Related papers: Using rational numbers to key nested sets

Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…

Targeting in-memory one-dimensional search keys, we propose a novel DIstribution-driven Learned Index tree (DILI), where a concise and computation-efficient linear regression model is used for each node. An internal node's key range is…

A Concept Tree is a structure for storing knowledge where the trees are stored in a database called a Concept Base. It sits between the highly distributed neural architectures and the distributed information systems, with the intention of…

We study the problem of generating, ranking and unranking of unlabeled ordered trees whose nodes have maximum degree of $\Delta$. This class of trees represents a generalization of chemical trees. A chemical tree is an unlabeled tree in…

In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational…

Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…

We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…

We address the problem of semantic querying of relational databases (RDB) modulo knowledge bases using very expressive knowledge representation formalisms, such as full first-order logic or its various fragments. We propose to use a…

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

Some researchers claim that language acquisition is critically dependent on experiencing linguistic input in order of increasing complexity. We set out to test this hypothesis using a simple recurrent neural network (SRN) trained to predict…

In the first place, a novel, yet straightforward in-place integer value-sorting algorithm is presented. It sorts in linear time using constant amount of additional memory for storing counters and indices beside the input array. The…

We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it…

A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques…

Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…

The problems that scientists face in creating well designed databases intersect with the concerns of data curation. Entity-relationship modeling and its variants have been the basis of most relational data modeling for decades. However,…

Link-based data structures, such as linked lists and binary search trees, have many well-known rearrangement steps allowing for efficient implementations of insertion, deletion, and other operations. We describe a rearrangement primitive…

Recently, the text-to-table generation task has attracted increasing attention due to its wide applications. In this aspect, the dominant model formalizes this task as a sequence-to-sequence generation task and serializes each table into a…