BACKGROUND In elite sports, the growing availability of doping substances identical to those naturally produced by the human body seriously limits the ability of drug-testing regimes to ensure fairness and protection of health. CONTENT The Athlete Biological Passport (ABP), the new paradigm in testing based on the personalized monitoring of biomarkers of doping, offers the enormous advantage of being independent of this endless pharmaceutical race. Doping triggers physiological changes that provide physiological enhancements. In the same way that disease-related biomarkers are invaluable tools that assist physicians in the diagnosis of pathology, specifically selected biomarkers can be used to detect doping. SUMMARY The ABP is a new testing paradigm with immense potential value in the current climate of rapid advancement in biomarker discovery. In addition to its original aim of providing proof of a doping offense, the ABP can also serve as a platform for a Rule of Sport, with the presentation before competition of the ABP to objectively demonstrate that the athlete will participate in a healthy physiological condition that is unaltered by performance-enhancing drugs. Finally, the decision-support system used today for the biological monitoring of world top-level athletes can also be advantageously transferred to other areas of clinical practice to reach the goal of personalized medicine.

In the fight against doping, disciplinary sanctions have up to now been primarily based on the discovery of an exogenous substance in a biological fluid of the athlete. However, indirect markers of altered erythropoiesis can provide enough evidence to differentiate between natural variations and blood doping. Forensic techniques for the evaluation of the evidence, and more particularly Bayesian networks, allow antidoping authorities to take into account firstly the natural variations of indirect markers - through a mathematical formalism based on probabilities - and secondly the complexity due to the multiplicity of causes and confounding effects - through a distributed and flexible graphical representation. The information stored in an athlete's biological passport may be then sufficient to launch a disciplinary procedure against the athlete. The strength of the passport is that it relies on a statistical approach based on sound empirical testing on large populations and justifiable protocols. Interestingly, its introduction coincides with the paradigm shift that is materializing today in forensic identification science, from archaic assumptions of absolute certainty and perfection to a more defensible empirical and probabilistic foundation.

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of Ϸ0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.