Related papers: Using rational numbers to key nested sets
For the elements of a numerical semigroup which are larger than the Frobenius number, we introduce the definition of, seed, by broadening the notion of generator. This new concept allows us to explore the semigroup tree in an alternative…
Uncovering causal relationships in data is a major objective of data analytics. Causal relationships are normally discovered with designed experiments, e.g. randomised controlled trials, which, however are expensive or infeasible to be…
Search trees are commonly used to implement access operations to a set of stored keys. If this set is static and the probabilities of membership queries are known in advance, then one can precompute an optimal search tree, namely one that…
The "ordered set" abstract data type with operations "insert", "erase", "find", "min", "max", "next" and "prev" is ubiquitous in computer science. It is usually implemented with red-black trees, $B$-trees, or $B^+$-trees. We present our…
Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for {\it bicombining tree-child networks}…
A random-key genetic algorithm is an evolutionary metaheuristic for discrete and global optimization. Each solution is encoded as a vector of N random keys, where a random key is a real number randomly generated in the continuous interval…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…
Any secured system can be modeled as a capability-based access control system in which each user is given a set of secret keys of the resources he is granted access to. In some large systems with resource-constrained devices, such as sensor…
Given a gene tree and a species tree, ancestral configurations represent the combinatorially distinct sets of gene lineages that can reach a given node of the species tree. They have been introduced as a data structure for use in the…
Text clustering holds significant value across various domains due to its ability to identify patterns and group related information. Current approaches which rely heavily on a computed similarity measure between documents are often limited…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
We introduce a framework for generating Chain-of-Thought (CoT) rationales to enhance text-to-SQL model fine-tuning. These rationales consist of intermediate SQL statements and explanations, serving as incremental steps toward constructing…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
We propose a method to identify all the nodes that are relevant to compute all the conditional probability distributions for a given set of nodes. Our method is simple, effcient, consistent, and does not require learning a Bayesian network…
For a numerical semigroup, we encode the set of primitive elements that are larger than its Frobenius number and show how to produce in a fast way the corresponding sets for its children in the semigroup tree. This allows us to present an…
As closed-loop materials discovery systems scale to produce millions of candidate compounds, the credibility of the novelty they reward becomes a critical concern. Novelty is commonly assessed against databases of ordered crystal…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…