Related papers: Strong Emergence Arising from Weak Emergence
Several modifications of the famous mathematical Game of Life are introduced by making Game of Life rules stochastic and mutual influence of cells in their 8-neighborhood on a rectangular lattice spatially non-uniform. Results are reported…
Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…
Despite major advances in climate science over the last 30 years, persistent uncertainties in projections of future climate change remain. Climate projections are produced with increasingly complex models which attempt to represent key…
A broad range of natural and social systems from human microbiome to financial markets can go through critical transitions, where the system suddenly collapses to another stable configuration. Critical transitions can be unexpected, with…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
How many parameters are required for a model to execute a given task? It has been argued that large language models, pre-trained via self-supervised learning, exhibit emergent capabilities such as multi-step reasoning as their number of…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
Causal emergence is the theory that macroscales can reduce the noise in causal relationships, leading to stronger causes at the macroscale. First identified using the effective information and later the integrated information in model…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet…
Short-term survival and an exuberant plunge into building our future are generating a new kind of unintended consequence -- hidden fragility. This is a direct effect of the sophistication and structural complexity of the socio-technical…
Societies experience politically stable and unstable phases along history, whereas political power is usually passed to new elite groups by these changes. Structural dynamics of the elites in a society have been proposed to be one of the…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
Will a large economy be stable? Building on Robert May's original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in…
We explore how physical scale and population size shape the emergence of complex behaviors in open-ended ecological environments. In our setting, agents are unsupervised and have no explicit rewards or learning objectives but instead evolve…
Many systems in chemistry, biology, finance and social sciences present emerging features which are not easy to guess from the elementary interactions of their microscopic individual components. In the past, the macroscopic behavior of such…
In models for the evolution of predation from initially purely competitive species interactions, the propensity of predation is most often assumed to be a direct consequence of the relative morphological and physiological traits of…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
Emergence is a concept in complexity science that describes how many-body systems manifest novel higher-level properties, properties that can be described by replacing high-dimensional mechanisms with lower-dimensional effective variables…