Zipf and Type-Token rules for the English, Spanish, Irish and Latin languages

The Zipf curves of log of frequency against log of rank for a large English corpus of 500 million word tokens, 689,000 word types and for a large Spanish corpus of 16 million word tokens, 139,000 word types are shown to have the usual slope close to –1 for rank less than 5,000, but then for a higher rank they turn to give a slope close to –2. This is apparently mainly due to foreign words and place names. Other Zipf curves for highlyinflected Indo-European languages, Irish and ancient Latin, are also given. Because of the larger number of word types per lemma, they remain flatter than the English curve maintaining a slope of –1 until turning points of about ranks 30,000 for Irish and 10,000 for Latin. A formula which calculates the number of tokens given the number of types is derived in terms of the rank at the turning point, 5,000 for both English and Spanish, 30,000 for Irish and 10,000 for Latin.

Depressed mood and dietary fish intake: Direct relationship or indirect relationship as a result of diet and lifestyle?

Previous studies have suggested an association between depressed mood and the dietary intake of fish. In all cases, however, dietary fish intake has been considered at the exclusion of all other aspects of the diet. This analysis investigates associations between depressed mood and dietary fish intake, while also concurrently investigating intake of a number of other dietary components. The analysis is conducted on data from 10,602 men from Northern Ireland and France screened for inclusion into the PRIME cohort study. Depressed mood was assessed using a self-report questionnaire based on the Welsh Pure Depression sub-scale of the Minnesota Multiphasic Personality Inventory, diet was assessed using a Food Frequency Questionnaire, and limited demographics were also measured. Using regression, depressed mood is initially inversely associated with dietary fish intake. On inclusion of all other dietary variables, the strength of this relationship reduces but remains, and significant associations with a number of other foods are also found. On additional inclusion of all demographic variables, the strength of the above relationships again reduces, and associations with various measures of socio-economic status and education are also significant. These findings suggest that depressed mood is associated with fish intake both directly, and indirectly as part of a diet that is associated with depression and as part of a lifestyle that is associated with depression. Additional support for these conclusions is also provided in the pattern of associations between depressed mood and diet in the two countries. The relative contributions of fish intake to depressed mood both directly and indirectly are yet to be determined. However, while diet is not measured and until lifestyle can be adequately measured, the potential roles of diet and lifestyle in the association between depressed mood and dietary fish intake should not be ignored.

Transmission loss allocation in a deregulated electrical energy market

This paper presents a new method for transmission loss allocation in a deregulated electrical power market. The proposed method is based on physical flow through transmission lines. The contributions of individual loads to the line flows are used as basis for allocating transmission losses to different loads. With minimum assumptions, that sound to be reasonable and cannot be rejected, a novel loss allocation formula is derived. The assumptions made are: a number of currents sharing a transmission line distribute themselves over the cross section in the same manner; that distribution causes the minimum possible power loss. Application of the proposed method is straightforward. It requires only a solved power flow and any simple algorithm for power flow tracing. Both active and reactive powers are considered in the loss allocation procedure. Results of application show the accuracy of the proposed method compared with the commonly used procedures.