Noncommutative Yang-Mills-Higgs actions from derivation-based differential calculus

Derivations of a noncommutative algebra can be used to construct differential calculi, the so-called derivation-based differential calculi. We apply this framework to a version of the Moyal algebra ${\cal{M}}$. We show that the differential calculus, generated by the maximal subalgebra of the derivation algebra of ${\cal{M}}$ that can be related to infinitesimal symplectomorphisms, gives rise to a natural construction of Yang-Mills-Higgs models on ${\cal{M}}$ and a natural interpretation of the covariant coordinates as Higgs fields. We also compare in detail the main mathematical properties characterizing the present situation to those specific of two other noncommutative geometries, namely the finite dimensional matrix algebra $M_n({\mathbb{C}})$ and the algebra of matrix valued functions $C^\infty(M)\otimes M_n({\mathbb{C}})$. The UV/IR mixing problem of the resulting Yang-Mills-Higgs models is also discussed.Comment: 23 pages, 2 figures. Improved and enlarged version. Some references have been added and updated. Two subsections and a discussion on the appearence of Higgs fiels in noncommutative gauge theories have been adde

"To Sponsor or not to Sponsor: Sponsored Search Auctions with Organic Links"

In 2010 sponsored search advertisements generated over $12 billion in revenue for search engines in the US market and accounted for 46% of online advertising revenue. A substantial portion of this revenue was generated by the sale of search keywords using auction mechanism. We analyze a game-theoretic model to understand the interplay between organic and sponsored links in keyword auctions. Our model allows both the relevance of the advertising firm as well as the position of its sponsored link to impact click-through-rates. Our results demonstrate how the presence of organic links (links generated by the search engine algorithm) may lead to either more or less aggressive bidding for sponsored link positions depending on consumers attitudes toward sponsored links and the extent to which sponsored and organic links are complements or substitutes. In contrast to equilibrium results in existing literature, the firm with the highest value per click does not necessarily win the first spot in the sponsored search listing. It also may be optimal for a firm to bid an amount greater than the expected value (or sale) from a click.sponsored search, organic search, online advertising, keyword auction

Set identified linear models

We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictions E(z T (x β−y)) = E(z Tu(z)) where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a set-up. Second, we show that these conditions set identify β where the identified set B is bounded and convex. We provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters. We derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar Sargan condition. Third, we provide new results on the asymptotics of analog estimates constructed from the identification results. When B is a strictly convex set, we also construct a test of the null hypothesis, β 0 ε B, whose size is asymptotically correct and which relies on the minimization of the support function of the set B − { β 0 }. Results of some Monte Carlo experiments are presented.

Proposition and validation of an original MAC layer with simultaneous medium accesses for low latency wireless control/command applications

Control/command processes require a transmission system with some characteristics like high reliability, low latency and strong guarantees on messages delivery. Concerning wire networks, field buses technologies like FIP offer this kind of service (periodic tasks, real time constraints...). Unfortunately, few wireless technologies can propose a communication system which respects such constraints. Indeed, wireless transmissions must deal with medium characteristics which make impossible the direct translation of mechanisms used with wire networks. The purpose of this paper is to present an original Medium Access Control (MAC) layer for a real time Low Power-Wireless Personal Area Network (LP-WPAN). The proposed MAC-layer has been validated by several complementary methods; in this paper, we focus on the specific Simultaneous Guaranteed Time Slot (SGTS) part