Quadratic Surplus

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
Convex Analysis ◽  
Scalar Product ◽  
Optimal Transport ◽  
Point Of View ◽  
Factorization Theorem ◽  
Polar Factorization

This chapter considers the case when the attributes are d-dimensional vectors and the surplus is the scalar product; it assumes that the distribution of the workers' attributes is continuous, but it relaxes the assumption that the distribution of the firms' attributes is discrete. This setting allows us to entirely rediscover convex analysis, which is introduced from the point of view of optimal transport. As a consequence, Brenier's polar factorization theorem is given, which provides a vector extension for the scalar notions of quantile and rearrangement.

More General Surplus

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
General Result ◽  
Convex Analysis ◽  
Scalar Product ◽  
Sufficient Conditions ◽  
General Function ◽  
Existence Of A Solution ◽  
Generalize Convex ◽  
Monge Problem ◽  
Natural Way

This chapter considers a case with a more general surplus function. It shows that when the scalar-product surplus is replaced by a more general function, much of the machinery put in place in Chapter 6 goes through. In particular, it is possible to generalize convex analysis in a natural way, and to obtain generalized notions of convex conjugates, of convexity, and of a subdifferential that are perfectly suited to the problem. A general result on the existence of dual minimizers is given, as well as sufficient conditions for the existence of a solution to the Monge problem.

scholarly journals Maximum Entropy on the Mean approach to solve generalized inverse problems with an application in computational thermodynamics.

2021 ◽  
Author(s):  
Eva Lawrence ◽  
Fabrice Gamboa ◽  
Thierry Klein ◽  
Christine Guéneau
Keyword(s):  
Inverse Problems ◽  
Maximum Entropy ◽  
Convex Analysis ◽  
Generalized Inverse ◽  
Point Of View ◽  
Multidimensional Case ◽  
General Integral ◽  
The Mean ◽  
Entropy Maximisation ◽  
Analysis Point

In this paper, we study entropy maximisation problems in order to reconstruct functions or measures subject to very general integral constraints. Our work has a twofold purpose. We first make a global synthesis of entropy maximisation problems in the case of a single reconstruction (measure or function) from the convex analysis point of view, as well as in the framework of the embedding into the Maximum Entropy on the Mean (MEM) setting. We further propose an extension of the entropy methods for a multidimensional case.

Information Geometry for Regularized Optimal Transport and Barycenters of Patterns

2019 ◽  
Vol 31 (5) ◽  
pp. 827-848 ◽  
Author(s):  
Shun-ichi Amari ◽  
Ryo Karakida ◽  
Masafumi Oizumi ◽  
Marco Cuturi
Keyword(s):  
Optimal Transport ◽  
Probability Distributions ◽  
Information Geometry ◽  
Wasserstein Distance ◽  
Point Of View ◽  
Transport Cost ◽  
Translation Invariance ◽  
Proper Distance ◽  
Leibler Divergence ◽  
Entropic Regularization

We propose a new divergence on the manifold of probability distributions, building on the entropic regularization of optimal transportation problems. As Cuturi ( 2013 ) showed, regularizing the optimal transport problem with an entropic term is known to bring several computational benefits. However, because of that regularization, the resulting approximation of the optimal transport cost does not define a proper distance or divergence between probability distributions. We recently tried to introduce a family of divergences connecting the Wasserstein distance and the Kullback-Leibler divergence from an information geometry point of view (see Amari, Karakida, & Oizumi, 2018 ). However, that proposal was not able to retain key intuitive aspects of the Wasserstein geometry, such as translation invariance, which plays a key role when used in the more general problem of computing optimal transport barycenters. The divergence we propose in this work is able to retain such properties and admits an intuitive interpretation.

On Redfield's Range-Correspondences

1966 ◽  
Vol 18 ◽  
pp. 1060-1071 ◽  
Author(s):  
H. O. Foulkes
Keyword(s):  
Symmetric Group ◽  
Scalar Product ◽  
Point Of View ◽  
Combinatorial Analysis ◽  
Important Paper ◽  
Group Reduction ◽  
Linear Graphs

In an important paper (7), long overlooked, J. H. Redfield dealt with several aspects of enumerative combinatorial analysis. In a previous paper (1) I showed the relation between a certain repeated scalar product of a set of permutation characters of a symmetric group and Redfield's composition of his group reduction functions. Here I consider, from a group representational point of view, Redfield's idea of a range-correspondence and its application to enumeration of linear graphs. The details of the application of these ideas to more general enumerations are also given.

scholarly journals Institutional and Non-Institutional Governance Initiatives in Urban Transport Planning: The Paradigmatic Case of the Post-Collapse of the Morandi Bridge in Genoa

2021 ◽  
Vol 13 (11) ◽  
pp. 5930
Author(s):  
Ilaria Delponte
Keyword(s):  
Optimal Transport ◽  
Point Of View ◽  
Urban Transport ◽  
Institutional Governance ◽  
The Public ◽  
Public Transport System ◽  
Emergency Event ◽  
The Moment ◽  
Modes Of Governance ◽  
Institutional Initiatives

The relationship between the institutional (established in law) and non-institutional initiatives (not supported by law) that improve the public transport system is currently a debated topic. The purpose of this paper is to identify the most relevant aspects of this relationship during an emergency event, namely the paradigmatic case study of the collapse of the Morandi Bridge in Genoa, which occurred in August 2018. The investigation, according to a consistent methodology widely used in the literature, is made up of a selection of interviews with professional figures particularly involved in institutional structures, drawing on qualitative results, and compared with official statistics. The events that occurred in Genoa, during the phase of reorganization of the urban transport service and the circulation in the city, underlined how the response of citizenship is a crucial element, including from the governance point of view. Analytic and observational findings reveal that non-institutional initiatives smooth major criticalities where formal institutions can only produce sub-optimal transport solutions (because of the limited means they own by virtue of the moment of emergency), providing evidence that the two modes of governance are absolutely complementary.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

How a sheperd guides a sheep herd?

1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg
Keyword(s):  
Point Of View ◽  
Single Ring ◽  
Damping Effects ◽  
Ring Particle

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.

The growth of mica polytypes as studied by conventional and high-resolution TEM

1983 ◽  
Vol 41 ◽  
pp. 174-177
Author(s):  
A. Baronnet ◽  
M. Amouric
Keyword(s):  
Water Pressure ◽  
Point Of View ◽  
Temperature Fields ◽  
Natural Occurrence ◽  
Growth Mechanisms ◽  
Long Period ◽  
High Resolution Tem ◽  
Layer Stacking ◽  
Experimental Works ◽  
Potential Use

The origin of mica polytypes has long been a challenging problem for crystal- lographers, mineralogists and petrologists. From the petrological point of view, interest in this field arose from the potential use of layer stacking data to furnish further informations about equilibrium and/or kinetic conditions prevailing during the crystallization of the widespread mica-bearing rocks. From the compilation of previous experimental works dealing with the occurrence domains of the various mica "polymorphs" (1Mr, 1M, 2M1, 2M2 and 3T) within water-pressure vs temperature fields, it became clear that most of these modifications should be considered as metastable for a fixed mica species. Furthermore, the natural occurrence of long-period (or complex) polytypes could not be accounted for by phase considerations. This highlighted the need of a more detailed kinetic approach of the problem and, in particular, of the role growth mechanisms of basal faces could play in this crystallographic phenomenon.

Radiation Damage in Ceramics

1982 ◽  
Vol 40 ◽  
pp. 600-603
Author(s):  
T. E. Mitchell ◽  
M. R. Pascucci ◽  
R. A. Youngman
Keyword(s):  
Radiation Damage ◽  
Outer Space ◽  
Point Of View ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Storage Media ◽  
Transmission Electron ◽  
Fundamental Point ◽  
Small Defect ◽  
Present Understanding

1. Introduction. Studies of radiation damage in ceramics are of interest not only from a fundamental point of view but also because it is important to understand the behavior of ceramics in various practical radiation enyironments- fission and fusion reactors, nuclear waste storage media, ion-implantation devices, outer space, etc. A great deal of work has been done on the spectroscopy of point defects and small defect clusters in ceramics, but relatively little has been performed on defect agglomeration using transmission electron microscopy (TEM) in the same kind of detail that has been so successful in metals. This article will assess our present understanding of radiation damage in ceramics with illustrations using results obtained from the authors' work.

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