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not in nite-precision points for the cumulative distribution function but intervals in the unit interval. Any nite-length sequence of symbols can be said to correspond to a subinterval of the unit interval. The objective of the arithmetic coding algorithm is to represent a sequence of random variables by a subinterval in [0, 1]. As the algorithm observes more input symbols, the length of the subinterval corresponding to the input sequence decreases. As the top end of the interval and the bottom end of the interval get closer, they begin to agree in the rst few bits. These will be rst few bits of the output sequence. As soon as the two ends of the interval agree, we can output the corresponding bits. We can therefore shift these bits out of the calculation and effectively scale the remaining intervals so that entire calculation can be done with nite precision. We will not go into the details here there is a very good description of the algorithm and performance considerations in Bell et al. [41] Example 13.3.2 (Arithmetic coding for a ternary input alphabet) Consider a random variable X with a ternary alphabet {A, B, C}, which are assumed to have probabilities 0.4, 0.4, and 0.2, respectively. Let the sequence to be encoded by ACAA. Thus, Fl ( ) = (0, 0.4, 0.8) and Fh ( ) = (0.4, 0.8, 1.0). Initially, the input sequence is empty, and the corresponding interval is [0, 1). The cumulative distribution function after the rst input symbol is shown in Figure 13.2. It is easy to calculate that the interval in the algorithm without scaling after the rst symbol A is

Degrees Celsius (= degrees centigrade)

In his study, participants were presented with an array of visual stimuli, one of which (the target stimulus) changed color In one condition, participants were required to point to the target stimulus the moment the array disappeared from screen, and at the same time speak aloud the number corresponding to the target location Pointing errors in this verbalization condition were aligned with the surrounding stimulus array, indicating that the participants used allocentric information that specified target location relative to the other stimuli By contrast, nonverbalization and task-irrelevant verbalization conditions resulted in egocentric pointing errors (ie, errors that were aligned with the movement direction) Verbalization during action execution thus appeared to have encouraged ventral pathway involvement in normally dorsal movement control.

functional movement behaviors (for exceptions, see Beek, 1989; Bootsma & van Wieringen, 1990; Newell, 1989). In this chapter, we seek to redress this deficiency in the literature. We note that preference for more complex experimental models from sports and physical pastimes has accelerated rapidly in recent years. Consequently, detailed insights into the adaptive nature of movement behavior are now being provided by a large number of studies, ranging from apparently superficial and frivolous cultural activities such as playground swinging (Post, Peper, & Beek, 2003), hula-hooping (Balasubramaniam & Turvey, 2004), and pedalo paddle boating (Chen, Liu, Mayer-Kress, & Newell, 2005) to more traditional sporting tasks such as javelin and discus throwing (Sch llhorn, 2003), rowing (Daffertshofer, Huys, & Beek, 2004; Shuttleworth, 2004), and long jumping run-ups (Montagne, Cornus, Glize, Quaine, & Laurent, 2000). HOW DEGENERATE BRAINS AND INDETERMINATE BEHAVIORS SUPPORT FUNCTIONAL BEHAVIORS IN DYNAMIC ENVIRONMENTS In this chapter, we argue that the increasing popularity of movement models from sports is associated with the powerful influence of a functionalist philosophical perspective viewing decision making and the control of action as adaptive, emergent behaviors that self-organize under constraints. Recognizing the apparent indeterminate (not completely predictable) nature of solutions to many behavioral tasks has amplified the utility of relativist theoretical perspectives on brain and behavior (Glimcher, 2005). Virtually all previous decision-making studies in sport psychology have knowingly or unknowingly adopted a

Unlike an implicit learner, a novice who consciously invokes explicit knowledge (perhaps based on instructions from a coach) would be expected to demonstrate a relatively strong reliance on the ventral pathway The dedicated dorsal pathway would be fully responsible for control only after the action had become highly automatized (see Milner & Goodale, 1995) In such a scenario, learning would be characterized not only by a declining awareness of the movement during execution, but also by a concurrent change in guidance from allocentric to egocentric information (van der Kamp et al, 2003; Willingham, 1998) For example, actions may become progressively less susceptible to visual illusions In this respect, it is noticeable that the highly automatized actions of grasping and reaching appear much less sensitive to illusions than hopping, which is arguably a less commonly performed action (Glover & Dixon, 2004) In these terms, implicit skill learning would.

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