Related papers: Probabilistic Methods in the Study of Topological …
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We present an evaluation of the performance of an automated classification of the Hipparcos periodic variable stars into 26 types. The sub-sample with the most reliable variability types available in the literature is used to train…
We propose random hinge forests, a simple, efficient, and novel variant of decision forests. Importantly, random hinge forests can be readily incorporated as a general component within arbitrary computation graphs that are optimized…
The Harary index of a graph $G$ is recently introduced topological index, defined on the reverse distance matrix as $H(G)=\sum_{u,v \in V(G)}\frac{1}{d(u,v)}$, where $d(u,v)$ is the length of the shortest path between two distinct vertices…
We study tree-indexed random walks as introduced by Benjamini, H\"aggstr\"om, and Mossel, i.e. labelings of a tree for which adjacent vertices have labels differing by 1. It is a conjecture of those authors that the distribution of the…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…
In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs); a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space.…
In this paper, topological indices play a significant role in the analysis of caterpillar trees, especially due to their applications in chemical graph theory. We presented a study on topological indices related to the Sigma index, which we…
We study a random recursive tree model featuring complete redirection called the random friend tree and introduced by Saram\"aki and Kaski. Vertices are attached in a sequential manner one by one by selecting an existing target vertex and…
Making use of a majorization technique for a suitable class of graphs, we derive upper and lower bounds for some topological indices depending on the degree sequence over all vertices, namely the first general Zagreb index and the first…
We derive sharp lower bounds for the first and the second Zagreb indices ($M_1$ and $M_2$ respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. $M_1$ is minimized by a tree with all…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
In this paper, we have studied bounds based on topological indicators, from which we selected Albertson index $\mathrm{irr}$ and the Sigma index $\sigma$. The Sigma index was defined through the following relationship: \[…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
Topological indices play a significant role in mathematical chemistry. Given a graph $\mathcal{G}$ with vertex set $\mathcal{V}=\{1,2,\dots,n\}$ and edge set $\mathcal{E}$, let $d_i$ be the degree of node $i$. The degree-based topological…
We consider topological indices I that are sums of f(deg(u)) f(deg(v)), where {u,v} are adjacent vertices and f is a function. The Randi{\'c} connectivity index or the Zagreb group index are examples for indices of this kind. In earlier…
Staged trees are probabilistic graphical models capable of representing any class of non-symmetric independence via a coloring of its vertices. Several structural learning routines have been defined and implemented to learn staged trees…
Let $\mathcal {T}^{\Delta}_n$ denote the set of trees of order $n$, in which the degree of each vertex is bounded by some integer $\Delta$. Suppose that every tree in $\mathcal {T}^{\Delta}_n$ is equally likely. For any given subtree $H$,…
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric terms, the model consists of points inside a toric variety.…