Symmetry, Volume 7, Issue 4

We define the operation of Petrie duality for maps, describing its general properties both geometrically and algebraically. We give a number of examples and applications, including the construction of a pair of regular maps, one orientable of genus 1...

The Estrada index of a graph \(G\) of \(n\) vertices is defined by \(EE(G)=\sum_{i=1}^ne^{\lambda_i}\), where \(\lambda_1,\lambda_2,\cdots,\lambda_n\) are the eigenvalues of \(G\). In this paper, we give upper and lower bounds of \(EE(G)\) for almost...

Asymmetry of brain function is known to be widespread amongst vertebrates, and it seems to have appeared very early in their evolution. In fact, recent evidence of functional asymmetry in invertebrates suggests that even small brains benefit from the...

Let \(\mathbf{H}\) be the quaternion algebra. Let \(\mathfrak{g}\) be a complex Lie algebra and let \(U(\mathfrak{g})\) be the enveloping algebra of \(\mathfrak{g}\). The quaternification \(\mathfrak{g}^{\mathbf{H}}=\)\(\,(\,\mathbf{H}\otimes U(\math...

We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them thro...

Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal...

Animal development relies on repeated symmetry breaking, e.g., during axial specification, gastrulation, nervous system lateralization, lumen formation, or organ coiling. It is crucial that asymmetry increases during these processes, since this will...

Fullerenes are molecules of carbon that are modeled by trivalent plane graphs with only pentagonal and hexagonal faces. Scaling up a fullerene gives a notion of similarity, and fullerenes are partitioned into similarity classes. In this expository ar...

We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.

Somatic stem cells are rare cells with unique properties residing in many organs and tissues. They are undifferentiated cells responsible for tissue regeneration and homeostasis, and contain both the capacity to self-renew in order to maintain their...