title: Lie theory and separation of variables. 11. The EPD equation

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: We show that the Euler–Poisson–Darboux equation {∂tt -∂rr – [(2m+1)/r]∂r}Ө=0
separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second-order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second-order operators in the enveloping algebra of SL(2,C).

text: Lie theory and separation of variables. 11. The EPD equation We show that the Euler–Poisson–Darboux equation {∂tt -∂rr – [(2m+1)/r]∂r}Ө=0
separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second-order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second-order operators in the enveloping algebra of SL(2,C).

year: 1976-03

title: Transformers for multi-label classification of medical text: an empirical comparison

authors: Yogarajan, Vithya

subjects: computer science

abstract: Recent advancements in machine learning-based multi-label medical text classification techniques have been used to help enhance healthcare and aid better patient care. This research is motivated by transformers’ success in natural language processing tasks, and the opportunity to further improve performance for medical-domain specific tasks by exploiting models pre-trained on health data. We consider transfer learning involving fine-tuning of pre-trained models for predicting medical codes, formulated as a multi-label problem. We find that domain-specific transformers outperform state-of-the-art results for multi-label problems with the number of labels ranging from 18 to 158, for a fixed sequence length. Additionally, we find that, for longer documents and/or number of labels greater than 300, traditional neural networks still have an edge over transformers. These findings are obtained by performing extensive experiments on the semi-structured eICU data and the free-form MIMIC III data, and applying various transformers including BERT, RoBERTa, and Longformer variations. The electronic health record data used in this research exhibits a high level of label imbalance. Considering individual label accuracy, we find that for eICU data medical-domain specific RoBERTa models achieve improvements for more frequent labels. For infrequent labels, in both datasets, traditional neural networks still perform better.

text: Transformers for multi-label classification of medical text: an empirical comparison Recent advancements in machine learning-based multi-label medical text classification techniques have been used to help enhance healthcare and aid better patient care. This research is motivated by transformers’ success in natural language processing tasks, and the opportunity to further improve performance for medical-domain specific tasks by exploiting models pre-trained on health data. We consider transfer learning involving fine-tuning of pre-trained models for predicting medical codes, formulated as a multi-label problem. We find that domain-specific transformers outperform state-of-the-art results for multi-label problems with the number of labels ranging from 18 to 158, for a fixed sequence length. Additionally, we find that, for longer documents and/or number of labels greater than 300, traditional neural networks still have an edge over transformers. These findings are obtained by performing extensive experiments on the semi-structured eICU data and the free-form MIMIC III data, and applying various transformers including BERT, RoBERTa, and Longformer variations. The electronic health record data used in this research exhibits a high level of label imbalance. Considering individual label accuracy, we find that for eICU data medical-domain specific RoBERTa models achieve improvements for more frequent labels. For infrequent labels, in both datasets, traditional neural networks still perform better.

year: 2021

title: On equality and colourblindness

authors: Robertson, Neville

subjects: Maori

abstract: "I have a dream that my four children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character." So said Martin Luther King, Jr, just over 40 years ago, in a speech that galvanised the US civil rights movement. King spoke of the United States but his dream is equally relevant in New Zealand. Has it been achieved? Some people would argue that not only has it been achieved but that the tables have been turned and now white folk are the ones who are oppressed. What is needed, they argue, is a level playing field. But how level is the playing field?

text: On equality and colourblindness "I have a dream that my four children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character." So said Martin Luther King, Jr, just over 40 years ago, in a speech that galvanised the US civil rights movement. King spoke of the United States but his dream is equally relevant in New Zealand. Has it been achieved? Some people would argue that not only has it been achieved but that the tables have been turned and now white folk are the ones who are oppressed. What is needed, they argue, is a level playing field. But how level is the playing field?

year: 2004