Related papers: Meta-universality classes at criticality
The robustness of the universality class concept of the chaotic transition was investigated by analytically obtaining its critical exponent for a wide class of maps. In particular, we extended the existing one-dimensional chaotic maps,…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
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…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large…
A model for opinion dynamics (Model I) has been recently introduced in which the binary opinions of the individuals are determined according to the size of their neighboring domains (population having the same opinion). The coarsening…
At the point of a second order phase transition also termed as a critical point, systems display long range order and their macroscopic behaviors are independent of the microscopic details making up the system. Due to these properties, it…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
We present a new paradigm in the study of brain mental dynamics on the basis of the stable transient activity neural networks observed in experiments. This new approach is in contrast to traditional system analysis usually adopted in…
The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition.…
Highly correlated brain dynamics produces synchronized states with no behavioral value, while weakly correlated dynamics prevent information flow. In between these states, the unique dynamical features of the critical state endow the brain…
In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum…
Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a…
Understanding how the test risk scales with model complexity is a central question in machine learning. Classical theory is challenged by the learning curves observed for large over-parametrized deep networks. Capacity measures based on…
Coarse-grained descriptions can be used to account for physical processes in which information is lost or not entirely accessible. In this paper, we start by proposing a connection between effective, coarse-grained descriptions of quantum…
Extended numerical simulations of threshold models have been performed on a human brain network with N=836733 connected nodes available from the Open Connectome project. While in case of simple threshold models a sharp discontinuous phase…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…