Related papers: Detecting properties from descriptions of groups

We first show that every group-theoretical category is graded by a certain double coset ring. As a consequence, we obtain a necessary and sufficient condition for a group-theoretical category to be nilpotent. We then give an explicit…

Causal effect identification typically requires a fully specified causal graph, which can be difficult to obtain in practice. We provide a sufficient criterion for identifying causal effects from a candidate set of Markov equivalence…

We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…

We develop an algorithm for recognizing whether a character belongs to $\Sigma^m$. In order to apply it we just need to know that the ambient group is of type $\mathrm{FP}_m$ or of type $\mathrm{F}_2$ and that the word problem is solvable…

Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

Neural networks for computer vision extract uninterpretable features despite achieving high accuracy on benchmarks. In contrast, humans can explain their predictions using succinct and intuitive descriptions. To incorporate explainability…

Almost all modern imperative programming languages include operations for dynamically manipulating the heap, for example by allocating and deallocating objects, and by updating reference fields. In the presence of recursive procedures and…

This paper describes the automation of a new text categorization task. The categories assigned in this task are more syntactically, semantically, and contextually complex than those typically assigned by fully automatic systems that process…

Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's…

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for…

Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment…

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…

Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…

Communities are not static; they evolve, split and merge, appear and disappear, i.e. they are product of dynamical processes that govern the evolution of the network. A good algorithm for community detection should not only quantify the…

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…

Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…

It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$…

Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…