An examination of the metabolic processes underpinning critical swimming in Atlantic cod (Gadus morhua L.) using in vivo 31P-NMR spectroscopy.

Traditionally, critical swimming speed has been defined as the speed when a fish can no longer propel itself forward, and is exhausted. To gain a better understanding of the metabolic processes at work during a U(crit) swim test, and that lead to fatigue, we developed a method using in vivo (31)P-NMR spectroscopy in combination with a Brett-type swim tunnel. Our data showed that a metabolic transition point is reached when the fish change from using steady state aerobic metabolism to non-steady state anaerobic metabolism, as indicated by a significant increase in inorganic phosphate levels from 0.3+/-0.3 to 9.5+/-3.4 mol g(-1), and a drop in intracellular pH from 7.48+/-0.03 to 6.81+/-0.05 in muscle. This coincides with the point when the fish change gait from subcarangiform swimming to kick-and-glide bursts. As the number of kicks increased, so too did the Pi concentration, and the pH(i) dropped. Both changes were maximal at U(crit). A significant drop in Gibbs free energy change of ATP hydrolysis from -55.6+/-1.4 to -49.8+/-0.7 kJ mol(-1) is argued to have been involved in fatigue. This confirms earlier findings that the traditional definition of U(crit), unlike other critical points that are typically marked by a transition from aerobic to anaerobic metabolism, is the point of complete exhaustion of both aerobic and anaerobic resources.

New Algorithms for M-Estimation of Multivariate Scatter and Location

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and to devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.