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This thesis presents a discussion of motion of a six-legged walking machine following removal of one leg constraint. To take a step, one leg must be lifted and placed at some other position. As soon as the constraint provided by the leg is removed, however the machine begins to fall. This falling motion can be represented as screw motion of the body center of mass and of body-leg attachments. First a study of body workspace of the machine was done with all six feet on the ground. Body workspace is the intersection of kinematic and force workspaces. Kinematic workspace is the volume in space where the center of mass can be placed such that all joint angles of legs are within specified limits; and force workspace is the volume in space where the force in all legs is compressive. The affect of various foot positions, pitches and heights of the center of mass were investigated to find a set of three symmetric foot positions that might constitute acceptable intermediate positions in a walking sequence. Motion of the center of mass in the forward direction is limited in the force workspace by two points at which the force on a pair of legs goes to zero. With the center of mass at each of these two positions, the screw parameters resulting from the release of force on one leg (front, middle and hind individually) could be determined. Dynamic simulation of these body and foot positions used the commercial software SD/FAST. Code was written in C to do both static and dynamic simulation of machine and merged with code generated by SD/FAST. Code was also written in Auto Lisp to plot the falling motion of machine. Screw parameters found in this study were such that sustained forward motion of the body could not be achieved using the falling motion alone. Other measures such as extending one or more of the remaining five legs would be needed for effective forward body motion. / Graduation date: 1994

Recent years have seen extensive studies on the pricing problem, as well as its many variances. They have found important applications in computational economics. Nowadays typical applications can be found in internet advertising, Google’s Auction for TV ads and many other resource allocation problems in electronic markets. In electronic markets, thousands of trading activities are processed in the internet or done automatically by computer programs. It is highly required that the trading mechanisms are efficient enough. In the thesis, we will study various pricing problems from different perspectives. The first problem we study is the design of auction mechanism when bidders are unit-demand. It can be applied in internet advertising. Thousand of advertisers bid for space in webpages to show their advertisements. We model the new problem and apply the General Second Price (GSP) mechanism to the problem. GSP is an efficient mechanism with linear time complexity. Moreover, we show that GSP has an envy-free equilibrium which can maximize the profit of advertisers. Auction mechanisms where bidders can bid for multiple items are also studied. A famous example of such auction is the Dutch flower auction. Such multi-unit auctions are widely studied these years. But budget constraints are not considered in many previous works. We study the scenario that each bidder has a budget on the money paid to the auctioneer and the valuation functions of bidders are non-linear. For the model, we design an adaptive clinching auction mechanism. The mechanism is proved to be incentive-compatible, which encourages bidders to reveal their true values, and Pareto-optimal, which ensures that no bidder can improve her utility without decreasing those of others. In some auctions, the items on sale are not available at the same time. For example, TV stations sell time-slots for advertisements on a daily basis. The advertisers are arriving and departing online and bidding for a set of timeslots. For the auction, we design a competitive mechanism which is truthful, i.e., all bidders have the incentive to submit their true private values to the auctioneer. Another important property the mechanism achieves is promptness, which makes sure that any advertiser that wins some time-slots could learn her payment immediately after winning these time-slots. In some pricing problems, upon the arrival of a new buyer, the seller needs to decide immediately whether he will sell his goods or not and what is the price. When buyers are unit-demand and each seller has b items on sale, the online pricing problem can be modelled by online weighted b-matching problem. For the problem, we show a randomized algorithm which achieves near-optimal competitive ratio. When buyers are not unit-demand, things are much more complicated. We consider a general model in which each buyer wants to buy a bundle of items and has a non-increasing valuation function for those items. We design a randomized algorithm which achieves low competitive ratio and derive a non-trivial lower bound on the competitive ratios. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

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There is no abstract available for this dissertation. / Department of Physics and Astronomy