Related papers: A computer based classification of caps in PG(4,3)
We study edge-to-edge tilings of the sphere by edge congruent pentagons, under the assumption that there are tiles with all vertices having degree 3. We develop the technique of neighborhood tilings and apply the technique to completely…
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…
We present a powerful method to extract per-point semantic class labels from aerialphotogrammetry data. Labeling this kind of data is important for tasks such as environmental modelling, object classification and scene understanding. Unlike…
Three-dimensional (3D) point cloud analysis has become one of the attractive subjects in realistic imaging and machine visions due to its simplicity, flexibility and powerful capacity of visualization. Actually, the representation of scenes…
We classify edge-to-edge tilings of the sphere by congruent almost equilateral pentagons, in which four edges have the same length. Together with our earlier classifications of edge-to-edge tilings of the sphere by congruent equilateral…
In this paper we classify all capable finite $p$-groups with derived subgroup of order $p$ and $G/G'$ of rank $n-1$.
In this work we solve the packing problem for complete (n,3)-arcs in PG(2,16), determining that the maximum size is 28 and the minimum size is 15. We also performed a partial classification of the extremal size of complete (n,3)-arcs in…
Every polygon $P$ can be companioned by a cap polygon $\hat P$ such that $P$ and $\hat P$ serve as two parts of the boundary surface of a polyhedron $V$. Pairs of vertices on $P$ and $\hat P$ are identified successively to become vertices…
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…
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…
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…
Capsule networks (see e.g. Hinton et al., 2018) aim to encode knowledge and reason about the relationship between an object and its parts. In this paper we specify a \emph{generative} model for such data, and derive a variational algorithm…
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…
Reporting on a computer--assisted search for nonpositively curved CW complexes of intermediate rank conducted some years ago. Not intended for publication.
Learning a powerful representation from point clouds is a fundamental and challenging problem in the field of computer vision. Different from images where RGB pixels are stored in the regular grid, for point clouds, the underlying semantic…
We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.
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…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
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…
Fine-grained visual classification aims to recognize images belonging to multiple sub-categories within a same category. It is a challenging task due to the inherently subtle variations among highly-confused categories. Most existing…