Related papers: On growing connected beta-skeletons
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
By Brook's Theorem, every n-vertex graph of maximum degree at most Delta >= 3 and clique number at most Delta is Delta-colorable, and thus it has an independent set of size at least n/Delta. We give an approximate characterization of graphs…
We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3.…
Let $\mathcal{G}$ be a $k$-uniform hypergraph, $\mathcal{L}_{\mathcal{G}}$ be its Laplacian tensor. And $\beta( \mathcal{G})$ denotes the maximum number of linearly independent nonnegative eigenvectors of $\mathcal{L}_{\mathcal{G}}$…
We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing…
For $\beta \geq 1$, the \emph{$\beta$-skeleton depth} ($\SkD_\beta$) of a query point $q\in \mathbb{R}^d$ with respect to a distribution function $F$ on $\mathbb{R}^d$ is defined as the probability that $q$ is contained within the…
A simplified model of clonal plant growth is formulated, motivated by observations of spatial structures in Posidonia oceanica meadows in the Mediterranean Sea. Two levels of approximation are considered for the scale-dependent feedback…
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by…
The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$.…
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
Urban populations exhibit fractal organization and systematic scaling regularities, yet the scaling exponents reported across cities vary substantially, challenging existing theory. Using 100~m gridded population maps for 477 urban areas…
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
Given an Orthogonal-Buekenhout-Metz unital $U_{\alpha,\beta}$, embedded in $PG(2,q^2)$, and a point $P\notin U_{\alpha,\beta}$, we study the set of feet, $\tau_{P}(U_{\alpha,\beta})$, of $P$ in $U_{\alpha,\beta}$. We characterize…
This paper deals with a problem which describes tuberculosis granuloma formation \begin{align*} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v) - uv - u + \beta, &x \in \Omega,\ t>0, \\ v_t = \Delta v + v -uv + \mu w, &x \in…
We construct random metric spaces by gluing together an infinite sequence of pointed metric spaces that we call blocks. At each step, we glue the next block to the structure constructed so far by randomly choosing a point on the structure…