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341
Stability properties of Plethysm: new approach with combinatorial proofs (Extended abstract)
Published 2015-01-01“…We show that these other plethysm coefficients count integer points in polytopes and we prove stability for them by exhibiting bijections between the corresponding sets of integer points of each polytope.…”
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342
Subword Complexes and Nil-Hecke Moves
Published 2013-01-01“…We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke monoid corresponding to W. If the complex is polytopal, we also describe such transformations for the dual polytope. …”
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343
All tight correlation Bell inequalities have quantum violations
Published 2020-02-01“…In geometric terms, this means that any correlation Bell inequality for which the classical and quantum maximum values coincide, does not define a facet, i.e., a face of maximum dimension, of the local (Bell) polytope. Indeed, using semidefinite programming duality, we prove upper bounds on the dimension of these faces, bounding it far away from the maximum. …”
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344
Algebraic shifting and strongly edge decomposable complexes
Published 2008-01-01“…Kalai and Sarkaria conjectured that if $\Gamma$ is a simplicial sphere then its algebraic shifting also satisfies (c) $\Delta (\Gamma) \subset \Delta (C(n,d))$, where $C(n,d)$ is the boundary complex of the cyclic $d$-polytope with $n$ vertices. We show this conjecture for strongly edge decomposable spheres introduced by Nevo. …”
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345
Subword Complexes and Nil-Hecke Moves
Published 2013-12-01“…We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke monoid corresponding to W. If the complex is polytopal, we also describe such transformations for the dual polytope. …”
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346
Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions
Published 2023-10-01“…The existence of a positively invariant polytope is shown and its size is calculated depending on the parameters of this cancer model. …”
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347
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348
Robust H-infinity filtering of stationary continuous-time linear systems with stochastic uncertainties
Published 2001“…The method proposed is also applied to the case where, in addition to the stochastic uncertainty, other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope. The problem of mixed H2/H∞ filtering for the above system is also treated. …”
Journal article -
349
Approximate counting in SMT and value estimation for probabilistic programs
Published 2017“…<p>#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains (quantitative information flow, static analysis of probabilistic programs). …”
Journal article -
350
Higher-order singular value decomposition and the reduced density matrices of three qubits
Published 2020“…Furthermore, we showed that it is possible to construct a polytope that encapsulates all the special states of three qubits by LU operations with HOSVD.…”
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351
Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates
Published 2024-01-01“…The biaxial-nematic and cyclic phases exhibit discrete polytope symmetries featuring non-Abelian vortices and we investigate a pair of noncommuting line defects within the context of a topological interface. …”
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352
Improved local models and new Bell inequalities via Frank-Wolfe algorithms
Published 2023-10-01“…We make our entire code accessible as a julia library called BellPolytopes.jl.…”
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353
Prescriptive unitarity from positive geometries
Published 2024-03-01“…Remarkably, at one loop it is a curvy version of a simple polytope, whose vertices are specified by maximal cuts of the amplitude. …”
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354
The short toric polynomial
Published 2011-01-01“…This formula implies Gessel's formula for the toric h-vector of a cube, and may be used to prove that the nonnegativity of the toric h-vector of a simple polytope is a consequence of the Generalized Lower Bound Theorem holding for simplicial polytopes.…”
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355
Universal Polynomials for Severi Degrees of Toric Surfaces
Published 2012-01-01“…An important ingredient in the proof is the polynomiality of the discrete volume of a variable facet-unimodular polytope.…”
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356
The moduli space of Harnack curves in toric surfaces
Published 2021-01-01“…This compactification has a natural stratification with the same poset as the secondary polytope of $\Delta $.…”
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357
Positive Configuration Space
Published 2022“…This space has a natural stratification by positive Chow cells, and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions of the hypersimplex into positroid polytopes, (b) the set of cones in the positive tropical Grassmannian, and (c) the set of cones in the positive Dressian. …”
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358
Valid Inequalities and Facets of the Capacitated Plant Location Problem
Published 2004“…We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.…”
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Working Paper -
359
A Definition of Type Domain of a Parallelotope
Published 2013-01-01“…<p>Each convex polytope P = P(α) can be described by a set of linear inequalities determined by vectors p and right hand sides α(p). …”
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360
Arnold’s Piecewise Linear Filtrations, Analogues of Stanley–Reisner Rings and Simplicial Newton Polyhedra
Published 2022-11-01“…Assuming that Newtons polytope is <i>simplicial</i> and <i>super-convenient</i> (that is, containing some neighborhood of the origin), the author strengthens the 1974 result by explicitly specifying the set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">B</mi><mrow><mi>s</mi><mi>h</mi></mrow></msup></semantics></math></inline-formula> of monomials of cardinality <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>!…”
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