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Tenorio and Cason (2002) nd similar deviations from rationality by recording choices made on the television game show The Price Is Right When it comes to spinning the big wheel, which determines who gets to go to the showcase showdown and compete for the big prizes, three contestants spin the wheel and the one closest to $100 without going over wins They spin once, and then they can choose whether or not to spin again There is an optimal strategy to this game, but Tenorio and Cason show that contestants spin more than the mathematically optimal number of times Pollsters need to constantly keep in mind the following when taking opinion polls It is not just the questions that are asked, but the order in which they are asked, that will in uence the results.

of the passive beam formers, such as the Butler BFN and Rotman lens BFN discussed before. To understand the basic operation of a DBF, we consider an analog equivalent of a DBF. Consider a receiving array of N elements receiving a signal from an angular direction , as shown in Figure 12.26. The BFN consists of N phase shifters and a power combiner block. A DBF essentially utilizes a similar concept, but the phase delaying and power combining are conducted in the digital domain instead of the analog domain. To better understand this, let us first consider the operation principle of a digital phase shifter. 12.6.1 Digital Phase Shifter An analog phase shifter typically utilizes a delay line causing a phase delay or phase shift. A delay line of a given length provides only a fixed amount of phase shift (unless a switching mechanism is introduced). However, by using a 90 hybrid and two amplifiers one can generate any amount of phase shift, as shown in the block diagram of Figure 12.27. The 90 hybrid essentially is a 3-dB power divider and provides 90 phase difference between two output signals represented by cosine and sine functions.

Hence, the restriction (always satis ed in the case of nite systems) expressed in the following proposition PROPOSITION 141 Let us consider a symmetric Kripke structure with a nite branching degree, then there is an invalidating path in the ordinary synchronized product iff there is an invalidating path in the quotient synchronized product..

Consider the question poll that asks: Are you con dent in our local treasurer It is different from the twoquestion poll that asks: Are you aware that our local treasurer was indicted for tax evasion Are you con dent in our local treasurer The last question in each poll is identical, but the answers one will receive will be drastically different Past experience, new information, and even the gender of the pollster will change the results of the poll We therefore cannot expect the same people to be rational automatons when they become stock market investors To compensate for the errors humans can make, a branch of literature on bounded rationality and learning models has emerged These researchers try to model the individual who is not able to do complex mathematical calculations instantaneously when making decisions but is able to either approximate the solution, or learn the solution over time.

Since the variable values are represented in binary, there must be a way of converting continuous values into binary, and visa versa. Quantization samples a continuous range of values and categorizes the samples into nonoverlapping subranges. Then a unique discrete value is assigned to each subrange. The difference between the actual function value and the quantization level is known

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Fig. 5.13 Examples of applications of the logistic growth curve. (a) Growth of yeast populations in culture. From Allee et al. (1949) reprinted in Maynard Smith (1974). (b) Growth of Drosophila melanogaster populations: (i) wild type, (ii) heterozygous or homozygous individuals for ve recessive mutations including vestigial wing and (iii) wild type in half volume of (i). (c) Growth of Moina macrocarpa populations at three different temperatures. (b) and (c) reprinted from Hutchinson (1978).