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381
Limitations of entropic inequalities for detecting nonclassicality in the postselected Bell causal structure
Published 2020-07-01“…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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382
Geometry of Multiprimary Display Colors I: Gamut and Color Control
Published 2021-01-01“…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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383
Structure of temporal correlations of a qubit
Published 2018-01-01“…We first characterize the polytope of temporal quantum correlations coming from the most general measurements. …”
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384
Continuous Maps from Spheres Converging to Boundaries of Convex Hulls
Published 2021-01-01“…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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385
Variational Barycentric Coordinates
Published 2024“…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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386
Provable preimage under-approximation for neural networks
Published 2024“…We present a sound and complete algorithm for the former, which exploits our disjoint union of polytopes representation to provide formal guarantees. …”
Conference item -
387
Diverging exchange force and form of the exact density matrix functional
Published 2019“…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. …”
Journal article -
388
A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids
Published 2021-02-01“…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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389
Computational Techniques for Investigating Information Theoretic Limits of Information Systems
Published 2021-02-01“…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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390
On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
Published 2019“…We also consider the different toric fiber types that arise in the polytopes of elliptic Calabi-Yau threefolds.…”
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391
First-order orbit queries
Published 2020“…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.…”
Journal article -
392
Finite-Time Fuzzy Fault-Tolerant Control for Nonlinear Flexible Spacecraft System with Stochastic Actuator Faults
Published 2024-02-01“…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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393
Practical sampling of constraint-based models: Optimized thinning boosts CHRR performance.
Published 2023-08-01“…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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394
Mechanisms for Robust Local Differential Privacy
Published 2024-03-01“…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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395
Geometry of Multiprimary Display Colors II: Metameric Control Sets and Gamut Tiling Color Control Functions
Published 2021-01-01“…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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396
Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
Published 2020-06-01“…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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397
On the Chvátal–Gomory closure of a compact convex set
Published 2019“…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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398
Uniqueness of Gibbs measures for continuous hardcore models
Published 2021“…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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399
Lifts of Convex Sets and Cone Factorizations
Published 2014“…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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400
Universal aspects of perturbative gauge theory
Published 2020“…The faces of an ABHY polytope are themselves isomorphic to ABHY polytopes of lower dimension. …”
Thesis