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The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution
, 2004
"... There is a fundamental underlying structure in models of stochastic evolution called the emergent seed. Relative to this structure the stochastic potential of a limit set can be found without optimization, and the stochastically stable limit set can be found using local analysis. This representation ..."
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There is a fundamental underlying structure in models of stochastic evolution called the emergent seed. Relative to this structure the stochastic potential of a limit set can be found without optimization, and the stochastically stable limit set can be found using local analysis. This representation can be used to find two measures of waiting time–the coheight and the censored coradius.. We show the usefulness of the emergent seed by reanalyzing several applications in the literature and by showing how most applications in the literature could have been solved using this technique.
Limiting Conditional Distributions: Imprecision and Relation to the Hazard Rate
, 2009
"... Many Markov chains with a single absorbing state have a unique limiting conditional distribution (LCD) to which they converge, conditioned on nonabsorption, regardless of the initial distribution. If this limiting conditional distribution is used as the initial distribution over the nonabsorbing s ..."
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Many Markov chains with a single absorbing state have a unique limiting conditional distribution (LCD) to which they converge, conditioned on nonabsorption, regardless of the initial distribution. If this limiting conditional distribution is used as the initial distribution over the nonabsorbing states, then the probability distribution of the process at time n, conditioned on nonabsorption, is equal for all values of n> 0. Such an initial distribution is known as the quasistationary distribution (QSD). Thus the LCD and QSD are equal. These distributions can be found in both the discretetime and continuoustime case. In this thesis we consider finite Markov chains which have one absorbing state, and for which all other states form a set which is a single communicating class. In addition, every state is aperiodic. These conditions ensure the existence of a unique LCD. We first consider continuous Markov chains in the context of survival analysis. We consider the hazard rate, a function which measures the risk of instantaneous failure of a system at time t conditioned on the system not having failed before t. It is well
ABSTRACT Title of dissertation: LEARNING IN ENGINEERED MULTIAGENT SYSTEMS
"... Consider the problem of maximizing the total power produced by a wind farm. Due to aerodynamic interactions between wind turbines, each turbine maximizing its individual power—as is the case in presentday wind farms—does not lead to optimal farmlevel power capture. Further, there are no good model ..."
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Consider the problem of maximizing the total power produced by a wind farm. Due to aerodynamic interactions between wind turbines, each turbine maximizing its individual power—as is the case in presentday wind farms—does not lead to optimal farmlevel power capture. Further, there are no good models to capture the said aerodynamic interactions, rendering model based optimization techniques ineffective. Thus, modelfree distributed algorithms are needed that help turbines adapt their power production online so as to maximize farmlevel power capture. Motivated by such problems, the main focus of this dissertation is a distributed modelfree optimization problem in the context of multiagent systems. The setup comprises of a fixed number of agents, each of which can pick an action and observe the value of its individual utility function. An individual’s utility function may depend on the collective action taken by all agents. The exact functional form (or model) of the agent utility functions, however, are unknown; an agent can only measure the numeric value of its utility. The objective of the multiagent system is to optimize the welfare function (i.e. sum of the individual utility functions).