最优传输(Optimal Transport)是多个学科交叉的研究领域,包括概率、分析以及优化等。最优传输研究的主要目标是建立有效比较概率分布的几何工具。以法国数学家蒙日(Monge)在二百多年前给出的问题为例:当给定两个沙盘时(每盘沙子可以代表一个概率分布),可以通过很多方式将一个沙盘传输(Transport or Reshape)到另一个沙盘。
最优传输（Optimal Transport）这一研究领域，融合了概率、分析与优化等多个学科，其核心在于开发有效的比较概率分布的几何工具。由法国数学家蒙日在二百多年前提出的问题，即如何以最低成本将一个沙盘的沙子传输至另一个沙盘，直观展示了最优传输的基本理念。通过计算传输单个沙粒的局部花费，进而求解整体花...
Computational Optimal Transport 作者:Gabriel Peyré/Marco Cuturi 出版社:Now Publishers Inc 副标题:With Applications to Data Science 出版年:2019-5-1 页数:274 定价:$99.00 装帧:Paperback 丛书:Foundations and Trends® in Machine Learning ISBN:9781680835502...
Computational Optimal Transport笔记——第二章(2) 技术标签:算法 符号说明 耦合矩阵 coupling matrix: P∈R+n×mP \in R^{n \times m}_{+}P∈R+n×m,其中Pi,jP_{i,j}Pi,j代表从 bin iii 移动到 bin jjj(或者在离散情况下从xix_ixi移动到yjy_jyj)的质量。 Admissible coupling: ...
uence of transport, logistics, and s- ply chain management on the modern economy and society has been growing steadily over the last few decades. The worldwide division of labor, the conn- tion of distributed production centers, and the increased mobility of individuals lead to an increased ...
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT problems numerically. First, we show that AOT problems are ...
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aResults of mapping spatial data to single-cell data using the optimal transport plan. Spatial scatter pie plot displays the well-structured cluster composition in adult mouse brain anterior slice.bLists of canonical cerebral cortical neuron types with scaled proportion.cSpatial deconvolution result of ...
Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer Water’s pivotal role is tied to the quantum nature of its hydrogen bond dynamics. Here, the authors investigate the thermal behavior of the protonated water hexamer through accurate path integral ...
optimal transport colocalization, which measures the minimal transporting cost below a given spatial scale to match two protein intensity distributions. Its validity on simulated data as well as on dual-color STED recordings of yeast and mammalian cells is demonstrated. We also extend the optimal ...