Related papers: Issues in data expansion in understanding critical…
When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models…
In this article, a correlation metric $\kappa_C$ is proposed for the inference of the dynamical state of neuronal networks. $\kappa_C$ is computed from the scaling of the correlation length with the size of the observation region, which…
Biological systems with many components often exhibit seemingly critical behaviors, characterized by atypically large correlated fluctuations. Yet the underlying causes remain unclear. Here we define and examine two types of criticality.…
The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order…
Shedding light onto how biological systems represent, process and store information in noisy environments is a key and challenging goal. A stimulating, though controversial, hypothesis poses that operating in dynamical regimes near the edge…
We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
We study relaxation processes in spin systems near criticality after a quench from a high-temperature initial state. Special attention is paid to the stage where universal behavior, with increasing order parameter emerges from an early…
The brain forms and stores distributed representations from sparse external input that compete for neuronal resources with already stored memory traces. It is unclear what dynamical properties of neural systems allow formation and…
Dynamic processes on networks are fundamental to understanding modern-day phenomena such as information diffusion and opinion polarization on the internet or epidemics spreading through society. However, such processes are notoriously…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
One of the important techniques of Data mining is Classification. Many real world problems in various fields such as business, science, industry and medicine can be solved by using classification approach. Neural Networks have emerged as an…
In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…
Despite their widespread utility across domains, basic network models face fundamental limitations when applied to complex biological systems, particularly in neuroscience. This paper critically examines these limitations and explores…
Two dimensional condensed matter is realised in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic…
Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic,…
The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both…
The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…
In this sequel paper we explore how macroscopic quantum phenomena can be measured or understood from the behavior of quantum correlations which exist in a quantum system of many particles or components and how the interaction strengths…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
The dynamics based on information transfer is proposed as an underlying mechanism for the scale-invariant dynamic critical behavior observed in a variety of systems. We apply the dynamics to the globally-coupled Ising model, which is…