Generic elements in isometry groups of Polish ultrametric spaces

This paper presents a study of generic elements in full isometry groups of Polish ultrametric spaces. We obtain a complete characterization of Polish ultrametric spaces X whose isometry group Iso(X) contains an open subgroup H with ample generics. It also gives a characterization of the existence of an open subgroup in Iso(X) with a comeager conjugacy class. We also study the transfinite sequence defined by the projection of a Polish ultrametric space X on the ultrametric space of orbits of X under the action of Iso(X)

On derived equivalence classification of gentle two-cycle algebras

We classify, up to derived (equivalently, tilting-cotilting) equivalence all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case

Obituary: Jarema Malicki (1965-2019).

Jarema Malicki, a pioneer in developmental studies of the vertebrate retina, died on 4th January 2019, shortly after being diagnosed with cancer. Here, I reflect on Jarema's life and work, with a particular focus on his research interests in zebrafish as a model organism for vertebrate retinogenesis and human ciliopathies

Cooperative Boolean systems with generically long attractors II

We prove that cooperativity in Boolean networks precludes a strong notion of sensitive dependence on initial conditions. Weaker notions of sensitive dependence are shown to be consistent with cooperativity, but if each regulatory functions is binary AND or binary OR, in N-dimensional networks they impose an upper bound of approximately sqrt(3)^N on the lengths of attractors that can be reached from a fraction p approaching 1 of initial conditions. The upper bound is shown to be sharp