title: Visualizing class probability estimators

authors: Frank, Eibe

subjects: Science & Technology

abstract: Inducing classifiers that make accurate predictions on future data is a driving force for research in inductive learning. However, also of importance to the users is how to gain information from the models produced. Unfortunately, some of the most powerful inductive learning algorithms generate “black boxes”—that is, the representation of the model makes it virtually impossible to gain any insight into what has been learned. This paper presents a technique that can help the user understand why a classifier makes the predictions that it does by providing a two-dimensional visualization of its class probability estimates. It requires the classifier to generate class probabilities but most practical algorithms are able to do so (or can be modified to this end).

text: Visualizing class probability estimators Inducing classifiers that make accurate predictions on future data is a driving force for research in inductive learning. However, also of importance to the users is how to gain information from the models produced. Unfortunately, some of the most powerful inductive learning algorithms generate “black boxes”—that is, the representation of the model makes it virtually impossible to gain any insight into what has been learned. This paper presents a technique that can help the user understand why a classifier makes the predictions that it does by providing a two-dimensional visualization of its class probability estimates. It requires the classifier to generate class probabilities but most practical algorithms are able to do so (or can be modified to this end).

year: 2003-01-01

title: The gcd-sum function

authors: Broughan, Kevin A.

subjects: mathematics

abstract: The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sumi=1..n (i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms.

text: The gcd-sum function The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: g(n) = sumi=1..n (i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms.

year: 2001

title: What Do Secondary School Rugby Players Think About Concussion?

authors: Murphy, Karen Jane

subjects: rugby

abstract: Traumatic Brain Injury (TBI) is a dominant and growing public health concern globally. Sport is an arena in which people are at high risk of TBI. In New Zealand the popular sport of rugby is played by many, particularly during school years. These school aged players are at particular risk of TBI because of the contact nature of the sport and the maturational stage of the brain which is still developing during the teenage years.  Moves to increase safety depend on an awareness of what these players know about TBI and their attitude towards TBI.
A sample of 456 secondary school rugby players in New Zealand were surveyed to gather information about their knowledge of, and attitude towards concussion. Rugby union and rugby league playing participants were mainly recruited through direct contact with schools. Participants were invited to access the survey online or could complete a paper copy. The survey was made up of items which had already been used in previous studies and this allowed for a comparison of findings with previous research. Some items related to knowledge of concussion while others related to attitude towards concussion, in particular attitudes to returning to play following concussion.
	Participants had good knowledge of symptoms, and almost all participants knew there was a risk to long term health and a risk of death if a second concussion was sustained before a first concussion had healed. However, there were some gaps in knowledge about treatment and recovery time.
Participants self-reported attitudes to concussion were consistently and significantly safer than the attitudes they predicted ‘most players’ would hold.
More than half of the participants had a relatively safe attitude to all but one of the items relating to concussion attitude. The least safe attitudes were around who should make a decision to returning to play after concussion and the safety of attitudes declined as the importance of a rugby match increased. 
Ethnicity consistently influenced knowledge and attitude on all the measures used within the survey. Those identifying as Māori ethnicity scored lower on all knowledge and attitude scales than those identifying as Pakeha ethnicity. Self-rated knowledge of concussion and the number of concussions experienced also had a positive effect on knowledge of concussion. 
There are several educational tools and regulatory documents aimed at minimising the incidence, severity and outcome of concussion in rugby but there is little research guiding how these resources are tailored to their intended audience in the secondary school population. Also, little is known about the gaps in knowledge and understanding of concussion in this population. It is tentatively stated that the findings from this study could be used to inform strategies which are aimed at increasing knowledge and making attitudes safer in secondary school rugby players in New Zealand.

text: What Do Secondary School Rugby Players Think About Concussion? Traumatic Brain Injury (TBI) is a dominant and growing public health concern globally. Sport is an arena in which people are at high risk of TBI. In New Zealand the popular sport of rugby is played by many, particularly during school years. These school aged players are at particular risk of TBI because of the contact nature of the sport and the maturational stage of the brain which is still developing during the teenage years.  Moves to increase safety depend on an awareness of what these players know about TBI and their attitude towards TBI.
A sample of 456 secondary school rugby players in New Zealand were surveyed to gather information about their knowledge of, and attitude towards concussion. Rugby union and rugby league playing participants were mainly recruited through direct contact with schools. Participants were invited to access the survey online or could complete a paper copy. The survey was made up of items which had already been used in previous studies and this allowed for a comparison of findings with previous research. Some items related to knowledge of concussion while others related to attitude towards concussion, in particular attitudes to returning to play following concussion.
	Participants had good knowledge of symptoms, and almost all participants knew there was a risk to long term health and a risk of death if a second concussion was sustained before a first concussion had healed. However, there were some gaps in knowledge about treatment and recovery time.
Participants self-reported attitudes to concussion were consistently and significantly safer than the attitudes they predicted ‘most players’ would hold.
More than half of the participants had a relatively safe attitude to all but one of the items relating to concussion attitude. The least safe attitudes were around who should make a decision to returning to play after concussion and the safety of attitudes declined as the importance of a rugby match increased. 
Ethnicity consistently influenced knowledge and attitude on all the measures used within the survey. Those identifying as Māori ethnicity scored lower on all knowledge and attitude scales than those identifying as Pakeha ethnicity. Self-rated knowledge of concussion and the number of concussions experienced also had a positive effect on knowledge of concussion. 
There are several educational tools and regulatory documents aimed at minimising the incidence, severity and outcome of concussion in rugby but there is little research guiding how these resources are tailored to their intended audience in the secondary school population. Also, little is known about the gaps in knowledge and understanding of concussion in this population. It is tentatively stated that the findings from this study could be used to inform strategies which are aimed at increasing knowledge and making attitudes safer in secondary school rugby players in New Zealand.

year: 2015