Efficient construction of nonorthogonal localized molecular orbitals in large systems.

Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Antisense Gene Silencing and Bacteriophages as Novel Disinfection Processes for Engineered Systems

The growth and proliferation of invasive bacteria in engineered systems is an ongoing problem. While there are a variety of physical and chemical processes to remove and inactivate bacterial pathogens, there are many situations in which these tools are no longer effective or appropriate for the treatment of a microbial target. For example, certain strains of bacteria are becoming resistant to commonly used disinfectants, such as chlorine and UV. Additionally, the overuse of antibiotics has contributed to the spread of antibiotic resistance, and there is concern that wastewater treatment processes are contributing to the spread of antibiotic resistant bacteria.

Due to the continually evolving nature of bacteria, it is difficult to develop methods for universal bacterial control in a wide range of engineered systems, as many of our treatment processes are static in nature. Still, invasive bacteria are present in many natural and engineered systems, where the application of broad acting disinfectants is impractical, because their use may inhibit the original desired bioprocesses. Therefore, to better control the growth of treatment resistant bacteria and to address limitations with the current disinfection processes, novel tools that are both specific and adaptable need to be developed and characterized.

In this dissertation, two possible biological disinfection processes were investigated for use in controlling invasive bacteria in engineered systems. First, antisense gene silencing, which is the specific use of oligonucleotides to silence gene expression, was investigated. This work was followed by the investigation of bacteriophages (phages), which are viruses that are specific to bacteria, in engineered systems.


For the antisense gene silencing work, a computational approach was used to quantify the number of off-targets and to determine the effects of off-targets in prokaryotic organisms. For the organisms of Escherichia coli K-12 MG1655 and Mycobacterium tuberculosis H37Rv the mean number of off-targets was found to be 15.0 + 13.2 and 38.2 + 61.4, respectively, which results in a reduction of greater than 90% of the effective oligonucleotide concentration. It was also demonstrated that there was a high variability in the number of off-targets over the length of a gene, but that on average, there was no general gene location that could be targeted to reduce off-targets. Therefore, this analysis needs to be performed for each gene in question. It was also demonstrated that the thermodynamic binding energy between the oligonucleotide and the mRNA accounted for 83% of the variation in the silencing efficiency, compared to the number of off-targets, which explained 43% of the variance of the silencing efficiency. This suggests that optimizing thermodynamic parameters must be prioritized over minimizing the number of off-targets. In conclusion for the antisense work, these results suggest that off-target hybrids can account for a greater than 90% reduction in the concentration of the silencing oligonucleotides, and that the effective concentration can be increased through the rational design of silencing targets by minimizing off-target hybrids.

Regarding the work with phages, the disinfection rates of bacteria in the presence of phages was determined. The disinfection rates of E. coli K12 MG1655 in the presence of coliphage Ec2 ranged up to 2 h-1, and were dependent on both the initial phage and bacterial concentrations. Increasing initial phage concentrations resulted in increasing disinfection rates, and generally, increasing initial bacterial concentrations resulted in increasing disinfection rates. However, disinfection rates were found to plateau at higher bacterial and phage concentrations. A multiple linear regression model was used to predict the disinfection rates as a function of the initial phage and bacterial concentrations, and this model was able to explain 93% of the variance in the disinfection rates. The disinfection rates were also modeled with a particle aggregation model. The results from these model simulations suggested that at lower phage and bacterial concentrations there are not enough collisions to support active disinfection rates, which therefore, limits the conditions and systems where phage based bacterial disinfection is possible. Additionally, the particle aggregation model over predicted the disinfection rates at higher phage and bacterial concentrations of 108 PFU/mL and 108 CFU/mL, suggesting other interactions were occurring at these higher concentrations. Overall, this work highlights the need for the development of alternative models to more accurately describe the dynamics of this system at a variety of phage and bacterial concentrations. Finally, the minimum required hydraulic residence time was calculated for a continuous stirred-tank reactor and a plug flow reactor (PFR) as a function of both the initial phage and bacterial concentrations, which suggested that phage treatment in a PFR is theoretically possible.

In addition to determining disinfection rates, the long-term bacterial growth inhibition potential was determined for a variety of phages with both Gram-negative and Gram-positive bacteria. It was determined, that on average, phages can be used to inhibit bacterial growth for up to 24 h, and that this effect was concentration dependent for various phages at specific time points. Additionally, it was found that a phage cocktail was no more effective at inhibiting bacterial growth over the long-term than the best performing phage in isolation.

Finally, for an industrial application, the use of phages to inhibit invasive Lactobacilli in ethanol fermentations was investigated. It was demonstrated that phage 8014-B2 can achieve a greater than 3-log inactivation of Lactobacillus plantarum during a 48 h fermentation. Additionally, it was shown that phages can be used to protect final product yields and maintain yeast viability. Through modeling the fermentation system with differential equations it was determined that there was a 10 h window in the beginning of the fermentation run, where the addition of phages can be used to protect final product yields, and after 20 h no additional benefit of the phage addition was observed.

In conclusion, this dissertation improved the current methods for designing antisense gene silencing targets for prokaryotic organisms, and characterized phages from an engineering perspective. First, the current design strategy for antisense targets in prokaryotic organisms was improved through the development of an algorithm that minimized the number of off-targets. For the phage work, a framework was developed to predict the disinfection rates in terms of the initial phage and bacterial concentrations. In addition, the long-term bacterial growth inhibition potential of multiple phages was determined for several bacteria. In regard to the phage application, phages were shown to protect both final product yields and yeast concentrations during fermentation. Taken together, this work suggests that the rational design of phage treatment is possible and further work is needed to expand on this foundation.

Component Neural Systems for the Creation of Emotional Memories during Free Viewing of a Complex, Real-World Event.

To investigate the neural systems that contribute to the formation of complex, self-relevant emotional memories, dedicated fans of rival college basketball teams watched a competitive game while undergoing functional magnetic resonance imaging (fMRI). During a subsequent recognition memory task, participants were shown video clips depicting plays of the game, stemming either from previously-viewed game segments (targets) or from non-viewed portions of the same game (foils). After an old-new judgment, participants provided emotional valence and intensity ratings of the clips. A data driven approach was first used to decompose the fMRI signal acquired during free viewing of the game into spatially independent components. Correlations were then calculated between the identified components and post-scanning emotion ratings for successfully encoded targets. Two components were correlated with intensity ratings, including temporal lobe regions implicated in memory and emotional functions, such as the hippocampus and amygdala, as well as a midline fronto-cingulo-parietal network implicated in social cognition and self-relevant processing. These data were supported by a general linear model analysis, which revealed additional valence effects in fronto-striatal-insular regions when plays were divided into positive and negative events according to the fan's perspective. Overall, these findings contribute to our understanding of how emotional factors impact distributed neural systems to successfully encode dynamic, personally-relevant event sequences.

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.