Related papers: A computer based classification of caps in PG(4,2)
We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, (relative) $\Delta^0_\alpha$ bi-embeddable categoricity, and degrees of…
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the…
We solve the equivalence problem for vacuum PP-wave spacetimes by employing the Karlhede algorithm. Our main result is a suite of Cartan invariants that allows for the complete invariant classification of the vacuum pp-waves. In particular,…
We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.
We define a \textit{cap} in the affine geometry $AG(n,2)$ to be a subset in which any collection of 4 points is in general position. In this paper we classify, up to affine equivalence, all caps in $AG(n,2)$ of size $k \leq 9$. As a result,…
Capsule Network (CapsNet) is among the promising classifiers and a possible successor of the classifiers built based on Convolutional Neural Network (CNN). CapsNet is more accurate than CNNs in detecting images with overlapping categories…
We perform the analytic classification of plane branches of multiplicity less or equal than four.
In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning…
Capsule networks are a type of neural network that identify image parts and form the instantiation parameters of a whole hierarchically. The goal behind the network is to perform an inverse computer graphics task, and the network parameters…
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
Let $\A$ be the incidence matrix of lines and points of the classical projective plane $PG(2,q)$ with $q$ odd. With respect to a conic in $PG(2,q)$, the matrix $\A$ is partitioned into 9 submatrices. The rank of each of these submatices…
Deep convolutional neural networks have shown high efficiency in computer visions and other applications. However, with the increase in the depth of the networks, the computational complexity is growing exponentially. In this paper, we…
The present paper is devoted to the complete classification of $4$-dimensional complex Poisson algebras, taking into account a classification, up to isomorphism, of the complex commutative associative algebras of dimension $4$, as well as…
Clouds classification is a great challenge in meteorological research. The different types of clouds, currently known and present in our skies, can produce radioactive effects that impact on the variation of atmospheric conditions, with the…
We present a new algorithm to compute all the chiral polytopes that have a given group $G$ as full automorphism group. This algorithm uses a new set of generators that characterize the group, all of them except one being involutions. It…
We classify up to equivalence the gradings on Hurwitz superalgebras and on symmetric composition superalgebras, over any field. Also, classifications up to isomorphism are given in case the field is algebraically closed. By grading, here we…
Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. The paper also…
On example of tasks of class NP the questions concerning accuracy of work of already existing and possible in the future algorithms for the solution of tasks on discrete structures are considered.
Let $A \subseteq E$ be a given extension of Hopf (respectively Lie) algebras. We answer the \emph{classifying complements problem} (CCP) which consists of describing and classifying all complements of $A$ in $E$. If $H$ is a given…
Working over the field of order 2 we consider those complete caps (maximal sets of points with no three collinear) which are disjoint from some codimension 2 subspace of projective space. We derive restrictive conditions which such a cap…