Action Potential Onset Dynamics and the Response Speed of Neuronal Populations

The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to understand how the properties of coding at the level of neuronal populations are determined by the dynamics of single neuron AP generation. Here we analyze how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals. We analyze a generalization of the $\theta$-neuron, the normal form of the dynamics of Type-I excitable membranes. Using a novel sparse matrix representation of the Fokker-Planck equation, which describes the ensemble dynamics, we calculate the transmission functions for small modulations of the mean current and noise noise amplitude. In the high-frequency limit the transmission function decays as $\omega^{-\gamma}$, where $\gamma$ surprisingly depends on the phase $\theta_{s}$ at which APs are emitted. In a physiologically plausible regime up to 1kHz the typical response speed is, however, independent of the high-frequency limit and is set by the rapidness of the AP onset, as revealed by the full transmission function. In this regime modulations of the noise amplitude can be transmitted faithfully up to much higher frequencies than modulations in the mean input current. We finally show that the linear response approach used is valid for a large regime of stimulus amplitudes.Comment: Submitted to the Journal of Computational Neuroscienc

Second-order linear differential equations with two irregular singular points of rank three: the characteristic exponent

For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the characteristic exponent of the multiplicative solutions. The Stokes multipliers are represented by converging series with terms for which limit formulas as well as more detailed asymptotic expansions are available. Here certain new, recursively known coefficients enter, which are closely related to but different from the coefficients of the formal solutions at one of the irregular singular points of the differential equation. The coefficients of the formal solutions then appear as finite sums over subsets of the new coefficients. As a by-product, the leading exponential terms of the asymptotic behaviour of the late coefficients of the formal solutions are given, and this is a concrete example of the structural results obtained by Immink in a more general setting. The formulas displayed in this paper are not of merely theoretical interest, but they also are complete in the sense that they could be (and have been) implemented for computing accurate numerical values of the characteristic exponent, although the computational load is not small and increases with the rank of the singular point under consideration.Comment: 33 page

KEY PARAMETERS OF THE 2nd FLIGHTPHASE OF THE TSUKAHARA WITH SALTO BACKWARD PIKED

For a high final score the gymnast need a high difficulty, but this is equivalent to a potential injury risk. Therefor purpose of this study was to identify key parameters of the 2nd flight phase for a safety execution of the Tsukahara with salto backward piked. Nine world class athletes were selected from Videos of two competitions with international participation. Each vault was examined with a 2D kinematic analysis from contact phase of the vaulting table up to the landing. With the help of these evaluated reference values coaches and scientist are able to compare the execution of their gymnasts with the help of a motion analysis to check for their safety and the successful learning of the vault

POSTURE CONTROL AFTER LONGITUDINAL ROTATIONS IN DIFFERENT DIRECTIONS

Fast rotations induce load on the human organism. Hanging vertical, young figure skaters perform rotations around the longitudinal axis. After the rotations we investigated the posture control. The differences between the direction of rotations will be explored. There were no differences between the rotations to preferred and not preferred direction of the rotations, but there were individual exceptions. Angular velocity about 500 deg/sec were reached. The results of the posture control show an effect of the rotations. But there is also no effect on the direction. The postural sway after rotation to preferred direction were not different to the postural sway after rotations to the opposite direction. Further investigations will use the results of this pilot study

DEVELOPMENT OF A COMPLEX MEASURING UNIT FOR SPRINGBOARD DIVING

Based on a springboard with a force platform a complex measuring unit was developed to be used in springboard diving. The platform is composed of three plates, and based on the principle of strain measurement for vertical and horizontal forces. Using a computer based video system as a new component the board's angle of inclination can be measured automatically. After locating two markers of the springboard in the first picture, the video system tracks the markers during the board movement itself. Feedback pictures for the diver will be selected for defined events because of the synchronized data from force measuring and the board inclination. With this image of the diver and an added reference picture (model stick-figure) the difference between the model and the actual performance were shown to the athletes

MOTOR CONTROL BY VISUAL PERCEPTION IN DIVING?

To perform the movement from tucked to straight position of the body for the entry into the water in springboard and platform diving different sensory inputs can be used. Visual control, based on visual perception, is one concept of getting information about the divers own movement. Special exercises and training programs (de Mers, 1983) were designed to get a better performance. Own investigations (Naundorf, Krug & Lattke, 2002) reported positive effect of using a somersault simulator in visual perception training. But in this study we look only at visual perception, but not on motor control. Another study of our group (Naundorf, Krug & Lattke, 2004) focused on using the somersault simulator for improving the technique of preparation for the water entry. Based on this we look for combination of improving visual perception and technique