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We define a novel quantitative strategy inspired by the ecological notion of nestedness to single out the scale at which innovation complexity emerges from the aggregation of specialized building blocks. Our analysis not only suggests that…
The laws of thermodynamics apply to biophysical systems on the nanoscale as described by the framework of stochastic thermodynamics. This theory provides universal, exact relations for quantities like work, which have been verified in…
Nature's many complex systems--physical, biological, and cultural--are islands of low-entropy order within increasingly disordered seas of surrounding, high-entropy chaos. Energy is a principal facilitator of the rising complexity of all…
The metaphor of a potential epigenetic differentiation landscape broadly suggests that during differentiation a stem cell follows the steepest descending gradient toward a stable equilibrium state which represents the final cell type. It…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
We study the hydrodynamic description of collective dynamics driven by velocity {\it alignment}. It is known that such Euler alignment systems must flock towards a limiting ``flocking'' velocity, provided their solutions remain globally…
Uncertainty is an important feature of dynamic systems, and entropy has been widely used to measure this attribute. In this Letter, we prove that state aggregation and decomposition can decrease and increase the entropy, respectively, of…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
The present work employs the Linder parametrization of a constant growth index \cite{linder/index} to investigate the evolution of growth rate of clustering and the dissipation of configurational entropy in some of the most widely studied…
We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing…
An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
We examine the temporal evolution of the modular entropy and capacity (in particular, the fluctuation of the entanglement entropy) for systems of time-dependent oscillators coupled by a (time-dependent) parameter. Such models, through the…
Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
The tendency of irreversible processes to generate entropy is the ultimate driving force for the evolution of nature. In engineering, entropy production is often used as a measure of usable energy losses. In this study we show that the…
The local Universe displays a rich hierarchical pattern of galaxy clusters and superclusters. The early Universe, however, was almost smooth, with only slight 'ripples' seen in the cosmic microwave background radiation. Models of the…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
One of the most directly observable features of a transiting multi-planet system is their size-ordering when ranked in orbital separation. Kepler has revealed a rich diversity of outcomes, from perfectly ordered systems, like Kepler-80, to…