scholarly journals Finite space Kantorovich problem with an MCMC of table moves

2021 ◽  
Vol 15 (1) ◽  
pp. 880-907
Author(s):  
Giovanni Pistone ◽  
Fabio Rapallo ◽  
Maria Piera Rogantin
Keyword(s):  
Finite Space ◽  
Kantorovich Problem

scholarly journals ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS

2021 ◽  
pp. 1-37
Author(s):  
Florian F. Gunsilius
Keyword(s):  
Convergence Rate ◽  
Poincaré Inequality ◽  
Optimal Transportation ◽  
Matching Theory ◽  
Economic Research ◽  
Poincare Inequality ◽  
Optimal Transportation Problem ◽  
Minimax Rate ◽  
The Cost ◽  
Kantorovich Problem

The theory of optimal transportation has experienced a sharp increase in interest in many areas of economic research such as optimal matching theory and econometric identification. A particularly valuable tool, due to its convenient representation as the gradient of a convex function, has been the Brenier map: the matching obtained as the optimizer of the Monge–Kantorovich optimal transportation problem with the euclidean distance as the cost function. Despite its popularity, the statistical properties of the Brenier map have yet to be fully established, which impedes its practical use for estimation and inference. This article takes a first step in this direction by deriving a convergence rate for the simple plug-in estimator of the potential of the Brenier map via the semi-dual Monge–Kantorovich problem. Relying on classical results for the convergence of smoothed empirical processes, it is shown that this plug-in estimator converges in standard deviation to its population counterpart under the minimax rate of convergence of kernel density estimators if one of the probability measures satisfies the Poincaré inequality. Under a normalization of the potential, the result extends to convergence in the $L^2$ norm, while the Poincaré inequality is automatically satisfied. The main mathematical contribution of this article is an analysis of the second variation of the semi-dual Monge–Kantorovich problem, which is of independent interest.

A casuality group in finite space-time

1972 ◽  
Vol 10 (1) ◽  
pp. 19-36 ◽  
Author(s):  
A. A. Blasi ◽  
F. Gallone ◽  
A. Zecca ◽  
V. Gorini
Keyword(s):  
Space Time ◽  
Finite Space

Full-wave finite space model of open-ended coaxial line for dielectric spectroscopy of liquids

2017 ◽  
Vol 88 (8) ◽  
pp. 084703 ◽  
Author(s):  
D. Jablonskas ◽  
S. Lapinskas ◽  
S. Rudys ◽  
M. Ivanov ◽  
J. Banys
Keyword(s):  
Dielectric Spectroscopy ◽  
Coaxial Line ◽  
Space Model ◽  
Full Wave ◽  
Finite Space

scholarly journals Video analysis of fish schooling behavior in finite space using a mathematical model

2003 ◽  
Vol 60 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Katsuya Suzuki ◽  
Tsutomu Takagi ◽  
Tomonori Hiraishi
Keyword(s):  
Mathematical Model ◽  
Video Analysis ◽  
Schooling Behavior ◽  
Finite Space ◽  
Fish Schooling

Mathematic Model and Method for Solving the Heat-Exchange Problem in Electron-Beam Welding of Arbitrary Areas

2019 ◽  
Vol 291 ◽  
pp. 173-182
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Electron Beam ◽  
Electron Beam Welding ◽  
Integral Transformation ◽  
Mathematic Model ◽  
Convergent Series ◽  
Dirichlet Boundary Conditions ◽  
Temperature Fields ◽  
The Finite Element Method ◽  
Finite Space ◽  
First Time

For the first time in this article, a mathematical model has been developed for calculating the temperature fields in arbitrary areas in electron-beam welding; this model was created in the form of a boundary value problem of mathematical physics for a parabolic equation of heat conductivity with Dirichlet boundary conditions. A new integral transformation was constructed for a two-dimensional finite space, with the use of which, as well as the finite element method and Galerkin's method, a temperature field has been determined in the form of a convergent series.

The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body

2018 ◽  
Vol 277 ◽  
pp. 168-177
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Temperature Field ◽  
Dirichlet Problem ◽  
Heat Exchange ◽  
Angular Velocity ◽  
Integral Transformation ◽  
Mathematic Model ◽  
Constant Angular Velocity ◽  
Temperature Fields ◽  
Finite Velocity ◽  
Finite Space

It is the first generalized 3D mathematic model, which is created for calculating temperature fields in the empty isotropic rotary body, which is restricted by end surfaces and lateral surface of rotation and rotates with constant angular velocity around the axis OZ, with taking into account finite velocity of the heat conductivity in the form of the Dirichlet problem. In this work, an integral transformation was formulated for the 2D finite space, with the help of which a temperature field in the empty isotropic rotary body was determined in the form of convergence series by the Fourier functions.

scholarly journals Causality constraints on hadron production in high energy collisions

2014 ◽  
Vol 23 (04) ◽  
pp. 1450019 ◽  
Author(s):  
Paolo Castorina ◽  
Helmut Satz
Keyword(s):  
Baryon Number ◽  
Heavy Ion ◽  
High Energy ◽  
Hadron Production ◽  
Space Time ◽  
Horizon Problem ◽  
Ion Interactions ◽  
Quantum Numbers ◽  
High Energy Collisions ◽  
Finite Space

For hadron production in high energy collisions, causality requirements lead to the counterpart of the cosmological horizon problem: the production occurs in a number of causally disconnected regions of finite space-time size. As a result, globally conserved quantum numbers (charge, strangeness, baryon number) must be conserved locally in spatially restricted correlation clusters. This provides a theoretical basis for the observed suppression of strangeness production in elementary interactions (pp, e+e-). In contrast, the space-time superposition of many collisions in heavy ion interactions largely removes these causality constraints, resulting in an ideal hadronic resonance gas in full equilibrium.

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