We investigate a degree-biased cutting process on random recursive trees, where each vertex is deleted with probability proportional to its degree. We establish the splitting property and derive the explicit distribution of the number of vertices del...
On a convex polyhedron P, the cut locus C(x) with respect to a point x is a tree of geodesic segments (shortest paths) on P that includes every vertex. We say that P has a skeletal cut locus if there is some x in P such that C(x) subset Sk(P), where...
UE4 - Runtime terrain editor with vertex paint functionality (⭐ 51)
In geometry, an angle is formed by two lines that meet at a point. Each line is called a side of the angle, and the point they share is called the vertex
We consider the algorithmic decision problem that takes as input an $n$-vertex $k$-uniform hypergraph $H$ with minimum codegree at least $m-c$ and decides whether it has a matching of size $m$. We show that this decision problem is fixed parameter tr...
We show that, contrarily to recent claims, data from the Wilson (unimproved) fermionic action at three different beta values demonstrate the presence of a large Goldstone boson contribution in the quark pseudoscalar vertex, quantitatively close to...
We say that a pure $d$-dimensional simplicial complex $Δ$ on $n$ vertices is \emph{shelling completable} if $Δ$ can be realized as the initial sequence of some shelling of $Δ_{n-1}^{(d)}$, the $d$-skeleton of the $(n-1)$-dimensional simplex. A wel...
Let $Y$ be the subdivided claw, the $7$-vertex tree obtained from a claw $K_{1,3}$ by subdividing each edge exactly once. We characterize the graphs (finite and infinite) that do not have $Y$ as a subgraph, or, equivalently, do not have $Y$ as a mino...
We introduce a continuous space limit of the Vertex Reinforced Jump Process (VRJP) in dimension one, which we call Linearly Reinforced Motion (LRM) on $\R$. It is constructed out of a convergent Bass-Burdzy flow. The proof goes through the represent...
Cone, in mathematics, the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex). The path, to be definite, is directed by some closed plane curve …
What is a cone? A cone is a 3-D shape that has a flat, circular base and a curved surface that angles toward a single point called a vertex or apex. The curved surface of the cone is also called the lateral …
A cone is a 3D shape with a flat circular base and a curved surface that forms a sharp point at the top called vertex. Learn the definition, parts, formulas, & more.
For integers m >= 1, s >= 0, and t >= 1, let K_s + mK_t denote the join of a clique K_s and m vertex-disjoint copies of K_t. We prove that for fixed m >= 1, t >= 1, and s >= 0, R(K_s + mK_t, K_n) = O( n^{s+t-1} / (log n)^{s+t-2} ). This settles a pro...
In this paper, we use normal surface theory to study Dehn filling on a knot-manifold. First, it is shown that there is a finite computable set of slopes on the boundary of a knot-manifold that bound normal and almost normal surfaces in a one-vertex...
The Merrifield-Simmons conjectures states a relation between the distance of vertices in a simple graph $G$ and the number of independent sets, denoted as $σ(G)$, in vertex-deleted subgraphs. Namely, that the sign of the term $σ(G_{-u}) \cdot σ(G_...
Let $G = (V, E)$ be a graph and $σ(G)$ the number of independent (vertex) sets in $G$. Then the Merrifield-Simmons conjecture states that the sign of the term $σ(G_{-u}) \cdot σ(G_{-v}) - σ(G) \cdot σ(G_{-u-v})$ only depends on the parity of the...
This is the seventh part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VII), we give sufficient conditions for the...
jQuery.Feyn is a tool for drawing Feynman diagrams with Scalable Vector Graphics (SVG), written in JavaScript and runs in modern browsers. It features predefined propagator styles, vertex types, and symbols. Math formulae can be included as external...
Recommender systems benefit us in tackling the problem of information overload by predicting our potential choices among diverse niche objects. So far, a variety of personalized recommendation algorithms have been proposed and most of them are based...
Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is an image-based disease progression model with single-vertex resolution, designed to reconstruct long-term patterns of brain pathology from short-term longitudinal data sets....