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Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach [PDF]
Entropy, 2020 We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework.
Carlos Islas +2 more
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Pluricomplex Green's functions and Fano manifolds [PDF]
Épijournal de Géométrie Algébrique, 2019 We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere ...
Nicholas McCleerey, Valentino Tosatti
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A monotonicity approach to Pogorelov's Hessian estimates for Monge- Ampère equation
Mathematics in Engineering, 2023 We present an integral approach to Pogorelov's Hessian estimates for the Monge-Ampère equation, originally obtained via a pointwise argument.
Yu Yuan
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Computing Three-Dimensional Freeform Reflectors with a Scattering Surface [PDF]
EPJ Web of Conferences, 2023 We present a novel approach to computing reflectors with a scattering surface in illumination optics. A scattering model governed by a Fredholm integral equation is derived.
Kronberg Vì C.E. +3 more
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Advanced Nonlinear Studies, 2023 We consider the asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao et al. [Monge-Ampère equation on exterior domains, Calc. Var PDE.
Liu Zixiao, Bao Jiguang
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Electronic Research Archive, 2023 In the present paper, we prove the existence of smooth solutions to a $ L_p $ Aleksandrov problem for Codazzi tensor with a log-convex measure in compact Riemannian manifolds $ (M, g) $ with positive constant sectional curvature under suitable conditions.
Zhengmao Chen
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Design of optical surfaces conform the hyperbolic Monge-Ampère equation [PDF]
EPJ Web of Conferences, 2022 We present a method for designing freeform optical surfaces for illumination optics. By the laws of reflection, refraction and conservation of energy, a fully nonlinear PDE, the Monge-Ampere equation, is derived for the optical surface.
Bertens M.W.M.C. +3 more
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Advances in Nonlinear Analysis, 2021 In this paper, we establish the second boundary behavior of the unique strictly convex solution to a singular Dirichlet problem for the Monge-Ampère ...
Wan Haitao, Shi Yongxiu, Liu Wei
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An adaptive least-squares algorithm for the elliptic Monge–Ampère equation
Comptes Rendus. Mécanique, 2023 We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach.
Caboussat, Alexandre +2 more
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Freeform design of a two-reflector system to collimate and shape a point source distribution [PDF]
EPJ Web of Conferences, 2021 We present a method to design a freeform two-reflector system to collimate and shape a beam from a point source. An important generalization compared to previous research is that the output beam can be in an arbitrary direction.
van Roosmalen A.H. +3 more
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