomials do have saturated Newton polytopes by Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi, Jonathan Montaño

“…We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. …”
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Entropies from Coarse-graining: Convex Polytopes vs. Ellipsoids by Nikos Kalogeropoulos

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Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering by Benjamin Braun, Kaitlin Bruegge, Matthew Kahle

“…Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. …”
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The Relationship between the Stasheff Polytope and Painted Trees Using Tubings by Shatha Asaad Salman, Anwar Khaleel Faraj, Alaa Sabeeh Dawood

Subjects: “…stasheff polytope…”
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Polytopal Rearrangement Governing Stereochemistry of Bicyclic Oxime Ether Synthesis by Zlatan Spahić, Tomica Hrenar, Ines Primožič

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Quantum sensing using multiqubit quantum systems and the Pauli polytope by Irma Avdic, LeeAnn M. Sager-Smith, Indranil Ghosh, Olivia C. Wedig, Jacob S. Higgins, Gregory S. Engel, David A. Mazziotti

“…Qubit occupations of a pure state obey generalized Pauli exclusion constraints that define a convex set known as the Pauli polytope, and hence violation of one of these constraints—a facet of the polytope—reveals a mixed state from the interaction of a quantum system with its environment without performing full-state tomography. …”
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Toric matrix Schubert varieties and root polytopes (extended abstract) by Laura Escobar, Karola Mészáros

“…We characterize when the ideal defining Xπ is toric (with respect to a 2n − 1-dimensional torus) and study the associated polytope of its projectivization. We construct regular triangulations of these polytopes which we show are geometric realizations of a family of subword complexes. …”
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The Nearest Polytope Problem: Algorithms and Application to Controlling Hybrid Systems by Wu, Albert, Sadraddini, Sadra, Tedrake, Russ

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The Nearest Polytope Problem: Algorithms and Application to Controlling Hybrid Systems by Wu, Albert, Sadraddini, Sadra, Tedrake, Russell L

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Enlargement of polytopic terminal region in NMPC by interpolation and partial invariance by Cannon, M, Kouvaritakis, B, Deshmukh, V, AAC, AAC

“…Polytopic invariant sets have significant advantages over ellipsoidal invariant sets in the design of constrained control laws due to their potential for greater flexibility in shape. …”

How fast can you escape a compact polytope? by D'Costa, J, Lefaucheux, E, Ouaknine, J, Worrell, J

“…The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. …”

Enlargement of polytopic terminal region in NMPC by interpolation and partial invariance by Cannon, M, Kouvaritakis, B, Deshmukh, V

“…This paper uses the concept of partial invariance to derive a sequence of linear programs in order to maximize offline the volume of an invariant polytopic set with an arbitrary predefined number of vertices subject to a bound on closed-loop performance. …”

Interhelical H-Bonds Modulate the Activity of a Polytopic Transmembrane Kinase by Juan Cruz Almada, Ana Bortolotti, Jean Marie Ruysschaert, Diego de Mendoza, María Eugenia Inda, Larisa Estefanía Cybulski

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All Tight Descriptions of 3-Stars in 3-Polytopes with Girth 5 by Borodin Oleg V., Ivanova Anna O.

Subjects: “…3-polytope…”
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Robust linear parameter varying induction motor control with polytopic models by Dalila Khamari, Abdessalem Makouf, Said Drid, Chrifi-Alaoui Larbi

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

“…<p>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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Locating-dominating number of certain infinite families of convex polytopes with applications by Sakander Hayat, Naqiuddin Kartolo, Asad Khan, Mohammed J.F. Alenazi

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