Percolation Theory Using Python
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Percolation Theory Using Python
Author: Anders Malthe-Sørenssen
language: en
Publisher: Springer Nature
Release Date: 2024-06-29
This course-based open access textbook delves into percolation theory, examining the physical properties of random media—materials characterized by varying sizes of holes and pores. The focus is on both the mathematical foundations and the computational and statistical methods used in this field. Designed as a practical introduction, the book places particular emphasis on providing a comprehensive set of computational tools necessary for studying percolation theory. Readers will learn how to generate, analyze, and comprehend data and models, with detailed theoretical discussions complemented by accessible computer codes. The book's structure ensures a complete exploration of worked examples, encompassing theory, modeling, implementation, analysis, and the resulting connections between theory and analysis. Beginning with a simplified model system—a model porous medium—whose mathematical theory is well-established, the book subsequently applies the same framework to realistic random systems. Key topics covered include one- and infinite-dimensional percolation, clusters, scaling theory, diffusion in disordered media, and dynamic processes. Aimed at graduate students and researchers, this textbook serves as a foundational resource for understanding essential concepts in modern statistical physics, such as disorder, scaling, and fractal geometry.
Quantitative Biosciences Companion in Python
Author: Joshua S. Weitz
language: en
Publisher: Princeton University Press
Release Date: 2024-01-09
A hands-on lab guide in the Python programming language that enables students in the life sciences to reason quantitatively about living systems across scales This lab guide accompanies the textbook Quantitative Biosciences, providing students with the skills they need to translate biological principles and mathematical concepts into computational models of living systems. This hands-on guide uses a case study approach organized around central questions in the life sciences, introducing landmark advances in the field while teaching students—whether from the life sciences, physics, computational sciences, engineering, or mathematics—how to reason quantitatively in the face of uncertainty. Draws on real-world case studies in molecular and cellular biosciences, organismal behavior and physiology, and populations and ecological communities Encourages good coding practices, clear and understandable modeling, and accessible presentation of results Helps students to develop a diverse repertoire of simulation approaches, enabling them to model at the appropriate scale Builds practical expertise in a range of methods, including sampling from probability distributions, stochastic branching processes, continuous time modeling, Markov chains, bifurcation analysis, partial differential equations, and agent-based simulations Bridges the gap between the classroom and research discovery, helping students to think independently, troubleshoot and resolve problems, and embark on research of their own Stand-alone computational lab guides for Quantitative Biosciences also available in R and MATLAB
Practical Social Network Analysis with Python
This book focuses on social network analysis from a computational perspective, introducing readers to the fundamental aspects of network theory by discussing the various metrics used to measure the social network. It covers different forms of graphs and their analysis using techniques like filtering, clustering and rule mining, as well as important theories like small world phenomenon. It also presents methods for identifying influential nodes in the network and information dissemination models. Further, it uses examples to explain the tools for visualising large-scale networks, and explores emerging topics like big data and deep learning in the context of social network analysis. With the Internet becoming part of our everyday lives, social networking tools are used as the primary means of communication. And as the volume and speed of such data is increasing rapidly, there is a need to apply computational techniques to interpret and understand it. Moreover, relationships in molecular structures, co-authors in scientific journals, and developers in a software community can also be understood better by visualising them as networks. This book brings together the theory and practice of social network analysis and includes mathematical concepts, computational techniques and examples from the real world to offer readers an overview of this domain.