Search results for "Algebra"
showing 10 items of 4129 documents
Discovering unbounded unions of regular pattern languages from positive examples
1996
The problem of learning unions of certain pattern languages from positive examples is considered. We restrict to the regular patterns, i.e., patterns where each variable symbol can appear only once, and to the substring patterns, which is a subclass of regular patterns of the type xαy, where x and y are variables and α is a string of constant symbols. We present an algorithm that, given a set of strings, finds a good collection of patterns covering this set. The notion of a ‘good covering’ is defined as the most probable collection of patterns likely to be present in the examples, assuming a simple probabilistic model, or equivalently using the Minimum Description Length (MDL) principle. Ou…
SORT-CC: A procedure for the statistical treatment of free sorting data
2008
International audience; A statistical approach for the analysis of free sorting data is discussed. In a first stage, the sorting data from each subject are arranged into a dataset consisting of indicator variables which reflect the memberships of the stimuli to the groups formed by the subject under consideration. Thereafter, an appropriate standardization is applied on these data and a three way statistical method, namely Common Components and Specific Weights Analysis, is performed on the datasets thus obtained. This makes it possible to take account of the individual differences among the subjects and to depict graphical displays showing the relationships among the stimuli on the one han…
Compound conditionals as random quantities and Boolean algebras
2022
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalised from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued object, with betting-based semantics, and its related approach as random quantity as mainly developed by two of the authors. Compound conditionals have been studied in the literature, but not in full generality. In this paper we provide a natural procedure to explicitly attach conditional random quantities to arbitrary compound conditionals that also allows us to compute their previsions. By studying the properties of these random quantities, we show that, in f…
Bodies Making Spaces: Understanding the Airport as a Site of Dissonance
2019
AbstractTrakilović theorizes the airport as a site where cultural/European notions of belonging are negotiated and controlled. Focusing on Schiphol airport in Amsterdam, the chapter approaches both the airport itself as well as its nearby detention center as one complex cultural phenomenon, from which Schiphol emerges as a site of heritage dissonance. Taking a phenomenological approach, the chapter explores what it means to be an embodied subject at the airport, taking the narrative of a Syrian newcomer who is relocated to the detention center as well as the author’s own experience of the airport as its analytical starting points. The selective processes of in- and exclusion at the airport …
Sense Equivalence in plWordNet to Princeton WordNet Mapping
2019
Abstract Though the interest in use of wordnets for lexicography is (gradually) growing, no research has been conducted so far on equivalence between lexical units (or senses) in inter-linked wordnets. In this paper, we present and validate a procedure of sense-linking between plWordNet and Princeton WordNet. The proposed procedure employs a continuum of three equivalence types: strong, regular and weak, distinguished by a custom-designed set of formal, semantic and translational features. To validate the procedure, three independent samples of 120 sense pairs were manually analysed with respect to the features. The results show that synsets from the two wordnets linked by interlingual syno…
Multi-class Text Complexity Evaluation via Deep Neural Networks
2019
Automatic Text Complexity Evaluation (ATE) is a natural language processing task which aims to assess texts difficulty taking into account many facets related to complexity. A large number of papers tackle the problem of ATE by means of machine learning algorithms in order to classify texts into complex or simple classes. In this paper, we try to go beyond the methodologies presented so far by introducing a preliminary system based on a deep neural network model whose objective is to classify sentences into more of two classes. Experiments have been carried out on a manually annotated corpus which has been preprocessed in order to make it suitable for the scope of the paper. The results sho…
A numerical property of Hilbert functions and lex segment ideals
2017
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the Osequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called fractal functions, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.
On the Betti numbers of three fat points in P1 × P1
2019
In these notes we introduce a numerical function which allows us to describe explicitly (and nonrecursively) the Betti numbers, and hence, the Hilbert function of a set Z of three fat points whose support is an almost complete intersection (ACI) in P1 × P1 . A nonrecursively formula for the Betti numbers and the Hilbert function of these configurations is hard to give even for the corresponding set of five points on a special support in P2 and we did not find any kind of this result in the literature. Moreover, we also give a criterion that allows us to characterize the Hilbert functions of these special set of fat points.
Infinitesimal deformations of double covers of smooth algebraic varieties
2003
The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi--Yau threefolds which are non--singular models of do…
OPERADS AND JET MODULES
2005
Let $A$ be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of $A$-modules. We define certain symmetric product functors of such modules generalising the tensor product of modules over commutative algebras, which we use to define the notion of a jet module. This in turn generalises the notion of a jet module over a module over a classical commutative algebra. We are able to define Atiyah classes (i.e. obstructions to the existence of connections) in this generalised context. We use certain model structures on the category of $A$-modules to study the properties of these Atiyah classes. The purpose of the paper is not to present any really de…