Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.

A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.

Advanced Aerogel Composites for Oil Remediation and Recovery

Oil spills in marine environments often damage marine and coastal life if not remediated rapidly and efficiently. In spite of the strict enforcement of environmental legislations (i.e., Oil Pollution Act 1990) following the Exxon Valdez oil spill (June 1989; the second biggest oil spill in U.S. history), the Macondo well blowout disaster (April 2010) released 18 times more oil. Strikingly, the response methods used to contain and capture spilled oil after both accidents were nearly identical, note that more than two decades separate Exxon Valdez (1989) and Macondo well (2010) accidents.

The goal of this dissertation was to investigate new advanced materials (mechanically strong aerogel composite blankets-Cabot® Thermal Wrap™ (TW) and Aspen Aerogels® Spaceloft® (SL)), and their applications for oil capture and recovery to overcome the current material limitations in oil spill response methods. First, uptake of different solvents and oils were studied to answer the following question: do these blanket aerogel composites have competitive oil uptake compared to state-of-the-art oil sorbents (i.e., polyurethane foam-PUF)? In addition to their competitive mechanical strength (766, 380, 92 kPa for Spaceloft, Thermal Wrap, and PUF, respectively), our results showed that aerogel composites have three critical advantages over PUF: rapid (3-5 min.) and high (more than two times of PUF’s uptake) oil uptake, reusability (over 10 cycles), and oil recoverability (up to 60%) via mechanical extraction. Chemical-specific sorption experiments showed that the dominant uptake mechanism of aerogels is adsorption to the internal surface, with some contribution of absorption into the pore space.

Second, we investigated the potential environmental impacts (energy and chemical burdens) associated with manufacturing, use, and disposal of SL aerogel and PUF to remove the oil (i.e., 1 m3 oil) from a location (i.e., Macondo well). Different use (single and multiple use) and end of life (landfill, incinerator, and waste-to-energy) scenarios were assessed, and our results demonstrated that multiple use, and waste-to-energy choices minimize the energy and material use of SL aerogel. Nevertheless, using SL once and disposing via landfill still offers environmental and cost savings benefits relative to PUF, and so these benefits are preserved irrespective of the oil-spill-response operator choices.

To inform future aerogel manufacture, we investigated the different laboratory-scale aerogel fabrication technologies (rapid supercritical extraction (RSCE), CO2 supercritical extraction (CSCE), alcohol supercritical extraction (ASCE)). Our results from anticipatory LCA for laboratory-scaled aerogel fabrication demonstrated that RSCE method offers lower cumulative energy and ecotoxicity impacts compared to conventional aerogel fabrication methods (CSCE and ASCE).

The final objective of this study was to investigate different surface coating techniques to enhance oil recovery by modifying the existing aerogel surface chemistries to develop chemically responsive materials (switchable hydrophobicity in response to a CO2 stimulus). Our results showed that studied surface coating methods (drop casting, dip coating, and physical vapor deposition) were partially successful to modify surface with CO2 switchable chemical (tributylpentanamidine), likely because of the heterogeneous fiber structure of the aerogel blankets. A possible solution to these non-uniform coatings would be to include switchable chemical as a precursor during the gel preparation to chemically attach the switchable chemical to the pores of the aerogel.

Taken as a whole, the implications of this work are that mechanical deployment and recovery of aerogel composite blankets is a viable oil spill response strategy that can be deployed today. This will ultimately enable better oil uptake without the uptake of water, potential reuse of the collected oil, reduced material and energy burdens compared to competitive sorbents (e.g., PUF), and reduced occupational exposure to oiled sorbents. In addition, sorbent blankets and booms could be deployed in coastal and open-ocean settings, respectively, which was previously impossible.