Common notation

Several important symbols and their cross-appendix conventions are collected below.

Symbol Meaning First defined
\(\insrate , \delrate \) TKF insertion / deletion rates (per link) §A
\(\ext \) TKF92 fragment-extension probability §A
\(\alphabet \) residue alphabet (\(A = |\alphabet | = 20\) for proteins) §A
\(\eqm , \exch , \symsub \) GTR stationary, asymmetric, exchangeability matrices §A
\(\revsub \) substitution rate matrix (generator) §A
\(\dom , \frag , \class \) domain, fragment, and substitution-class indices (MixDom) §C
\(\eta _s\) per-site gamma rate multiplier §D
\(z_s, c_s, h_{cc'}\) key, site-class, Potts-atom indices (TKF-DP) §D
\(\alpha _z, \alpha _c, \alpha _H\) key/class/atom Dirichlet-process concentrations §D
\(\Q , \Hh \) generator and Potts coupling tensor §D
\(\tkftrans \) TKF91 Pair HMM transition matrix §A
\(\exptrans \) exploded \(7{\times }7\) MixDom top-level transitions with null states §C
\(\nonemptytrans \) effective \(5{\times }5\) MixDom top-level matrix (nulls summed out) §C
\(\transnest \) final nested MixDom Pair HMM transition matrix §C
\(N_a, N_g\) alive / gravestone counts (TKF-DP) §D
\(F_0, F_1, F_2\) TKF92 Pair HMM 0/1/2-cell marginal partition functions §E
\(\pi _{\!M}\) CRP partition of Match cells (infinite Pair HMM) §E