LinKnot - Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics. The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves. Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.

This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.

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The increasing demand for ubiquitous data service sets high expectations on future cellular networks. They should not only provide data rates that are higher by orders of magnitude than today's systems, but also have to guarantee high coverage and reliability. Thereby, sophisticated interference management is inevitable. The focus of this work is to develop cooperative transmission schemes that can be applied to cellular networks of the next generation and beyond. For this, conventional network architectures and communication protocols have to be challenged and new concepts need to be developed. Starting from cellular networks with base station cooperation, this thesis investigates how classical network architectures can evolve to future networks in which the mobile stations are no longer served by base stations in their close vicinity, but by a dynamic and flexible heterogeneity of different nodes. With the transition from classical cell-based networks to relay enabled post-cellular networks, we trade off node complexity with density. Aggressive spatial multiplexing can thereby deliver high data rates to large areas in a very efficient way, even when the backhaul capacity is limited or when in certain areas no backhaul access is available at all. The beneficial performance scaling shows that such post-cellular networks can offer a flexible and dynamic solution for mobile communication of future generations.

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More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.

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