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Tuberous sclerosis occurs in about 1 per 12,000 children (de Vries et al., 2005); across age groups, it is estimated to occur in 1 in 14,500 people (Zaroff et al., 2004). Accurate incidence and prevalence is complicated by the variability in severity, extent of symptoms, and the age range at which the syndrome is identi ed. Furthermore, in individuals of average cognitive ability, diagnosis may not be made until (unless) the child develops a more severe form of the syndrome (Webb & Osborne, 1995; Zaroff et al., 2004).

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Approaches to optimization are akin to root or zero nding methods, only harder. Bracketing the root or optimum is a major step in hunting it down. For the one-variable case, nding one positive point and one negative point brackets the zero. On the other hand, bracketing a minimum requires three points, with the middle point having a lower value than either end point. In the mathematical approach, root nding searches for zeros of a function, while optimization nds zeros of the function derivative. Finding the function derivative adds one more step to the optimization process. Many times the derivative does not exist or is very dif cult to nd. We like the simplicity of root nding problems, so we teach root nding techniques to students of engineering, math, and science courses. Many technical problems are formulated to nd roots when they might be more naturally posed as optimization problems; except the toolbox containing the optimization tools is small and inadequate. Another dif culty with optimization is determining if a given minimum is the best (global) minimum or a suboptimal (local) minimum. Root nding doesn t have this dif culty. One root is as good as another, since all roots force the function to zero. Finding the minimum of a nonlinear function is especially dif cult. Typical approaches to highly nonlinear problems involve either linearizing the problem in a very con ned region or restricting the optimization to a small region. In short, we cheat. 1.1.3 Categories of Optimization

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This protection is used to protect a generator against phase-to-phase faults downstream of the generator. It is particularly useful when the generator does not have a system for maintaining the short-circuit current at approximately 3 In (see section 4.1.2). As described in section 4.1.2, the short-circuit current downstream of a generator develops according to the three following periods: subtransient ( X ''d ): lasting 10 to 20 ms after the start of the fault; transient ( X 'd ): lasting up to 100 to 400 ms; synchronous ( X d ): steady-state or synchronous reactance to be considered after the transient period. The synchronous reactance occurs after a period of approximately 100 to 400 ms. It has a value of roughly 200 to 350% (see Tables 4-3, 4-4 and 4-5). 1 We therefore have a permanent three-phase short-circuit current I sc = In , X d (%) equal to between 0.3 and 0.5 In , as long as the generator is not fitted with a system allowing the short-circuit current to be held at approximately 3 In (see section 4.1.2). Note: the minimum permanent short-circuit current is obtained for a three-phase short-circuit and is, in this specific case, lower than the phase-to-phase short-circuit current clear of earth. Indeed, according to section 4.2.3, the phase-to-phase shortcircuit current clear of earth is:

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