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Since we rejected the approaches that suggest themselves immediately, we face the task to provide an alternative. There actually is one and it is surprisingly simple [Borgelt 1995]. The rationale underlying it is that in most applications calculi to handle imprecision and uncertainty are employed to support decision making. That is, it is often the goal to decide on one course of action and to decide in such a way as to optimize the expected benefit. The best course of action, obviously, depends on the obtaining situation, but usually there is only imperfect (that is, incomplete or uncertain) knowledge, so that the obtaining situation cannot be identified with certainty. In a probabilistic setting it is plausible that we should decide on that action that corresponds to the most probable situation at least, if each situation requires a different course of action and if all costs are equal because this decision strategy guarantees that in the long run we make the smallest number of mistakes (and thus incur the lowest costs). In the possibilistic setting the commonly used decision rule is directly analogous, namely to decide on that course of action that corresponds to the situation with the highest degree of possibility. It may be argued that this situation can be least excluded , since the probability of those contexts in which it can be excluded is smallest. However, this possibilistic decision rule is open to criticism, especially, if the decision is compared to one derived from the basic probability assignment computed by applying the insufficient reason principle (cf. Section 2.4.3). In Section 2.4.12, in which we discuss open problems, we briefly consider possible points of criticism. For the other parts of this book, however, we accept this decision rule, although we share most doubts whether it is reasonable.

Second, physical information travels only nite distance: this means that computation is local and we can assume that the nonlinear medium is a spatial arrangement of elementary processing units connected locally; that is, each unit interacts with closest neighbors Third, nature is governed by waves and spreading patterns: computation is therefore spatial Reaction diffusion computers give us best examples of unconventional computers; their features follow Jonathan Mills classi cation of convention versus unconventional [32]: wetware, nonsilicon computing substrate; parallel processing; computation occurring everywhere in substrate space; computation is based on analogies; spatial increase in precision; holistic and spatial programming; visual structure; and implicit error correcting A theory of reaction diffusion computing was established and a range of practical applications are outlined in the work by Adamatzky [1]; recent discoveries are published in a collective monograph [5].

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Best, SR On the Signi cance of Current Vector Alignment in Establishing the Resonant Frequency of Small Space-Filling Wire Antennas IEEE Ant Wireless Propagation Lett Vol 2, 2003b, pp 201 204 Best, SR The Foster Reactance Theorem and Quality Factor for Antennas IEEE Ant Wireless Propagation Lett Vol 3, 2004a, pp 306 309 Best, SR The Radiation Properties of Electrically Small Folded Spherical Helix Antennas Trans IEEE Vol AP-52, April 2004b, pp 953 960 Best, SR A Discussion on the Quality Factor of Impedance Matched Electrically Small Wire Antennas Trans IEEE Vol AP-53, Jan 2005a, pp 502 508; correction Jun 2005, p 2133 Best, SR, Low Q Electrically Small Linear and Elliptical Polarized Spherical Dipole Antennas Trans IEEE Vol AP-53, March 2005b, pp 1047 1053 Best, SR and Morrow, JD The Effectiveness of Space-Filling Fractal Geometry in Lowering Resonant Frequency.

In thinking about how this reorientation of the audit function will be played out, Marks foresees a much different audit landscape in the future:

The chapter in no way serves as a substitute for these books but rather an introduction to the eld and a case study of several characteristic examples The chapter is populated with cellular automaton examples of reaction diffusion processes We have chosen cellular automatons to study computation in reaction diffusion media because cellular automatons can provide just the right fast prototypes of reaction diffusion models The examples of best practice include models of BZ reactions and other excitable systems [21,31], chemical systems exhibiting Turing patterns [54,56,58], precipitating systems [5], calcium wave dynamics [55], and chemical turbulence [23] We therefore consider it reasonable to interpret the cellular automaton local update rules in terms of reaction diffusion chemical systems and reinterpret the cellular automaton rules in novel designs of the chemical laboratory reaction diffusion computers.

As noted above, the physical position of the retailer is brought into balance in the short-term markets. The process begins in the day-ahead market and continues through to delivery time. We rst present a description of the retailer s position. Afterwards, retailer behavior for a simple portfolio without market instruments is examined.

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