Related papers: Two lilypond systems of finite line-segments
We address the question of how a localized microscopic defect, especially if it is small with respect to certain dynamic parameters, affects the macroscopic behavior of a system. In particular we consider two classical exactly solvable…
We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…
We prove that a set $A$ of at most $q$ non-collinear points in the finite plane $\mathbb{F}_{q}^{2}$ spans at least $\approx\frac{|A|}{\sqrt{q}}$ directions: this is based on a lower bound contained in [FST13], which we prove again together…
We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various…
This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth rates. These include the location in the complex plane of…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
For a projective variety $X$ defined over a non-Archimedean complete non-trivially valued field $k$, and a semipositive metrized line bundle $(L, \phi)$ over it, we establish a metric extension result for sections of $L^{\otimes n}$ from a…
We consider the "Touch and Stop" cluster growth percolation (CGP) model on the two dimensional square lattice. A key-parameter in the model is the fraction p of occupied "seed" sites that act as nucleation centers from which a particular…
Recent researches on complex systems highlighted the so-called super-linear growth phenomenon. As the system size $P$ measured as population in cities or active users in online communities increases, the total activities $X$ measured as GDP…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
We introduce a bond percolation procedure on a $D$-dimensional lattice where two neighbouring sites are connected by $N$ channels, each operated by valves at both ends. Out of a total of $N$, randomly chosen $n$ valves are open at every…
We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton through one cell of…
The two-type Richardson model describes the growth of two competing infections on $\mathbb{Z}^d$ and the main question is whether both infection types can simultaneously grow to occupy infinite parts of $\mathbb{Z}^d$. For bounded initial…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard…
Liesegang patterns emerge from precipitation processes and may be used to build bulk structures at submicron lengthscales. Thus they have significant potential for technological applications provided adequate methods of control can be…
The simplest way to obtain continuous interpolation between two points in high dimensional space is to draw a line between them. While previous works focused on the general connectivity between model parameters, we explored linear…