Related papers: Unveiling the Link between Complexity and Symmetry…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\em and} the (physical) states. For infinitely extended systems the states fall into physically…
The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. It…
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…
This work builds on a rich discourse surrounding the social brain hypothesis as well as the definition and quantification of social complexity. We believe this manuscript provides a new perspective on the topic by pairing a conceptual…
We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are often not effective and sufficient to contain them. Many common approaches do…
Classic economic science is reaching the limits of its explanatory powers. Complexity science uses an increasingly larger set of different methods to analyze physical, biological, cultural, social, and economic factors, providing a broader…
The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity.…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data.…
This preprint deals with the symmetry of parametrized families of systems and the changes therein as the parameter changes. There are (at least ?) two kinds of symmetry: generic and specific which behave in almost totally opposite ways as…
The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…