A proof of Waldhausen's uniqueness of splittings of S^3 (after Rubinstein and Scharlemann)

In [Topology 35 (1996) 1005--1023] J H Rubinstein and M Scharlemann, using Cerf Theory, developed tools for comparing Heegaard splittings of irreducible, non-Haken manifolds. As a corollary of their work they obtained a new proof of Waldhausen's uniqueness of Heegaard splittings of S^3. In this note we use Cerf Theory and develop the tools needed for comparing Heegaard splittings of S^3. This allows us to use Rubinstein and Scharlemann's philosophy and obtain a simpler proof of Waldhausen's Theorem. The combinatorics we use are very similar to the game Hex and requires that Hex has a winner. The paper includes a proof of that fact (Proposition 3.6).Comment: This is the version published by Geometry & Topology Monographs on 3 December 200

Signaling in First-Price Auctions

It is commonly assumed in private value auctions that bidders have no information about the realization of the other bidders' valuations. Nevertheless, an informative public signal about the realization may be released by a bidder while he learns his own valuation. Using a simple discrete asymmetric first-price auction setting, we show that a bidder may indeed benefit from the presence of an informative signal about his own valuation. We characterize the optimal signal and show that a signal is not beneficial if it is too precise. The latter result carries over to a general continuous asymmetric first-price auction model. Finally, we use a specific signaling structure with uniform distributions to show that signaling need not be beneficial for any precision of the signal.asymmetric auction, first-price auction, signaling

Thin position for a connected sum of small knots

We show that every thin position for a connected sum of small knots is obtained in an obvious way: place each summand in thin position so that no two summands intersect the same level surface, then connect the lowest minimum of each summand to the highest maximum of the adjacent summand below.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-14.abs.htm

False memory and aging: an event-related potential study

The DRM paradigm is used to examine false memory—when a list of highly associated words (e.g. SEWING, THREAD, THIMBLE) is studied, a nonpresented but associated false target (e.g. NEEDLE) is often confidently (but incorrectly) identified as having been studied. An ERP study was conducted with a sample of young and older adults to examine age differences in false memory and neurological distinctions between true and false recognition. DRM words were presented in a lateralized fashion, with the prediction that a contralateral sensory signature would be present for true but not false memories. ERP data was largely inconclusive, but does suggest that processing during the DRM paradigm may largely be carried out in the left hemisphere.Paul Verhaeghen - Faculty Mentor ; Audrey Duarte - Committee Member/Second Reade

Information Disclosure in Innovation Contests

In innovation contests, the progress of the competing firms in the innovation process is usually their private information. We analyze an innovation contest in which research firms have a stochastic technology to develop innovations at a fixed cost, but their progress is publicly announced. We make a comparison with the case of no information revelation: if the progress is disclosed, the expected profit of the firms is higher, but the expected profit of the sponsor is lower. Additionally, we show that firms may voluntarily reveal their information.contest, innovation, information revelation

The Heegaard genus of bundles over S^1

This paper explores connections between Heegaard genus, minimal surfaces, and pseudo-Anosov monodromies. Fixing a pseudo-Anosov map phi and an integer n, let M_n be the 3-manifold fibered over S^1 with monodromy phi^n. JH Rubinstein showed that for a large enough n every minimal surface of genus at most h in M_n is homotopic into a fiber; as a consequence Rubinstein concludes that every Heegaard surface of genus at most h for M_n is standard, that is, obtained by tubing together two fibers. We prove this result and also discuss related results of Lackenby and Souto.Comment: This is the version published by Geometry & Topology Monographs on 3 December 200