We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut into two pieces each, and they may no...

We study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be efficiently discussed and solved. This solution determines the master field for the model in the 'C-representation.

Large-scale deletions of mitochondrial DNA (mtDNA) are common events that have been found to occur in human ageing and in patients with mitochondrial myopathies. The mechanisms by which these deletions occur remain unclear, but several mechanisms have been proposed, such as slipped-mispairing, illegitimate recombination, and oxidative reactions elicited by free radicals. In addition, the DNA to...

We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 7→ 012, 1 7→ 02, 2 7→ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds applications in several fields such as combinatorics on words; for example, in pattern avoidance it is often used to construct infinite words avoiding given patterns. It has b...

Motivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian–Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium. The method is based on following tracelines, so it is stable independent of any CFL constraint. The mai...