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To quantify swimwear-induced differences under triathlon-specific conditions, we compare the swimming performance, the metabolic cost, and the standardised passive drag of well-trained triathletes when wearing (1) five speedsuit models by different manufacturers from 2017, (2) usual swimming trunks/swimsuits (men/women), and (3) individually preferred competition trisuits. Because of the complexity of the underlying hydrodynamic and biomechanical effects, three separate experimental stages were realized, each with 6–12 well-trained short- and middle-distance triathletes (male and female, mean age 22 ± 5 years) from the German national elite or junior elite level. All measurements were conducted on the basis of real athletes’ motion in the water to correctly account for all relevant effects, including skin and muscle vibrations. First, the athletes took part in a series of 100 m short-distance tests at maximal effort in a long-course pool to quantify swim-time differences in absolute terms. Second, the subjects completed multiple submaximal 400 m tests at 95% of their individual maximal speed in a swimming flume, with their swimwear-related differences in metabolic load being explored in terms of blood lactate and heart rate. Third, the passive drag of the triathletes was measured in the flume during a towing test under standardised conditions in velocity steps of 0.2 m/s within the triathlon-relevant range of 1.1–1.7 m/s. In all three test stages, the speedsuits exhibited performance advantages over trunks/swimsuits: in the 100 m maximal test, the mean swim time with speedsuits decreased by 0.99 ± 0.30 s (≙ − 1.5%). During the 400 m submaximal flume test, the mean heart rate showed a reduction of 7 ± 2 bpm (≙ − 4.0%), while the post-exercise blood lactate accumulation decreased by 1.0 ± 0.2 mmol/L (≙ − 26.2%). Similarly, the passive drag in the towing test was lowered by 3.2 ± 1.0 W (≙ − 6.9% as for normalised power and − 5.2% as for normalised force) for the speedsuits. Wearing speedsuits instead of usual trunks/swimsuits is shown to improve the swimming performance and to reduce the metabolic cost for well-trained triathletes under triathlon-specific test conditions. The reduction in passive drag of the passively towed athlete’s body due specific speedsuit surface textures seems to be only one reason for performance advantages: the effective reduction in muscular, soft tissue, and skin vibrations at the trunk and thighs during active propulsive motion of the swimmer seems to further contribute substantially.

Zusammenfassung Die Stressfraktur des Kreuzbeins stellt eine oftmals fehldiagnostizierte Uberlastungsverletzung bei Sportlern dar. Sie ausert sich in ihrer Initialphase latent und sehr unspezifisch als tiefsitzender, oftmals einseitiger Schmerz im LWS-/ISG- bzw. Gesas-/Huft-/Beckenbereich. Eine gesicherte Diagnose gelingt derzeit nur per MRT. Hierauf sowie auf ihre erfolgreiche konservative Therapie mittels Alternativtraining wird anhand zweier Kasuistiken aus dem Jahr 2016 (Elite-Langstreckenlaufer und Amateur-Triathlet) eingegangen. Basierend auf einer verlaufsbegleitenden MRT-Diagnostik wird die radiologische Zeitskala der Knochenreparaturprozesse dargestellt und eine Halbwertszeit des ossaren Odemvolumens von 31±7 Tagen abgeleitet. Aus therapeutischer Sicht wird insbesondere auf den Einsatz eines Teilschwerelosigkeitslaufbands (AlterG®) eingegangen. Ein Vergleich der unterschiedlichen individuellen Verlaufe der beiden beschriebenen Falle lasst vermuten, dass sich bei fruhzeitiger Erkennung, adaquater Therapie und einem spezifischen Trainingswiedereinstieg die Heilungszeit verkurzen und der Trainingsruckstand deutlich reduzieren lassen konnen.

We investigate formal power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of two-dimensional languages to a quantitative setting. We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will be a picture series. We introduce weighted 2-dimensional on-line tessellation automata (W2OTA) and prove that for commutative semirings, the class of picture series defined by sentences of the weighted logics coincides with the family of picture series that are computable by W2OTA. Moreover, we show that the family of behaviors of W2OTA coincide precisely with the class of picture series characterized by weighted (quadrapolic) picture automata and consequently, the notion of weighted recognizability presented here is robust. However, the weighted structures can not be used to get better decidability properties than in the language case. For every commutative semiring, it is undecidable whether a given MSO formula has restricted structure or whether the semantics of a formula has empty support.

In this paper we consider transformations on formal power series and extend well-known results in terms of homomorphisms to rational functions. Using these results we prove a Kleene-Schutzenberger Theorem for formal power series over rational monoids. It extends a result of Sakarovitch.

Words and finite automata over words are central notions in computer science. They model the sequential executions of systems. However, both the world in its own and computer science have to cope with another phenomenon as well: concurrency. Then not all events have to be ordered but some actions may appear independently. On the other hand, words can be seen as one-dimensional objects, but higher-dimensional objects like two-dimensional rectangles or pictures have to be handled as well. This chapter is concerned with weighted automata that describe quantitative aspects of partially ordered sets and of pictures. More specifically, we first consider weighted asynchronous cellular automata that compute semiring valuations of Mazurkiewicz traces. In a similar spirit, weighted branching automata associate weights to series-parallel pomsets. Thirdly, weighted picture automata describe quantitative aspects of two-dimensional arrays of colors. We characterize the expressive power of these automata by rational expressions and by monadic second-order logics.