title: Orthogonal trades in complete sets of MOLS

authors: Cavenagh, Nicholas J.

subjects: mathematics

abstract: Let Bₚ be the Latin square given by the addition table for the integers modulo an odd prime p (i.e. the Cayley table for (Zₚ, +)). Here we consider the properties of Latin trades in Bₚ which preserve orthogonality with one of the p−1 MOLS given by the finite field construction. We show that for certain choices of the orthogonal mate, there is a lower bound logarithmic in p for the number of times each symbol occurs in such a trade, with an overall lower bound of (log p)² / log log p for the size of such a trade. Such trades imply the existence of orthomorphisms of the cyclic group which differ from a linear orthomorphism by a small amount. We also show that any transversal in Bₚ hits the main diagonal either p or at most p − log₂ p – 1 times. Finally, if p ≡ 1 (mod 6) we show the existence of a Latin square which is orthogonal to Bₚ and which contains a 2 × 2 subsquare.

text: Orthogonal trades in complete sets of MOLS Let Bₚ be the Latin square given by the addition table for the integers modulo an odd prime p (i.e. the Cayley table for (Zₚ, +)). Here we consider the properties of Latin trades in Bₚ which preserve orthogonality with one of the p−1 MOLS given by the finite field construction. We show that for certain choices of the orthogonal mate, there is a lower bound logarithmic in p for the number of times each symbol occurs in such a trade, with an overall lower bound of (log p)² / log log p for the size of such a trade. Such trades imply the existence of orthomorphisms of the cyclic group which differ from a linear orthomorphism by a small amount. We also show that any transversal in Bₚ hits the main diagonal either p or at most p − log₂ p – 1 times. Finally, if p ≡ 1 (mod 6) we show the existence of a Latin square which is orthogonal to Bₚ and which contains a 2 × 2 subsquare.

year: 2017

title: The economic consequences of ‘brain drain’ of the best and brightest: Microeconomic evidence from five countries

authors: McKenzie, David

subjects: brain drain

abstract: Brain drain has long been a common concern for migrant-sending countries, particularly for small countries where high-skilled emigration rates are highest. However, while economic theory suggests a number of possible benefits, in addition to costs, from skilled emigration, the evidence base on many of these is very limited. Moreover, the lessons from case studies of benefits to China and India from skilled emigration may not be relevant to much smaller countries. This paper presents the results of innovative surveys which tracked academic high achievers from five countries to wherever they moved in the world in order to directly measure at the micro level the channels through which high-skilled emigration affects the sending country. The results show that there are very high levels of emigration and of return migration among the very highly skilled; the income gains to the best and brightest from migrating are very large, and an order of magnitude or more greater than any other effect; there are large benefits from migration in terms of postgraduate education; most high-skilled migrants from poorer countries send remittances; but that involvement in trade and foreign direct investment is a rare occurrence. There is considerable knowledge flow from both current and return migrants about job and study opportunities abroad, but little net knowledge sharing from current migrants to home country governments or businesses. Finally, the fiscal costs vary considerably across countries, and depend on the extent to which governments rely on progressive income taxation.

text: The economic consequences of ‘brain drain’ of the best and brightest: Microeconomic evidence from five countries Brain drain has long been a common concern for migrant-sending countries, particularly for small countries where high-skilled emigration rates are highest. However, while economic theory suggests a number of possible benefits, in addition to costs, from skilled emigration, the evidence base on many of these is very limited. Moreover, the lessons from case studies of benefits to China and India from skilled emigration may not be relevant to much smaller countries. This paper presents the results of innovative surveys which tracked academic high achievers from five countries to wherever they moved in the world in order to directly measure at the micro level the channels through which high-skilled emigration affects the sending country. The results show that there are very high levels of emigration and of return migration among the very highly skilled; the income gains to the best and brightest from migrating are very large, and an order of magnitude or more greater than any other effect; there are large benefits from migration in terms of postgraduate education; most high-skilled migrants from poorer countries send remittances; but that involvement in trade and foreign direct investment is a rare occurrence. There is considerable knowledge flow from both current and return migrants about job and study opportunities abroad, but little net knowledge sharing from current migrants to home country governments or businesses. Finally, the fiscal costs vary considerably across countries, and depend on the extent to which governments rely on progressive income taxation.

year: 2010-08

title: Evidence of swarm intelligence in collective cultures: Identifying the use of the swarm goal directive of productivity in Pacific organisation systems as well as getween genders

authors: Arun, Natalie M.

subjects: Maori

abstract: Intrigued by the existence of societies outside that of the human population, scientists have ventured to study social aggregations within insects to seek insights on effective colonizing. The most popular of these social aggregations are colonies of ants and bees. In studying these groups of social insects researchers have developed algorithms loosely termed swarm intelligence that increase work efficiency within businesses and other social organizations (Bonabeau & Meyer, 2001). A subsequent proliferation of research in surrounding fields has allowed for investigation of key variables that improve work on a global scale (Bonabeau & Meyer, 2001). James Kennedy (1999), an initiator of swarm research, has suggested that there is a high correlation between systems that rely on each other for information and greater task accomplishment.

text: Evidence of swarm intelligence in collective cultures: Identifying the use of the swarm goal directive of productivity in Pacific organisation systems as well as getween genders Intrigued by the existence of societies outside that of the human population, scientists have ventured to study social aggregations within insects to seek insights on effective colonizing. The most popular of these social aggregations are colonies of ants and bees. In studying these groups of social insects researchers have developed algorithms loosely termed swarm intelligence that increase work efficiency within businesses and other social organizations (Bonabeau & Meyer, 2001). A subsequent proliferation of research in surrounding fields has allowed for investigation of key variables that improve work on a global scale (Bonabeau & Meyer, 2001). James Kennedy (1999), an initiator of swarm research, has suggested that there is a high correlation between systems that rely on each other for information and greater task accomplishment.

year: 2008