Jingli Ren – författare

Mathematical Methods in Data Science covers a broad range of mathematical tools used in data science, including calculus, linear algebra, optimization, network analysis, probability and differential equations. Based on the authors' recently published and previously unpublished results, this book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations for dataanalysis and prediction. With data science being used in virtually every aspect of our society, the book includes examples and problems arising in data science and the clear explanation of advanced mathematical concepts, especially data-driven differential equations, making it accessible to researchers and graduate students in mathematics and data science.

Combines a broad spectrum of mathematics, including linear algebra, optimization, network analysis and ordinary and partial differential equations for data science Written by two researchers who are actively applying mathematical and statistical methods as well as ODE and PDE for data analysis and prediction Highly interdisciplinary, with content spanning mathematics, data science, social media analysis, network science, financial markets, and more Presents a wide spectrum of topics in a logical order, including probability, linear algebra, calculus and optimization, networks, ordinary differential and partial differential equations

Mathematical Methods in Data Science covers a broad range of mathematical tools used in data science, including calculus, linear algebra, optimization, network analysis, probability and differential equations. Based on the authors'' recently published and previously unpublished results, this book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations for dataanalysis and prediction. With data science being used in virtually every aspect of our society, the book includes examples and problems arising in data science and the clear explanation of advanced mathematical concepts, especially data-driven differential equations, making it accessible to researchers and graduate students in mathematics and data science.- Combines a broad spectrum of mathematics, including linear algebra, optimization, network analysis and ordinary and partial differential equations for data science- Written by two researchers who are actively applying mathematical and statistical methods as well as ODE and PDE for data analysis and prediction- Highly interdisciplinary, with content spanning mathematics, data science, social media analysis, network science, financial markets, and more- Presents a wide spectrum of topics in a logical order, including probability, linear algebra, calculus and optimization, networks, ordinary differential and partial differential equations

This book begins by exploring the fundamental concepts of dynamical systems and machine learning modeling, elucidating the workflow of these two modeling approaches. While primarily tailored as an introductory textbook for both undergraduate and graduate students, its broader aim is to captivate the interest of seasoned ecologists and life scientists, beckoning them to explore the realm of modeling. The introduction and development of each section adhere to a practical problem-driven approach, aiming to address real-world issues. The focus is on addressing how to establish and evolve appropriate models based on practical problems or data.Throughout the book, the authors deliver rich content and diverse models. A detailed overview of the workflow for both machine learning and dynamical system modeling is provided, covering topics such as stability and bifurcation theory, fundamentals of machine learning algorithms, data processing, and visualization methods. Regarding dynamical systems, the authors encompass various types of models, including delay, diffusion, continuous, and discrete models. For machine learning, both black-box and interpretable models are covered in this book, including neural network model, ensemble learning model, SHAP, LIME, and more.Ecologists, life scientists, and applied mathematicians might find this book helpful. It can be also used as a textbook for both undergraduate and graduate students.This book is related to SDG 15: Life on Land

This book begins by exploring the fundamental concepts of dynamical systems and machine learning modeling, elucidating the workflow of these two modeling approaches. While primarily tailored as an introductory textbook for both undergraduate and graduate students, its broader aim is to captivate the interest of seasoned ecologists and life scientists, beckoning them to explore the realm of modeling. The introduction and development of each section adhere to a practical problem-driven approach, aiming to address real-world issues. The focus is on addressing how to establish and evolve appropriate models based on practical problems or data.Throughout the book, the authors deliver rich content and diverse models. A detailed overview of the workflow for both machine learning and dynamical system modeling is provided, covering topics such as stability and bifurcation theory, fundamentals of machine learning algorithms, data processing, and visualization methods. Regarding dynamical systems, the authors encompass various types of models, including delay, diffusion, continuous, and discrete models. For machine learning, both black-box and interpretable models are covered in this book, including neural network model, ensemble learning model, SHAP, LIME, and more.Ecologists, life scientists, and applied mathematicians might find this book helpful. It can be also used as a textbook for both undergraduate and graduate students.This book is related to SDG 15: Life on Land