\nobreakspace {}\hfill {{\bfseries Page}}
\contentsline {front}{{Abstract}}{iii}{chapter*.1}
\contentsline {front}{{Dedication}}{iv}{section*.2}
\contentsline {front}{{Acknowledgments}}{v}{chapter*.3}
\contentsline {front}{{Vita}}{vii}{chapter*.4}
\contentsline {front}{{List of Tables}}{xi}{chapter*.6}
\contentsline {front}{List of Figures}{xii}{chapter*.7}
\vskip 1.0em plus 1pt \hskip -\parindent Chapters:\vskip 0.25em\rm 
\contentsline {chapter}{\numberline {1.}Introduction}{1}{chapter.1}
\contentsline {chapter}{\numberline {2.}Model of a Solitary Agent}{3}{chapter.2}
\contentsline {subsubsection}{Terminology: Agents, Tasks, and Currency}{4}{section*.8}
\contentsline {subsubsection}{Behavioral Optimization: Making the Best Choices}{4}{section*.9}
\contentsline {subsubsection}{Approach Motivation: Finite Lifetime Analysis and Design}{5}{section*.10}
\contentsline {section}{\numberline {2.1}The Generalized Solitary Agent Model}{6}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}Model Assumptions}{6}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}Task-Type Parameters}{8}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}Actual Processing Gains, Costs, and Times}{12}{subsection.2.1.3}
\contentsline {subsection}{\numberline {2.1.4}Important Technical Notes}{12}{subsection.2.1.4}
\contentsline {section}{\numberline {2.2}Classical OFT Analysis: Encounter-Based Approach}{13}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}Processes Generated from Merged Encounters}{13}{subsection.2.2.1}
\contentsline {subsubsection}{Merged Task-Type Processes}{14}{section*.11}
\contentsline {subsubsection}{Net Gain, Cost, and Time Processes}{15}{section*.12}
\contentsline {subsection}{\numberline {2.2.2}Markov Renewal Process}{16}{subsection.2.2.2}
\contentsline {subsubsection}{Encounter Times: Statistics and Stochastic Limits}{17}{section*.13}
\contentsline {subsection}{\numberline {2.2.3}Markov Renewal-Reward Processes}{18}{subsection.2.2.3}
\contentsline {subsection}{\numberline {2.2.4}Reward Process Statistics}{18}{subsection.2.2.4}
\contentsline {subsubsection}{Stochastic Limits of Net Gain Processes}{19}{section*.14}
\contentsline {subsubsection}{Variance Under Pseudo-Deterministic Conditions}{20}{section*.15}
\contentsline {section}{\numberline {2.3}Finite Lifetime Analysis: Processing-Based Approach}{22}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}Poisson Encounters of Processed Tasks of One Type}{22}{subsection.2.3.1}
\contentsline {subsubsection}{Poisson Encounters of All Processed Tasks}{23}{section*.16}
\contentsline {subsubsection}{Merged Task-Type Processes}{23}{section*.17}
\contentsline {subsection}{\numberline {2.3.2}Process-Only Markov Renewal Process}{24}{subsection.2.3.2}
\contentsline {subsubsection}{Cumulative Reward Processes and Their Statistics}{26}{section*.18}
\contentsline {subsubsection}{Limits of Cumulative Reward Processes}{26}{section*.19}
\contentsline {subsubsection}{Variance Under Pseudo-Deterministic Conditions}{27}{section*.20}
\contentsline {section}{\numberline {2.4}Relationship Between Analysis Approaches}{29}{section.2.4}
\contentsline {section}{\numberline {2.5}Weaknesses of the Model}{30}{section.2.5}
\contentsline {chapter}{\numberline {3.}Statistical Optimization Objectives for Solitary Behavior}{33}{chapter.3}
\contentsline {section}{\numberline {3.1}Objective Function Structure}{34}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}Statistics of Interest}{34}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}Optimization Constraints}{36}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}Impact of Function Choice on Optimal Behaviors}{38}{subsection.3.1.3}
\contentsline {section}{\numberline {3.2}Classical OFT Approach to Optimization}{39}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Maximization of Long-Term Rate of Net Gain}{39}{subsection.3.2.1}
\contentsline {subsubsection}{Opportunity Cost and Pareto Optimality}{41}{section*.21}
\contentsline {subsubsection}{Equilibrium Renewal Process as an Attractive Alternative}{42}{section*.22}
\contentsline {subsubsection}{Graphical Interpretation of Rate Maximization}{43}{section*.23}
\contentsline {subsection}{\numberline {3.2.2}Minimization of Net Gain Shortfall}{44}{subsection.3.2.2}
\contentsline {subsubsection}{Maximization of Reward-to-Variability Ratio}{45}{section*.24}
\contentsline {paragraph}{Location-Scale Justification:}{46}{section*.25}
\contentsline {paragraph}{Analogous Results from Economics:}{46}{section*.26}
\contentsline {paragraph}{Links to Risk-Sensitive Dynamic Optimization:}{47}{section*.27}
\contentsline {subsubsection}{Graphical Interpretation of Risk Minimization}{47}{section*.28}
\contentsline {subsection}{\numberline {3.2.3}Criticisms of the OFT Approach}{48}{subsection.3.2.3}
\contentsline {section}{\numberline {3.3}Generalized Optimization of Solitary Agent Behavior}{49}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}Finite Task Processing}{50}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}Tradeoffs as Ratios}{51}{subsection.3.3.2}
\contentsline {subsubsection}{Rate Maximization with Gain Threshold}{52}{section*.29}
\contentsline {subsubsection}{Efficiency}{55}{section*.30}
\contentsline {subsubsection}{Risk-Sensitivity: Reward-to-Variability Ratios}{58}{section*.31}
\contentsline {subsubsection}{Reward-to-Variance Ratios}{61}{section*.32}
\contentsline {subsection}{\numberline {3.3.3}Generalized Pareto Tradeoffs}{63}{subsection.3.3.3}
\contentsline {subsubsection}{Gain and Time}{64}{section*.33}
\contentsline {subsubsection}{Efficiency}{64}{section*.34}
\contentsline {subsubsection}{Risk-Sensitivity: Mean and Standard Deviation}{65}{section*.35}
\contentsline {subsubsection}{Risk-Sensitivity: Mean, Variance, and Expected Utility}{65}{section*.36}
\contentsline {subsection}{\numberline {3.3.4}Constraints}{66}{subsection.3.3.4}
\contentsline {subsubsection}{Gain and Time}{67}{section*.37}
\contentsline {subsubsection}{Efficiency}{68}{section*.38}
\contentsline {subsubsection}{Risk-Sensitivity: Mean, Standard Deviation, and Variance}{68}{section*.39}
\contentsline {paragraph}{Standard Deviation:}{69}{section*.40}
\contentsline {section}{\numberline {3.4}Future Directions Inspired by PMPT}{70}{section.3.4}
\contentsline {subsection}{\numberline {3.4.1}Lower Partial Moments}{70}{subsection.3.4.1}
\contentsline {subsection}{\numberline {3.4.2}Stochastic Dominance}{72}{subsection.3.4.2}
\contentsline {chapter}{\numberline {4.}Finite-Lifetime Optimization Results}{74}{chapter.4}
\contentsline {section}{\numberline {4.1}Optimization of a Rational Objective Function}{74}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}The Generalized Problem}{75}{subsection.4.1.1}
\contentsline {subsubsection}{The Decision Variables and Constraints}{75}{section*.41}
\contentsline {subsubsection}{Generalized Advantage, Disadvantage, and Objective}{76}{section*.42}
\contentsline {subsubsection}{Notation}{76}{section*.43}
\contentsline {subsection}{\numberline {4.1.2}The Optimization Procedure}{76}{subsection.4.1.2}
\contentsline {subsubsection}{First-Order Necessary Conditions}{78}{section*.44}
\contentsline {paragraph}{Preference Probabilities:}{79}{section*.45}
\contentsline {paragraph}{Processing Times:}{80}{section*.46}
\contentsline {subsubsection}{Second-Order Necessary Conditions}{81}{section*.47}
\contentsline {paragraph}{Elimination of Active Preference Probability Constraints:}{81}{section*.48}
\contentsline {paragraph}{Elimination of Active Processing Time Constraints:}{81}{section*.49}
\contentsline {paragraph}{Elimination of Off-Diagonal Terms:}{82}{section*.50}
\contentsline {paragraph}{Impact of Inactive Preference Probability Diagonals:}{83}{section*.51}
\contentsline {paragraph}{Definiteness from Inactive Processing Time Diagonals:}{83}{section*.52}
\contentsline {subsubsection}{Second-Order Sufficiency Conditions}{83}{section*.53}
\contentsline {paragraph}{The Extreme-Preference Rule:}{84}{section*.54}
\contentsline {paragraph}{Problems with Sufficiency at Zero Preference Probability:}{84}{section*.55}
\contentsline {subsection}{\numberline {4.1.3}Solutions to Special Cases}{84}{subsection.4.1.3}
\contentsline {subsubsection}{Constant Disadvantage Case}{85}{section*.56}
\contentsline {subsubsection}{Decreasing Advantage-to-Disadvantage Ratio}{87}{section*.57}
\contentsline {section}{\numberline {4.2}Optimization of Specific Objective Functions}{90}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}Maximization of Rate of Excess Net Point Gain}{90}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}Maximization of Discounted Net Gain}{91}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}Maximization of Rate of Excess Efficiency}{92}{subsection.4.2.3}
\contentsline {chapter}{\numberline {5.}Conclusion}{93}{chapter.5}
\contentsline {section}{\numberline {5.1}Contributions to Engineering}{93}{section.5.1}
\contentsline {section}{\numberline {5.2}Contributions to Biology}{94}{section.5.2}
\contentsline {section}{\numberline {5.3}Future Directions}{96}{section.5.3}
\contentsline {section}{\numberline {5.4}The Value of Collaboration}{97}{section.5.4}
\vskip 1.0em plus 1pt \hskip -\parindent Appendices:\hfill \vskip 0.25em\rm 
\contentsline {chapter}{\numberline {A.}Limits of Markov Renewal Processes}{98}{appendix.A}
\contentsline {chapter}{Bibliography}{100}{section*.58}
\contentsline {chapter}{List of Acronyms}{106}{appendix*.61}
\contentsline {chapter}{List of Terms}{107}{appendix*.63}
\contentsline {chapter}{List of Symbols}{109}{appendix*.65}
\contentsline {chapter}{Index}{114}{section*.67}
\contentsline {chapter}{People}{121}{section*.69}