Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes. Given the widespread use of bundling in real-life markets, we study its role as a stabilizing and coordinating device by considering the notion of \emph{competitive bundling equilibrium}: a competitive equilibrium over the market induced by partitioning the goods for sale into fixed bundles. Compared to other equilibrium concepts involving bundles, this notion has the advantage of simulatneous succinctness ($O(m)$ prices) and market clearance. Our first set of results concern welfare guarantees. We show that in markets where consumers care only about the number of goods they receive (known as multi-unit or homogeneous markets), even in the presence of complementarities, there always exists a competitive bundling equilibrium that guarantees a logarithmic fraction of the optimal welfare, and this guarantee is tight. We also establish non-trivial welfare guarantees for general markets, two-consumer markets, and markets where the consumer valuations are additive up to a fixed budget (budget-additive). Our second set of results concern revenue guarantees. Motivated by the fact that the revenue extracted in a standard competitive equilibrium may be zero (even with simple unit-demand consumers), we show that for natural subclasses of gross substitutes valuations, there always exists a competitive bundling equilibrium that extracts a logarithmic fraction of the optimal welfare, and this guarantee is tight. The notion of competitive bundling equilibrium can thus be useful even in markets which possess a standard competitive equilibrium

The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Biophysical Measurements of Cells, Microtubules, and DNA with an Atomic Force Microscope

Atomic force microscopes (AFMs) are ubiquitous in research laboratories and have recently been priced for use in teaching laboratories. Here we review several AFM platforms (Dimension 3000 by Digital Instruments, EasyScan2 by Nanosurf, ezAFM by Nanomagnetics, and TKAFM by Thorlabs) and describe various biophysical experiments that could be done in the teaching laboratory using these instruments. In particular, we focus on experiments that image biological materials and quantify biophysical parameters: 1) imaging cells to determine membrane tension, 2) imaging microtubules to determine their persistence length, 3) imaging the random walk of DNA molecules to determine their contour length, and 4) imaging stretched DNA molecules to measure the tensional force.Comment: 29 page preprint, 7 figures, 1 tabl

Sixteen years of Collaborative Learning through Active Sense-making in Physics (CLASP) at UC Davis

This paper describes our large reformed introductory physics course at UC Davis, which bioscience students have been taking since 1996. The central feature of this course is a focus on sense-making by the students during the five hours per week discussion/labs in which the students take part in activities emphasizing peer-peer discussions, argumentation, and presentations of ideas. The course differs in many fundamental ways from traditionally taught introductory physics courses. After discussing the unique features of CLASP and its implementation at UC Davis, various student outcome measures are presented showing increased performance by students who took the CLASP course compared to students who took a traditionally taught introductory physics course. Measures we use include upper-division GPAs, MCAT scores, FCI gains, and MPEX-II scores.Comment: Also submitted to American Journal of Physic

Webteaching: sequencing of subject matter in relation to prior knowledge of pupils

Two experiments are discussed in which the sequencing procedure of webteaching is compared with a linear sequence for the presentation of text material.\ud \ud In the first experiment variations in the level of prior knowledge of pupils were studied for their influence on the sequencing mode of text presentation. Prior knowledge greatly reduced the effect of the size of sequencing procedures.\ud \ud In the second experiment pupils with a low level of prior knowledge studied a text, following either a websequence or a linear sequence. Webteaching was superior to linear teaching on a number of dependent variables. It is concluded that webteaching is an effective sequencing procedure in those cases where substantial new learning is required

The mating-specific Gα interacts with a kinesin-14 and regulates pheromone-induced nuclear migration in budding yeast

As a budding yeast cell elongates toward its mating partner, cytoplasmic microtubules connect the nucleus to the cell cortex at the growth tip. The Kar3 kinesin-like motor protein is then thought to stimulate plus-end depolymerization of these microtubules, thus drawing the nucleus closer to the site where cell fusion and karyogamy will occur. Here, we show that pheromone stimulates a microtubule-independent interaction between Kar3 and the mating-specific Gα protein Gpa1 and that Gpa1 affects both microtubule orientation and cortical contact. The membrane localization of Gpa1 was found to polarize early in the mating response, at about the same time that the microtubules begin to attach to the incipient growth site. In the absence of Gpa1, microtubules lose contact with the cortex upon shrinking and Kar3 is improperly localized, suggesting that Gpa1 is a cortical anchor for Kar3. We infer that Gpa1 serves as a positional determinant for Kar3-bound microtubule plus ends during mating. © 2009 by The American Society for Cell Biology