Related papers: Critical P\'olya urn
The critical brain hypothesis posits that neural systems operate near a phase transition, optimizing the processing of information. While scale invariance and non-Gaussian dynamics--hallmarks of criticality--have been observed in brain…
In Probabilistic Risk Management, risk is characterized by two quantities: the magnitude (or severity) of the adverse consequences that can potentially result from the given activity or action, and by the likelihood of occurrence of the…
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of…
The dynamics of critical slope self-organized critical models is studied, using a previous mapping into a linear interface depinning model dragged at one end. The model is solved obtaining the complete set of scaling exponents. Some results…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…
Self-organized criticality is a well-established phenomenon, where a system dynamically tunes its structure to operate on the verge of a phase transition. Here, we show that the dynamics inside the self-organized critical state are…
We present two models of competitive learning, which are respectively interfacial and cooperative learning. This learning is outcome-related, so that spatially and temporally local environments influence the conversion of a given site…
Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with non-equilibrium problems, however, the distinction in…
Numerous online services are data-driven: the behavior of users affects the system's parameters, and the system's parameters affect the users' experience of the service, which in turn affects the way users may interact with the system. For…
Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme…
We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous…
Deterministic chaos is commonly associated with spectral criticality: exponential sensitivity is expected when Jacobian eigenvalues exceed unity in parts of the attractor, producing the local expansion that offsets contraction elsewhere. We…
We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but closer examination of the mechanism reveals that it…
We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the…
Self-organizing system is studied whose behavior is governed by field of an order parameter, a fluctuation amplitude of conjugate field and a couple of Grassmannian conjugated fields that define the entropy as a control parameter. Within…
Recurrent neural networks are convenient and efficient models for language modeling. However, when applied on the level of characters instead of words, they suffer from several problems. In order to successfully model long-term…
Criticality has been conjectured as an integral part of neuronal network dynamics. Operating at a critical threshold requires precise parameter tuning and a corresponding mechanism remains an open question. Recent studies have suggested…
Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Moreover, experimental studies of morphology indicate that neurons develop a network of small-world-like connections, with the…