Related papers: The linear nature of pseudowords
Issues concerning intelligent data analysis occurring in machine learning are investigated. A scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order…
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…
In this paper we consider linear combinations of two trivariate homogeneous polynomials of second degree. We formulate and solve two problems: i) Characterization of polynomials for which all linear combinations are factorizable. ii) How…
In this paper, the Identity Problem for certain groups, which asks if the subsemigroup generated by a given finite set of elements contains the identity element, is related to problems regarding ordered groups. Notably, the Identity Problem…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if…
This note shows how iteration of the standard process of adjoining identities and zeros to semigroups gives rise naturally to the lexicographical ordering on the additive semigroup of n-tuples of nonnegative integers and n-tuples of…
This paper focuses on generalized pseudostandard words, defined by de Luca and De Luca in 2006. In every step of the construction, the involutory antimorphism to be applied for the pseudopalindromic closure changes and is given by a so…
Motivated by applications to information retrieval, we study the lattice of antichains of finite intervals of a locally finite, totally ordered set. Intervals are ordered by reverse inclusion; the order between antichains is induced by the…
Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y =…
In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We show that every continuous homogeneous quasimorphism on a finite-dimensional 1-connected simple Lie group arises as the relative growth of any continuous bi-invariant partial order on that group. More generally we show, that an arbitrary…
We give a short and self-contained proof of Levi's Extension Lemma for pseudoline arrangements.
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…
An element of a group is said to be reversible if it is conjugate to its inverse. We characterise the reversible elements in the group of diffeomorphisms of the real line, and in the subgroup of order preserving diffeomorphisms.
Given an infinite linear group with a finite set of generators, we show that the shortest word length of an element of infinite order has an upper bound that depends only on the number of generators and the degree. This provides a…
Establishing dense correspondences across semantically similar images remains a challenging task due to the significant intra-class variations and background clutters. Traditionally, a supervised learning was used for training the models,…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
Recent advances in semi-supervised object detection (SSOD) are largely driven by consistency-based pseudo-labeling methods for image classification tasks, producing pseudo labels as supervisory signals. However, when using pseudo labels,…