Let be a finite field of order which is a prime power. In the finite field setting, we say that a function is a Mattila-Sjölin type function in if for any with , we have . The main purpose of this talk is to present …
An intersection digraph is a digraph where every vertex is represented by an ordered pair of sets such that there is an edge from to if and only if and intersect. An intersection digraph is reflexive if for every vertex . Compared to well-known undirected …
The preservation of symmetry is one of the key tools for designing data-efficient neural networks. A representative example is convolutional neural networks (CNNs); they preserve translation symmetries, and this symmetry preservation is often attributed to their success in real-world applications. In the machine-learning community, there is a growing body of work that explores a new …
In this talk, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations in terms of the entries in the first row with integer coefficients. Using these conditions we show the invertibility of some family of circulant matrices with particular forms of …
