Related papers: Classification from a Computable Viewpoint

We classify gradings on matrix algebras by a finite abelian group. A grading is called good if all elementary matrices are homogeneous. For cyclic groups, all gradings on a matrix algebra over an algebraically closed field are good. We can…

We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…

Classifying journals or publications into research areas is an essential element of many bibliometric analyses. Classification usually takes place at the level of journals, where the Web of Science subject categories are the most popular…

Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…

Constellations are partial algebras that are one-sided generalisations of categories. It has previously been shown that the category of inductive constellations is isomorphic to the category of left restriction semigroups. Here we consider…

Big Data concern large-volume, growing data sets that are complex and have multiple autonomous sources. Earlier technologies were not able to handle storage and processing of huge data thus Big Data concept comes into existence. This is a…

Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically…

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…

Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…

We initiate the computability-theoretic study of ringed spaces and schemes. In particular, we show that any Turing degree may occur as the least degree of an isomorphic copy of a structure of these kinds. We also show that these structures…

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…

We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…

Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability,…

Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

One of the most powerful ideas in the study and classification of algebraic varieties is the notion of a model: that is, to single out an object, in the appropriate isomorphism class, with nice properties. This survey aims to define and…

This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…

Data classification, the process of analyzing data and organizing it into categories, is a fundamental computing problem of natural and artificial information processing systems. Ideally, the performance of classifier models would be…