Alexander Mehler

Frank Emmert-Streib

Matthias Dehmer

For over a decade, complex networks have steadily grown as an important tool across a broad array of academic disciplines, with applications ranging from physics to social media. A tightly organized collection of carefully-selected papers on the subject, Towards an Information Theory of Complex Networks: Statistical Methods and Applications presents theoretical and practical results about information-theoretic and statistical models of complex networks in the natural sciences and humanities. The book's major goal is to advocate and promote a combination of graph-theoretic, information-theoretic, and statistical methods as a way to better understand and characterize real-world networks. This volume is the first to present a self-contained, comprehensive overview of information-theoretic models of complex networks with an emphasis on applications. As such, it marks a first step toward establishing advanced statistical information theory as a unified theoretical basis of complex networks for all scientific disciplines and can serve as a valuable resource for a diverse audience of advanced students and professional scientists. While it is primarily intended as a reference for research, the book could also be a useful supplemental graduate text in courses related to information science, graph theory, machine learning, and computational biology, among others.

Statistical Methods and Applications

Towards an Information Theory of Complex Networks

Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.

From Biology to Linguistics

Analysis of Complex Networks

This interdisciplinary text offers theoretical and practical results of information theoretic methods used in statistical learning. It presents a comprehensive overview of the many different methods that have been developed in numerous contexts.

Information Theory and Statistical Learning

Xueliang Li

Zengqiang Chen

Yongtang Shi

This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.

Mathematical Foundations and Applications of Graph Entropy

Armin Graber

Armindo Salvador

The book introduces to the reader a number of cutting edge statistical methods which can e used for the analysis of genomic, proteomic and metabolomic data sets. In particular in the field of systems biology, researchers are trying to analyze as many data as possible in a given biological system (such as a cell or an organ). The appropriate statistical evaluation of these large scale data is critical for the correct interpretation and different experimental approaches require different approaches for the statistical analysis of these data. This book is written by biostatisticians and mathematicians but aimed as a valuable guide for the experimental researcher as well computational biologists who often lack an appropriate background in statistical analysis.

Methods in Systems Biology

Applied Statistics for Network Biology

The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical technique

Mathematical Foundations and Applications

Quantitative Graph Theory

This book is the first to focus on the application of mathematical networks for analyzing microarray data. This method goes well beyond the standard clustering methods traditionally used. From the contents: * Understanding and Preprocessing Microarray Data * Clustering of Microarray Data * Reconstruction of the Yeast Cell Cycle by Partial Correlations of Higher Order * Bilayer Verification Algorithm * Probabilistic Boolean Networks as Models for Gene Regulation * Estimating Transcriptional Regulatory Networks by a Bayesian Network * Analysis of Therapeutic Compound Effects * Statistical Methods for Inference of Genetic Networks and Regulatory Modules * Identification of Genetic Networks by Structural Equations * Predicting Functional Modules Using Microarray and Protein Interaction Data * Integrating Results from Literature Mining and Microarray Experiments to Infer Gene Networks The book is for both, scientists using the technique as well as those developing new analysis techniques.

A Network-Based Approach

Analysis of Microarray Data

Salissou Moutari

In order best exploit the incredible quantities of data being generated in most diverse disciplines data sciences increasingly gain worldwide importance. The book gives the mathematical foundations to handle data properly. It introduces basics and functionalities of the R programming language which has become the indispensable tool for data sciences. Thus it delivers the reader the skills needed to build own tool kits of a modern data scientist.

Mathematical Foundations of Data Science Using R

Abbe Mowshowitz

A well-balanced overview of mathematical approaches to complex systems ranging from applications in chemistry and ecology to basic research questions on network complexity. Matthias Dehmer, Abbe Mowshowitz, and Frank Emmert-Streib, well-known pioneers in the fi eld, have edited this volume with a view to balancing classical and modern approaches to ensure broad coverage of contemporary research problems. The book is a valuable addition to the literature and a must-have for anyone dealing with network compleaity and complexity issues.

Advances in Network Complexity

The aim of the book is to help students become data scientists. Since this requires a series of courses over a considerable period of time, the book intends to accompany students from the beginning to an advanced understanding of the knowledge and skills that define a modern data scientist. The book presents a comprehensive overview of the mathematical foundations of the programming language R and of its applications to data science.

Stefan Pickl

This comprehensive introduction to computational network theory as a branch of network theory builds on the understanding that such networks are a tool to derive or verify hypotheses by applying computational techniques to large scale network data. The highly experienced team of editors and high-profile authors from around the world present and explain a number of methods that are representative of computational network theory, derived from graph theory, as well as computational and statistical techniques. With its coherent structure and homogenous style, this reference is equally suitable for courses on computational networks.

Theoretical Foundations and Applications

Computational Network Theory

Modern and Interdisciplinary Problems in Network Science: A Translational Research Perspective covers a broad range of concepts and methods, with a strong emphasis on interdisciplinarity. The topics range from analyzing mathematical properties of network-based methods to applying them to application areas. By covering this broad range of topics, the book aims to fill a gap in the contemporary literature in disciplines such as physics, applied mathematics and information sciences.

A Translational Research Perspective

Modern and Interdisciplinary Problems in Network Science

Frontiers in Data Science deals with philosophical and practical results in Data Science. A broad definition of Data Science describes the process of analyzing data to transform data into insights. This also involves asking philosophical, legal and social questions in the context of data generation and analysis. In fact, Big Data also belongs to this universe as it comprises data gathering, data fusion and analysis when it comes to manage big data sets. A major goal of this book is to understand data science as a new scientific discipline rather than the practical aspects of data analysis alone.

Frank Emmert-Streib

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