scholarly journals VIRASORO MODULE STRUCTURE OF LOCAL MARTINGALES OF SLE VARIANTS

2007 ◽  
Vol 19 (05) ◽  
pp. 455-509 ◽  
Author(s):  
KALLE KYTÖLÄ
Keyword(s):  
Generating Function ◽  
Coulomb Gas ◽  
Module Structure ◽  
Multiple Sle ◽  
Straightforward Approach

Martingales often play an important role in computations with Schramm–Loewner Evolutions (SLEs). The purpose of this article is to provide a straightforward approach to the Virasoro module structure of the space of local martingales for variants of SLEs. In the case of ordinary chordal SLE, it has been shown in Bauer and Bernard's Phys. Lett. B557 that polynomial local martingales form a Virasoro module. We will show for more general variants that the module of local martingales has a natural submodule [Formula: see text] that has the same interpretation as the module of polynomial local martingales of chordal SLE, but it is in many cases easy to find more local martingales than that. We discuss the surprisingly rich structure of the Virasoro module [Formula: see text] and construction of the "SLE state" or "martingale generating function" by Coulomb gas formalism. In addition, Coulomb gas or Feigin–Fuchs integrals will be shown to transparently produce candidates for multiple SLE pure geometries.

CNN-based Classification of Degraded Images

2020 ◽  
Vol 2020 (10) ◽  
pp. 28-1-28-7 ◽  
Author(s):  
Kazuki Endo ◽  
Masayuki Tanaka ◽  
Masatoshi Okutomi
Keyword(s):  
Neural Networks ◽  
Image Restoration ◽  
Image Classification ◽  
Convolutional Neural Networks ◽  
Deep Convolutional Neural Networks ◽  
Alternative Approach ◽  
Degraded Image ◽  
Degraded Images ◽  
Straightforward Approach

Classification of degraded images is very important in practice because images are usually degraded by compression, noise, blurring, etc. Nevertheless, most of the research in image classification only focuses on clean images without any degradation. Some papers have already proposed deep convolutional neural networks composed of an image restoration network and a classification network to classify degraded images. This paper proposes an alternative approach in which we use a degraded image and an additional degradation parameter for classification. The proposed classification network has two inputs which are the degraded image and the degradation parameter. The estimation network of degradation parameters is also incorporated if degradation parameters of degraded images are unknown. The experimental results showed that the proposed method outperforms a straightforward approach where the classification network is trained with degraded images only.

Effect of OCA properties on foldable AMOLED panel with a module structure

2019 ◽  
pp. 1627
Author(s):  
Yali Liu ◽  
Yongzhen Jia ◽  
Zhengzhou Liu ◽  
Di Wu ◽  
Haoqun Li ◽  
...  
Keyword(s):  
Module Structure

Algorithm for detecting module structure in complex networks based on node type

2009 ◽  
Vol 28 (10) ◽  
pp. 2590-2593
Author(s):  
Wei SHI ◽  
Zheng ZHAO ◽  
Gui-xiang XUE
Keyword(s):  
Complex Networks ◽  
Module Structure ◽  
Node Type

Bank Loans Valuation: a Straightforward Approach

2019 ◽  
Author(s):  
Bünyamin Erkan ◽  
Damien Pouponneau
Keyword(s):  
Bank Loans ◽  
Straightforward Approach

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

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