Many scientific disciplines rely on observational data of systems for which it is difficult (or impossible) to implement controlled experiments. Data analysis techniques are required for identifying causal information and relationships directly from such observational data. This need has led to the development of many different time series causality approaches and tools including transfer entropy, convergent cross-mapping (CCM), and Granger causality statistics. A practicing analyst can explore the literature to find many proposals for identifying drivers and causal connections in time...

This book is a brief introduction to negative quantum channels, i.e., linear, trace-preserving (and consistent) quantum maps that are not completely positive. The flat and sharp operators are introduced and explained. Complete positivity is presented as a mathematical property, but it is argued that complete positivity is not a physical requirement of all quantum operations. Negativity, a measure of the lack of complete positivity, is proposed as a tool for empirically testing complete positivity assumptions. Table of Contents: Preface / Acknowledgments / Introduction and Definition of...