Georgia Institute of Technology College of Sciences

Pricing and allocating goods to buyers with complex preferences in order to maximize some desired objective (e.g., social welfare or profit) is a central problem in Algorithmic Mechanism Design. In this talk I will discuss some particularly simple algorithms that are able to achieve surprisingly strong guarantees for a range of problems of this type. As one example, for the problem of pricing resources, modeled as goods having an increasing marginal extraction cost to the seller, a simple approach of pricing the i-th unit of each good at a value equal to the anticipated extraction cost of the 2i-th unit gives a constant-factor approximation to social welfare for a wide range of cost curves and for arbitrary buyer valuation functions. I will also discuss simple algorithms with good approximation guarantees for revenue, as well as settings having an opposite character to resources, namely having economies of scale or decreasing marginal costs to the seller.

(algebraic statistics reading seminar)

Annual Joseph Ford Commemorative Lecture: I will describe several models for running insects, from an energy-conserving biped, through a muscle-actuated hexapod driven by a neural central pattern generator, to a reduced phase-oscillator model that captures the dynamics of unperturbed gaits and of impulsive perturbations. I will argue that both simple models and large simulations are necessary to understand biological systems. The models show that piecewise-holonomic constraints due to intermittent foot contacts confer asymptotic stability on the feedforward system, while leg force sensors modulate motor outputs to mitigate large perturbations. Phase response curves and coupling functions help explain reflexive feedback mechanisms. The talk will draw on joint work with Einat Fuchs, Robert Full, Raffaele Ghigliazza, Raghu Kukillaya, Josh Proctor, John Schmitt, and Justin Seipel. Research supported by NSF and the J. Insley Blair Pyne Fund of Princeton University.