Related papers: Garside and quadratic normalisation: a survey
We consider the natural monoid structure on the set of quadratic rings over an arbitrary base scheme and characterize this monoid in terms of discriminants.
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
We investigate various aspects of the "weighted" greedy algorithm with respect to a Schauder basis. For a weight w, we describe w-greedy, w-almost-greedy and w-partially-greedy bases, and show some properties of w-semi-greedy bases. To…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
We present the natural arguments for the rationality of a recently proposed simple approach for renormalization which is based solving differential equations. The renormalization group equation is also derived in a natural way and…
A base for a permutation group $G$ acting on a set $\Omega$ is a sequence $\mathcal{B}$ of points of $\Omega$ such that the pointwise stabiliser $G_{\mathcal{B}}$ is trivial. Denote the minimum size of a base for $G$ by $b(G)$. There is a…
We propose to study the infrared behaviour of polymerised (or tethered) random manifolds of dimension D interacting via an exclusion condition with a fixed impurity in d-dimensional Euclidean space in which the manifold is embedded. We…
In this paper we will present the results of Artin--Markov on braid groups by using the Groebner--Shirshov basis. As a consequence we can reobtain the normal form of Artin--Markov--Ivanovsky as an easy corollary.
This note documents the specification of normal forms in cubical type theory. The definition is already present in the proof of normalization for cubical type theory, but we present it in a more traditional style explicitly for reference.
The purpose of this paper is to introduce $\omega$-Chebyshev-greedy and $\omega$-partially greedy approximation classes and to study their relation with $\omega$-approximation spaces, where the latter are a generalization of the classical…
In this paper we introduce the framed pure braid group on $n$ strands of an oriented surface, a topological generalisation of the pure braid group $P_n$. We give different equivalents definitions for framed pure braid groups and we study…
We consider a Bayesian hierarchical version of the normal theory general linear model which is practically relevant in the sense that it is general enough to have many applications and it is not straightforward to sample directly from the…
Consider a collection of weighted subsets of a ground set N. Given a query subset Q of N, how fast can one (1) find the weighted sum over all subsets of Q, and (2) sample a subset of Q proportionally to the weights? We present a tree-based…
We develop, in the context of general relativity, the notion of a geoid -- a surface of constant "gravitational potential". In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general…
We propose a new computationally efficient method for quantizing the weights of pre- trained neural networks that is general enough to handle both multi-layer perceptrons and convolutional neural networks. Our method deterministically…
Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to…
Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss…
We develop a rigidity theory for bar-joint frameworks in Euclidean $d$-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class.…
In this work, we address a question posed by Dehornoy et al. in the book "Foundations of Garside Theory" that asks for a theory of groups of $\mathrm{I}_G$-type when $G$ is a Garside group. In this article, we introduce a broader notion…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…