Principles of Stakes Fairness in Sport

Fairness in sport is not just about assigning the top prizes to the worthiest competitors. It is also about the way the prize structure itself is organised. For many sporting competitions, although it may be acceptable for winners to receive more than losers, it can seem unfair for winners to take everything and for losers to get nothing. Yet this insight leaves unanswered some difficult questions about what stakes fairness requires and which principles of stakes fairness are appropriate for particular competitions. In this article I specify a range of different principles of stakes fairness (ten in total) that could regulate sporting competitions. I also put forward a theoretical method for pairing up appropriate principles of stakes fairness with given sporting competitions. Specifically, I argue that the underlying rationales for holding sporting competitions can provide useful guides for identifying appropriate principles of stakes fairness. I then seek to clarify and work through some of the implications of this method for a sample of real world controversies over sporting prize structures. I also attempt to refine the method in response to two possible objections from indeterminacy and relativism. Finally, I compare and contrast my conclusions with more general philosophical debates about justice

Metabolomic markers reveal novel pathways of ageing and early development in human populations

BACKGROUND Human ageing is a complex, multifactorial process and early developmental factors affect health outcomes in old age. METHODS Metabolomic profiling on fasting blood was carried out in 6055 individuals from the UK. Stepwise regression was performed to identify a panel of independent metabolites which could be used as a surrogate for age. We also investigated the association with birthweight overall and within identical discordant twins and with genome-wide methylation levels. RESULTS We identified a panel of 22 metabolites which combined are strongly correlated with age (R(2) = 59%) and with age-related clinical traits independently of age. One particular metabolite, C-glycosyl tryptophan (C-glyTrp), correlated strongly with age (beta = 0.03, SE = 0.001, P = 7.0 × 10(-157)) and lung function (FEV1 beta = -0.04, SE = 0.008, P = 1.8 × 10(-8) adjusted for age and confounders) and was replicated in an independent population (n = 887). C-glyTrp was also associated with bone mineral density (beta = -0.01, SE = 0.002, P = 1.9 × 10(-6)) and birthweight (beta = -0.06, SE = 0.01, P = 2.5 × 10(-9)). The difference in C-glyTrp levels explained 9.4% of the variance in the difference in birthweight between monozygotic twins. An epigenome-wide association study in 172 individuals identified three CpG-sites, associated with levels of C-glyTrp (P < 2 × 10(-6)). We replicated one CpG site in the promoter of the WDR85 gene in an independent sample of 350 individuals (beta = -0.20, SE = 0.04, P = 2.9 × 10(-8)). WDR85 is a regulator of translation elongation factor 2, essential for protein synthesis in eukaryotes. CONCLUSIONS Our data illustrate how metabolomic profiling linked with epigenetic studies can identify some key molecular mechanisms potentially determined in early development that produce long-term physiological changes influencing human health and ageing

Minimal fine limits on trees

Let T be the set of vertices of a tree. We assume that the Green function is finite and G(s, t) → 0 as |s| →∞ for each vertex t. For v positive superharmonic on T and E a subset of T, the reduced function of v on E is the pointwise infimum of the set of positive superharmonic functions that majorize v on E. We give an explicit formula for the reduced function in case E is finite as well as several applications of this formula. We define the minimal fine filter corresponding to each boundary point of the tree and prove a tree version of the Fatou-Naïm-Doob limit theorem, which involves the existence of limits at boundary points following the minimal fine filter of the quotient of a positive superharmonic by a positive harmonic function. We deduce from this a radial limit theorem for such functions. We prove a growth result for positive superharmonic functions from which we deduce that, if the trees has transition probabilities all of which lie between δ and 1/2 - δ for some δ∈ (0, 1/2) (for example homogeneous trees with isotropic transition probabilities), then any real-valued function on T which has a limit at a boundary point following the minimal fine filter necessarily has a nontangential limit there. We give an example of a tree for which minimal fine limits do not imply nontangential limits, even for positive superharmonic functions. Motivated by work on potential theory on halfspaces and Brelot spaces, we define the harmonic fine filter corresponding to each boundary point of the tree. In contrast to the classical setting, we are able to show that it is the same as the minimal fine filter

Fractal functions with no radial limits in Bergman spaces on trees

For each p > 0 we provide the construction of a harmonic function on a homogeneous isotropic tree T in the Bergman space A(p) (sigma) with no finite radial limits anywhere. Here, sigma is an analogue of the Lebesgue measure on the tree. With the appropriate modifications, the construction yields a function in A(1) (sigma) when T is a rooted radial tree such that the number of forward neighbors increases so slowly that their reciprocals are not summable

Bergman Spaces and Carleson Measures on Homogeneous Isotropic Trees

Hastings studied Carleson measures for non-negative subharmonic functions on the polydisk and characterized them by a certain geometric condition relative to Lebesgue measure \s. Cima \& Wogen and Luecking proved analogous results for weighted Bergman spaces on the unit ball and other open subsets of \mathC^n. We consider a similar problem on a homogeneous tree, and study how the characterization and properties of Carleson measures for various function spaces depend on the choice of reference measure $\sigma$

ERP responses to images of abstract artworks, photographs of natural scenes, and artificially created uncomfortable images.

The idea of efficient coding in the visual brain allows for predictions for the processing of various types of images, including certain artworks, natural images and uncomfortable images. Efficient processing is thought to result in lower responses compared to less efficient processing. The efficiency of the processing is suggested to depend on the architecture of the visual system and the properties of the input image. In this study, neural responses were estimated using EEG across the categories of a set of five images of abstract artworks, a set of five photographs of natural images and a set of five computer-generated uncomfortable images. EEG responses to contrast-matched images were found to be lower for the set of five abstract artworks used in the study compared to the set of photographs of natural images, lending preliminary support for the idea that certain abstract artworks, for example the work of Pollock, may be processed efficiently