Efficient Networks in Models of Player and Partner Heterogeneity

This paper contributes to the literature on centrality measures in economics by defining a team game and identifying the key players in the game. As an illustration of the theory we create a unique data set from the UEFA Euro 2008 tournament. To capture the interaction between players we create the passing network of each team. This all allows us to identify the key player and key groups of players for both teams in each game. We then use our measure to explain player ratings by experts and their market values. Our measure is significant in explaining expert ratings. We also find that players having higher intercentrality measures, regardless of their field position have significantly higher market values.

An Explicit Proof of the Generalized Gauss-Bonnet Formula

In this paper we construct an explicit representative for the Grothendieck fundamental class [Z] of a complex submanifold Z of a complex manifold X, under the assumption that Z is the zero locus of a real analytic section of a holomorphic vector bundle E. To this data we associate a super-connection A on the exterior algebra of E, which gives a "twisted resolution" of the structure sheaf of Z. The "generalized super-trace" of A^{2r}/r!, where r is the rank of E, is an explicit map of complexes from the twisted resolution to the Dolbeault complex of X, which represents [Z]. One may then read off the Gauss-Bonnet formula from this map of complexes.Comment: 21 pages. Paper reorganized to improve exposition. To appear in Asterisqu

Constructing homologically trivial actions on products of spheres

We prove that if a finite group $G$ has a representation with fixity $f$, then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of $f+1$ spheres. This shows, in particular, that every finite group acts freely and homologically trivially on some finite CW-complex homotopy equivalent to a product of spheres

Fusion systems and group actions with abelian isotropy subgroups

We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on M \times \bbS^{n_1} \times...\times \bbS^{n_k} for some positive integers $n_1,...n_k$. We construct these actions using a recursive method, introduced in an earlier paper, that involves abstract fusion systems on finite groups. As another application of this method, we prove that every finite solvable group acts freely and smoothly on some product of spheres with trivial action on homology.Comment: 13 pages. Last two sections of the previous version are removed for further study. To appear in Proceedings of the Edinburgh Mathematical Societ

Digital microarrays: single-molecule readout with interferometric detection of plasmonic nanorod labels

DNA and protein microarrays are a high-throughput technology that allow the simultaneous quantification of tens of thousands of different biomolecular species. The mediocre sensitivity and limited dynamic range of traditional fluorescence microarrays compared to other detection techniques have been the technology’s Achilles’ heel and prevented their adoption for many biomedical and clinical diagnostic applications. Previous work to enhance the sensitivity of microarray readout to the single-molecule (“digital”) regime have either required signal amplifying chemistry or sacrificed throughput, nixing the platform’s primary advantages. Here, we report the development of a digital microarray which extends both the sensitivity and dynamic range of microarrays by about 3 orders of magnitude. This technique uses functionalized gold nanorods as single-molecule labels and an interferometric scanner which can rapidly enumerate individual nanorods by imaging them with a 10× objective lens. This approach does not require any chemical signal enhancement such as silver deposition and scans arrays with a throughput similar to commercial fluorescence scanners. By combining single-nanoparticle enumeration and ensemble measurements of spots when the particles are very dense, this system achieves a dynamic range of about 6 orders of magnitude directly from a single scan. As a proof-of-concept digital protein microarray assay, we demonstrated detection of hepatitis B virus surface antigen in buffer with a limit of detection of 3.2 pg/mL. More broadly, the technique’s simplicity and high-throughput nature make digital microarrays a flexible platform technology with a wide range of potential applications in biomedical research and clinical diagnostics.The authors wish to thank Oguzhan Avci and Jacob Trueb for thoughtful comments and suggestions regarding numerical optimization of the optical system. This work was funded in part by a research contract with ASELSAN, Inc. and the Wallace H. Coulter Foundation 2010 Coulter Translational Award. (ASELSAN, Inc.; Wallace H. Coulter Foundation Coulter Translational Award)Accepted manuscrip

Key Players and Key Groups in Teams

This paper contributes to the literature on centrality measures in economics by defining a team game and identifying the key players in the game. As an illustration of the theory we create a unique data set from the UEFA Euro 2008 tournament. To capture the interaction between players we create the passing network of each team. This all allows us to identify the key player and key groups of players for both teams in each game. We then use our measure to explain player ratings by experts and their market values. Our measure is significant in explaining expert ratings. We also find that players having higher intercentrality measures, regardless of their field position have significantly higher market values.

Key Players and Key Groups in Teams: A Network Approach Using Soccer Data

This paper provides a way of evaluating a player's contribution to her team and relates her effort to her salaries. We collect data from UEFA Euro 2008 Tournament and construct the passing network of each team. Then we determine the key player in the game while ranking all the other players too. Next, we identify key groups of players to determine which combination of players played more important role in the match. Using 2010 market values and observable characteristics of the players, we show that players having higher intercentrality measures regardless of their field position have significantly higher market values.Social networks, team game, centrality measures