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11141 Normal Forms A relation is in rst normal form (1NF) if and only if every domain in the relation contains only simple values if and only if each domain is equivalent to an SIA attribute type or equivalent to an SNA attribute type Luckily, there are very simple techniques that we can use to transform a relation that is not already in 1NF into a 1NF relation If a relation is not in 1NF, then it must have one or more domains that are nonsimple If we transform every nonsimple domain into a simple domain, then we have achieved 1NF Sometimes, there will be extremely nonsimple domains, where these techniques need to be applied more than once we will not discuss those cases, but careful application of these techniques can always (eventually) bring us to a set of one or more relations in 1NF.

Dzau, V J (1994) Pathobiology of atherosclerosis and plaque complication American Heart Journal, 128, 1300 1309 Eagle, K A, Guyton, R A, Davidoff, R, Ewy, G A, Fonger, J, Gardner, T J, et al (1999) ACC/AHA guidelines for coronary artery bypass graft surgery: Executive summary and recommendations: A report of the American College of Cardiology, American Heart Association Task Force on Guidelines Committee for Coronary Artery Bypass Surgery Circulation, 100, 1464 1480 Eaker, E D, Pinsky, J, & Castelli, W P (1992) Myocardial infarction and coronary death among women: Psychosocial predictors from 20-year follow-up of women in the Framingham Study American Journal of Epidemiology, 135, 854 864 Egolf, B, Lasker, J, Wolf, S, & Potvin, L (1992) The Roseto effect: A 50-year comparison of mortality rates American Journal of Public Health, 82, 1089 1092 Eisenberg, D M.

Merely following the forward generation rules discussed in the previous sections will usually result in 1NF relations 11142 Second Normal Form In order for a relation to be in second normal form (2NF), it must already be in 1NF as a precondition To determine if a relation that is already in 1NF is also in 2NF, we must explore the dependencies between the domains in the relation and the PK The concept used for this is called a functional dependency (FD) A domain has an FD upon another domain if the other domain determines the value for it In order for a relation to be in 2NF, every domain that is not part of the PK must have an FD upon the PK (but not an FD on merely some subset of the PK).

If it is dependent on only part of the PK, we say that there is a partial functional dependency (PFD) When the domain is only functionally dependent on the whole PK, we say that there is a fully functional dependency (FFD) In order to be in 2NF, each domain that is not part of the PK must have an FFD upon the PK of the relation 11143 Third Normal Form and Beyond In order for a relation to be in third normal form (3NF), it must already be in 2NF as a precondition To determine if a relation that is already in 2NF is also in 3NF, we must explore the dependencies further and look for transitive dependencies A transitive dependency (TD) occurs when some domain has an FD upon another domain, which has in turn has an FFD upon the PK.

In order to be in 3NF, every domain in the relation that is not part of the PK must have an FFD upon the PK, and no TDs can exist for these domains The last level of normalization we will discuss is referred to as Boyce Codd normal form (BCNF) Because 3NF did not consider TDs for domains that are part of the PK, a new normal form called BCNF was de ned to address the situation In order for a relation to be in BCNF, it must rst be in 3NF Additionally, BCNF requires that no TDs exist for the domains that are part of the PK There are additional normal forms de ned, but most relational data models are only concerned with these four forms (1NF, 2NF, 3NF, and BCNF), so we will not discuss the other forms beyond BCNF here..

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, Delbanco, T L, Berkey, S C, Kkaptchuk, T J, Kupelnick, B, Kuhl, J, et al (1993) Cognitive behavioral techniques for hypertension: Are they effective Annals of Internal Medicine, 188, 964 972..

At rst sight, information theory and gambling seem to be unrelated. But as we shall see, there is strong duality between the growth rate of investment in a horse race and the entropy rate of the horse race. Indeed, the sum of the growth rate and the entropy rate is a constant. In the process of proving this, we shall argue that the nancial value of side information is equal to the mutual information between the horse race and the side information. The horse race is a special case of investment in the stock market, studied in 16. We also show how to use a pair of identical gamblers to compress a sequence of random variables by an amount equal to the growth rate of wealth on that sequence. Finally, we use these gambling techniques to estimate the entropy rate of English. 6.1 THE HORSE RACE

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