Limitations of entropic inequalities for detecting nonclassicality in the postselected Bell causal structure by V. Vilasini, Roger Colbeck

“…In addition, for the bipartite Bell scenario with two inputs and three outputs we find the vertex description of the polytope of nonsignalling distributions that satisfy all of the CHSH-type inequalities, which is one of the main regions of investigation in this work.…”
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Geometry of Multiprimary Display Colors I: Gamut and Color Control by Gaurav Sharma, Carlos Eduardo Rodriguez-Pardo

“…For multiprimary displays, the gamut, i.e., the range of colors that can be rendered using additive combinations of an arbitrary number of light sources (primaries) with modulated intensities, is known to be a zonotope, which is a specific type of convex polytope. We develop a complete, cohesive, and directly usable mathematical characterization of the geometry of the multiprimary gamut zonotope. …”
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Structure of temporal correlations of a qubit by Jannik Hoffmann, Cornelia Spee, Otfried Gühne, Costantino Budroni

“…We first characterize the polytope of temporal quantum correlations coming from the most general measurements. …”
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Continuous Maps from Spheres Converging to Boundaries of Convex Hulls by Joseph Malkoun, Peter J. Olver

“…We prove this theorem using techniques from convex geometry of (spherical) polytopes and set-valued homology. We further establish an interesting relationship with the Gauss map of the polytope B, appropriately defined. …”
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Variational Barycentric Coordinates by Dodik, Ana, Stein, Oded, Sitzmann, Vincent, Solomon, Justin

“…In contrast, we directly parameterize the continuous function that maps any coordinate in a polytope's interior to its barycentric coordinates using a neural field. …”
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Provable preimage under-approximation for neural networks by Zhang, X, Wang, B, Kwiatkowska, M

“…We present a sound and complete algorithm for the former, which exploits our disjoint union of polytopes representation to provide formal guarantees. …”

Diverging exchange force and form of the exact density matrix functional by Schilling, C, Schilling, R

“…Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope E^1_N = P^1_N, described by linear constraints D^{(j)}(n)⩾0. …”

A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids by Alejandro Garces, Walter Gil-González, Oscar Danilo Montoya, Harold R. Chamorro, Lazaro Alvarado-Barrios

“…The power flow equations are linearized, and the combinatorial part is represented using a Birkhoff polytope <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">B</mi><mn>3</mn></msub></semantics></math></inline-formula> that allows the selection of phase swapping in each node. …”
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Computational Techniques for Investigating Information Theoretic Limits of Information Systems by Chao Tian, James S. Plank, Brent Hurst, Ruida Zhou

“…Based on this reduced linear program, we consider four techniques to investigate the fundamental limits of information systems: (1) computing an outer bound for a given linear combination of information measures and providing the values of information measures at the optimal solution; (2) efficiently computing a polytope tradeoff outer bound between two information quantities; (3) producing a proof (as a weighted sum of known information inequalities) for a computed outer bound; and (4) providing the range for information quantities between which the optimal value does not change, i.e., sensitivity analysis. …”
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On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds by Huang, Yu-Chien, Taylor IV, Washington

“…We also consider the different toric fiber types that arise in the polytopes of elliptic Calabi-Yau threefolds.…”
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First-order orbit queries by Almagor, S, Ouaknine, J, Worrell, J

“…On the other hand, previous work has shown that in dimension d = 4, giving a decision procedure for the special case of the Orbit Problem with singleton source set S and polytope target set T would entail major breakthroughs in Diophantine approximation.…”

Finite-Time Fuzzy Fault-Tolerant Control for Nonlinear Flexible Spacecraft System with Stochastic Actuator Faults by Jiao Xu, Tao Song, Jiaxin Wang

“…To effectively manage the intricacies introduced by these factors, the nonhomogeneous Markov process is represented as a polytope set. The proposed solution involves the development of a nonhomogeneous matrix transformation, accompanied by the introduction of adaptable parameters. …”
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Practical sampling of constraint-based models: Optimized thinning boosts CHRR performance. by Johann F Jadebeck, Wolfgang Wiechert, Katharina Nöh

“…Our guideline is validated using three (out-of-sample) large-scale networks and we show that it allows sampling convex polytopes uniformly to convergence in a fraction of time, thereby unlocking the rigorous investigation of hitherto intractable models. …”
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Mechanisms for Robust Local Differential Privacy by Milan Lopuhaä-Zwakenberg, Jasper Goseling

“…By analyzing the structure of this set and approximating it with a polytope, we can use robust optimization to find mechanisms with high utility. …”
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Geometry of Multiprimary Display Colors II: Metameric Control Sets and Gamut Tiling Color Control Functions by Carlos Eduardo Rodriguez-Pardo, Gaurav Sharma

“…Specifically, we show that MCS is a convex polytope whose vertices are control vectors obtained from (parallelepiped) tilings of the gamut, i.e., the range of colors that the display can produce. …”
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Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes by Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, Robert W. Spekkens

“…We prove that the set of free operations forms a polytope, which in turn allows us to derive an efficient algorithm for deciding whether one resource can be converted to another. …”
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On the Chvátal–Gomory closure of a compact convex set by Dadush, Daniel, Dey, Santanu S., Vielma Centeno, Juan Pablo

“…In this paper, we show that the Chvátal–Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver (Ann Discret Math 9:291–296, 1980) for irrational polytopes, and generalizes the same result for the case of rational polytopes (Schrijver in Ann Discret Math 9:291–296, 1980), rational ellipsoids (Dey and Vielma in IPCO XIV, Lecture Notes in Computer Science, vol 6080. …”
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Uniqueness of Gibbs measures for continuous hardcore models by Gamarnik, David, Ramanan, Kavita

“…In this version the state or "spin value" xu of any node u of the graph lies in the interval [0, 1], the hardcore constraint xu + xv ≤ 1 is satisfied for every edge (u, v) of the graph, and the space of feasible configurations is given by a convex polytope. When the graph is a regular tree, we show that there is a unique Gibbs measure associated to each activity parameter λ > 0. …”
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Lifts of Convex Sets and Cone Factorizations by Parrilo, Pablo A., Thomas, Rekha R., Gouveia, João

“…This generalizes a theorem of Yannakakis that established a connection between polyhedral lifts of a polytope and nonnegative factorizations of its slack matrix. …”
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Universal aspects of perturbative gauge theory by Frost, H

“…The faces of an ABHY polytope are themselves isomorphic to ABHY polytopes of lower dimension. …”