The Collected Mathematical Papers: On Monge's “Mémoire sur la théorie des déblais et des remblais”

By A. Cayley. 2009

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Citations in the corpus

Model Fusion via Optimal Transport (2019, methodology): “Our method relies on optimal transport (OT) [1, 2], to minimize the transportation cost of neurons present in the layers of individual models, measured by the similarity of activations or incoming weights.”
Theoretical Analysis of Domain Adaptation with Optimal Transport (2016, background): “Optimal transportation theory was ﬁrst introduced in [17] to study the problem of resource allocation.”
Overcoming Negative Transfer: A Survey (2020, background): “The Monge version [71] of the optimal transport distance is seeking for a map T ∗ : ΩS → ΩT that pushes μS towards μT , defined as:”
Differentiable Top-k with Optimal Transport (2020, methodology): “We first show that the standard top-k operator can be parameterized in terms of the solution of an Optimal Transport (OT) problem (Monge, 1781; Kantorovich, 1960).”
Fast geometric learning with symbolic matrices (2020, unknown): “Optimal transport (OT) is a generalization of sorting to spaces of dimension D > 1 [81, 107].”
{Euclidean, metric, and Wasserstein} gradient flows: an overview (2016, methodology): “This generalized problem by Kantorovich is much easier to handle than the original one proposed by Monge: for instance in the Monge case we would need existence of at least a map T satisfying the constraints.”
Optimal Mass Transport: Signal processing and machine-learning applications (2017, unknown): “The problem was initially studied by the French mathematician Gaspard Monge in his seminal work “Mémoire sur la théorie des déblais et des remblais” [35] in 1781.”
Statistical Aspects of Wasserstein Distances (2018, background): “1 Univariate Measures We shall identify measures μ on the real line (X = R), with their distribution function F ; the empirical distribution function corresponding to μn is Fn(t) = n−1 ∑n i=1 1{Xi ≤ t}. Thus Xi ∼ F , Yj ∼ G and we slightly abuse notation by writing Wp(F,G) for Wp(μ, ν). Munk & Czado”
Regularity of Optimal Maps on the Sphere: the Quadratic Cost and the Reflector Antenna (2013, methodology): “The problem of regularity of optimal maps is related to the problem of regularity of solutions of the associated elliptic Monge-Ampére type equation.”
Lipschitz Functions Have Lp-Stable Persistence (2010, background): “This notion of distance between distributions is popular in computer vision; see also the Monge-Kantorovich transportation problem [10] [11] .”
Logical, Metric, and Algorithmic Characterisations of Probabilistic Bisimulation (2011, background): “Monge in 1781 [45], consists of finding an optimal way of shovelling a pile of sand into a hole of the same volume.”