12 papers
Sums of units in finite rings and applications to Cayley graphs
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
The question of whether a ring is additively generated by its units has been studied from several perspectives in ring theory and algebraic graph theory. In this paper, we investig…
Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
Arthur S. Powanwe, Luisa H. B. Liboni, Anif N. Shikder +7
We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption…
Maximal -extensions of Pythagorean fields and Right Angled Artin Groups
Oussama Hamza, Christian Maire, Ján Mináč +1
In this paper, we describe minimal presentations of maximal pro- quotients of absolute Galois groups of formally real Pythagorean fields of finite type. For this purpose, we int…
On divisibility relation graphs
Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1
For each positive integer , we define the divisibility relation graph whose vertex set is the set of divisors of , and in which two vertices are adjacent if one is a di…
Geometric perspective of linear stability in finite networks of nonlinear oscillators
Yashee Sinha, Priya B. Jain, Antonio Mihara +4
We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematic…
A complete classification of perfect unitary Cayley graphs
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of math…
On the strong Massey property for number fields
Christian Maire, Ján Mináč, Ravi Ramakrishna +1
Let . We show that for every number field with , the absolute and tame Galois groups of satisfy the strong -fold Massey property relative to .…
On the gcd graphs over polynomial rings
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
Gcd-graphs over the ring of integers modulo are a natural generalization of unitary Cayley graphs. The study of these graphs has foundations in various mathematical fields, inc…
The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one
Sunil K. Chebolu, Ján Mináč, Cihan Okay +2
The famous Bloch--Kato conjecture implies that for a field containing a primitive th root of unity, the cohomology ring of the absolute Galois group of with $\math…
Theory of transient chimeras in finite Sakaguchi-Kuramoto networks
Roberto C. Budzinski, James W. C. Graham, Ján Mináč +1
Chimera states are a phenomenon in which order and disorder can co-exist within a network that is fully homogeneous. Precisely how transient chimeras emerge in finite networks of K…
On the arithmetic of the join rings over finite fields
Sunil K. Chebolu, Jonathan Merzel, Ján Mináč +3
Given a collection of finite groups and a ring , we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1,…
An algebraic approach to spike-time neural codes in the hippocampus
Federico W. Pasini, Alexandra N. Busch, Ján Mináč +2
Although temporal coding through spike-time patterns has long been of interest in neuroscience, the specific structures that could be useful for spike-time codes remain highly uncl…