Related papers: On growing connected beta-skeletons
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
Previous works have shown the universality of allometric scalings under density and total value at city level, but our understanding about the size effects of regions on them is still poor. Here, we revisit the scaling relations between…
The following is an open problem in topology: Determine whether the Stone-\v{C}ech compactification of a widely-connected space is necessarily an indecomposable continuum. Herein we describe properties of $X$ that are necessary and…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
Understanding what types of phenomena lead to discontinuous phase transitions in the connectivity of random networks is an outstanding challenge. Here we show that a simple stochastic model of graph evolution leads to a discontinuous…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how…
An independent dominating set of a graph, also known as a maximal independent set, is a set $S$ of pairwise non-adjacent vertices such that every vertex not in $S$ is adjacent to some vertex in $S$. We prove that for $\Delta=4$ or…
The stability number of a graph G is the cardinality of a stability system of G (that is of a stable set of maximum size of G). A graph is alpha-stable if its stability number remains the same upon both the deletion and the addition of any…
Let $\Gamma$ be a distance-regular graph with classical parameters $(D, b, \alpha, \beta)$ satisfying $b\geq 2$ and $D\geq 3$. Let $r=1+b+b^2+\cdots+b^{D-1}$. In 1999, K. Metsch showed that there exists a positive constant $C(\alpha,b)$…
The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a nonlinear, stochastic…
Metabolic networks consist of linked functional components, or modules. The mechanism underlying metabolic network modularity is of great interest not only to researchers of basic science but also to those in fields of engineering. Previous…
Beta decay is a well-established and efficient probe of nuclear structure and provides important information also for halo nuclei. Detailed decay studies of near-dripline nuclei are challenging, but are now feasible due to the technical…
We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are…
In this note we show that $\beta'_*$, the $\beta$-function slopes in the electric and magnetic theories are equal at the corresponding infrared fixed points. This follows from the scaling of the correlators of the trace of the energy…
Flat sheets encoded with patterns of contraction/elongation morph into curved surfaces. If the surfaces bear Gauss curvature, the resulting actuation can be strong and powerful. We deploy the Gauss-Bonnet theorem to deduce the Gauss…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
Given the amino acid sequence of a protein, researchers often infer its structure and function by finding homologous, or evolutionarily-related, proteins of known structure and function. Since structure is typically more conserved than…