Related papers: A computer based classification of caps in PG(4,2)
A constructive characterization of the class of uniformly $4$-connected graphs is presented. The characterization is based on the application of graph operations to appropriate vertex and edge sets in uniformly $4$-connected graphs, that…
Flocks are an important topic in the field of finite geometry, with many relations with other objects of interest. This paper is a contribution to the difficult problem of classifying flocks up to projective equivalence. We complete the…
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
The $P$ versus $NP$ problem is still unsolved. But there are several oracles with $P$ unequal $NP$ relative to them. Here we will prove, that $P\not=NP$ relative to a $P$-complete oracle. In this paper, we use padding arguments as the proof…
We describe and implement an algorithm to find all post-critically finite (PCF) cubic polynomials defined over $\mathbb{Q}$, up to conjugacy over $\text{PGL}_2(\bar{\mathbb{Q}})$. We describe normal forms that classify equivalence classes…
Several text classification tasks such as sentiment analysis, news categorization, multi-label classification and opinion classification are challenging problems even for modern deep learning networks. Recently, Capsule Networks (CapsNets)…
In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then,…
When creating the ranking based on the pairwise comparisons very often, we face difficulties in completing all the results of direct comparisons. In this case, the solution is to use the ranking method based on the incomplete PC matrix. The…
Capsule networks (CapsNets) have recently shown promise to excel in most computer vision tasks, especially pertaining to scene understanding. In this paper, we explore CapsNet's capabilities in optical flow estimation, a task at which…
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
Most image-search approaches today are based on the text based tags associated with the images which are mostly human generated and are subject to various kinds of errors. The results of a query to the image database thus can often be…
Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…
The rapid increase in data on galaxy images at low and high redshift calls for re-examination of the classification schemes and for new automatic objective methods. Here we present a classification method by Artificial Neural Networks. We…
2834 inequivalent spreads under the group $\mathrm{P}\Gamma\mathrm{L}(4,8)$. Therefore there are the same number of translation planes of order 64 with kernel containing $\mathrm{GF}(8)$, and we describe various properties of these planes.…
This paper introduces the 3DCapsule, which is a 3D extension of the recently introduced Capsule concept that makes it applicable to unordered point sets. The original Capsule relies on the existence of a spatial relationship between the…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Theoretical results are known about the completeness of a planar algebraic cubic curve as a (n,3)-arc in PG(2,q). They hold for q big enough and sometimes have restriction on the characteristic and on the value of the j-invariant. We…
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems…
Integrated Gradients (IG) and PatternAttribution (PA) are two established explainability methods for neural networks. Both methods are theoretically well-founded. However, they were designed to overcome different challenges. In this work,…