Related papers: A computer based classification of caps in PG(4,2)
In this paper, we propose a capsule-based neural network model to solve the semantic segmentation problem. By taking advantage of the extractable part-whole dependencies available in capsule layers, we derive the probabilities of the class…
We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements.…
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].
This paper presents an empirical exploration of the use of capsule networks for text classification. While it has been shown that capsule networks are effective for image classification, their validity in the domain of text has not been…
We classify the planar cubic Cayley graphs of connectivity 2, providing an explicit presentation and embedding for each of them. Combined with [9] this yields a complete description of all planar cubic Cayley graphs.
In the projective space $\mathrm{PG}(N,q)$ over the Galois field of order $q$, $N\ge3$, an iterative step-by-step construction of complete caps by adding a new point on every step is considered. It is proved that uncovered points are evenly…
In this work we construct a new class of maximal partial spreads in $PG(4,q)$, that we call $q$-added maximal partial spreads. We obtain them by depriving a spread of a hyperplane of some lines and adding $q+1$ lines not of the hyperplane…
We consider point sets in $\mathbb{Z}_n^2$ where no three points are on a line - also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear…
Point clouds, being the simple and compact representation of surface geometry of 3D objects, have gained increasing popularity with the evolution of deep learning networks for classification and segmentation tasks. Unlike human, teaching…
In this paper, we propose a topological classification of points for 2D discrete binary images. This classification is based on the values of the calculus of topological numbers. Six classes of points are proposed: isolated point, interior…
Reporting on a computer--assisted search for nonpositively curved CW complexes of intermediate rank conducted some years ago. Not intended for publication.
Several classes of near-MDS codes of ${\rm PG}(3,q)$ are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of a symplectic polar space ${\cal W}(3, q)$ or starting from…
The paper presents a novel type of capsule network (CAP) that uses custom-defined neural network (NN) layers for blind classification of digitally modulated signals using their in-phase/quadrature (I/Q) components. The custom NN layers of…
Minimal 1-saturating sets in the projective plane $PG(2,q)$ are considered. They correspond to covering codes which can be applied to many branches of combinatorics and information theory, as data compression, compression with distortion,…
Theoretical foundations of a new algorithm for determining the p-capitulation type kappa(K) of a number field K with p-class rank rho=2 are presented. Since kappa(K) alone is insufficient for identifying the second p-class group…
Explicit constructions of infinite families of scattered ${\mathbb F}_q$--linear sets in $PG(r-1,q^t)$ of maximal rank $\frac{rt}2$, for $t$ even, are provided. When $q=2$ and $r$ is odd, these linear sets correspond to complete caps in…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
Using the computer algebra program GAP, we show that all crystallographic groups in dimensions at most 4 are distinguished from each other by their sets of finite quotients.
Explicit bases for the spaces of holomorphic cusp forms of all even positive weights and all orders are constructed. The dimensions of these spaces are computed.
In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…