The Fanaroff-Riley Transition and the Optical Luminosity of the Host Elliptical Galaxy

We show that a model for radio source dynamics we had earlier proposed can readily reproduce the relationship between the radio power division separating the two Fanaroff-Riley classes of extragalactic radio sources and the optical luminosity of the host galaxy, as found by Owen and Ledlow (1994). In our scenario, when less powerful jets eventually slow down to the point that the advance of the working surface (i.e., hotspot) becomes subsonic with respect to the external gas, the jet's collimation is severely weakened. This criterion distinguishes the powerful and well collimated FR II sources from the weaker sources producing the less collimated FR I type morphologies.Comment: 6 pages, 1 figure; typo corrected; refs updated; now published in A&

The context-dependence of mutations: a linkage of formalisms

Defining the extent of epistasis - the non-independence of the effects of mutations - is essential for understanding the relationship of genotype, phenotype, and fitness in biological systems. The applications cover many areas of biological research, including biochemistry, genomics, protein and systems engineering, medicine, and evolutionary biology. However, the quantitative definitions of epistasis vary among fields, and its analysis beyond just pairwise effects remains obscure in general. Here, we show that different definitions of epistasis are versions of a single mathematical formalism - the weighted Walsh-Hadamard transform. We discuss that one of the definitions, the backgound-averaged epistasis, is the most informative when the goal is to uncover the general epistatic structure of a biological system, a description that can be rather different from the local epistatic structure of specific model systems. Key issues are the choice of effective ensembles for averaging and to practically contend with the vast combinatorial complexity of mutations. In this regard, we discuss possible approaches for optimally learning the epistatic structure of biological systems.Comment: 6 pages, 3 figures, supplementary informatio