On the number of types in sparse graphs

We prove that for every class of graphs $\mathcal{C}$ which is nowhere dense, as defined by Nesetril and Ossona de Mendez, and for every first order formula $\phi(\bar x,\bar y)$, whenever one draws a graph $G\in \mathcal{C}$ and a subset of its nodes $A$, the number of subsets of $A^{|\bar y|}$ which are of the form $\{\bar v\in A^{|\bar y|}\, \colon\, G\models\phi(\bar u,\bar v)\}$ for some valuation $\bar u$ of $\bar x$ in $G$ is bounded by $\mathcal{O}(|A|^{|\bar x|+\epsilon})$, for every $\epsilon>0$. This provides optimal bounds on the VC-density of first-order definable set systems in nowhere dense graph classes. We also give two new proofs of upper bounds on quantities in nowhere dense classes which are relevant for their logical treatment. Firstly, we provide a new proof of the fact that nowhere dense classes are uniformly quasi-wide, implying explicit, polynomial upper bounds on the functions relating the two notions. Secondly, we give a new combinatorial proof of the result of Adler and Adler stating that every nowhere dense class of graphs is stable. In contrast to the previous proofs of the above results, our proofs are completely finitistic and constructive, and yield explicit and computable upper bounds on quantities related to uniform quasi-wideness (margins) and stability (ladder indices)

View-dependent accuracy in body mass judgements of female bodies

A fundamental issue in testing body image perception is how to present the test stimuli. Previous studies have almost exclusively used images of bodies viewed in front-view, but this potentially obscures key visual cues used to judge adiposity reducing the ability to make accurate judgements. A potential solution is to use a three-quarter view, which combines visual cues to body fat that can be observed in front and profile. To test this hypothesis, 20 female observers completed a 2-alternative forced choice paradigm to determine the smallest difference in body fat detectable in female bodies in front, three-quarter, and profile view. There was a significant advantage for three-quarter and profile relative to front-view. Discrimination accuracy is predicted by the saliency of stomach depth, suggesting that this is a key visual cue used to judge body mass. In future, bodies should ideally be presented in three-quarter to accurately assess body size discrimination

Implementation of sustainability in innovation management: The Idea to People, Planet and Profit (I2P3®) Process

Assessing the sustainability of the innovation portfolio is a particular challenge for industries. The two main issues are the lack of data at the early stage of project development and the high number of ideas and projects that are developed. This paper provides an overview of the I2P³® process (Idea to People, Planet and Profit®) which was developed by Evonik Creavis GmbH, the strategic innovation unit of Evonik Industries AG, in order to integrate sustainability into its innovation process. This process is based on a holistic approach to assess the three dimensions of sustainability (economical, environmental, and societal). The paper includes a detailed description of each stage of the process, with the categories and criteria used to assess these three dimensions, from idea generation to market launch. Following this, difficulties faced in the implementation process and improvement options are discussed