Related papers: Nests, and their Role in the Orderability Problem
We formalize the notion of nesting probabilistic programming queries and investigate the resulting statistical implications. We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed,…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
Systems of randomly packed, macroscopic elements, from jammed spherical grains to tangled long filaments, represent a broad class of disordered meta-materials with a wide range of applications and manifestations in nature. A `bird nest'…
This paper have two parts. In the first part we discuss word embeddings. We discuss the need for them, some of the methods to create them, and some of their interesting properties. We also compare them to image embeddings and see how word…
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
The Ordered Set Theory is a branch of Mathematics that studies partially ordered sets (usually posets) and lattices. The meaning of dimension is one of the main parts of this eld. Dimensions of partially ordered sets and lattices have been…
We introduce the notion of a nest-representable tolerance and show that some results from our former paper "From congruence identities to tolerance identities" [CT] can be extended to this more general setting.
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
This note is developing, and we will include many additions in the near future. Our purpose here is to highlight that there is plenty of space for a topological development of the Fermat Real Line.
The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts.…
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
Sentence ordering is the task of arranging the sentences of a given text in the correct order. Recent work using deep neural networks for this task has framed it as a sequence prediction problem. In this paper, we propose a new framing of…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
We consider here the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem…
We characterize the order of principal congruences of a bounded lattice as a bounded ordered set. We also state a number of open problems in this new field.
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…
In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices $n=2^m$ we define the set of all the possible…