Hardness of Parameter Estimation in Graphical Models by Bresler, Guy, Gamarnik, David, Shah, Devavrat

“…Our reduction entails showing that the marginal polytope boundary has an inherent repulsive property, which validates an optimization procedure over the polytope that does not use any knowledge of its structure (as required by the ellipsoid method and others).…”
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A Solution of the Energy Minimization Problem for Codes of Codimension 1 by Zhang, Yichi

“…We also investigate the polytope of quasicodes, where we give a symmetry and a list of vertices in some special cases.…”
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Design of Processor Array Based on an Optimized Multiprojection Approach by CAMPOS, J.-M, CUMPLIDO, R.

“…In this work, an optimized multiprojection approach based on the Polytope model is proposed as well as an automated way for getting the scheduler and the allocator vectors. …”
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Topological superfluid defects with discrete point group symmetries by Y. Xiao, M. O. Borgh, A. Blinova, T. Ollikainen, J. Ruostekoski, D. S. Hall

“…Here the authors demonstrate, in atomic spinor Bose–Einstein condensates, previously unobserved vortex line defects with discrete polytope symmetries, which are of interest to quantum information applications.…”
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On the stability of certain perturbed systems of differential equations and the relationship with the magnitude of the perturbation by Efrén Vázquez Silva, Celso Monteiro Chissoca Chitungo

“…In this work we consider a class of polytopes of third order square matrices, studied early. …”
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Extending the Birkhoff-von Neumann switching strategy to multicast switching by Sundararajan, Jay Kumar, 1982-

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Combinatorial aspects of scattering amplitudes: amplituhedra, T-duality, and cluster algebras by Parisi, M

“…On one side, the hypersimplex Delta_{k+1,n} – a polytope which has been studied in connection with the moment map, torus orbits in the Grassmannian, tropical geometry and cluster algebras. …”

Quick eVALUATION OF THE INTERVAL STABILITY OF THE LINEAR ASSIGNMENT problem SOLUTIONS by M. P. Revotjuk, M. K. Qaraleh, P. M. Batura

“…Economical one-step transition to the nearest vertex of the polytope of problem one for all the edges of the optimal perfect matching is almost an order of magnitude reduces the computational complexity of evaluating the stability of the current optimal solution.…”
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Invariant sets for feedback linearisation based nonlinear predictive control by Bacic, M, Cannon, M, Kouvaritakis, B

“…This paper describes a method for calculating invariant/feasible sets with respect to feedback linearising control law for input-affine nonlinear systems. Polytope simplification and partial invariance/feasibility are used to reduce the conservativeness of the affine difference inclusion. …”

Feynman diagrams in four-dimensional holomorphic theories and the Operatope by Kasia Budzik, Davide Gaiotto, Justin Kulp, Jingxiang Wu, Matthew Yu

“…We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”). …”
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A lattice point counting generalisation of the Tutte polynomial by Amanda Cameron, Alex Fink

“…This polynomial is constructed using lattice point counts in the Minkowski sum of the base polytope of a polymatroid and scaled copies of the standard simplex. …”
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An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts by Candelas, P, Constantin, A, Skarke, H

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

Profinite and residual properties of fibred groups by Kudlinska, M

“…We explain how to construct the polytopes using topological representatives of the monodromy. …”

Cosmology meets cohomology by Shounak De, Andrzej Pokraka

“…Abstract The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. …”
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A general method for the manipulability analysis of serial robot manipulators by Zhihong Zou

“…In this article, a general methodology of using manipulability polytopes to characterize the manipulator’s capability to generate velocities, forces, and accelerations at the end-effector is proposed. …”
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Positive Configuration Space by Arkani-Hamed, Nima, Lam, Thomas, Spradlin, Marcus

“…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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On efficient computation of low-complexity controlled invariant sets for uncertain linear systems by Blanco, T, Cannon, M, De Moor, B

“…A method is presented for determining invariant low-complexity polytopic sets and associated linear feedback laws for linear systems with polytopic uncertainty. …”

Equivariant Seidel maps and a flat connection on equivariant symplectic cohomology by Liebenschutz-Jones, T

“…As an application, we compute these algebraic structures for a few specific examples and provide a method to compute them for toric manifolds using the moment polytope.…”

Fusions of Consciousness by Donald D. Hoffman, Chetan Prakash, Robert Prentner

“…The possible dynamics of <i>n</i> agents form an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional polytope with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>n</mi><mi>n</mi></msup></semantics></math></inline-formula> vertices—the <i>Markov polytope</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">M</mi><mi>n</mi></msub></semantics></math></inline-formula>. …”
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Local hidden variable values without optimization procedures by Dardo Goyeneche, Wojciech Bruzda, Ondřej Turek, Daniel Alsina, Karol Życzkowski

“…In particular, this problem is the first step towards characterizing the LHV polytope of a given scenario. In this work, we establish a relation between the LHV value of bipartite Bell inequalities and the mathematical notion of excess of a matrix. …”
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