Covariation analysis of sets of aligned sequences for RNA molecules is relatively successful in elucidating RNA secondary structure, as well as some aspects of tertiary structure [Gutell et al. (1992)]. Covariation analysis of sets of aligned sequences for protein molecules is successful in certain instances in elucidating certain structural and functional links [Korber et al. (1993)], but in general, pairs of sites displaying highly covarying mutations in protein sequences do not necessarily correspond to sites that are spatially close in the protein structure [Gobel et al. (1994), Clarke (1995), Shindyalov et al. (1994), Thomas et al. (1996, Taylor &;Hatrick (1994), Neher (1994]. In this paper we identify two reasons why naive use of covariation analysis for protein sequences fails to reliably indicate sequence positions that are spatially proximate. The first reason involves the bias introduced in calculation of covariation measures due to the fact that biological sequences are generally related by a non-trivial phylogenetic tree. We present a null-model approach to solve this problem. The second reason involves linked chains of covariation which can result in pairs of sites displaying significant covariation even though they are not spatially proximate. We present a maximum entropy solution to this classic problem of "causation versus correlation". The methodologies are validated in simulation.1 Research supported by the Department of Energy under contract W-7405-ENG-36 A MS 1991 subject classifications. Primary 62F03 secondary 62P10, 92D20.

Local scale transformations are made to vary the long range properties of harmonic oscillator orbitals conventionally used in model structure calculations of nuclear systems. The transformations ensure that those oscillator states asymptotically have exponentially decaying forms consistent with chosen single nucleon binding energies, leaving the structure essentially unchanged within the body of the nucleus. Application has been made to the radioactive nuclei 6,8He and 11Li and the resulting wave functions are used to generate g-folding optical potentials for elastic scattering of those ions from hydrogen. As a consistency test, application has been made to form wave functions for 40Ca and they have been used also to specify relevant proton-40Ca optical potentials with which elastic scattering has been predicted. The need for appropriate specifications of single particle binding energies in exotic nuclei is discussed.Comment: 24 pages, 16 figures, RevTex

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