Related papers: Trees of definable sets over the p-adics
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case of three-graphs (that is, hypergraphs whose edges have…
We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic…
Let $t$ be a rooted tree and $n_i(t)$ the number of nodes in $t$ having $i$ children. The degree sequence $(n_i(t),i\geq 0)$ of $t$ satisfies $\sum_{i\ge 0} n_i(t)=1+\sum_{i\ge 0} in_i(t)=|t|$, where $|t|$ denotes the number of nodes in…
In this paper, we investigate the structures of an extremal tree which has the minimal number of subtrees in the set of all trees with the given degree sequence of a tree. In particular, the extremal trees must be caterpillar and but in…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
We construct a notion of p-adic measure on Artin n-stacks which are strongly of finite type over the ring of p-adic integers. We also prove the rationality of of the Poincare series and the Serre series associated with such stacks. Finally,…
The status of a vertex $v$ in a connected graph is the sum of the distances from $v$ to all other vertices. The status sequence of a connected graph is the list of the statuses of all the vertices of the graph. In this paper we investigate…
A few notes about infinite trees in a descriptive set-theoretic setting.
Contour trees have been developed to visualize or encode scalar data in imaging technologies and scientific simulations. Contours are defined on a continuous scalar field. For discrete data, a continuous function is first interpolated,…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
We introduce a family of mathematical objects called $\mathcal{P}$-schemes, where $\mathcal{P}$ is a poset of subgroups of a finite group $G$. A $\mathcal{P}$-scheme is a collection of partitions of the right coset spaces $H\backslash G$,…
Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of context-specific Bayesian networks. In this paper, we…
We introduce essential subtrees for terms (trees) and tree automata . There are some results concerning independent sets of subtrees and separable sets for a tree and an automaton.
In this paper, based on results of exact learning, test theory, and rough set theory, we study arbitrary infinite families of concepts each of which consists of an infinite set of elements and an infinite set of subsets of this set called…
Ensemble trees are a popular machine learning model which often yields high prediction performance when analysing structured data. Although individual small decision trees are deemed explainable by nature, an ensemble of large trees is…
The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…