Related papers: Forest Fire Model on $\mathbb{Z}_{+}$ with Delays

We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree…

Forest fires may cause considerable damages both in ecosystems and lives. This proposal describes the application of Internet of Things and wireless sensor networks jointly with multi-hop routing through a real time and dynamic monitoring…

In this paper we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for…

We show there exist UV-complete field-theoretic models in general dimension, including $2+1$, with the spontaneous breaking of a global symmetry, which persists to the arbitrarily high temperatures. Our example is a conformal vector model…

The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…

Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…

In this paper we study the complexity of the firefighter problem and related problems on trees when more than one firefighter is available at each time step, and answer several open questions of Finbow and MacGillivray 2009. More precisely,…

Consider critical site percolation on a "nice" planar lattice: each vertex is occupied with probability $p = p_c$, and vacant with probability $1 - p_c$. Now, suppose that additional vacancies ("holes", or "impurities") are created,…

In this paper we developed the model for the carbon dioxide emission from forest fire. The master equation for the spreading of the carbon dioxide to atmosphere is the hyperbolic diffusion equation. In the paper we study forest fire ignited…

We consider a new IDLA - particle system model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. We prove that almost surely all trees are finite.

We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…

We study the distribution of ages in the mean field forest fire model introduced by R\'ath and T\'oth. This model is an evolving random graph whose dynamics combine Erd\H{o}s-R\'enyi edge-addition with a Poisson rain of lightning strikes.…

We reconsider a model introduced by Bak, Chen, and Tang (Phys. Rev. A 38, 364 (1988)) as a supposedly self-organized critical model for forest fires. We verify again that the model is not critical in 2 dimensions, as found also by previous…

A few notes about infinite trees in a descriptive set-theoretic setting.

We have explored in three dimensions the fate of a massive white dwarf as a function of different initial locations of carbon ignition, with the aid of a SPH code. The calculated models cover a variety of possibilities ranging from the…

We investigate the growth of clusters within the forest fire model of R\'{a}th and T\'{o}th [22]. The model is a continuous-time Markov process, similar to the dynamical Erd\H{o}s-R\'{e}nyi random graph but with the addition of so-called…

It is well known that in Zermelo-Fraenkel (ZF) set theory any finite set is decidable. In this paper we discuss an extension of ZF where this result is no longer valid. Such an extension is quasi-set theory and it has its origin on problems…

For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…

Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…

Machine learning (ML)-based wildfire detection methods have been developed in recent years, primarily using deep learning (DL) models trained on large collections of wildfire images and videos. However, peatland fires exhibit distinct…