Mathematical Modeling and Supercomputer Technologies. 22nd International Conference, MMST 2022 Nizhny Novgorod, Russia, November 14–17, 2022 Revised Selected Papers

Preface
Organization
Contents
Computational Methods for Mathematical Models Analysis
Diffusion in the Phase Space of the Autooscillatory System, Demonstrating the Stochastic Web in the Conservative Limit: Numerical Investigation
	1 Introduction
	2 Methods of the Investigation
	3 Dependence of Average Ensemble Energy on Time
	4 Conclusion
	References
Aberrator Shape Identification from 3D Ultrasound Data Using Convolutional Neural Networks and Direct Numerical Modeling
	1 Introduction
	2 Direct Problem
		2.1 Problem Statement
		2.2 Mathematical Model and Numerical Method
		2.3 Numerical Results for the Direct Problem
	3 Inverse Problem
		3.1 Problem Statement
		3.2 Neural Network Architecture
		3.3 Dataset and Training
	4 Numerical Experiments and Discussion
	5 Conclusions and Future Work
	References
Complex Dynamics of the Implicit Maps Derived from Iteration of Newton and Euler Methods
	1 Introduction
	2 Basic Model
	3 Numerical Simulation
		3.1 Repellers
		3.2 Attractors
	4 Conclusion
	References
Recognition of Vertical Migrations for Two Age Groups of Zooplankton
	1 Introduction
	2 Materials and Methods
	3 Results
		3.1 Fitness Identification
		3.2 Neural Network
		3.3 Construction of the Training Sample
	4 Summary
	References
Nonintegrability of the Problem of Motion of an Ellipsoidal Body with a Fixed Point in a Flow of Particles
	1 Introduction. V.V. Kozlov\'s Theorem on the Nonexistence of Analytic First Integral Near the Equilibrium Position of Hamiltonian System
	2 Formulation of the Problem. Hamilton Function of the Problem
	3 Application of V.V. Kozlov\'s Theorem 1
	4 Conclusions
	References
Numerical and Analytical Investigation of the Dynamics of a Body Under the Action of a Periodic Piecewise Constant External Force
	1 Introduction
	2 Problem Setting
	3 Solution Method
	4 Numerical Study of the Dynamics of a Body
	5 Conclusion
	References
Motif of Two Coupled Phase Equations with Inhibitory Couplings as a Simple Model of the Half-Center Oscillator
	1 Introduction
	2 The Model
	3 The Results
		3.1 Maps of Temporal Patterns
		3.2 Analytical Study of Bifurcation Transitions
	4 Conclusion
	References
Solutions of Multidimensional Hydrodynamic Evolution Equations Using the Fast Legendre Transformation
	1 Introduction
	2 Evolution Equations of Multidimensional Flows and Growth of Surfaces
	3 Results of Numerical Simulation of Surface Growth and Multidimensional Velocity Field Using the Two-Dimensional Fast Legendre Transform Algorithm
		3.1 Using the Fast Legendre Transform for the Numerical Calculation of Evolutionary Nonlinear Equations
		3.2 Results of Numerical Simulation
	References
An Iterative Method for Solving a Nonlinear System of the Theory of Radiation Transfer and Statistical Equilibrium in a Plane-Parallel Layer
	1 Introduction
	2 Problem Statement and Main Results
	3 Proofs of Theorems
		3.1 Preliminary Statements
		3.2 Proof of Theorem 3
		3.3 Proof of Theorems 1, 2
	4 Numerical Solution of the Transfer Equation
		4.1 Difference Approximation of the Kinetic Equation
		4.2 Properties of the Difference Dcheme
	5 Computational Results
	References
Role of Abnormal Calcium Signaling and Liver Tissue Structure in Glucose and Lipid Metabolism: Mathematical Modeling
	1 Introduction
		1.1 Main Processes
		1.2 Hormonal Regulation
		1.3 Calcium Regulation
		1.4 Mathematical Models
	2 Model Description
	3 Results
	4 Discussion
	References
On the Period Length Modulo p of the Numerators of Convergents for the Square Root of a Prime Number p
	1 Introduction
	2 Preliminaries
	3 The Main Result
	4 Related Works
	5 Conclusion
	References
Investigation of a Queueing System with Two Classes of Jobs, Bernoulli Feedback, and a Threshold Switching Algorithm
	1 Introduction
	2 The Problem Statement
	3 Essays on Solving the Stationary Equations
		3.1 Priority Algorithm (Case L=0)
		3.2 Case L =1
		3.3 Some Observations Concerning the Case L=2
		3.4 Numerical Example
	References
Coexistence of Dissipative and Conservative Regimes in Unidirectionally Coupled Maps
	1 Introduction
	2 Model Description
	3 Jacobian of System
	4 Conclusion
	References
Regulation of Neural Network Activity by Extracellular Matrix Molecules
	1 Introduction
	2 Materials
		2.1 Mathematical Model of Single Neuron
		2.2 Mathematical Model of ECM
	3 Results
		3.1 Neural Network
		3.2 Quasi-synchronous Neural Network Activity
	4 Conclusion
	References
Investigation of Ice Rheology Based on Computer Simulation of Low-Speed Impact
	1 Introduction
	2 Problem Formulation
	3 Simulation Results
	4 Conclusion
	References
Computation in Optimization and Optimal Control
Global Optimization Method Based on the Survival of the Fittest Algorithm
	1 Introduction
	2 Materials and Methods
		2.1 Differential Evolution
		2.2 The New Algorithm SoFDE
	3 Results
		3.1 Convergence Proof for SoFDE
		3.2 Comparison of Evolutionary Algorithms
	4 Summary
	References
Solving of the Static Output Feedback Synthesis Problem in a Class of Block-Homogeneous Matrices of Input and Output
	1 Introduction
	2 Formulation of the Problem
	3 Synthesis of Controllers in a Class of Block-Homogeneous Input and Output Matrices
	4 Synthesis of Controllers with Arbitrary Input and Output Matrices
	5 Conclusion
	References
Weak Penalty Decomposition Algorithm for Sparse Optimization in High Dimensional Space
	1 Introduction
	2 Weak Penalty Decomposition Method in Hilbert Spaces
		2.1 The Cardinality Constrained Optimization Problem
		2.2 The Weak Penalty Decomposition Algorithm
		2.3 Convergence Analysis
		2.4 Empirical Results
	3 Conclusion
	References
Mathematical Modelling and Optimization of Scheduling for Processing Beet in Sugar Production
	1 Introduction
	2 Mathematical Model and Statement of the Problem
	3 Optimal Scheduling
		3.1 Does Mixing Beet Varieties Lead to Maximizing the Objective Function?
		3.2 ``Hungarian Algorithm\'\' for Solving the Optimization Problem
		3.3 Analytical Solutions
	4 Numerical Results
	5 Conclusion
	References
Integration of Information Systems Data to Improve the Petroleum Product Blends Quality
	1 Introduction
	2 Experiment
	3 Results and Discussions
	4 Conclusion
	References
Supercomputer Simulation
High-Performance Graph Coloring on Intel CPUs and GPUs Using SYCL and KOKKOS
	1 Introduction
	2 Background and Related Work
	3 Implementation of Coloring Algorithms on OpenMP, SYCL and KOKKOS
		3.1 Overview
		3.2 Implementation on C++
		3.3 Implementation on SYCL
		3.4 Implementation on KOKKOS
		3.5 Optimizations
	4 Numerical Results
		4.1 Preliminaries
		4.2 Experiments on CPU
		4.3 Experiments on GPU
	5 Conclusion
	References
Automated Debugging of Fragmented Programs in LuNA System
	1 Fragmented Programs and the LuNA System
	2 Errors in the LuNA-Programs
	3 Methods and Tools of Automated Debugging. The Analysis of Applicability to the LuNA
	4 The Tool for Analysis Hangups of the LuNA-Programs
	5 Overhead Evaluation
	6 Conclusion and Future Work
	References
Multi-GPU GEMM Algorithm Performance Analysis for Nvidia and AMD GPUs Connected by NVLink and PCIe
	1 Introduction
	2 Related Work
	3 Performance Model Overview
	4 Testing Platforms
	5 Results
	6 Discussion
	7 Conclusions
	References
Numerical Simulation of Quantum Dissipative Dynamics of a Superconducting Neuron
	1 Introduction
	2 Phisical Model
	3 Numerical Implementation and Acceleration
	4 Conclusion
	References
Using Coarray Fortran for Design of Hydrodynamics Code on Nested Grids
	1 Introduction
	2 Numerical Model
	3 Parallel Implementation
	4 Sedov\'s Blast Wave Problem
	5 Conclusions
	References
Author Index