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We must be very careful with the concept of adjacency. The components of a device may be adjacent in different ways: They may be physically wired to one another, they may be electromagnetically adjacent, or they may be thermally adjacent, to illustrate three different notions of adjacency. If a system de nition of adjacency is not modeled appropriately, model-based reasoning may render inappropriate and incorrect recommendations. Model-based reasoning is sometimes known by other names, the most notable of which is reasoning from rst principles, a term used to signify that reasoning is based on basic principles of causality, and deep reasoning, a term intended to distinguish model-based reasoning from more surface-oriented forms of reasoning such as rule-based, associational reasoning.5 Other related terms include qualitative reasoning and commonsense reasoning, terms that have been closely associated in the arti cial intelligence world with qualitative physics, or reasoning about the physical world. Let us now look more closely at how we may apply these principles to solving problems. We will rst look at model-based diagnosis, or determining which component of a system is responsible for a system malfunction. Then we will explore how model-based reasoning can be used to help us design network models.

As long as the transaction is turned on again soon, it is also unlikely that anyone will notice that the resulting inventory records indicate quantities that are somewhat higher than what is actually in stock..

between the patient and the consultant, helping both parties to interpret the other's questions and statements. The advocacy offered by the second healthcare worker can be immensely helpful and reassuring to the patient daunted by personal medical concerns, the medical jargon, and, if that is not enough, the technology. This support role is not necessarily a part of the healthcare worker's normal activity, however, and some prior training may be needed to develop the interpersonal skills to discharge it effectively. It is also vital that the consultant is satisfied that the healthcare professional with the patient is competent to carry out any treatment that is delegated to him or her [45, 741, including those procedures that cannot be carried out in the teleconsultation itself or are left to later. This requirement includes the ability to capture the information needed for treatment-a competence that should be confirmed before the teleconsultation begins. It may well be useful for other healthcare workers to be present at the consultation so that they can acquire the skills for future participation. These training sessions should be documented carefully to determine the skill levels and evaluation procedures of all involved. One interesting consequence of such local skilling (tele-education) is that it may make the telemedicine link redundant. In describing the essential features of teleconsultation (Section 2.2.1) we noted Tachakra and Haig's [45] prerequisites for success. Where there are frequent changes of healthcare personnel it can be helpful to document the teleconsultation procedure by providing either a process gzrideliize or template of the steps involved, or a protocol or pathway for the medical treatment [45]. A process guideline consists of a detailed checklist that might include the following stages:

Erasures can also sometimes be declared using concatenated coding techniques, where an outer code declares erasures at some symbol positions, which an inner code can then correct. Consider the erasure capability for a code of distance dfin. A single erased symbol removed from a code (with no additional errors) leaves a code with a minimum distance at least dfin - 1. Thus f erased symbols can be filled provided that f < dfin. For example, a Hamming code with dmin = 3 can correct up to 2 erasures. Now suppose that there are both errors and erasures. For a code with d ~ experiencing n a single erasure, there are still n - 1 unerased coordinates and the codewords are separated by a distance of at least dfin - 1. More generally, if there are f erased symbols, then the distance among the remaining digits is at least d f i n - f . Letting tf denote the random error decoding distance in the presence of f erasures, we can correct up to

More information available from http://www-ra.informatik.uni-tuebingen.de/SNNS/. More information available from http://www.nd.com. A search on the web for Neural Network FAQ will give a variety of pages pointing to the valuable neural network reference.

(in millions)