Related papers: Quantifying Complexity: An Object-Relations Approa…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…
Entanglement entropy, which is a measure of quantum correlations between separate parts of a many-body system, has emerged recently as a fundamental quantity in broad areas of theoretical physics, from cosmology and field theory to…
Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify…
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…
This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics…
We present a quantum information-inspired framework for analyzing complex systems through multivariate time series. In this approach the system's state is encoded into a density matrix, providing a compact representation of higher-order…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states.…
CoCoE stands for Complexity, Coherence and Entropy, and presents an extensible methodology for empirical analysis of Linked Open Data (i.e., RDF graphs). CoCoE can offer answers to questions like: Is dataset A better than B for knowledge…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
Computational modeling of a complex system is limited by the parts of the system with the least information. While detailed models and high-resolution data may be available for parts of a system, abstract relationships are often necessary…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We introduce Complexity as Advantage (CAA), a framework that defines the complexity of a system relative to a family of observers. Instead of measuring complexity as an intrinsic property, we evaluate how much predictive regret a system…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…