Bilevel Optimization of Taxing Strategies for Carbon Emissions Using Fuzzy Random Matrix Generators

2022 ◽  
pp. 210-234
Author(s):  
Timothy Ganesan ◽  
Irraivan Elamvazuthi
Keyword(s):  
Power Generation ◽  
Carbon Emissions ◽  
Random Matrix ◽  
Matrix Theory ◽  
Stackelberg Game ◽  
Cuckoo Search ◽  
Bilevel Optimization ◽  
Tax Rates ◽  
The Novel ◽  
Fuzzy Random

Bilevel (BL) optimization of taxing strategies in consideration of carbon emissions was carried out in this work. The BL optimization problem was considered with two primary targets: (1) designing an optimal taxing strategy (imposed on power generation companies) and (2) developing optimal economic dispatch (ED) schema (by power generation companies) in response to tax rates. The resulting interaction was represented using Stackelberg game theory – where the novel fuzzy random matrix generators were used in tandem with the cuckoo search (CS) technique. Fuzzy random matrices were developed by modifying certain aspects of the original random matrix theory. The novel methodology was tailored for tackling complex optimization systems with intermediate complexity such as the application problem tackled in this work. Detailed performance and comparative analysis are also presented in this chapter.

scholarly journals Random Matrix Generators for Optimizing a Fuzzy Biofuel Supply Chain System

2020 ◽  
Vol 4 (1) ◽  
pp. 33 ◽  
Author(s):  
Timothy Ganesan ◽  
Pandian Vasant ◽  
Pratik Sanghvi ◽  
Joshua Thomas ◽  
Igor Litvinchev
Keyword(s):  
Supply Chain ◽  
Random Matrix ◽  
Large Scale ◽  
Matrix Theory ◽  
Fuzzy Optimization ◽  
Cuckoo Search ◽  
Supply Chain System ◽  
Creative Commons ◽  
Biofuel Supply Chain ◽  
Biomass Power Plant

Complex industrial systems often contain various uncertainties. Hence sophisticated fuzzy optimization (metaheuristics) techniques have become commonplace; and are currently indispensable for effective design, maintenance and operations of such systems. Unfortunately, such state-of-the-art techniques suffer several drawbacks when applied to largescale problems. In line of improving the performance of metaheuristics in those, this work proposes the fuzzy random matrix theory (RMT) as an add-on to the cuckoo search (CS) technique for solving the fuzzy large-scale multiobjective (MO) optimization problem; biofuel supply chain. The fuzzy biofuel supply chain problem accounts for uncertainties resulting from fluctuations in the annual electricity generation output of the biomass power plant [kWh/year]. The details of these investigations are presented and analyzed.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

SSA, Random Matrix Theory, and Noise-Reduced Correlations

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang ◽  
Mario Bondioli ◽  
Harvey J. Stein
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory

History—an overview

2018 ◽  
Author(s):  
Oriol Bohigas ◽  
Hans A. Weidenmüller
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
The Past ◽  
History Of ◽  
And Mathematics

An overview of the history of random matrix theory (RMT) is provided in this chapter. Starting from its inception, the authors sketch the history of RMT until about 1990, focusing their attention on the first four decades of RMT. Later developments are partially covered. In the past 20 years RMT has experienced rapid development and has expanded into a number of areas of physics and mathematics.

scholarly journals Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 976
Author(s):  
R. Aguilar-Sánchez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Random Matrix ◽  
Adjacency Matrix ◽  
Matrix Theory ◽  
Computational Study ◽  
Random Networks ◽  
Geometric Graphs ◽  
Theory Approach ◽  
Complexity Measures ◽  
Random Geometric Graphs ◽  
Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

scholarly journals Extremal correlators and random matrix theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Alba Grassi ◽  
Zohar Komargodski ◽  
Luigi Tizzano
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Matrix Model ◽  
Effective Field Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Effective Field ◽  
Random Matrix Model ◽  
Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

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