Related papers: Critical P\'olya urn
This work concerns the long-term dynamics of a spatiotemporal many-body deterministic model that exhibits emergence and self-organization, and which has been recently proposed as a new paradigm for Artificial Life. Collective structures…
Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian brain, the complex dynamics that spontaneously emerge from neuronal interactions have been characterized as neuronal avalanches, a…
The possible control of competitive invasion by infection of the invader and multiplicative noise is studied. The basic model is the Lotka-Volterra competition system with emergent carrying capacities. Several stationary solutions of the…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
Neural networks with equal excitatory and inhibitory feedback show high computational performance. They operate close to a critical point characterized by the joint activation of large populations of neurons. Yet, in macaque motor cortex we…
The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of…
The hypothesis that living systems can benefit from operating at the vicinity of critical points has gained momentum in recent years. Criticality may confer an optimal balance between exceedingly ordered and too noisy states. We here…
P{\'o}lya urns are urns where at each unit of time a ball is drawn and is replaced with some other balls according to its colour. We introduce a more general model: The replacement rule depends on the colour of the drawn ball and the value…
We study the role played by topological textures and antitextures during the phase ordering of a two-dimensional system described by the discretised nonlinear O(3) sigma model with purely dissipative dynamics. We identify and characterise…
We propose an elementary but effective approach to studying a general class of Poissonized tenable and balanced urns on two colors. We characterize the asymptotic behavior of the process via a partial differential equation that governs the…
We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kind of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate…
Cognitive function requires the coordination of neural activity across many scales, from neurons and circuits to large-scale networks. As such, it is unlikely that an explanatory framework focused upon any single scale will yield a…
As a promising computational paradigm, occurrence of critical states in artificial and biological neural networks has attracted wide-spread attention. An often-made explicit or implicit assumption is that one single critical state is…
In this paper we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a…
Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
In this paper, we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the \emph{negatively…
We consider a class of models of opinion formation where the dissemination of individual opinions occurs through the spreading of local consensus and disagreement. We study the emergence of full collective consensus or maximal disagreement…