An analysis of the Kimura 3ST model of DNA sequence evolution is given on the basis of its continuous Lie symmetries. The rate matrix commutes with a U(1)×U(1)×U(1) phase subgroup of the group GL(4) of 4× 4 invertible complex matrices acting on a linear space spanned by the 4 nucleic acid base letters. The diagonal ‘branching operator’ representing speciation is defined, and shown to intertwine...

The symmetry reduction of the equation u 0 +∇ u − 4 5 ∇u = 0 to ordinary differential equations with respect to all subalgebras of rank three of the algebra A E (1) ⊕ AC (3) is carried out. New invariant solutions are constructed for this equation.

Motivated by D-brane scenarios, we consider a non-supersymmetric model based on the gauge symmetry U (3) C ×U (3) L ×U (3) R which is equivalent to the SU (3) 3 " trinification " model supplemented by three U (1)s. Two U (1) combinations are anomalous while the third U (1) Z ′ is anomaly free and contributes to the hypercharge generator. This hypercharge embedding correspods to sin 2 θ W = 6 19...

Recently an unlinkable version of the U-Prove attributebased credential scheme was proposed at Financial Crypto ’14 [9]. Unfortunately, the new scheme is forgeable: if sufficiently many users work together then they can construct new credentials, containing any set of attributes of their choice, without any involvement of the issuer. In this note we show how they can achieve this and we point o...

Geography of the Family by Kai A. Konrad, Harald Künemund, Kjell Erik Lommerud and Julio R. Robledo We study the residential choice of siblings who are altruistic towards their parents. The first-born child’s location choice influences the behavior of the second-born child and can shift some of the burden of providing care for the parents from one child to the other. These strategic considerati...