"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

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 an 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 consumer 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 …rm with the highest value per click does not necessarily win the first spot in the sponsored search listings. It also may be optimal for a firm to bid an amount greater than the expected value (or sale) from a click.

Two-phase flow in a chemically active porous medium

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species -- in a one-dimensional macroscopic description --, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor.Comment: 13 pages, 10 figure

A New Spin on Color Quantization

We address the problem of image color quantization using a Maximum Entropy based approach. Focusing on pixel mapping we argue that adding thermal noise to the system yields better visual impressions than that obtained from a simple energy minimization. To quantify this observation, we introduce the coarse-grained quantization error, and seek the optimal temperature which minimizes this new observable. By comparing images with different structural properties, we show that the optimal temperature is a good proxy for complexity at different scales. Finally, noting that the convoluted error is a key observable, we directly minimize it using a Monte Carlo algorithm to generate a new series of quantized images. Adopting an original approach based on the informativity of finite size samples, we are able to determine the optimal convolution parameter leading to the best visuals.Comment: 8 pages, 5 figure

Rational points on Erdős–Selfridge superelliptic curves

Given k⩾2k⩾2, we show that there are at most finitely many rational numbers xx and y≠0y≠0 and integers ℓ⩾2ℓ⩾2 (with (k,ℓ)≠(2,2)(k,ℓ)≠(2,2)) for which \begin{eqnarray}x(x+1)\cdots (x+k-1)=y^{\ell }.\end{eqnarray} In particular, if we assume that ℓℓ is prime, then all such triples (x,y,ℓ)(x,y,ℓ) satisfy either y=0y=0 or ℓ<exp(3k)ℓ<exp⁡(3k)