Related papers: Critical P\'olya urn
Universal critical properties can manifest themselves not only in spatial but also in temporal directions. It has been found that critical point with emergent symmetry exhibits intriguing spatial critical properties characterized by two…
The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic…
We comprehend the role of imperfections in materials consisting of interacting particles, arising from different origins on their universal features. Specifically, we report the static and dynamic responses in a cluster of Coulomb…
Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…
Many biological and cognitive systems do not operate deep within one or other regime of activity. Instead, they are poised at critical points located at phase transitions in their parameter space. The pervasiveness of criticality suggests…
We report avalanche criticality of thermal relaxation in glassy systems after a rapid quench by molecular simulation. Our analysis of the energy landscape and the scaling reveals that particle rearrangement is critical. The critical…
The critical behavior of many physical systems involves two competing $n^{}_1-$ and $n^{}_2-$component order-parameters, ${\bf S}^{}_1$ and ${\bf S}^{}_2$, respectively, with $n=n^{}_1+n^{}_2$. Varying an external control parameter $g$,…
The critical dynamics of conformal field theories on random surfaces is investigated beyond the previously studied dynamics of the overall area and the genus. It is found that the evolution of the order parameter in physical time performs a…
The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
Generic higher character Lifshitz critical behaviors are described using field theory and $\epsilon_{L}$-expansion renormalization group methods. These critical behaviors describe systems with arbitrary competing interactions. We derive the…
We propose two new evolutionary rules that is not mimic evolution of strategies based on the spatial Prisoner's Dilemma (PD). The former follows the selfish evolutionary rule and then the coexistence phase appears with weak phase transition…
In the present paper we prove that the probabilities of the P\'olya urn distribution (with negative replacement) satisfy a monotonicity property similar to that of the binomial distribution (P\'olya urn distribution with no replacement). As…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the…
Using cyclic shear to drive a two dimensional granular system, we determine the structural characteristics for different inter-particle friction coefficients. These characteristics are the result of a competition between mechanical…
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger,…
We study decoherence induced by a dynamic environment undergoing a quantum phase transition. Environment's susceptibility to perturbations - and, consequently, efficiency of decoherence - is amplified near a critical point. Over and above…