Optimal Real-Time Bidding Strategies

The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions -- throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators (KPI). The optimization problems faced by companies building bidding strategies are new and interesting for the community of applied mathematicians. In this article, we introduce a stochastic optimal control model that addresses the question of the optimal bidding strategy in various realistic contexts: the maximization of the inventory bought with a given amount of cash in the framework of audience strategies, the maximization of the number of conversions/acquisitions with a given amount of cash, etc. In our model, the sequence of auctions is modeled by a Poisson process and the \textit{price to beat} for each auction is modeled by a random variable following almost any probability distribution. We show that the optimal bids are characterized by a Hamilton-Jacobi-Bellman equation, and that almost-closed form solutions can be found by using a fluid limit. Numerical examples are also carried out

Treatment needs and impact of oral health screening of athletes with intellectual disability in Belgium

Background: Special Olympics Special Smiles (SOSS) is an initiative created for oral health data collection and education in oral hygiene for athletes with an intellectual disability. The aims of this study were to evaluate treatment needs of participants of Special Olympics in Belgium 2013 in comparison with those from 2008 and to assess the impact of screening and referral within the SOSS in a group of athletes who participated in two consecutive events, 2012 and 2013. Methods: Data were collected following a standardized protocol developed by the U.S. Centres for Disease Control and Prevention, Division of Oral Health. Oral hygiene habits, treatment urgency and reports of oral pain, gingival signs, sealants, untreated caries, missing and filled teeth were recorded. Data analysis of data from 2013 consisted in descriptive statistics followed by the analysis of the data by univariable and multivariable logistic regression. This data was compared with data from 2008 published by Leroy et al., 2012 using Chi square tests. Data from athletes who participated in both Special Olympics events (2012 and 2013) were compared using Exact McNemar's test and Chi-square test for homogeneity of proportions. The level of significance for all tests was set at a p-value < 0.05. Results: A total of 627 athletes with intellectual disability participated to the SOSS program in 2013, while 132 athletes met the inclusion criteria of being a participant at both SO Belgium 2012 and 2013. The prevalence of gingival signs was 44.3 % in 2013, slightly higher than in 2008 (42.4 %). The burden of untreated decay affected 27.1 % of the population showing a net increase in comparison to 2008 (20.9 %). McNemar's test and Chi-square test revealed that there were no statistically significant differences in the proportions of all compared parameters between 2012 and 2013. Conclusion: Special Olympics results from 2013 indicate a considerable unmet treatment need among Belgian Special Olympics Athletes, persistent from 2008 to 2013. Moreover, SO intervention had no impact in the oral health of athletes who participated in 2012 and 2013 events. Continuous efforts for preventive and restorative oral health care are needed for this population

Prediction of destructive properties using descriptive analysis of nd measurements

Three groups of measurements related to peach maturity were acquired through destructive (D) mechanical tests (Magness Taylor Firmness, MTF), mechanical non destructive (ND) tests, and ND optical spectroscopy (Optical indexes). The relationship between these groups of variables was studied in order to estimate D mechanical measurements (MTF, with higher instrumental and sampling variability, time consuming, generally used as a reference for the assessment of peach handling), from ND measurements (quick, applicable on line, dealing better with the high variability found in fruit products). Multivariate exploratory analysis was used to extract the structure of the data. The information about the data structure of ND measurements, the relationship of MTF with the space defined by ND variables, and the expert knowledge regarding to the dataset was then used for modelling MTF (R 2 =0.72 and standard error on validation 5.73 N