27 citations · 60 across the 16 of their papers we have counts for
17 papers
On prime Cayley graphs
Maria Chudnovsky, Michal Cizek, Logan Crew +4
The decomposition of complex networks into smaller, interconnected components is a central challenge in network theory with a wide range of potential applications. In this paper, w…
Fekete polynomials of principal Dirichlet characters
Shiva Chidambaram, Ján Mináč, Tung T. Nguyen +1
Fekete polynomials associated to quadratic Dirichlet characters have interesting arithmetic properties, and have been studied in many works. In this paper, we study a seemingly sim…
Spectral perturbation by rank- matrices
Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1
Let and designate matrices with coefficients in a field . In this paper, we completely answer the following question: For fixed, what are the possible ch…
Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators
Priya B. Jain, Tung T. Nguyen, Ján Mináč +2
Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study…
On the Paley graph of a quadratic character
Ján Mináč, Lyle Muller, Tung T. Nguyen +1
Paley graphs form a nice link between the distribution of quadratic residues and graph theory. These graphs possess remarkable properties which make them useful in several branches…
Broadcasting solutions on networked systems of phase oscillators
Tung T. Nguyen, Roberto C. Budzinski, Federico W. Pasini +3
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the…
Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays
Roberto C. Budzinski, Tung T. Nguyen, Gabriel B. Benigno +4
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstra…
Joins of normal matrices, their spectrum, and applications
Jan Mináč, Lyle Muller, Tung T. Nguyen +1
Motivated by studies of oscillator networks, we study the spectrum of the join of several normal matrices with constant row sums. We apply our results to compute the characteristic…
On the arithmetic of generalized Fekete polynomials
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
For each prime number one can associate a Fekete polynomial with coefficients or except the constant term, which is 0. These are classical polynomials that have been s…
Quaternion algebras and square power classes over biquadratic extensions
Frank Chemotti, Jan Minac, Tung T. Nguyen +3
Recently the Galois module structure of square power classes of a field has been computed under the action of in the case where is the Klein…
Spectral perturbation by rank one matrices
Jon Merzel, Jan Minac, Lyle Muller +2
Let be a matrix of size over an algebraically closed field and a monic polynomial of degree . In this article, we describe the necessary and sufficie…
Joins of circulant matrices
Jacqueline Doan, Jan Minac, Lyle Muller +2
We study the spectrum of the join of several circulant matrices. We apply our results to compute explicitly the spectrum of certain graphs obtained by joining several circulant gra…
Fekete polynomials, quadratic residues, and arithmetic
Jan Minac, Tung T. Nguyen, Nguyen Duy Tan
Fekete polynomials associate with each prime number a polynomial with coefficients or except the constant term, which is 0. These coefficients reflect the distribution…
Equilibria in Kuramoto oscillator networks: An algebraic approach
Tung T. Nguyen, Roberto C. Budzinski, Jacqueline Doan +3
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions rema…
Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
Roberto C. Budzinski, Tung T. Nguyen, Jacqueline Doan +3
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductor…
Further insights into the mysteries of the values of zeta functions at integers
Ján Mináč, Nguyen Duy Tân, Nguyen Tho Tung
We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to a…
Integer solutions of
Tien Nam Le, Tung Tho Nguyen
In this article we will show different proofs for the fact that there exist relatively prime positive integers such that: .