The American vaccine pricing market has many actors, making it a complex system to model. Because of this, previous papers have chosen to model only vaccine manufacturers while leaving out the government. However, the government is also an important actor in the market, since it buys over half of vaccines produced. In this work, we aim to introduce the government into vaccine pricing models to better recommend pricing strategies to the Centers for Disease Control and Prevention.

Roughgarden et al. (2006) proposed a theory called social selection as a behavioral game theoretic model for sexual reproduction that incorporates both competition and cooperation in 2006. Players oscillate between playing competitively to maximize their individual fitness, leading to a Nash Competitive Equilibrium, and playing cooperatively to maximize a team fitness function, leading to a Nash Bargaining Solution. Roughgarden et al. (2006) gives rates of change for both the competitive state and the cooperative state, but does not explain her rates or how to switch between the states in sufficient detail. We test and rederive the rates, critiquing an assumption that the derivation of such a rate must make, as well as create a probabilistic model that switches between the two states. We test our model on the reproductive behaviors of Symphodus tinca, the peacock wrasse. The results follow the trajectory of the reproductive strategies for the wrasse throughout the breeding system, suggesting that cooperation could be a mechanism through which wrasse change their reproductive behaviors. However, the inputs to the model need to be analyzed more critically. Future work could include deriving rates for competitive play and cooperative play that do not rely on assumptions of being able to quantify strategy allocation proportion and refining the model and drawing generalized conclusions about it.

This thesis focuses on decentralized deadbeat output regulation of discrete-time nonlinear plants that are composed of multiple agents. These agents interact, via scalar-valued signals, in a known structured way represented with a graph. This work is motivated by applications where it is infeasible and/or undesirable to introduce control action within each plant agent; instead, control agents are introduced to interact with certain plant agents, where each control agent focuses on regulating a specific plant agent, called its target. Then, two analyses are carried out to determine if regulation is achieved: targeting analysis is used to determine if control laws can be found to regulate all target agents, then growing analysis is used to determine the effect of those control laws on non-target plant agents. The strength of this novel approach is the intuitively-appealing notion of each control agent focusing on the regulation of just one plant agent. This work goes beyond previous research by generalizing the class of allowable plant dynamics, considering not only arbitrary propagation times through plant agents, but also allowing for non-symmetrical influence between the agents. Moreover, new necessary and sufficient algebraic conditions are derived to determine when targeting succeeds. The main contribution of this work, however, is the development of new easily-verifiable conditions necessary for targeting and/or growing to succeed. These new conditions are valuable due to their simplicity and scalability to large systems. They concern the positioning of control agents and targets as well as the propagation time of signals through the plant, and they help significantly with design decisions. Various graph structures (such as queues, grids, spiders, rings, etc.) are considered and for each, these conditions are used to develop a control scheme with the minimum number of control agents needed.

This thesis focuses on decentralized deadbeat output regulation of discrete-time nonlinear plants that are composed of multiple agents. These agents interact, via scalar-valued signals, in a known structured way represented with a graph. This work is motivated by applications where it is infeasible and/or undesirable to introduce control action within each plant agent; instead, control agents are introduced to interact with certain plant agents, where each control agent focuses on regulating a specific plant agent, called its target. Then, two analyses are carried out to determine if regulation is achieved: targeting analysis is used to determine if control laws can be found to regulate all target agents, then growing analysis is used to determine the effect of those control laws on non-target plant agents. The strength of this novel approach is the intuitively-appealing notion of each control agent focusing on the regulation of just one plant agent. This work goes beyond previous research by generalizing the class of allowable plant dynamics, considering not only arbitrary propagation times through plant agents, but also allowing for non-symmetrical influence between the agents. Moreover, new necessary and sufficient algebraic conditions are derived to determine when targeting succeeds. The main contribution of this work, however, is the development of new easily-verifiable conditions necessary for targeting and/or growing to succeed. These new conditions are valuable due to their simplicity and scalability to large systems. They concern the positioning of control agents and targets as well as the propagation time of signals through the plant, and they help significantly with design decisions. Various graph structures (such as queues, grids, spiders, rings, etc.) are considered and for each, these conditions are used to develop a control scheme with the minimum number of control agents needed.

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. Using this model for NBD2, we examine the consequence of single point mutations on NBD2. We collate the wildtype structure with eight of the most prevalent mutations and observe how the NBD2 is affected by each of these mutations.

The field of chemical graph theory utilizes simple graphs as models of molecules. These models are called molecular graphs, and quantifiers of molecular graphs are known as molecular descriptors or topological indices. Today's chemists use molecular descriptors to develop algorithms for computer aided drug designs, and computer based searching algorithms of chemical databases and the field is now more commonly known as combinatorial or computational chemistry. With the completion of the human genome project, related fields are emerging such as chemical genomics and pharmacogenomics. Recent advances in molecular biology are driving new methodologies and reshaping existing techniques, which in turn produce novel approaches to nucleic acid modeling and protein structure prediction. The origins of chemical graph theory are revisited and new directions in combinatorial chemistry with a special emphasis on biochemistry are explored. Of particular importance is the extension of the set of molecular descriptors to include graphical invariants. We also describe the use of artificial neural networks (ANNs) in predicting biological functional relationships based on molecular descriptor values. Specifically, a brief discussion of the fundamentals of ANNs together with an example of a graph theoretic model of RNA to illustrate the potential for ANN coupled with graphical invariants to predict function and structure of biomolecules is included.

Revenue Management (RM) is the practice of managing perishable assets by control-ling their availability and/or prices with an objective to maximize the total revenue. Seat inventory allocation falls in the purview of quantity-based RM. The liberalization of the aviation sector and the subsequent entrance of the low-cost carriers saw an ever-increasing customer base for the airline industry. Given the large number of buyers, firms were free to decide the price at which they would sell tickets. The low-cost carriers started to follow a third degree price discrimination and segmentation of the market, charging a higher price to the market with a relatively inelastic demand. Although a lot of work has been done in the area of seat inventory allocation under a monopolistic market scenario, we realized that not a lot of work had been done in a competitive market scenario. This thesis considers the problem of seat inventory allocation and pricing in a duopoly where each of the competing airlines have two fare-classes. We consider the possibility that the same fare-class may be priced differently by the two competing airlines and allow for the over flow of passengers between the airlines in the same fare-class. In the first part of our work, we develop a non-linear mathematical model for setting the booking limits for one of the two competing air-lines such that the revenue earned is maximized. We consider over flow of passengers from one airline to another in the same fare-class in response to a price differential and compare the results obtained from our model with the standard Expected Marginal Seat Revenue (EMSR) model under a monopolistic scenario. The results show that our model gives higher revenues than that obtained from the EMSR model. In the second part of our work, we consider a non-cooperative game between two competing airlines with price cutting as the strategy to increase their demand. Through numerical computations, we identify the pure strategy Nash equilibrium. From the results, we conclude that Nash equilibrium is achieved only when both the airlines follow the same pricing strategy indicating that individual price cutting will not be beneficial. This also indicates that unless the competitors enter into a cooperative coalition with each other, they would not benefit from deep discount offers. In the third and final part, we prove theoretically the existence of pure strategy Nash equilibrium in a two airline, two fare-class problem with price sensitive over flow of customers in the same fare-class that was computationally analysed earlier. The strategy / strategies at which Nash equilibrium is achieved are identified. We show that Nash equilibrium is only achieved when both the airlines price identically. Hence, our thesis concludes that differential pricing does not hold any significance for the competing airlines from an operational perspective.