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We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…
In the work [4] tree-rooted planar cubic maps with marked directed edge (not in this tree) were enumerated. The number of such objects with $2n$ vertices is $C_{2n}\cdot C_{n+1}$, where $C_k$ is Catalan number. In this work a marked…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant extension known as '$\Gamma$-species' which incorporates data about 'structural' group actions). This culminates…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
We give a summary of recent progress on the signed area enumeration of closed walks on planar lattices. Several connections are made with quantum mechanics and statistical mechanics. Explicit combinatorial formulae are proposed which rely…
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now…
Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…
Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total…
Spectral methods include a family of algorithms related to the eigenvectors of certain data-generated matrices. In this work, we are interested in studying the geometric landscape of the eigendecomposition problem in various spectral…
A common approach to aggregate classification estimates in an ensemble of decision trees is to either use voting or to average the probabilities for each class. The latter takes uncertainty into account, but not the reliability of the…
In this article we propose a heuristic algorithm to explore search space trees associated with instances of combinatorial optimization problems. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
There is a rising interest in mapping trees using satellite or aerial imagery, but there is no standardized evaluation protocol for comparing and enhancing methods. In dense canopy areas, the high variability of tree sizes and their spatial…
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher…
Random Forests and related tree-based methods are popular for supervised learning from table based data. Apart from their ease of parallelization, their classification performance is also superior. However, this performance, especially…
We develop a combinatorial model of paperfolding for the purposes of enumeration. A planar embedding of a graph is called a {\em crease pattern} if it represents the crease lines needed to fold a piece of paper into something. A {\em flat…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…