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Message Passing for Maximum Weight Independent Set
Published 2011“…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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424
Causal and causally separable processes
Published 2016-01-01“…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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425
Sparse sums of squares on finite abelian groups and improved semidefinite lifts
Published 2016“…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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426
New Theory and Algorithms for Convex Optimization with Non-Standard Structures
Published 2023“…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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Thesis -
427
Heterotic string models on smooth Calabi-Yau threefolds
Published 2013“…Any two half-polytopes over a given slice can be combined into a reflexive polytope. …”
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428
Discrete–geometric functions associated to polyhedral cones and point sets
Published 2012“…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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Thesis -
429
New Calabi–Yau manifolds from genetic algorithms
Published 2024-03-01“…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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430
New Calabi–Yau manifolds from genetic algorithms
Published 2024“…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. …”
Journal article -
431
On r-stacked triangulated manifolds
Published 2013-01-01“…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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432
Constrained control of SISO bilinear systems
Published 2003“…Then, it is shown that invariant polytopes based on bilinear controllers can be much larger. …”
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433
Robust MPC for linear systems with bounded multiplicative uncertainty
Published 2012“…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. …”
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434
Positive geometries for all scalar theories from twisted intersection theory
Published 2020-07-01“…We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. …”
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435
Affine Subspace Concentration Conditions
Published 2023-05-01“…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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436
Polypositroids
Published 2024-01-01“…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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437
Coxeter submodular functions and deformations of Coxeter permutahedra
Published 2021“…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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438
Coxeter submodular functions and deformations of Coxeter permutahedra
Published 2022“…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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439
Single nucleotide variants of filaggrin and glucocorticoid receptors genes in children suffering different phenotypes of atopic diseases
Published 2022-03-01“…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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440
The Lecture Hall Parallelepiped
Published 2015“…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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