The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Many physical systems lose or gain stability and pattern through bifurcation. Extensive
research of such bifurcation behavior is carried out in science and engineering. The study of …

For families of Hamiltonians defined by parts that are local, the most general definition of a
symmetry algebra is the commutant algebra, ie, the algebra of operators that commute with …

The field of network synchronization has seen tremendous growth following the introduction
of the master stability function (MSF) formalism, which enables the efficient stability analysis …

We present a technique for reducing the computational requirements by several orders of
magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum …

Motivated by recent interest in group-symmetry in semidefinite programming, we propose a
numerical method for finding a finest simultaneous block-diagonalization of a finite number …

We study cluster synchronization of networks and propose a canonical transformation for
simultaneous block diagonalization of matrices that we use to analyze the stability of the …

The dynamics of the brain results from the complex interplay of several neural populations
and is affected by both the individual dynamics of these areas and their connection structure …

An algorithm is given for the problem of finding the finest simultaneous block-diagonalization
of a given set of square matrices. This problem has been studied independently in the area …

An outstanding problem in the study of networks of heterogeneous dynamical units concerns
the development of rigorous methods to probe the stability of synchronous states when the …