title: Brocard's problem and variations

authors: Liu, Yi

abstract: This thesis examines the work which has been done on Brocard’s problem which is to study solutions to
n! + 1 = x²,

and related problems of the form
n! = f(x) or n! = f(x, y),

where f is a polynomial with integer coefficients. I also consider problems of the form
n! = f(x),

where there are apparently no solutions.

text: Brocard's problem and variations This thesis examines the work which has been done on Brocard’s problem which is to study solutions to
n! + 1 = x²,

and related problems of the form
n! = f(x) or n! = f(x, y),

where f is a polynomial with integer coefficients. I also consider problems of the form
n! = f(x),

where there are apparently no solutions.

year: 2013

title: Deep learning in diabetic foot ulcers detection: A comprehensive evaluation

authors: Yap, Moi Hoon

subjects: computer science

abstract: There has been a substantial amount of research involving computer methods and technology for the detection and recognition of diabetic foot ulcers (DFUs), but there is a lack of systematic comparisons of state-of-the-art deep learning object detection frameworks applied to this problem. DFUC2020 provided participants with a comprehensive dataset consisting of 2,000 images for training and 2,000 images for testing. This paper summarizes the results of DFUC2020 by comparing the deep learning-based algorithms proposed by the winning teams: Faster R–CNN, three variants of Faster R–CNN and an ensemble method; YOLOv3; YOLOv5; EfficientDet; and a new Cascade Attention Network. For each deep learning method, we provide a detailed description of model architecture, parameter settings for training and additional stages including pre-processing, data augmentation and post-processing. We provide a comprehensive evaluation for each method. All the methods required a data augmentation stage to increase the number of images available for training and a post-processing stage to remove false positives. The best performance was obtained from Deformable Convolution, a variant of Faster R–CNN, with a mean average precision (mAP) of 0.6940 and an F1-Score of 0.7434. Finally, we demonstrate that the ensemble method based on different deep learning methods can enhance the F1-Score but not the mAP.

text: Deep learning in diabetic foot ulcers detection: A comprehensive evaluation There has been a substantial amount of research involving computer methods and technology for the detection and recognition of diabetic foot ulcers (DFUs), but there is a lack of systematic comparisons of state-of-the-art deep learning object detection frameworks applied to this problem. DFUC2020 provided participants with a comprehensive dataset consisting of 2,000 images for training and 2,000 images for testing. This paper summarizes the results of DFUC2020 by comparing the deep learning-based algorithms proposed by the winning teams: Faster R–CNN, three variants of Faster R–CNN and an ensemble method; YOLOv3; YOLOv5; EfficientDet; and a new Cascade Attention Network. For each deep learning method, we provide a detailed description of model architecture, parameter settings for training and additional stages including pre-processing, data augmentation and post-processing. We provide a comprehensive evaluation for each method. All the methods required a data augmentation stage to increase the number of images available for training and a post-processing stage to remove false positives. The best performance was obtained from Deformable Convolution, a variant of Faster R–CNN, with a mean average precision (mAP) of 0.6940 and an F1-Score of 0.7434. Finally, we demonstrate that the ensemble method based on different deep learning methods can enhance the F1-Score but not the mAP.

year: 2021

title: Kiwi, kapai, and kuia: Māori loanwords in New Zealand English children's picture books published between 1995 and 2005

authors: Macdonald, Daryl Eveline

abstract: Māori loanwords are a distinctive characteristic of New Zealand English (Deverson, 1991). A previous study of the frequency of Māori loanwords in New Zealand English children’s picture books showed an incidence of 56 words per thousand in a corpus of 13 books published by a single publishing house between 1995 and 2005 (Daly, 2007). The current study determined the frequency, semantic categories, and textual representations of loanwords in a corpus of nearly 500 children’s picture books published in New Zealand between 1995 and 2005. Results showed an incidence of 13 Māori loanwords per thousand words of text. Reasons for this difference in frequency and the potential effects of a relatively high incidence of Māori loanwords in children’s picture books are discussed in terms of the language use of the readers, the changing character of New Zealand English, and New Zealand national identity.

text: Kiwi, kapai, and kuia: Māori loanwords in New Zealand English children's picture books published between 1995 and 2005 Māori loanwords are a distinctive characteristic of New Zealand English (Deverson, 1991). A previous study of the frequency of Māori loanwords in New Zealand English children’s picture books showed an incidence of 56 words per thousand in a corpus of 13 books published by a single publishing house between 1995 and 2005 (Daly, 2007). The current study determined the frequency, semantic categories, and textual representations of loanwords in a corpus of nearly 500 children’s picture books published in New Zealand between 1995 and 2005. Results showed an incidence of 13 Māori loanwords per thousand words of text. Reasons for this difference in frequency and the potential effects of a relatively high incidence of Māori loanwords in children’s picture books are discussed in terms of the language use of the readers, the changing character of New Zealand English, and New Zealand national identity.

year: 2013