Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

Evaluating functional network inference using simulations of complex biological systems.

MOTIVATION: Although many network inference algorithms have been presented in the bioinformatics literature, no suitable approach has been formulated for evaluating their effectiveness at recovering models of complex biological systems from limited data. To overcome this limitation, we propose an approach to evaluate network inference algorithms according to their ability to recover a complex functional network from biologically reasonable simulated data. RESULTS: We designed a simulator to generate data representing a complex biological system at multiple levels of organization: behaviour, neural anatomy, brain electrophysiology, and gene expression of songbirds. About 90% of the simulated variables are unregulated by other variables in the system and are included simply as distracters. We sampled the simulated data at intervals as one would sample from a biological system in practice, and then used the sampled data to evaluate the effectiveness of an algorithm we developed for functional network inference. We found that our algorithm is highly effective at recovering the functional network structure of the simulated system-including the irrelevance of unregulated variables-from sampled data alone. To assess the reproducibility of these results, we tested our inference algorithm on 50 separately simulated sets of data and it consistently recovered almost perfectly the complex functional network structure underlying the simulated data. To our knowledge, this is the first approach for evaluating the effectiveness of functional network inference algorithms at recovering models from limited data. Our simulation approach also enables researchers a priori to design experiments and data-collection protocols that are amenable to functional network inference.

Sea Urchin Body Plan Development and Evolution: An Integrative Transcriptomic Approach

My dissertation work integrates comparative transcriptomics and functional analyses to investigate gene expression changes underlying two significant aspects of sea urchin evolution and development: the dramatic developmental changes associated with an ecologically significant shift in life history strategy and the development of the unusual radial body plan of adult sea urchins.

In Chapter 2, I investigate evolutionary changes in gene expression underlying the switch from feeding (planktotrophic) to nonfeeding (lecithotrophic) development in sea urchins. In order to identify these changes, I used Illumina RNA-seq to measure expression dynamics across 7 developmental stages in three sea urchin species: the lecithotroph Heliocidaris erythrogramma, the closely related planktotroph Heliocidaris tuberculata, and an outgroup planktotroph Lytechinus variegatus. My analyses draw on a well-characterized developmental gene regulatory network (GRN) in sea urchins to understand how the ancestral planktotrophic developmental program was altered during the evolution of lecithotrophic development. My results suggest that changes in gene expression profiles occurred more frequently across the transcriptome during the evolution of lecithotrophy than during the persistence of planktotrophy. These changes were even more pronounced within the GRN than across the transcriptome as a whole, and occurred in each network territory (skeletogenic, endomesoderm and ectoderm). I found evidence for both conservation and divergence of regulatory interactions in the network, as well as significant changes in the expression of genes with known roles in larval skeletogenesis, which is dramatically altered in lecithotrophs. I further explored network dynamics between species using coexpression analyses, which allowed me to identify novel players likely involved in sea urchin neurogenesis and endoderm patterning.

In Chapter 3, I investigate developmental changes in gene expression underlying radial body plan development and metamorphosis in H. erythrogramma. Using Illumina RNA-seq, I measured gene expression profiles across larval, metamorphic, and post-metamorphic life cycle phases. My results present a high-resolution view of gene expression dynamics during the complex transition from pre- to post-metamorphic development and suggest that distinct sets of regulatory and effector proteins are used during different life history phases.

Collectively, my investigations provide an important foundation for future, empirical studies to investigate the functional role of gene expression change in the evolution of developmental differences between species and also for the generation of the unusual radial body plan of sea urchins.