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Mathematics
Showing 1-30 of 466 projects
Topic: Investigating the Asymptotic Behavior and Central Limit Theorems for Random W...
This work investigates the asymptotic behavior and central limit phenomena for random walks defined on non-Euclidean geometries, with a focus on hyperbolic, sph...
Optimal stopping times for stochastic processes with path-dependent payoff functions...
In this work, we investigate the problem of optimal stopping times for stochastic processes with path-dependent payoff functions, focusing on a broad class of M...
Optimal Transport Theory in High-Dimensional Data: Applications to Clustering and Ge...
In high-dimensional data analysis, optimal transport (OT) offers a principled framework to compare and align distributions, enabling robust clustering, dimensio...
Optimal control of nonlocal nonlinear differential equations on graphs using fractio...
We present a comprehensive study on the optimal control of nonlocal nonlinear differential equations defined on graphs, incorporating fractional calculus to mod...
Data-driven Spectral Methods for Solving High-Dimensional Partial Differential Equat...
Data-driven spectral methods offer a powerful framework for solving high-dimensional partial differential equations (PDEs) by combining the accuracy of spectral...
Topic: Investigating the Applications of Topological Data Analysis in Multivariate T...
This study explores the integration of Topological Data Analysis (TDA) with multivariate time series to enhance change-point detection and anomaly ranking in co...
Topic: Spectral Analysis of Graphs via Nonlinear Eigenvalue Problems and Application...
Spectral properties of graphs underpin fundamental processes on networks, yet classical linear eigenvalue methods often fall short in capturing nonlinearity ind...
Optimal Transport and Its Applications to Data Analysis: Theory, Algorithms, and App...
We present a comprehensive study of optimal transport (OT) frameworks and their transformative impact on data analysis in high-dimensional statistical inference...
Stochastic Analysis and Applications: Numerical Approximation of Solutions to Stocha...
This study advances the numerical treatment of stochastic differential equations (SDEs) driven by Lévy processes through the synthesis of Malliavin calculus te...
Topic: Topological Data Analysis for Time-Varying Manifolds: Stability, Computation,...
Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust geometric and topological features from complex data. This abstract pr...
A Multiscale Analysis of Fractional Differential Equations in Modeling Anomalous Dif...
We present a comprehensive study on the multiscale analysis of fractional differential equations (FDEs) to model anomalous diffusion processes on complex networ...
Spectral methods for solving nonlinear partial differential equations on irregular d...
Spectral methods provide a powerful framework for solving nonlinear partial differential equations (PDEs) on irregular domains by leveraging global basis functi...
Optimizing Spectral Clustering for High-Dimensional Data via Graph Laplacian Regular...
Spectral clustering is a powerful tool for discovering intrinsic structure in high-dimensional data, yet its performance often deteriorates in the presence of n...
Topological Data Analysis for Characterizing Phase Transitions in High-Dimensional R...
This study develops a novel framework combining topological data analysis (TDA), persistent homology, and machine learning to characterize phase transitions in ...
Numerical Methods for Solving Fractional Differential Equations with Applications to...
This study presents a comprehensive development of numerical methods for solving fractional differential equations (FDEs) arising in anomalous diffusion process...
Finite Difference Schemes and Stability Analysis for Nonlinear Partial Differential ...
Finite Difference Schemes and Stability Analysis for Nonlinear Partial Differential Equations on Irregular Domains presents a rigorous examination of numerical ...
Optimal Investment Portfolio Optimization under Stochastic Volatility with Receding ...
We propose a rigorous framework for optimizing investment portfolios under stochastic volatility using receding horizon control (RHC) to manage dynamic risk and...
A Unified Approach to Stability Analysis and Approximation of Nonlinear Dynamical Sy...
In this work, we present a unified framework for stability analysis and high-fidelity approximation of nonlinear dynamical systems by integrating fractional-ord...
Nonlinear Dynamics and Chaos in Predator-Prey Models with Time-Delay and Stochastic ...
Nonlinear dynamics and chaos in predator-prey systems are investigated in the presence of time delays and stochastic perturbations to elucidate the mechanisms d...
Topology of neural network loss landscapes and their implications for optimization i...
The optimization landscape of neural networks exhibits intricate topological features that profoundly influence learning dynamics, generalization, and robustnes...
Asymptotic Analysis and Numerical Methods for Fractional-Order Stochastic Differenti...
This study develops a rigorous framework for asymptotic analysis and numerical approximation of fractional-order stochastic differential equations (SDEs) arisin...
Analysis of Fractal Geometry in Natural Phenomena and Its Applications...
Fractal geometry, a branch of mathematics that studies complex patterns exhibiting self-similarity across different scales, has significantly advanced our under...
Applications of Fractal Geometry in Network Topology Optimization...
This study explores the innovative application of fractal geometry principles in optimizing network topologies, aiming to enhance the efficiency, scalability, a...
Advanced Optimization Techniques for Large-Scale Data Analysis...
This research explores and evaluates the effectiveness of advanced optimization techniques in enhancing the efficiency and accuracy of large-scale data analysis...
Application of Topological Data Analysis in High-Dimensional Data Clustering...
High-dimensional data sets have become increasingly prevalent across various scientific and technological fields, posing significant challenges for traditional ...
Analyzing the Application of Fractal Geometry in Modeling Natural Phenomena...
Fractal geometry has revolutionized the way natural phenomena are modeled, providing a framework to describe complex, irregular, and self-similar structures tha...
Optimizing Network Routing Algorithms Using Advanced Graph Theory Techniques...
This research explores the application of advanced graph theory techniques to optimize network routing algorithms with the aim of enhancing efficiency, reliabil...
Advanced Techniques for Optimizing Non-Linear Dynamic Systems Using Chaos Theory...
The study investigates innovative methodologies for optimizing non-linear dynamic systems by leveraging chaos theory, aiming to enhance the efficiency and predi...
Topology Optimization in Structural Design Using Machine Learning Techniques...
This research explores the innovative integration of machine learning techniques into the process of topology optimization to enhance structural design efficien...
Mathematical Modeling and Analysis of Epidemic Spread Using Differential Equations...
In recent years, the rapid proliferation of infectious diseases has underscored the critical need for precise mathematical frameworks to understand, predict, an...
