Related papers: A computer based classification of caps in PG(4,2)
In this paper we present the complete classification of caps in PG(4,3). These results have been obtained using a computer based exhaustive search that exploits projective equivalence.
In this paper we present the complete classification of caps in PG(5,2). These results have been obtained using a computer based exhaustive search that exploits projective equivalence.
We describe an algorithm for testing the completeness of caps in PG(r; q), q even. It allowed us to check that the 95256-cap in PG(12; 4) recently found by Fu el al. (see [14]) is complete.
In this paper we present and analyze computational results concerning small complete caps in the projective spaces $\mathrm{PG}(N,q)$ of dimension $N=3$ and $N=4$ over the finite field of order $q$. The results have been obtained using…
Some new families of small complete caps in $PG(N,q)$, $q$ even, are described. By using inductive arguments, the problem of the construction of small complete caps in projective spaces of arbitrary dimensions is reduced to the same problem…
We define a cap in the affine geometry AG(n,2) to be a subset in which every collection of four points is in general position. In this paper, we classify, up to affine equivalence, all caps in AG(7,2) of size k greater than or equal to 10.…
In this work complete caps in $PG(N,q)$ of size $O(q^{\frac{N-1}{2}}\log^{300} q)$ are obtained by probabilistic methods. This gives an upper bound asymptotically very close to the trivial lower bound $\sqrt{2}q^{\frac{N-1}{2}}$ and it…
In PG(2,32) the following two results are proven by a computer aided search. (i) Uniqueness of hyperfocused 12-arcs, up to projectivities; (ii) Non-existence of hyperfocused 14-arcs. The existence problem for hyperfocused 16-arcs remains…
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…
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…
Image classification has become one of the main tasks in the field of computer vision technologies. In this context, a recent algorithm called CapsNet that implements an approach based on activity vectors and dynamic routing between…
A complete classification of two-dimensional algebras over algebraically closed fields is provided
We give a complete classification, up to birational equivalence, of all fibrations by plane projective rational quartic curves in characteristic two.
Capsule networks are designed to present the objects by a set of parts and their relationships, which provide an insight into the procedure of visual perception. Although recent works have shown the success of capsule networks on simple…
In this paper, we deal with plane curves with cusps. It is well known that there are various types of cusps. Among them, we investigate criteria for $(n, n+1)$ cusps with respect to several differential conditions and relations between…
Image classification is a challenging problem which aims to identify the category of object in the image. In recent years, deep Convolutional Neural Networks (CNNs) have been applied to handle this task, and impressive improvement has been…
Point cloud completion aims to recover raw point clouds captured by scanners from partial observations caused by occlusion and limited view angles. This makes it hard to recover details because the global feature is unlikely to capture the…
Using class field theory one associates to each curve C over a finite field, and each subgroup G of its divisor class group, unramified abelian covers of C whose genus is determined by the index of G. By listing class groups of curves of…
We examine categoricity issues for computable algebraic fields. We give a structural criterion for relative computable categoricity of these fields, and use it to construct a field that is computably categorical, but not relatively…
We present a computer algorithm to explicitly compute the BGG resolution and its cohomology. We give several applications, in particular computation of various sheaf cohomology groups on flag varieties. An implementation of the algorithm is…