Root system chip-firing by Hopkins, Samuel F

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Trajectory planner for agile flights in unknown environments by Tordesillas Torres, Jesús.

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Message Passing for Maximum Weight Independent Set by Sanghavi, Sujay, Shah, Devavrat, Willsky, Alan S.

“…We show that each fixed-point estimate of max product can be mapped in a natural way to an extreme point of the linear programming (LP) polytope associated with the MWIS problem. However, this extreme point may not be the one that maximizes the value of node weights; the particular extreme point at final convergence depends on the initialization of max product. …”
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Causal and causally separable processes by Ognyan Oreshkov, Christina Giarmatzi

“…For a fixed number of settings and outcomes for each party, these correlations form a polytope whose facets define causal inequalities. The case of quantum correlations in this paradigm is captured by the process matrix formalism. …”
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Sparse sums of squares on finite abelian groups and improved semidefinite lifts by Fawzi, Hamza, Saunderson, James F, Parrilo, Pablo A

“…Putting N=d2 gives a family of polytopes in R2d with linear programming extension complexity Ω(d2) and semidefinite programming extension complexity O(dlog(d)). …”
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New Theory and Algorithms for Convex Optimization with Non-Standard Structures by Zhao, Renbo

“…In the second chapter, we present and analyze a new away-step Frank-Wolfe method for the convex optimization problem min𝑥∈𝒳 𝑓(A𝑥) + ⟨𝑐, 𝑥⟩, where 𝑓 is a 𝜃-logarithmically-homogeneous self-concordant barrier, A is a linear operator, ⟨𝑐, ·⟩ is a linear function and 𝒳 is a nonempty polytope. We establish the global linear convergence rate of our Frank-Wolfe method in terms of both the objective gap and the Frank-Wolfe gap. …”
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Heterotic string models on smooth Calabi-Yau threefolds by Constantin, A

“…Any two half-polytopes over a given slice can be combined into a reflexive polytope. …”

Discrete–geometric functions associated to polyhedral cones and point sets by Wang, Xinli

“…We present a close relationship between the function associated to integral cones and the classical Dedekind sums. The theory of the polytope algebra—the universal group for translation-invariant valuations—was developed by many mathematicians (see [MS83], [Bri97]). …”
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New Calabi–Yau manifolds from genetic algorithms by Per Berglund, Yang-Hui He, Elli Heyes, Edward Hirst, Vishnu Jejjala, Andre Lukas

“…Calabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. …”
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New Calabi–Yau manifolds from genetic algorithms by Berglund, P, He, Y-H, Heyes, E, Hirst, E, Jejjala, V, Lukas, A

“…Calabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. …”

On r-stacked triangulated manifolds by Satoshi Murai, Eran Nevo

“…The notion of $r$-stackedness for simplicial polytopes was introduced by McMullen and Walkup in 1971 as a generalization of stacked polytopes. …”
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Constrained control of SISO bilinear systems by Bacic, M, Cannon, M, Kouvaritakis, B

“…Then, it is shown that invariant polytopes based on bilinear controllers can be much larger. …”

Robust MPC for linear systems with bounded multiplicative uncertainty by Evans, M, Cannon, M, Kouvaritakis, B, IEEE

“…The tubes are defined by sequences of polytopic sets for which we propose two methods of construction, respectively employing low-complexity parallelotopes and polytopes of fixed but arbitrary complexity. …”

Positive geometries for all scalar theories from twisted intersection theory by Nikhil Kalyanapuram, Raghav G. Jha

“…We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. …”
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Affine Subspace Concentration Conditions by Kuang-Yu Wu

“…We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold for smooth and reflexive polytopes with barycenter at the origin. …”
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Polypositroids by Thomas Lam, Alexander Postnikov

“…We initiate the study of a class of polytopes, which we coin polypositroids, defined to be those polytopes that are simultaneously generalized permutohedra (or polymatroids) and alcoved polytopes. …”
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Coxeter submodular functions and deformations of Coxeter permutahedra by Ardila, Federico, Castillo, Federico, Eur, Christopher, Postnikov, Alexander

“…We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This class of polytopes contains important families such as weight polytopes, signed graphic zonotopes, Coxeter matroids, root cones, and Coxeter associahedra. …”
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Coxeter submodular functions and deformations of Coxeter permutahedra by Ardila, Federico, Castillo, Federico, Eur, Christopher, Postnikov, Alexander

“…We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This class of polytopes contains important families such as weight polytopes, signed graphic zonotopes, Coxeter matroids, root cones, and Coxeter associahedra. …”
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Single nucleotide variants of filaggrin and glucocorticoid receptors genes in children suffering different phenotypes of atopic diseases by V.O. Dityatkovsky, N.V. Naumenko, О.O. Alifirenko, N.L. Pinaeva, S.T. Taran, I.A. Filatova, O.Ye. Abaturov

“…The heterozygous variant A/G SNV rs10052957 of the NR3C1 gene is the most common in all AtD phenotypes, except for monotopic BA and polytopic AD+SAR(C)/PAR(C), and significantly, by 0.40 times (95% CI 0.18-0.93, p<0.05) reduces the risk of the polytopic phenotype related to AD. …”
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The Lecture Hall Parallelepiped by Liu, Fu, Stanley, Richard P.

“…The s-lecture hall polytopes P [subscript s] are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and Bousquet-Mélou. …”
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