Related papers: A computer based classification of caps in PG(5,2)
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…
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
In a geometry, a maximal cap is a collection of points of largest size containing no lines. In AG(4,3), maximal caps contain 20 points. The 81 points of AG(4,3) can be partitioned into 4 mutually disjoint maximal caps together with a single…
In this paper we prove the existence of a complete cap of ${\rm PG}(4n+1, q)$ of size $2(q^{2n+1}-1)/(q-1)$, for each prime power $q>2$. It is obtained by projecting two disjoint Veronese varieties of ${\rm PG}(2n^2+3n, q)$ from a suitable…
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…
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…
In this article, using the computer, are enumerated all locally-rigid packings by $N$ congruent circles (spherical caps) on the unit sphere ${\Bbb S}^2 $ with $N < 12.$ This is equivalent to the enumeration of irreducible spherical contact…
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…
We compute the Hilbert series of general weighted flag varieties and discuss a computer-aided method to determine their defining equations. We apply our results to weighted flag varieties coming from the Lie groups of type G_2 and GL(6), to…
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…
We give a complete classification, up to birational equivalence, of all fibrations by plane projective rational quartic curves in characteristic two.
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].
Reporting on a computer--assisted search for nonpositively curved CW complexes of intermediate rank conducted some years ago. Not intended for publication.
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 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…
In this paper, a deep convolutional neural network architecture for galaxies classification is presented. The galaxy can be classified based on its features into main three categories Elliptical, Spiral, and Irregular. The proposed deep…
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.
We develop a systematic method for computing the angle combinations at all vertices in an edge-to-edge tiling of the sphere by pentagons with the same five angles. The method is a useful and necessary step in many tiling problems about…
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…