We report on the calculation of the factorisable one-loop weak-interaction corrections to the initial and final states for three-jet observables in electron-positron annihilations. We show that such corrections are of a few percent at √ s = MZ . Hence, while their impact is not dramatic in the context of LEP1 and SLC, where the total error on the measured value of αS is larger, at a future Line...

The gauge action of the Lie groupG on the chiral WZNW phase spaceMǦ of quasiperiodic fields with Ǧ-valued monodromy, where Ǧ ⊂ G is an open submanifold, is known to be a Poisson-Lie (PL) action with respect to any coboundary PL structure on G, if the Poisson bracket on MǦ is defined by a suitable monodromy dependent exchange r-matrix. We describe the momentum map for these symmetries when G is ...

In linear system identification, optimal excitation signals can be determined using the Cramer-Rao bound. This problem has not been thoroughly studied for the nonlinear case. In this work, the Cramer-Rao bound for a factorisable Volterra model is derived. The analytical result is supported with simulation examples. The bound is then used to find the optimal excitation signal out of the class of...

We introduce a family of factorisable ribbon quasi-Hopf algebras Q(N) for N positive integer: as an algebra, is the semidirect product CZ2 with direct sum Graßmann and Clifford algebra in 2N generators. show that RepQ(N) equivalent to symplectic fermion category SF(N) was computed [54] from conformal blocks corresponding logarithmic field theory. The latter turn conjecturally representations Ve...

The Birkhoff polytope $\mathcal{B}_d$ consisting of all bistochastic matrices order $d$ assists researchers from many areas, including combinatorics, statistical physics and quantum information. Its subset $\mathcal{U}_d$ unistochastic matrices, determined by squared moduli unitary is a particular importance for theory as classical dynamical systems described transition can be quantised. In to ...