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Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources. [PDF]
Sci Rep, 2016 Blind Source Separation (BSS) is a powerful tool for analyzing composite data patterns in many areas, such as computational biology. We introduce a novel BSS method, Convex Analysis of Mixtures (CAM), for separating non-negative well-grounded sources ...
Zhu Y, Wang N, Miller DJ, Wang Y.
europepmc +3 more sources
Discrete convex analysis: A tool for economics and game theory [PDF]
Journal of Mechanism and Institution Design, 2016 This paper presents discrete convex analysis as a tool for use in economics and game theory. Discrete convex analysis is a new framework of discrete mathematics and optimization, developed during the last two decades.
Kazuo Murota
doaj +2 more sources
Convex analysis and financial equilibrium [PDF]
Mathematical Programming, 2014 Convexity has long had an important role in economic theory, but some recent developments have featured it all the more in problems of equilibrium. Here the tools of convex analysis are applied to a basic model of incomplete financial markets in which assets are traded and money can be lent or borrowed between the present and future.
A. Jofré, R. Rockafellar, R. Wets
semanticscholar +4 more sources
The correction range of lumbosacral curve vertebral body tilt in degenerative scoliosis for achieving postoperative coronal balance [PDF]
BMC Musculoskeletal DisordersPurpose To explore the relationship between lumbosacral curve vertebral body tilt correction and postoperative coronal balance in adult degenerative scoliosis to determine the ideal target values for the tilt correction.
Zehua Jiang +10 more
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Discrete-Convex-Analysis-Based Framework for Warm-Starting Algorithms with Predictions [PDF]
Neural Information Processing Systems, 2022 Augmenting algorithms with learned predictions is a promising approach for going beyond worst-case bounds. Dinitz, Im, Lavastida, Moseley, and Vassilvitskii~(2021) have demonstrated that a warm start with learned dual solutions can improve the time ...
Shinsaku Sakaue, Taihei Oki
semanticscholar +1 more source
Convex analysis on polyhedral spaces [PDF]
Mathematische Zeitschrift, 2022 AbstractWe introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
Botero, Ana Maria +2 more
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Anomaly Detection Based on Convex Analysis: A Survey
Frontiers in Physics, 2022 As a crucial technique for identifying irregular samples or outlier patterns, anomaly detection has broad applications in many fields. Convex analysis (CA) is one of the fundamental methods used in anomaly detection, which contributes to the robust ...
Tong Wang +8 more
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Sharpening Sparse Regularizers via Smoothing
IEEE Open Journal of Signal Processing, 2021 Non-convex sparsity-inducing penalties outperform their convex counterparts, but generally sacrifice the cost function convexity. As a middle ground, we propose the sharpening sparse regularizers (SSR) framework to design non-separable non-convex ...
Abdullah H. Al-Shabili +2 more
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A Convex Analysis Approach to Entropy Functions, Variational Principles and Equilibrium States [PDF]
Communications in Mathematical Physics, 2020 Using methods from Convex Analysis, for each generalized pressure function we define an upper semi-continuous affine entropy-like map, establish an abstract variational principle for both countably and finitely additive probability measures and prove ...
A. Biś +3 more
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Sparse Regularized Optimal Transport with Deformed q-Entropy
Entropy, 2022 Optimal transport is a mathematical tool that has been a widely used to measure the distance between two probability distributions. To mitigate the cubic computational complexity of the vanilla formulation of the optimal transport problem, regularized ...
Han Bao, Shinsaku Sakaue
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