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Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
In this paper, we generalize Ahlfors' lemma on logarithmic derivative to holomorphic tangent curves of directed projective manifolds intersecting closed subschemes. As a consequence, we obtain Algebro-Geometric Ahlfors' Lemma on Logarithmic…
We give a construction of Kirchberg algebras from graphs. By using product graphs in the construction we are able to provide models for general (UCT) Kirchberg algebras while maintaining the explicit generators and relations of the…
We study twisted derived equivalences of hyper-K\"ahler fourfolds. We describe when two hyper-K\"ahler fourfolds of $K3^{[2]}$-type of Picard rank $1$ with isomorphic transcendental lattices are derived equivalent. Then we present new…
We present a simple mechanism, which can be randomised, for constructing sparse $3$-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over $\mathbb{Z}_2^t$ and have vertex degree…
We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of…
We give a construction of two-sided invariant metrics on free products (possibly with amalgamation) of groups with two-sided invariant metrics and, under certain conditions, on HNN extensions of such groups. Our approach is similar to the…
Tensor diagrams are a handy way to depict complicated relationships between objects in projective geometry. One of the simpler ones takes two copies of a $3\times 3$ matrix and computes its adjugate. In this paper, we give a geometric…
We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.
In this paper we define a new product-like binary operation on directed graphs, and we discuss some of its properties. We also briefly discuss its application in constructing the subtyping relation in generic nominally-typed object-oriented…
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…
In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…
For any group $G$ with subgroup $H$ and a set of representatives $T$ from the set of cosets $G/H$, we develop a rewriting system from $G$ that bequeaths a product into the set decomposition $T\times H$ of $G$, converting it into a group. In…
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…
We extend a theorem, originally formulated by Blattner-Cohen-Montgomery for crossed products arising from Hopf algebras weakly acting on noncommutative algebras, to the realm of left Hopf algebroids. Our main motivation is an application to…
The cocycle bicrossed product construction allows certain freedom in producing examples of locally compact quantum groups. We give an overview of some recent examples of this kind having remarkable properties.
Conics and Cartesian ovals are very important curves in various fields of science. Also aspheric curves based on conics are useful in optics. Superconic curves recently suggested by A. Greynolds are extensions of both conics and Cartesian…