Related papers: Subregularity in infinitely labeled generating tre…
Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A_{2n}(2143) of alternating…
Multi-label classification consists in classifying an instance into two or more classes simultaneously. It is a very challenging task present in many real-world applications, such as classification of biology, image, video, audio, and text.…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
Multi-label classification is an important yet challenging task in natural language processing. It is more complex than single-label classification in that the labels tend to be correlated. Existing methods tend to ignore the correlations…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
The maximally clustered permutations are characterized by avoiding the classical permutation patterns 3421, 4312, and 4321. This class contains the freely-braided permutations and the fully-commutative permutations. In this work, we show…
Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete. To lower its complexity, many extensions of graph…
We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numerical semigroups, we analyze some of its properties and use…
In materials science, the challenge of rapid prototyping materials with desired properties often involves extensive experimentation to find suitable microstructures. Additionally, finding microstructures for given properties is typically an…
Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…
In this paper, we find an explicit formula for the generating function that counts the circular permutations of length n avoiding the pattern 23 4 1 whose enumeration was raised as an open problem by Rupert Li. This then completes in all…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
Handling imbalance in class distribution when building a classifier over tabular data has been a problem of long-standing interest. One popular approach is augmenting the training dataset with synthetically generated data. While classical…
Providing pretrained language models with simple task descriptions in natural language enables them to solve some tasks in a fully unsupervised fashion. Moreover, when combined with regular learning from examples, this idea yields…
Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data:…
Despite much work on advanced deep learning and generative modeling techniques for tabular data generation and imputation, traditional methods have continued to win on imputation benchmarks. We herein present UnmaskingTrees, a simple method…