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Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While…
In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller…
We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a…
Borrowing inspiration from Marcone and Mont\'{a}lban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an…
We study the compressed representation of a ranked tree by a (string) straight-line program (SLP) for its preorder traversal, and compare it with the well-studied representation by straight-line context free tree grammars (which are also…
Comparability graphs are the undirected graphs whose edges can be directed so that the resulting directed graph is transitive. They are related to posets and have applications in scheduling theory. This paper considers the problem of…
Lotuses are certain types of finite contractible simplicial complexes, obtained by identifying vertices of polygons subdivided by diagonals. As we explained in a previous paper, each time one resolves a complex reduced plane curve…
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
We consider the problem of lossless compression of binary trees, with the aim of reducing the number of code bits needed to store or transmit such trees. A lossless grammar-based code is presented which encodes each binary tree into a…
Trees are partial orderings where every element has a linearly ordered set of smaller elements. We define and study several natural notions of completeness of trees, extending Dedekind completeness of linear orders and Dedekind-MacNeille…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
Decision trees are renowned for their ability to achieve high predictive performance while remaining interpretable, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data…
We define a class of partially labeled trees and use them to find simple proofs for two recent enumeration results of Colin Defant concerning stack-sorting preimages of permutation classes.
We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
In this work, we propose a simple but effective method to interpret black-box machine learning models globally. That is, we use a compact binary tree, the interpretation tree, to explicitly represent the most important decision rules that…
This paper defines a notion of binding trees that provide a suitable model for second-order type systems with F-bounded quantifiers and equirecursive types. It defines a notion of regular binding trees that correspond in the right way to…