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Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including third and…
Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that…
Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…
A core feature of complex systems is that the interactions between elements in the present causally constrain each-other as the system evolves through time. To fully model all of these interactions (between elements, as well as ensembles of…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
The boundaries between physical and social networks have narrowed with the advent of the Internet and its pervasive platforms. This has given rise to a complex adaptive information ecosystem where individuals and machines compete for…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
Integrated Information Theory (IIT) is a prominent theory of consciousness that has at its centre measures that quantify the extent to which a system generates more information than the sum of its parts. While several candidate measures of…
Complex systems, from the human brain to the global economy, are made of multiple elements that interact in such ways that the behaviour of the `whole' often seems to be more than what is readily explainable in terms of the `sum of the…
Information theory is gaining popularity as a tool to characterize performance of biological systems. However, information is commonly quantified without reference to whether or how a system could extract and use it; as a result,…
Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…