We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pes...

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pesk...

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pesk...

To achieve high performance, autonomous systems, such as science explorers, should adapt to the environment to improve utility gained, as well as robustness. Flexibility during temporal plan execution has been explored extensively to improve robustness, where flexibility exists both in activity choices and schedules. These problems are framed as conditional constraint networks over temporal con...

Revenue maximization in combinatorial auctions (and other multidimensional selling settings) is one of the most important and most elusive problems in mechanism design. The design problem is NP-complete, and the optimal designs include features that are not acceptable in many applications, such as favoring some bidders over others and randomization. In this paper, we instead study a common reve...

Revenue maximization in combinatorial auctions (and other multidimensional selling settings) is one of the most important and elusive problems in mechanism design. The optimal design is unknown, and is known to include features that are not acceptable in many applications, such as favoring some bidders over others and randomization. In this paper, we instead study a common revenue-enhancement a...

The Birch and Swinnerton-Dyer conjecture states that the rank of the Mordell-Weil group of an elliptic curve E equals the order of vanishing at the central point of the associated L-function L(s, E). Previous investigations have focused on bounding how far we must go above the central point to be assured of finding a zero, bounding the rank of a fixed curve or on bounding the average rank in a ...

In this paper we consider the problem of making inference on a structural parameter in instrumental variables regression when the instruments are only weakly correlated with the endogenous explanatory variables. Adopting a local-to-zero assumption as in Staiger and Stock (1994) on the coe cients of the instruments in the rst stage equation, the asymptotic distributions of various test statistic...

In this thesis, I present a framework for achieving a stable bounding gait on the LittleDog robot over rough terrain. The framework relies on an accurate planar model of the dynamics, which I assembled from a model of the motors, a rigid body model, and a novel physically-inspired ground interaction model, and then identified using a series of physical measurements and experiments. I then used ...