We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the 1 : 6 : 1 integrable case quartic potential. A generalisation of the 1 : 6 : 8 case is sim...

Instead of studying Lax equations as such, a solution Z of a Lax equation is assumed to be given. Then Z is regarded as defining a constraint on a non-autonomous linear differential equation associated with the Lax equation. In generic cases, quadrature and sometimes algebraic formulae in terms of Z are then proved for solution x of the linear differential equation, and examples are given where...

We study lax epimorphisms in 2-categories, with special attention to Cat and V-Cat. show that any 2-category convenient colimits has an orthogonal LaxEpi-factorization system, we give a concrete description of this factorization Cat.

BACKGROUND Quantification of left ventricular (LV) volume from cardiovascular magnetic resonance images relies on subjective and often challenging selection of short-axis (SAX) slices. We hypothesized that this could be solved by defining mitral annular (MA) plane and apex in long-axis (LAX) views, which could be combined with automated LV volume analysis that does not rely on manual tracing of...

We investigate limits in the 2-category of strict algebras and lax morphisms for a 2-monad. This includes both the 2-category of monoidal categories and monoidal functors as well as the 2-category of monoidal categories and opomonoidal functors, among many other examples.

Probabilistic bisimulation is a widely studied equivalence relation for stochastic systems. However, it requires the behavior of the states to match on actions with matching labels. This does not allow bisimulation to capture symmetries in the system. In this thesis we define lax probabilistic bisimulation, in which actions are only required to match within given action equivalence classes. We ...