Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

Design of advanced reverse osmosis and nanofiltration membranes for water purification

Most commercially available reverse osmosis (RO) and nanofiltration (NF) membranes are based on the thin film composite (TFC) aromatic polyamide membranes. However, they have several disadvantages including low resistance to fouling, low chemical and thermal stabilities and limited chlorine tolerance. To address these problems, advanced RO/NF membranes are being developed from polyimides for water and wastewater treatments. The following three projects have resulted from my research. (1) Positively charged and solvent resistant NF membranes. The use of solvent resistant membranes to facilitate small molecule separations has been a long standing industry goal of the chemical and pharmaceutical industries. We developed a solvent resistant membrane by chemically cross-linking of polyimide membrane using polyethylenimine. This membrane showed excellent stability in almost all organic solvents. In addition, this membrane was positively charged due to the amine groups remaining on the surface. As a result, high efficiency (> 95%) and selectivity for multivalent heavy metal removal was achieved. (2) Fouling resistant NF membranes. Antifouling membranes are highly desired for “all” applications because fouling will lead to higher energy demand, increase of cleaning and corresponding down time and reduced life-time of the membrane elements. For fouling prevention, we designed a new membrane system using a coating technique to modify membrane surface properties to avoid adsorption of foulants like humic acid. A layer of water-soluble polymer such as polyvinyl alcohol (PVA), polyacrylic acid (PAA), polyvinyl sulfate (PVS) or sulfonated poly(ether ether ketone) (SPEEK), was adsorbed onto the surface of a positively charged membrane. The resultant membranes have a smooth and almost neutrally charged surface which showed better fouling resistance than both the positively charged NF membranes and commercially available negatively charged NTR-7450 membrane. In addition, these membranes showed high efficiency for removal of multivalent ions (> 95% for both cations and anions). Therefore, these antifouling surfaces can be potentially used for water softening, water desalination and wastewater treatment in a membrane bioreactor (MBR) process. (3) Thermally stable RO membranes. Commercial RO membranes cannot be used at temperature higher than 45°C due to the use of polysulfone substrate, which often limits their applications in industries. We successfully developed polyimides as the membrane substrate for thermally stable RO membranes due to their high thermal resistance. The polyimide-based composite polyamide membranes showed desalination performance comparable to the commercial TFC membrane. However, the key advantage of the polyimide-based membrane is its high thermal stability. As the feed temperature increased from 25oC to 95oC, the water flux increased 5 - 6 times while the salt rejection almost kept constant. This membrane appears to provide a unique solution for hot water desalination and also a feasible way to improve the water productivity by increasing the operating temperature without any drop in salt rejection.

Protein quality and distribution determines anabolic signaling, cellular energetics, and body composition

Building and maintaining muscle is critical to the quality of life for adults and elderly. Physical activity and nutrition are important factors for long-term muscle health. In particular, dietary protein – including protein distribution and quality – are under-appreciated determinants of muscle health for adults. The most unequivocal evidence for the benefit of optimal dietary protein at individual meals is derived from studies of weight management. During the catabolic condition of weight loss, higher protein diets attenuate loss of lean tissue and partition weight loss to body fat when compared with commonly recommended high carbohydrate, low protein diets. Muscle protein turnover is a continuous process in which proteins are degraded, and replaced by newly synthesized proteins. Muscle growth occurs when protein synthesis exceeds protein degradation. Regulation of protein synthesis is complex, with multiple signals influencing this process. The mammalian target of rapamycin (mTORC1) pathway has been identified as a particularly important regulator of protein synthesis, via stimulation of translation initiation. Key regulatory points of translation initiation effected by mTORC1 include assembly of the eukaryotic initiation factor 4F (eIF4F) complex and phosphorylation of the 70 kilodalton ribosomal protein S6 kinase (S6K1). Assembly of the eIF4F initiation complex involves phosphorylation of the inhibitory eIF4E binding protein-1 (4E-BP1), which releases the initiation factor eIF4E and allows it to bind with eIF4G. Binding of eIF4E with eIF4G promotes preparation of the mRNA for binding to the 43S pre-initiation complex. Consumption of the amino acid leucine (Leu) is a key factor determining the anabolic response of muscle protein synthesis (MPS) and mTORC1 signaling to a meal. Research from this dissertation demonstrates that the peak activation of MPS following a complete meal is proportional to the Leu content of a meal and its ability to elevate plasma Leu. Leu has also been implicated as an inhibitor of muscle protein degradation (MPD). In particular, there is evidence suggesting that in muscle wasting conditions Leu supplementation attenuates expression of the ubiquitin-proteosome pathway, which is the primary mode of intracellular protein degradation. However, this is untested in healthy, physiological feeding models. Therefore, an experiment was performed to see if feeding isonitrogenous protein sources with different Leu contents to healthy adult rats would differentially impact ubiquitin-proteosome (protein degradation) outcomes; and if these outcomes are related to the meal responses of plasma Leu. Results showed that higher Leu diets were able to attenuate total proteasome content but had no effect on ubiquitin proteins. This research shows that dietary Leu determines postprandial muscle anabolism. In a parallel line of research, the effects of dietary Leu on changes in muscle mass overtime were investigated. Animals consuming higher Leu diets had larger gastrocnemius muscle weights; furthermore, gastrocnemius muscle weights were correlated with postprandial changes in MPS (r=0.471, P<0.01) and plasma Leu (r=0.400, P=0.01). These results show that the effect of Leu on ubiquitin-proteosome pathways is minimal for healthy adult rats consuming adequate diets. Thus, long-term changes in muscle mass observed in adult rats are likely due to the differences in MPS, rather than MPD. Factors determining the duration of Leu-stimulated MPS were further investigated. Despite continued elevations in plasma Leu and associated translation initiation factors (e.g., S6K1 and 4E-BP1), MPS returned to basal levels ~3 hours after a meal. However, administration of additional nutrients in the form of carbohydrate, Leu, or both ~2 hours after a meal was able to extend the elevation of MPS, in a time and dose dependent manner. This effect led to a novel discovery that decreases in translation elongation activity was associated with increases in activity of AMP kinase, a key cellular energy sensor. This research shows that the Leu density of dietary protein determines anabolic signaling, thereby affecting cellular energetics and body composition.