title: Induced subarrays of Latin squares without repeated symbols

authors: Abel, R. Julian R.

subjects: Latin square

abstract: We show that for any Latin square L of order 2m, we can partition the rows and columns of L into pairs so that at most (m+3)/2 of the 2x2 subarrays induced contain a repeated symbol. We conjecture that any Latin square of order 2m (where m ≥ 2, with exactly five transposition class exceptions of order 6) has such a partition so that every 2x2 subarray induced contains no repeated symbol. We verify this conjecture by computer when m ≤ 4.

text: Induced subarrays of Latin squares without repeated symbols We show that for any Latin square L of order 2m, we can partition the rows and columns of L into pairs so that at most (m+3)/2 of the 2x2 subarrays induced contain a repeated symbol. We conjecture that any Latin square of order 2m (where m ≥ 2, with exactly five transposition class exceptions of order 6) has such a partition so that every 2x2 subarray induced contains no repeated symbol. We verify this conjecture by computer when m ≤ 4.

year: 2013

title: Utilizing popularity characteristics for product recommendation

authors: Ahn, Hyung Jun

subjects: automated product recommendation

abstract: This paper presents a novel approach to automated product recommendation based on the popularity characteristics of products. Popularity plays a significant role in the consumer purchasing process but has not been given much attention in recommendation research. A three-dimensional model of popularity is used to develop popularity classes of products. These are joined with the MovieLens dataset to create a hybrid movie recommendation system that combines genre and popularity information. As compared with collaborative filtering, the hybrid system shows positive results under the conditions of data sparsity and cold-starting. Many interesting issues for further research are suggested.

text: Utilizing popularity characteristics for product recommendation This paper presents a novel approach to automated product recommendation based on the popularity characteristics of products. Popularity plays a significant role in the consumer purchasing process but has not been given much attention in recommendation research. A three-dimensional model of popularity is used to develop popularity classes of products. These are joined with the MovieLens dataset to create a hybrid movie recommendation system that combines genre and popularity information. As compared with collaborative filtering, the hybrid system shows positive results under the conditions of data sparsity and cold-starting. Many interesting issues for further research are suggested.

year: 2006

title: Conclusion: Relationships of interdependence—Making the difference together

authors: Berryman, Mere

abstract: This chapter begins by taking a brief look at New Zealand history. It then presents two different Māori whakataukī as metaphors, both to reconnect to the beginning of the book and also to make connections throughout the book as a whole. These metaphors are used to bring the chapters together and to consider how inclusion, a term that is often highly contested and poorly understood (Wearmouth, 2009), might begin to be better understood and applied when working with Māori children and young people with disabilities, or special education needs, or both, and with their families.

text: Conclusion: Relationships of interdependence—Making the difference together This chapter begins by taking a brief look at New Zealand history. It then presents two different Māori whakataukī as metaphors, both to reconnect to the beginning of the book and also to make connections throughout the book as a whole. These metaphors are used to bring the chapters together and to consider how inclusion, a term that is often highly contested and poorly understood (Wearmouth, 2009), might begin to be better understood and applied when working with Māori children and young people with disabilities, or special education needs, or both, and with their families.

year: 2015