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# Bicycle Network Mandatory Helmet Review

The Bicycle Network is reviewing their bicycle helmet policy. I’ve been asked by BN CEO Craig Richards to comment on the questions:

Do you believe it should be mandatory to wear a helmet when riding a bicycle? What’s your reasons for your answer?

In the spirit of transparency, what follows is my response to Mr Richards.

Before I respond to this question, I would like to give my impressions regarding the motivations and methods used in this review.

1. It is quite reasonable for an organization such as the Bicycle Network (BN) to review their policies and/or advocacy positions. However, why advertise you are reviewing your policies to the media or anyone external to BN? I believe it would be quite rare for any organization to issue a media release and provide interviews to print and television media that they are reviewing their policies.
2. What is the population frame for the survey? Whatever it is, it should be informed by what the surveyors are trying to accomplish. If the purpose is to canvas the opinions of the BN, then the survey should have been restricted to BN members. If BN is trying to canvas opinions of Australian cyclists, then this has not been accomplished for the same reason. As far as I am aware, there was nothing in place to ensure responses were BN members or Australian residents or cyclists or even human (i.e., self-report cannot be validated).
3. It is well known and accepted that online polls lack scientific rigor. This cannot be changed by statistical analysis or restricting the sample of responders. Given these issues and perhaps the wording of the questions, it is unclear what is actually being measured and whether any of the results will be generalizable to any population. The Statistical Society of Australia has raised similar concerns regarding the Australian Marriage Law Postal Survey.
4. These points invalidate the survey results irrespective of whether they are favorable or unfavorable towards bike helmet legislation. In my view, it is an exercise in motivational reasoning and, at a minimum, propaganda to drum up support for a predetermined change in BN policy.
5. What is an expert? That is truly a difficult question to answer, but it certainly is not someone who wins a popularity contest. It is also not someone who has an opinion on a topic, including those with doctoral degrees but no formal training or established research record on this topic. It is someone who can evaluate the quality of evidence and not just selectively cite data supportive of their opinions.
6. It is well known from multiple surveys here and abroad that lack of cycling infrastructure and concerns for safety are the reasons people do not cycle. So, why have a huge, media-grabbing survey about helmet policy? Why are more important issues not being addressed?
7. If BN change their policy, are they prepared to properly evaluate its impact? What if there is no increase in cycling, yet cycling head injuries/fatalities increase? Will the BN accept the potential consequences of that decision?

The reason I support bicycle helmet legislation is because the peer-reviewed research evidence indicates:

1. Bicycle helmets are highly effective at mitigating head, serious head (roughly skull fractures and/or intracranial hemorrhage), fatal head, and facial injury,
2. Helmet wearing rates are low without helmet legislation and high with them,
3. Bicycle helmet legislation is associated with declines in cycling head injury and cycling fatality, and
4. There is no strong evidence supportive of common hypotheses presented by anti-helmet and anti-helmet helmet legislation advocates. These include no clear evidence for risk compensation, helmets increasing angular acceleration, helmet legislation deters cycling, helmet legislation is part of the causal pathway for the rise in obesity, or that removing existing helmet legislation will increase cycling or improve population health.

Bicycle helmet legislation is supported by professional societies including the Australasian College of Road Safety, the Australian Injury Prevention Network and the Royal Australasian College of Surgeons.

As an aside, arguments calling for mandatory helmets in cars or for pedestrians are Straw Man arguments. This discussion is about interventions to make cycling safer and not other road users. There are interventions such as lower posted speed limits that benefit all road users, but that is not what is being argued. Additionally, this view implies no measures should be taken to improve cycling safety unless injuries are eliminated for other road users. I find this view to be unethical.

I would also like to add that it is not uncommon for public health interventions to be opposed and debated. This is not unique to bicycle helmets or helmet legislation. However, this discussion should revolve around the available evidence and how “better” evidence may be collected if there are knowledge gaps. Instead, I find bike helmets to be less debate about evidence and more about choosing sides, standing one’s ground and ignoring quality evidence that disagrees with a predetermined position.

There is a misconception Australia is alone in bicycle helmet legislation. My colleagues and I count at least 271 country, state, territory, province or city bicycle helmet laws. That is, there were at 271 instances across the world where legislators proposed legislation, debated its merit, and decided to move forward with legislation.

Countries with bicycle helmet legislation include Argentina, Australia, Austria, parts of Canada, Chile, Croatia, Czech Republic, Estonia, Finland, France, Iceland, Israel, Japan, Jersey, Latvia, Lithuania, Malta, New Zealand, Slovakia, Slovenia, South Africa, South Korea, Spain, Sweden, United Arab Emirates and parts of the United States. These laws differ in terms of enforcement and many apply only to children below a certain age. Ten countries have bicycle helmet laws that apply to all ages (Argentina, Australia, some parts of Canada, Chile, Finland, Malta, New Zealand, South Africa, United Arab Emirates, and parts of the United States). There have only been two jurisdictions that have repealed helmet legislation (Mexico City and Bosnia & Herzegovina) and the impacts of these repeals have never been evaluated. The validity of the argument Australia is alone aside, the reader should be aware that appeals to popularity have no logical foundation.

Below is a list of peer-reviewed articles I have published with colleagues that have informed my position. Many of these papers are available publicly and I am happy to share copies privately. There is also research by others that I would happily point to for any interested reader.

1. Grzebieta RH, Olivier J & Boufous S. (2017) Reducing serious injury from road traffic crashes. Medical Journal of Australia, 207(6): 242-243.
2. Olivier J & Radun I. (2017) Bicycle helmet effectiveness is not overstated. Traffic Injury Prevention, 18: 755-760.
3. Schepers P, Stipdonk H, Methorst R & Olivier J. (2017) Bicycle fatalities: Trends in crashes with and without motor vehicles in The Netherlands. Transportation Research Part F: Traffic Psychology and Behaviour,46: 491-499.
4. Olivier J & Creighton P. (2017) Bicycle injuries and helmet use: A systematic review and meta-analysis. International Journal of Epidemiology, 46(1): 278-292.
5. Olivier J, Boufous S & Grzebieta R. (2016) No strong evidence bicycle helmet legislation deters cycling. Medical Journal of Australia, 205(2): 54-55.
6. Boufous S & Olivier J. (2016) Recent trends in cyclist fatalities in Australia. Injury Prevention, 22(4):284-287.
7. Olivier J, Creighton P & Mason CT. (2016) Evidence Bicycle Helmets Mitigate Intracranial Injury is Not Controversial. European Journal of Trauma and Emergency Surgery, 42:333-336.
8. Olivier J & Walter SR. (2015) Too much statistical power can lead to false conclusions: A response to Kary (2014). Injury Prevention, 21: 289.
9. Olivier J, Wang JJJ, Walter S & Grzebieta R. (2014) Anti-Helmet Arguments: Lies, damned lies and flawed statistics. Journal of the Australasian College of Road Safety, 25(4): 10-23.
10. Olivier J, Wang JJJ & Grzebieta R. (2014) A systematic review of methods used to assess mandatory bicycle helmet legislation in New Zealand. Journal of the Australasian College of Road Safety, 25(4): 24-31.
11. Olivier J. (2014) The apparent ineffectiveness of bicycle helmets: A case of selective citation (letter). Gaceta Sanitaria, 28: 254-255.
12. Wang J, Olivier J & Grzebieta R. (2014) Response to ‘Evaluation of New Zealand’s bicycle helmet law’ (letter). New Zealand Medical Journal, 127(1389): 106-108.
13. Olivier J & Walter SR. (2013) Bicycle helmet wearing is not associated with close overtaking: A reanalysis of Walker (2007). PLOS ONE, 8(9): e75424. Erratum in: PLOS ONE, 9(1).
14. Bambach MR, Mitchell RJ, Grzebieta RH & Olivier J. (2013) The effectiveness of helmets in bicycle collisions with motor vehicles: A case-control study. Accident Analysis and Prevention, 53: 78-88.
15. Walter SR, Olivier J, Churches T & Grzebieta R. (2013) The impact of compulsory cycle helmet legislation on cyclist head injuries in New South Wales, Australia: A response. Accident Analysis and Prevention, 52: 204-209.
16. Olivier J, Walter SR & Grzebieta RH. (2013) Long term bicycle related head injury trends for New South Wales, Australia following mandatory helmet legislation. Accident Analysis and Prevention, 50: 1128-1134.
17. Olivier J, Churches T, Walter S, McIntosh A & Grzebieta R. (2012) Response to Rissel and Wen, The possible effect on frequency of cycling if mandatory bicycle helmet legislation was repealed in Sydney, Australia: a cross sectional survey (letter). Health Promotion Journal of Australia, 23(1): 76.
18. Poulos RG, Chong SSS, Olivier J & Jalaludin B. (2012) Geospatial analyses to prioritize public health interventions: a case study of pedestrian and pedal cycle injuries in New South Wales, Australia. International Journal of Public Health, 57(3): 467-475.
19. Walter SR, Olivier J, Churches T & Grzebieta R. (2011) The impact of compulsory cycle helmet legislation on cyclist head injuries in New South Wales, Australia. Accident Analysis and Prevention, 43(6): 2064-2071.
20. Esmaeilikia M, Grzebieta R & Olivier J. (2017) A systematic review on the effects of bicycle helmet legislation on cycling. Proceedings of the 6th Annual International Cycling Safety Conference (extended abstract).
21. Olivier J & Terlich F. (2016) The use of propensity score stratification and synthetic data to address allocation bias when assessing bicycle helmet effectiveness. 2016 IRCOBI Conference Proceedings – International Research Council on the Biomechanics of Injury, IRC-16-29: 185-193.
22. Olivier J, Grzebieta R, Wang JJJ & Walter, S. (2013) Statistical Errors in Anti-Helmet Arguments. Proceedings of the Australasian College of Road Safety Conference.
23. Wang JJJ, Grzebieta R, Walter S & Olivier J. (2013) An evaluation of the methods used to assess the effectiveness of mandatory bicycle helmet legislation in New Zealand. Proceedings of the Australasian College of Road Safety Conference.
24. Olivier J, Wang JJJ, Walter S & Grzebieta R. (2013) On the use of empirical Bayes for comparative interrupted time series with an application to mandatory helmet legislation. Proceedings of the Australasian Road Safety, Research, Policing and Education Conference.
25. Wang JJJ, Walter S, Grzebieta R & Olivier J. (2013) A Comparison of Statistical Methods in Interrupted Time Series Analysis to Estimate an Intervention Effect. Proceedings of the Australasian Road Safety, Research, Policing and Education Conference.

# No One Thinks Helmets are a Panacea for Cycling Safety

Last week I published a post about an ABC Radio National piece about bicycle helmets. A colleague of mine contacted ABC’s Media Watch and ran a story about it. In the aftermath, I’ve been told the debate is not about whether bicycle helmets are effective or if helmet legislation has resulted in fewer bicycle related head injuries, the myth that was being debunked on the show Assumptions was whether helmet legislation should be the sole strategy for cycling safety.

The problem is that no one believes bicycle helmets are a panacea for cycling safety, mandatory or not. Helmets are designed to protect the head and therefore are not designed to protect other body parts. Head injuries may be very important, but it is possible for a cyclist to have serious or fatal injuries that do not involve the head. Clearly, other strategies are needed for a comprehensive cycling safety strategy.

On several occasions now, I’ve called for more research into other strategies besides helmet promotion or legislation like increased segregated cycling infrastructure and lower speed limits on roads commonly used by cyclists. Here are a few direct quotes from those papers.

Walter et al [1]

While helmet legislation appears to play an important role in the reduction of cyclist head injuries, further improvements in cyclist safety in general may be gained from a broader focus.  Cyclist safety is a complex issue driven by a range of factors. Cycling in Australia has changed with a considerable increase in recreational road cycling and mountain biking in recent years. Additional research into the diverse and changing risk profiles among these cycling subgroups would facilitate further safety improvements.

Olivier et al [2]

Our study shows that the beneficial effect of MHL in NSW has been maintained since enactment of the law over 20 years ago. This signals a need to focus on other aspects of bicycle safety in order to further reduce cycling-related injuries. Collisions involving motor vehicles clearly have a high risk of head injury indicating that the interaction between cyclists and MVs is a key area for intervention through further changes to transport infrastructure and modification of cyclist and motorist behaviour.

Walter et al [3]

Safety concerns tend to dominate media coverage of cycling in Australia (Rissel et al., 2010). This public discourse is often framed, or re-framed, around removal or relaxation of mandatory helmet laws (Piper et al., 2011), despite the wearing of helmets by cyclists forming only one part of the safety picture. In contrast, the high levels of cycling participation and the excellent cycling safety environment in northern European countries such as the Netherlands, Denmark and Germany appear to have been predicated on substantial and sustained investment in well-connected networks of thoughtfully designed bike lanes, bike paths and other cycling infrastructure. Other important factors are low speed limits on urban streets, the fostering of consideration and understanding between road users, and adequate legal protection for vulnerable road users, both cyclists and pedestrians alike. These are the essential elements for providing a cycling environment that encourages participation, with all its health, economic and environmental benefits, while maximising safety.

Olivier and Walter [4]

Risk compensation theory for helmet wearing while cycling has generated increased interest in the peer-reviewed literature, although there is little to no evidence to support the theory. Walker’s [2] argument that helmet wearing affects the behaviour of motor vehicle drivers does not support risk compensation theory upon reanalysis. Helmet wearing is associated with a small difference in passing distance and is not associated with close passing. The evidence from this study does not justify recommendations around helmet wearing, but rather highlights the more important factors of kerb distance, road characteristics and traffic type which may inform more effective cycling safety improvements.

Olivier [5]

Helmets, however, should not be viewed as a panacea and instead are an important part of any cycling safety strategy along with segregated cycling facilities and lower speed limits for motorised traffic. The benefits of each intervention are situational – helmets will help a cyclist in an accident and segregated cycling infrastructure will help avoid accidents. I therefore believe the decision to mandate helmet use should be in conjunction with a comprehensive strategy and not in isolation.

The current view of road safety is the safe system approach where many strategies are used in concert to minimize the risk and severity of injury. The notion of framing helmet promotion or legislation as an all-or-nothing strategy is very far from the truth. I stated just that in an article published last year.

Olivier et al [6]

Quite often arguments against helmet legislation are framed as an all-or-nothing safety intervention strategy that is in direct competition with creating segregated cycling infrastructure. In other words, it is believed a government will support one but not both. To wit, Ian Walker in a recent New York Times article states “Any solution to bicyclist safety should focus on preventing collisions from taking place, not seeking to minimize the damage after a collision has occurred” [35]. This strategy runs counter to the safe system approach supported by government and safety advocacy groups, where personal protection is seen as a critical component of the whole system to reducing vulnerable road user (cyclist and motorcyclist) injuries. There is also little support for focussing on injury avoidance alone in the injury record. In NSW from 1991 to 2010, only 12% and 23% of bicycle related head injury hospitalisations for children and adults respectively involve a motor vehicle. The goal of the safe system approach, on the other hand, would be to minimise the risk of a crash (crash avoidance) and to minimise the risk of injury when a crash occurs (personal protection), i.e., a holistic approach is used to reduce road trauma.

No one believes bicycle helmets are a panacea as a cycling safety strategy, and that includes me and my colleagues. There’s no myth to be busted.

1. Walter, S.R., Olivier, J., Churches, T., & Grzebeita, R. (2011). The impact of compulsory cycle helmet legislation on cyclist head injuries in New South Wales, Australia. Accident Analysis and Prevention, 43, 2064–2071.
2. Olivier, J., Walter, S.R., & Grzebieta, R.H. (2013). Long term bicycle related head injury trends for New South Wales, Australia following mandatory helmet legislation. Accident Analysis and Prevention, 50, 1128–1134.
3. Walter, S.R., Olivier, J., Churches, T. & Grzebieta, R. (2013). The impact of compulsory helmet legislation on cyclist head injuries in New South Wales, Australia: A response. Accident Analysis and Prevention, 52, 204-209.
4. Olivier, J. & Walter, S.R. (2013). Bicycle helmet wearing is not associated with close motor vehicle passing: A re-analysis of Walker, 2007. PLOS ONE, 8(9): e75424.
5. Olivier, J. (2014). The apparent ineffectiveness of bicycle helmets: A case of selective citation. Gaceta Sanitaria, 28, 254-255.
6. Olivier, J., Wang, J.J.J., Walter, S. & Grzebieta, R. (2015). Anti-helmet arguments: lies, damned lies and flawed statistics. Journal of the Australasian College of Road Safety, 25, 10-23.

# Media Watch Segment “Helmet claims under fire”

Alan Todd of Freestyle Cyclists was recently interviewed for an upcoming piece on ABC Radio National. Much of Todd’s responses were the same misleading information he gives in all his interviews (see here and here, for examples). I sent an email to host Susan Carland detailing some of the misinformation given by Todd and received no response.

A colleague forwarded my email to ABC’s Media Watch. They ran a segment on last night’s show. You can read the transcripts or watch the video here. Note the website includes links to responses from Alan Todd, ABC Radio National Manager Deborah Leavitt, Professor Raphael Grzebieta and Dr Andrew McIntosh.

I found Todd’s conclusion quite curious which seems to be a common argument by anti-helmet advocates.

In conclusion, it is now twenty five years since Victoria become the first place in the world to mandate helmets for cyclists. Since then, only three countries have introduced nationally enforced all ages helmet laws for cyclists. If the evidence for the benefits of such laws was indeed overwhelming, why have the other one hundred and ninety three countries not followed suit?

In my own view, this is a self fulfilling prophesy. There are several anti-helmet advocacy groups that are very vocal like FreestyleCyclists, the Bicycle Helmet Research Foundation and Cyclists Rights Action Group. They may seem like legitimate research organizations to the uninformed, but they are not comprised of experts from relevant fields like road safety, injury epidemiology, trauma surgery, biostatistics, etc. The ones who do have research backgrounds are from other disciplines like Dorothy Robinson (beef industry research) Nigel Perry (computer science) and John Adams (geography).

I don’t understand how it happened, but anti-helmet advocates have gained a foothold among some influential organizations including policy makers. This has likely stopped other jurisdictions from moving ahead with either helmet legislation or promotion.

To be clear, I’m not an advocate for helmet legislation in other jurisdictions. That is a decision the people of each country/state/city must make for themselves from an informed position. The problem is the spread of misinformation about helmets and helmet laws means that is unlikely to happen.

Note: The comments are full of the usual names like Colin Clarke and Chris Gillham. Neither are ever shy about promoting their anti-helmet views.

Update: Interesting Tweet from Wendy Carlisle who initially reported on the 2010 Voukelatos and Rissel paper that was later retracted.

# Colin Clarke’s Assessment of Australian Helmet Laws

Colin Clarke, a former engineering student, left a comment to my recent post regarding my experiences with Elsevier. Although this post was about an email I sent to Jennifer Mindell (editor in chief of the Journal of Transport and Health) and Chris Pringle (Elsevier Executive Publisher), Clarke took it upon himself to promote his views on bicycle helmets.

Since his comment was really not relevant to my post, I thought about rejecting his comment for quite a while. However, since I assume he would just criticize me somewhere else for censorship, I allowed his comment to be published.

I’ve had numerous online discussions with Clarke about bike helmets (see here, for example). Years ago, it seems Clarke wrote a standard criticism about helmets and, if you’ve ever read one, you’ve essentially read them all. I’ve pointed out fallacies in his arguments many times, and he continually ignores those criticisms.

Clarke’s primary argument is what I call the ‘helmet law as cycling deterrent’ hypothesis. There’s no real, solid evidence to support this hypothesis, yet it has not stopped those like Clarke to proclaim its truth to anyone who cares to listen.

In his comment, Clarke ‘estimates’ (and I’m being generous here) 413 cycling head injuries in NSW are expected in 1992 (this assumes a 30% drop in cycling from 1991 to 1992 and 590 head injuries reported in 1991, i.e., 590*0.7=413). Instead, there were 648 NSW head injury hospitalizations in 1992 (hospital data can be found here).

There are two problems with this approach. First, NSW adults were subject to helmet legislation for the entirety of 1991 and children for half. Clarke would have needed 1990/91 data to make that point (Jan-Dec for adults, Jul-Jun for children). This also assumes there aren’t any existing trends in cycling rates (no data exists to even attempt to estimate those secular trends, except for 1.5 years of pre-law hospital data that doesn’t support Clarke’s hypothesis). Second, if you apply the same logic to arm injuries, you get an expected 660*0.7=462 arm injuries in 1992 (there were 760). In fact, not adjusting for population, head injuries increased by 9.8% while arm injuries increased 15% between those years. None of this suggests Clarke’s hypothesis is true.

Importantly, the injury data comes from a census of medically diagnosed hospitalizations at that time and is therefore of high quality. To justify the drop in cyclists, Clarke relies on repurposed cycling counts from helmet use surveys. Standing on a street corner observing helmet use among cyclists is prone to bias when used as a measure of cycling exposure (this makes the Victoria and NSW helmet use surveys problematic if used for that purpose). Data collected in this way does not readily capture recreational cyclists (which is the backbone of Australian cycling) and does not/cannot account for changes in cycling routes or patterns (observation locations are fixed from year to year). It is known that many kids stopped cycling to school in Australia because either their parents or their schools started discouraging it or outright forbade it. This was not due to helmet legislation, although the two issues may share a common causal factor (i.e., parents/society concerned about cycling injury). This did not mean kids stopped cycling after school or on weekends.

Data collected through (stratified) random sampling does not suffer from those problems. The only such surveys in Australia, that I’m aware of around the time of helmet legislation, are from South Australia[1] and Western Australia[2]. Below is a summary of their results for proportion of responses to one of four categories of cycling frequency. (Note these reports do not seem to exist online and I’ve decided to host them on my webpage as I feel very few have ever read them or any other source material.)

 South Australia Western Australia 1990 1993 1989 1993 At least weekly 21.8 21.0 At least weekly 26.6 27.7 At least monthly 5.2 6.0 At least every 3 months 11.1 11.6 At least every 3 months 3.9 4.4 At least once per year 10.3 11.5 Less often or never 69.1 68.6 Never 52.0 49.2

The results indicate no change in cycling in either SA or WA. We also found that to be true for non-head cycling injury hospitalisations in NSW[3]. Neither arm nor leg injuries declined significantly following helmet legislation, and certainly not at the 20% rate cited by Clarke or the 30-40% figure quoted by others. If cycling in NSW dropped substantially after helmet legislation as suggested, I have always wondered why is there no evidence in the census of injury hospitalizations?

Clarke cites two of his own papers to justify his position. The first is a non-peer reviewed conference paper titled Evaluation of Australia’s bicycle helmet laws. I received numerous spam emails about this conference for months. Unfortunately, I get 10+ emails a day for such conferences or predatory publishers asking me to submit ‘my latest research’. Legitimate conferences and publishes do not need to advertise so aggressively.

As with much of his comments about other people’s work, Clarke’s paper is loaded with cherry-picked data and not a shred of statistical/analytic rigor. I’ll detail a few examples.

Figure 3 on page 6 are counts of cyclists from helmet use surveys in Victoria in 1990 and 1991. Back in June 2013, Tim Churches pointed out this figure omits the 1992 data and does not aggregate by age, which is important considering cycling numbers differ substantially across age groups. Below is a plot created using Tim’s R code.

The counts of cyclists for two age groups are virtually identical from 1990 to 1992 (age 5-11 and 18+). The only decline was for 12-17 year olds. If you assume this data is an accurate estimate of cycling exposure (keep in mind I don’t agree with this stance), the cycling decline is age dependent and not true overall.

Clarke also cites a WA report from Heathcote. I could not find a copy of this 1993 report anywhere; however, I did find a 1994 report by the same author[2]. According to 1994 report, the 1993 report concerned helmet use and “recommended the need for further research into cycling trends, and attitudes towards the helmet wearing law”. This was the motivation behind the 1994 report. Therefore, the later report is the more relevant here.

The numbers of recreational cyclists reported by Clarke are not found in the 1994 report; however, Table 8 summarizes Usual Destinations with 21.3% in 1989 and 17.4% in 1993 reporting “To a venue for sport/recreation”. This is not near a 57% reduction in recreation cycling as reported by Clarke and, when taken out of context, ignores that there was no real change in WA cycling frequency as was reported in the same surveys (see above table).

In his Table 13, Clarke reports proportions cycling to work in five year intervals (I discussed problems with how this data is interpreted in a previous post). In addition to the usual problems with this data, Clarke creates additional problems by “estimating” the proportion in 1990. He gives absolutely no justification for this figure except for links to anti-helmet advocacy websites. I guess he could have extrapolated that figure, but such an estimate would be fraught with problems from data taken over three days 5 years apart. Estimating trends from such data completely ignores day-to-day variability.

Clarke also cites his 2012 NZMJ paper. Note I have been critical of this paper on at least four occasions [4-7]. The last citation was a systematic review of the methods used to assess the New Zealand bicycle helmet law. Against quality criteria for assessing a population-based intervention, Clarke’s study scored the lowest of five included studies.

Clarke is quite active on the internet sharing his views on helmet legislation. This includes routine editing of the Wikipedia pages on bicycle helmets under the pseudonym “Colin at cycling” where his contributions have been to promote his NZMJ paper (see the edits page). Although I’m generally supportive of Wikipedia (even contributing money), I find it disturbing anti-helmet advocates like Clarke have taken control of the bicycle helmet content. Like Clarke, they all have conflicts of interest which are never reported (see Dorothy Robinson’s Wikipedia page for a flavor of what’s happened, she has a clear conflict of interest since she essentially promotes her own work and strongly opposes the inclusion of other studies that criticize her work).

If anything, Clarke is steadfast in his beliefs helmets are ‘bad’ and he’s not afraid to share his views. However, I’d be more willing to accept his points if he’d stop cherry-picking data and present a balanced view of the topic. My past experiences with him indicate that is highly unlikely.

1. Marshall, J. & White, M. (1994). Evaluation of the compulsory helmet wearing legislation for bicyclists in South Australia. South Australian Department of Transport, Walkerville, SA.
2. Heathcote, B. & Maisey, G. (1994) Bicyclist use and attitudes to the helmet wearing law. Traffic Board of Western Australia, Perth.
3. Walter, S.R., Olivier, J., Churches, T., & Grzebeita, R. (2011). The impact of compulsory cycle helmet legislation on cyclist head injuries in New South Wales, Australia. Accident Analysis and Prevention, 43, 2064–2071.
4. Olivier, J. (2012) Don’t blame mandatory helmets for cyclist deaths in New Zealand. The Conversation.
5.  Wang, J., Olivier, J. & Grzebieta, R. (2014). Response to ‘Evaluation of New Zealand’s bicycle helmet law’ article. The New Zealand Medical Journal, 127, 106-108.
6. Olivier, J., Wang, J.J.J., Walter, S. & Grzebieta, R. (2014). Anti-helmet arguments: lies, damned lies and flawed statistics. Journal of the Australasian College of Road Safety, 25, 10-23.
7. Olivier, J., Wang, J.J.J. & Grzebieta, R. (2014). A systematic review of methods used to assess mandatory bicycle helmet legislation in New Zealand. Journal of the Australasian College of Road Safety, 25, 24-31.

# Reflections on MJA and Elsevier

Virtually all members of the Medical Journal of Australia (MJA) editorial board have resigned in light of a decision to partner with publishing giant Elsevier to produce future issues of MJA. According to reports, 19 of 20 members of the MJA editorial advisory committee resigned after editor-in-chief Stephen Leeder was sacked. Leeder is quoted as saying dealing with Elsevier was “beyond the reach of my ethical tolerance,” while other members note it was an Elsevier journal that published the now infamous Andrew Wakefield MMR vaccine/autism study and Elsevier in the past created “fake” journals sponsored by drug companies.

This incidence has reminded me of an email exchange and online discussion I had with Jennifer Mindell, editor-in-chief of Elsevier’s Journal of Transport and Health (JTH), and Chris Pringle, an Executive Publisher at Elsevier for Geography & Transport. In my original post, I expressed doubt regarding the legitimacy of JTH as an unbiased source of research as the journal is affiliated with the anti-helmet advocacy group Transport and Health Study Group (THSG).

In her response regarding the debate around bike helmets, Mindell states

“I feel strongly that these issues need to be discussed in a respectful way in a scientific forum, rather than in a series of confidential emails full of allegations or in separate blogs, with difficulty in bringing all the evidence together in one place.”

In a long, detailed email, I detailed how I don’t trust Elsevier or Mindell to handle things in a unbaised manner. Specifically, a journal with ties to an anti-helmet organization should not be the host for the debate.

To perhaps contribute to the discussion around Elsevier and promote transparency, I’ve inserted my full response to Mindell and Pringle below. This was my explanation in regards to me declining an invitation to contribute a bike helmet article to JTH.

Email to Jennifer Mindell and Chris Pringle (16 April 2014)

Jennifer,

Perhaps some more background would help explain our decision not to contribute to the JTH cycle helmets issue.

I became involved in bicycle helmet research around 2010 because a student of mine at the time, Scott Walter, had an interest. Scott is a commuter cyclist (as was I until I needed to take our small child to daycare). Our interest was piqued by a paper by Alex Voukelatos and Chris Rissel in the Journal of the Australasian College of Road Safety (JACRS) and the published criticisms of that paper by Tim Churches. It was clear to us the Voukelatos/Rissel paper was weak because

(1) no statistical analysis was performed (they merely “eyeballed” their incorrectly drawn graphs to reach their conclusions, and unfortunately the human eye is not a well-defined nor reliable statistical procedure),

(2) the numbers literally didn’t add up (as pointed out by Tim, their results were numerically incorrect, as was the time-scale on the graph which formed the entire basis of their analysis, thus they based their conclusions on a graph that showed incorrect numbers at the wrong position on a date axis),

(3) there was a huge discrepancy between head injuries identified by ICD9 and ICD10 indicating incorrect usage of ICD codes (we accept they would likely not be identical, but Voukelatos/Rissel identified over twice as many head injuries using ICD10 than using ICD9 for 1998/99 (511 vs 1170), we were also never able to reproduce the injury counts reported in their paper, there was a clear problem there)

(4) the use of 1988/89 data was problematic as only one diagnosis code existed in the database at that time (so cyclists with both head and arm injuries would only be listed as one – and most likely head instead of arm thereby inflating the 1988/89 head/arm ratio)

(5) there was no comparison to other body parts and no clear justification arm injuries were a good comparator

As I’m sure you are all aware, the Voukelatos/Rissel paper was later retracted by the JACRS. Although there were clear problems with their study, Scott and I felt that the comparison of head and arm injuries over time was an interesting one and could help deal with the lack of exposure data. We were aware of the criticisms of past research on this topic and we felt this strategy had the best chance of addressing those issues in the most rigorous way possible (if the claims by some authors that helmet legislation led to a 30-40% drop in cycling are true, wouldn’t we see a corresponding decline in non-head injury?). This is certainly not a new strategy as psychologists would call the arm injury comparison a dependent, non-equivalent, no treatment control.

Our goal was to correct those issues and present the results as we found them – no matter if they were supportive or not supportive of helmet legislation. In the end, we reported a 29% decline in cycling head injuries (after adjusting for changes in arm and leg injury). Although we found significant declines in cycling head injury at exactly the time of helmet law introduction, we found no significant declines in cycling arm or leg injury at the time of the NSW helmet law commencement. Note that this change corresponded to approximately a 55% increase in helmet wearing. Thus, per “new” helmet wearer, the decline was actually about 0.29/0.55=52.3%. That figure is not unlike what is usually reported in case-control studies of cycling helmet effectiveness.

Note that our conclusion was not that every jurisdiction in the world should have helmet legislation, as reactionary critics have said that our paper recommends, but merely that the calls to repeal helmet legislation in NSW, Australia are not justified by our analysis. How exactly does that make us pro-helmet?

Once our paper was published, our research was attacked by anti-helmet groups like Helmet Freedom (www.helmetfreedom.com) and the Bicycle Helmet Research Foundation (www.cyclehelmets.org – your colleagues Malcolm Wardlaw and John Franklin are both editorial board members), and elsewhere on the blogosphere. It doesn’t seem to matter to these organisations whether their information is correct or not and, in my opinion, they resemble anti-vaccine and climate change denier websites. One site claims we used less than a year worth of data before the law (we had 18 months of data before the law and would’ve gone further back if usable data existed), while another suggested our paper was a government conspiracy to counter de Jong’s cycle helmets cost-benefit paper and Rissel and Wen’s cycle helmet attitudes survey. The latter claim is quite ludicrous considering our paper was published first of the three, and we actually cited a working draft of de Jong’s paper (as it was the only version available to us at the time), and we published a direct response to the Rissel and Wen paper
(http://www.publish.csiro.au/?act=view_file&file_id=HE12076.pdf). After pointing out to Rissel and Wen that they had misinterpreted their own logistic regression results and ignored their own results that run contrary to their conclusions, they state “Olivier et al. are unashamedly pro-helmet advocates,7,8”. The citations are our 2011 paper and Rissel’s rejoinder to our paper.

Rissel’s rejoinder to our 2011 Accident Analysis and Prevention (AAP) paper was published in 2012 in AAP (another Elsevier journal). The journal’s editors, Karl Kim and Rune Elvik, did not offer us the right of reply or even inform us his rejoinder existed. We found out about it after it was published. In his rejoinder, Rissel cites as primary evidence his own already retracted paper discussed above which is, quite frankly, rather bizarre academic behaviour, and in violation of COPE guidelines. The data and analysis used by Voukelatos and Rissel is clearly wrong and I find it troubling that Rissel was allowed to proclaim his conclusions were unaffected by incorrect data (he never corrected the data or the graph used in his analysis, so he had no evidence to even support his claim). Rissel also misquoted figures/analyses from other studies — a 2011 Rune Elvik paper (who was still editor-in-chief of AAP at the time, this is also the meta-analysis paper that has had at least two corrigendums), an assessment of the Western Australia helmet law (Hendrie et al), and an assessment of UK cycling fatalities (Hynd et al).

One of Rissel’s criticisms was we did not share our data. Since Rissel has an appointment with the NSW Ministry of Health, he is keenly aware of the privacy laws governing the sharing of hospitalisation data. Although we had access to unit record data, we were only approved to release the information contained in our paper, nothing more. I also found his request for our data strange considering he had access to the very same NSW hospitalisation data (even if he used it incorrectly in his paper). Our paper clearly listed the ICD9 codes we used, so he could have easily replicated the aggregated data identified from the unit records.

Additionally, Raphael Grzebieta and I had an email exchange with Chris Rissel two weeks before he submitted his rejoinder. Most of the criticisms found in his rejoinder were in his email. I responded in detail why his criticisms were unfounded. Rissel even alludes to this email exchange in his rejoinder where he states

“A somewhat arbitrary 18 months before and after the official start of the mandatory helmet legislation was used as the basis of regression modelling, limited by poor quality data prior to the legislation (Olivier, personal communication).”

This was actually in reference to there being only 18 months of usable NSW hospitalisation data before the helmet law and not hospitalisation data being of poor quality. Note that since our analysis used the same source data as Voukelatos and Rissel, their retracted paper and Rissel’s post-retraction contention the helmet law had no effect
suffers the same problem (as would any assessment of the NSW helmet law). Note that Rissel never received my permission for publishing the contents of our personal email exchange, and we find his failure to take any heed of our detailed response to the criticisms contained in his AAP rejoinder, which he received two weeks prior to submission of the rejoinder article, to be disingenuous in the extreme. Given these types of behaviour, you will understand our reluctance to submit to a journal with him on the editorial board.

Once we were aware of Rissel’s rejoinder and his bad faith in failing to modify his rejoinder in light of our prior correspondence with him, we alerted these and other issues to Karl Kim, Rune Elvik and, eventually, Chris Pringle. Kim and Elvik’s initial reaction was Rissel’s rejoinder should be retracted. However, Elsevier in the end decided not to
and offered us the option of replying to his criticisms which would go out to peer-review. Much of the response had already been written because we had already responded to Rissel through email.

Note that the retracted Voukelatos/Rissel paper is presently hosted by anti-helmet websites (for example, http://www.cycle-helmets.com/rissel.pdf and http://www.cyclehelmets.org/1146.html) without any indication of the retraction. These organisations, including the Bicycle Helmet Research Foundation – again, your colleagues Wardlaw and Franklin are editorial board members, would be in violation of COPE guidelines if they were, in fact, research organisations.

Tim has also made you aware of Elvik’s papers in AAP and Elsevier’s handling of that situation. I find it incredibly strange that the editor-in-chief of a journal can have the key results in a paper corrected in a major way not once, but twice, without having the paper retracted, nor having the paper re-submitted for peer-review, nor even modifying his conclusions or discussion in light of such major calculation errors. The whole episode reflects extremely poorly on Elsevier’s methods and ethical standards as a scientific publisher of repute.

There were also unfounded criticisms made by you, Malcolm Wardlaw and John Franklin in a THSG presentation (see attached [link: http://www.transportandhealth.
Cycling-safety.pptx]). You state you want the discussion of cycle helmets to be “less adversarial” as it “does not allow for defining common ground”, yet your actions indicate otherwise. Much of your presentation on helmets is a criticism of other people’s work. When I came across your presentation, it was clear right away that you had manipulated the axes and scales of a graph from our 2011 AAP paper to make your point (these are both massive no-no’s that are usually taught in introductory statistics courses). However, how was I supposed to react to your unfounded criticisms? You didn’t publish them in a journal or conference proceedings – I downloaded it from the THSG website (was it peer-reviewed?). As a researcher, how am I supposed to address such criticisms? You seem to be displeased I expressed my views about the THSG and JTH openly on my blog, yet isn’t that exactly what you did to our paper? If you don’t agree with my blog entry, you can at least leave a comment. We were not offered that courtesy by you.

In your presentation, you include the plot below. I’ve seen this plot elsewhere on anti-helmet websites. I find it interesting, not for what it presents but what it doesn’t. The effect of a trend is presented, but each point represents observations taken on one day taken five years apart. The information conveyed does not indicate how the weather affected census data done in some years and there’s no information about how modes of transportation are categorised. In earlier censuses, multiple modes of travel including a bicycle leg would be categorised as “cycling”. Yet, later years, the categorisation was by primary mode. So, someone taking the Manly ferry coupled with cycling trips to and from may be included with cycling in some censuses and not in others. It also ignores the fact that 1.14% of trips in Australian cities (where most people live and cycle) were by bicycle in the 1986 survey and this figure changed little (1.13%) by the next one in 1991. These are the two censuses on either side of when most Australians were subjected to helmet legislation. It also ignores declines in other modes of transportation except cars (see attached figure created by Tim Churches). Was helmet legislation also the causal factor for declines in other modes of transport?

I also note that your THSG co-chair and JTH editorial board member Stephen Watkins has stated “Mass helmet use has not reduced serious head injuries to a noticeable degree relative to general improvements in road safety seen for other road users (i.e. secular trends) (http://www.cyclist.ie/wp-content/uploads/2010/11/Transport-Health-Study-
Group-Cycle-Helmets.pdf). Another quote of his is “The most important is that it has been shown in a number of different jurisdictions that compulsory (and enforced) helmet-wearing reduces cycle use.” These statements are interesting when juxtaposed together. I wholly agree that separating out the effect of helmet legislation (or any other
intervention) from secular trends is important. We did just that in our 2011 analysis. However, this rigour never seems to apply to surveys used to draw conclusions about cycling numbers (whether designed for that purpose or not). There were 4 NSW cycling surveys taken in Oct 1990, Apr 1991, Apr 1992 and Apr 1993. The helmet law came
into effect on 1 Jan 1991 (adults) and 1 July 1991 (kids). The adult data, whose overall counts change little over the 4 surveys, is not found in any of Robinson’s work (it effectively doesn’t exist) and she uses only the 1991-1993 surveys for kids. That means only one data point is used pre-helmet law. How can anyone estimate secular trends in cycling from one data point? Two data points isn’t even realistic as only a line can be estimated.

In fact, trend data does exist for Australian metro areas dating back to 1900 (see attached). Cycling mode share increased up to WWII peaking at about 8-9% mode share. This was followed by a steady decline thereafter. The big change in cycling rates came at the expense of car travel and not helmet legislation.

I am confused when you say the THSG is “less likely” to revise their policy as a result of our declining your request to contribute to the JTH helmet issue. Shouldn’t revision of policy happen naturally as more evidence comes to light? Surely the evidence does not have to appear in the JTH in order to be considered by THSG. For example, in reference
of your comment that “many people in public health” believed helmets only protected against “minor issues such as grazes”, a recent article in Accident Analysis and Prevention (http://www.sciencedirect.com/science/article/pii/S000145751400061X) states

“Considering a realistic bicycle accident scenario documented in the literature (Fahlstedt et al., 2012) where a cyclist was thrown at 20 km/h (i.e. 5.6 m/s which corresponds to a drop height of approximately 1.5 m), our analysis indicates that a helmeted cyclist in this situation would have a 9% chance of sustaining the severe brain and skull injuries noted above whereas an unhelmeted cyclist would have sustained these injuries with 99.9% certainty. In other words, a helmet would have reduced the probability of skull fracture or life threatening brain injury from very likely to highly unlikely.”

We also published a paper earlier this year where we found helmets reduced the odds of severe head injury by up to 74% (these were NSW cyclists hospitalised after a motor vehicle crash and reported to the police from 2001-2009). Severe injuries included “Open wound of head with intracranial injury” (S01.83), “Multiple fractures involving skull
and facial bones” (S02.7), “Fracture of skull and facial bones, part unspecified” (S02.9), “Loss of consciousness [30 mins-24hrs]” (S06.03), “Loss of consciousness prolonged without return of consciousness ” (S06.05), “Traumatic cerebral oedema” (S06.1), “Diffuse brain injury” (S06.2), “Other diffuse cerebral & cerebellar injury” (S06.28), “Traumatic subdural haemorrhage” (S06.5), “Traumatic subarachnoid haemorrhage” (S06.6), “Other intracranial injuries” (S06.8), and “Intracranial injury, unspecified” (S06.9). None of these are minor injuries.

One of the main tenet’s of scientific discourse is to re-evaluate one’s position in light of new evidence. Shouldn’t you reflect on the THSG’s policy in light of this and other evidence? Whether we submit an article or not to the JTH?

It takes an awful lot of effort on the part of several researchers, while coordinating everyone’s busy schedules, to produce a high-quality research paper. There has been nothing in my experience with you, the THSG, the JTH or Elsevier that would indicate submitting a “pro-helmet” paper to JTH would be worth the effort. However, I suppose
that could change in light of new evidence

Regards,

Jake

# Psych Journal Bans Hypothesis Testing and Confidence Intervals

In a recent editorial, the scientific journal Basic and Applied Social Psychology have banned submissions that utilize null hypothesis significance testing (NHST) or confidence intervals (CI). Firstly, I can certainly appreciate what motivated the journal’s policy as I routinely read/review manuscripts that solely base decision making on p-values less than 5%, i.e., the (incorrect) belief research findings are important if p<0.05.

For example, I recently read a case-control study of helmet use and bicycle-related trauma by Heng et al.[1] One of their reported measures was alcohol use and they found “[a]lcohol consumption did not correlate with…helmet wearing” and report a p-value of “NS” (as in, not significant). A summary of that data is given below.

 Helmet Use Alcohol Involvement Yes No Yes 0 18 No 17 125

The p-value from this table is certainly greater than 5% by Fisher’s exact test. For a measure of effect size, it isn’t possible to compute an odds ratio in the usual way. Instead, a continuity corrected version can be computed by adding a half to each cell.

$OR_{cc}=\dfrac{(a+0.5)(d+0.5)}{(b+0.5)(c+0.5)}$

The above $2\times2$ table gives a continuity corrected odds ratio of $OR_{cc}=0.19$. In other words, there is an associated 81% reduction in the odds of alcohol involvement among helmet wearers versus those not wearing a helmet in this data set. That is not a trivial result and, perhaps, this is the type of situation the journal is trying to avoid. That is something I fully support.

On the other hand, I believe the journal has over-reached by banning NHST and CI. Granted there are problems with these methods of statistical inference, but I strongly disagree these methods are invalid. Perhaps the strengths and limitations of these methods are poorly understood, but they are certainly not invalid.

The journal does recommend an increased focus on descriptive statistics and correctly note they “become increasingly stable” as sample size increases. Of course, this does rely on descriptive statistics that are unbiased (at least asymptotically), otherwise you’ll get stable estimates that do not reliably estimate what you want estimated.

I also think there is a disconnect between the push for descriptive statistics and the ban on confidence intervals. So, for example, I may be encouraged to report the sample mean and its standard error

$\bar{x}$   and   $\dfrac{s}{\sqrt{n}}$

but I’m banned from combining these results as

$\bar{x}\pm{1.96}\times\dfrac{s}{\sqrt{n}}.$

The American Statistical Association is aware of this situation and has formed a committee to comment on the journal’s decision. I look forward to reading what they come up with.

1. Heng KWJ, Lee AHP, Zhu S, Tham KY, Seow E. (2006) Helmet use and bicycle-related trauma in patients presenting to an acute hospital in Singapore. Singapore Med J 47(5): 367-372.


text:
A YAML based configuration DSL and associated parser/validator.

## Project description

py-yacc
=======

Python implementation of a Yet Another Configuration Compiler.

Why? What about INI, XML, JSON, or plain Python?
------------------------------------------------

Except for XML and Python, the other options offer limited typing options.
XML is cumbersome. Plain Python is not platform independent.

Also, none of these provide solutions for defining configuration requirements.
Not options, requirements: things that must be provided inorder to have a
functional environment. E.g. external resources - databases, hostnames, etc.
that form the backbone of a modern cloud application.

Enter the YACC DSL.

The YACC DSL
------------

At the base is a configuration descriptor. This is a plain old YAML map document with a few additions:

- !spec: used to describe a setting value. It must have description, type, and value.
- !required: used as a value to identify something that MUST BE provided externally,
and validation of compiled parameters WILL fail.
- !optional: used to identify settings that may not be set at all. If not provided externally,
a compiled configuration will not contain this setting.
- !uri: a resource path that can be parsed as a URI. E.g. mongodb://host/db/collection

Example
-------

i_am_a_section:
i_am_a_default_setting: !spec
description: What I am used for
type: !!str ""
value: setting_value
i_am_a_required_setting: !spec
description: I am required by the application, and
I cannot have a default.
type: !!str ""
value: !required "where should I be set."
i_am_another_section:
i_am_a_map: !spec
description: What I am used for
type: {}
value:
some: thing
more: than
a: scalar
i_am_a_list: !spec
description: What I am used for
type: []
value: [ a, b, c]
i_am_a_uri: !spec
description: What I am used for
type: !uri

## Project details

Uploaded source

format: plain


text:
Hybrid Quantum-Classical simulations (QM/MM) with CP2K interface¶

In a molecular mechanics (MM) force field, the influence of electrons is expressed by empirical parameters that are assigned on the basis of experimental data, or on the basis of results from high-level quantum chemistry calculations. These are valid for the ground state of a given covalent structure, and the MM approximation is usually sufficiently accurate for ground-state processes in which the overall connectivity between the atoms in the system remains unchanged. However, for processes in which the connectivity does change, such as chemical reactions, or processes that involve multiple electronic states, such as photochemical conversions, electrons can no longer be ignored, and a quantum mechanical description is required for at least those parts of the system in which the reaction takes place.

One approach to the simulation of chemical reactions in solution, or in enzymes, is to use a combination of quantum mechanics (QM) and molecular mechanics (MM). The reacting parts of the system are treated quantum mechanically, with the remainder being modeled using the force field. The current version of GROMACS provides an interface to the popular Quantum Chemistry package CP2K 188.

Overview¶

GROMACS interactions between the QM and the MM subsystems are handled using the GEEP approach as described by Laino et al. 189. This method of evaluating interactions between the QM and MM subsystems is a variant of the “electrostatic embedding” scheme. The electrostatic interactions between the electrons of the QM region and the MM atoms and between the QM nuclei and the MM atoms are explicitly included into the Hamiltonian for the QM subsystem:

$H^{QM/MM} = H^{QM}_e-\sum_i^n\sum_J^M\frac{e^2Q_J}{4\pi\epsilon_0r_{iJ}}+\sum_A^N\sum_J^M\frac{e^2Z_AQ_J}{e\pi\epsilon_0R_{AJ}},$

where $$n$$ and $$N$$ are the number of electrons and nuclei in the QM region, respectively, and $$M$$ is the number of charged MM atoms. The first term on the right hand side is the original electronic Hamiltonian of an isolated QM system. The first of the double sums is the total electrostatic interaction between the QM electrons and the MM atoms. The total electrostatic interaction of the QM nuclei with the MM atoms is given by the second double sum. An important advantage of using the CP2K/GEEP combination is that it allows evaluation of forces for both QM-QM and QM-MM interactions, in the case of systems with periodic boundary conditions (PBC). To avoid double accounting for electrostatic interactions and LJ, classical MM charge on the QM atoms are zeroed out as well as LJ interactions between QM-QM atoms are excluded. It should be noted that LJ interactions between QM-MM atoms are kept and still calculated by GROMACS. Bonded interactions between QM and MM atoms are described at the MM level by the appropriate force-field terms. All bonds, consisting of 2 QM atoms, angles and settles containing 2 or 3 QM atoms, dihedrals containing 3 or 4 QM atoms are excluded from the forcefield evaluation. Broken chemical bonds between QM and MM subsystems needs to be capped in the QM calculation. This is done within CP2K by adding a hydrogen atom to complete the valence of the QM region. The force on this atom, which is present in the QM region only, is distributed over the two atoms of the bond. The cap atom is usually referred to as a link atom. Within the interface all described topology modifications are performed automatically during gmx grompp pre-processing.

Software prerequisites¶

CP2K version 8.1 (or later) should be linked into GROMACS as libcp2k. For a specific installation instructions please follow the Building with CP2K QM/MM support guide.

Limitations in simulation techniques¶

The QM/MM interface limits simulations in two ways. First, no topology modifications are possible during the simulations in the QM region. Second, interface completely ignores “B” state parameters in the topology, making double topology setups impossible, e.g. free-energy perturbation simulations (Free energy implementation).

In addition it should be noted that the contribution of forces from QM/MM to the system virial are not accounted for. The size of the effect on the pressure-coupling algorithm grows with the total summed force due to QM-MM interactions and might produce artifacts in simulations with the NPT ensemble.

Usage¶

QM/MM simulations with CP2K interface are controlled by setting mdp file options and, in some cases, providing an additional input file for gmx grompp with the -qmi command-line option. All options that are related to QM/MM simulations with CP2K are prefixed with qmmm-cp2k.

Setting qmmm-cp2k-active=true will trigger a QM/MM simulation using the whole system as QM part and default parameters for all other options.

Choosing atoms for QM calculation¶

The QM part of your system is chosen with a name that corresponds to an atom group in the index file of GROMACS to the qmmm-cp2k-qmgroup option in mdp file. The typical QM part should consist of atoms that are interesting from the chemical point of view, i.e. part of the system where reaction happens. To make computation of the QM part feasible, it should be small and as compact as possible in a space. DFT simulations often scale as 3rd order of the number of atoms in the QM part. This means increasing number of atoms in the QM part by a factor of 2 will slow down the simulation by a factor of 8.

In addition user should provide total charge of your QM subsystem with qmmm-cp2k-qmcharge option and spin-state (multiplicity) with qmmm-cp2k-qmmultiplicity option.

Supported QM methods¶

The QM method is chosen with qmmm-cp2k-qmmethod in the mdp file. Currently the following QM methods are supported:

1. qmmm-cp2k-qmmethod=PBE - DFT using PBE functional and DZVP-MOLOPT basis set.

2. qmmm-cp2k-qmmethod=BLYP - DFT using BLYP functional and DZVP-MOLOPT basis set.

That list will be updated with a new methods once they are tested and included into the interface.

Providing your own CP2K input file¶

In addition it is possible to use custom external CP2K input file with qmmm-cp2k-qmmethod=INPUT and providing file with gmx grompp with -qmi option. The external file will be incorporated into the tpr file of the simulation and are subject to the following restrictions:

1. RUN_TYPE option in the CP2K input should be equal to ENERGY_FORCE.

2. CHARGE option should be present.

3. MULTIPILICTY option should be present.

4. COORD_FILE_NAME option should be present pointing towards pdb file.

5. Both CHARGE_EXTENDED TRUE and COORD_FILE_FORMAT PDB options should be present.

6. Incremental includes (@INCLUDE directive) are not allowed in the CP2K input file .

Changing names of CP2K files¶

During gmx mdrun simulation additional files will be produced with .inp, .out and .pdb. They contain CP2K input, CP2K output and pdb file with point charges of MM atoms in the extended beta field. By default all CP2K related files names will be deduced from tpr simulation file name by adding _cp2k suffix. In order to change it manually qmmm-cp2k-qmfilenames option should be used.

Output¶

The energy output file will contain an additional “Quantum En.” term. This is the energy that is added to the system from the QM/MM interactions. In addition, a file containing CP2K output will appear in the simulation directory with the .out extension.

Future developments¶

support of additional DFT methods will be added in the future, as well as semi-empirical and DFTB description of the QM subsystem will be allowed. Support of the multiple time-stepping approach to speed-up simulation will be added. Excited state simulations will be implemented with TD-DFT description of the wavefunction.


text:
# Maxima/Minima

• December 2nd 2008, 05:13 AM
Jen1603
Maxima/Minima
A can of beans has internal radius r and height h. Given that Surface area is S = 2 pi r ( r + h ) and this is equal to 120 pi. Determine r and h such that the volume of beans in the can is a maximum.
• December 2nd 2008, 08:11 AM
Soroban
Hello, Jen1603!

Quote:

A can of beans has internal radius $r$ and height $h.$
Given that surface area is $S \:=\:2\pi r(r + h)$ and this is equal to $120\pi$,
determine $r$ and $h$ such that the volume of the can is a maximum.

We are given: . $2\pi(r^2+rh) \:=\:120\pi \quad\Rightarrow\quad h \:=\:\frac{60-r^2}{r}$ .[1]

The volume of a cylindrical can is: . $V \:=\:\pi r^2h$ .[2]

Substitute [1] into [2]: . $V \;=\;\pi r^2\left(\frac{60-r^2}{r}\right) \quad\Rightarrow\quad V \;=\;\pi(60r - r^3)$

Differentiate and equate to zero: . $V' \;=\;\pi(60-3r^2) \:=\:0$

. . and we have: . $3r^2\:=\:60\quad\Rightarrow\quad r^2 \:=\:20 \quad\Rightarrow\quad\boxed{ r \:=\:2\sqrt{5}}$

Substitute into [1]: . $h \;=\;\frac{60-20}{2\sqrt{5}} \quad\Rightarrow\quad\boxed{ h \:=\:4\sqrt{5}}$


text:
/ MATHEMATICS, STATISTICS, COVID-19, HEALTHCARE

# Bayes' Theorem and the Deathly Hallows

This article is an expanded version of the math part of an article I cowrote with marine biologist Dr. Andrew Rhyne about how many well-meaning public health professionals have misinterpreted the math behind test efficiency, Bayes’ Theorem. This misinterpretation has lead to dangerous public policy positions. Anyone with a math allergy is invited to read that article instead.

I and Dr. Andrew Rhyne, marine biologist and my longtime collaborator in fighting wildlife crime, have spent a lot of time in the last several months working on how best to fight the COVID-19 pandemic, especially in college communities like our own Roger Williams University.

## How understanding Bayes’ Theorem is crucial in informing health policies

Imagine a Venn diagram of intellectual ideas with three overlapping circles as depicted above. The first orange circle represents those ideas that are important for the well-being, smooth functioning, and progression of human society. In this circle, we find the germ theory of disease, the moral imperative of the Golden Rule, and basic arithmetic. The second blue circle represents ideas that are confusing or subtle. The Hegelian dialectic lives here alongside every book with the word semiotics in the title, and the Paradox of Indoor Ornithology, which claims that the sight of a green apple is evidence supporting the notion that all ravens are black ravens.1 If you just said, “What?,” I want to point out that that’s the point: these are difficult, confusing ideas. Finally, we have the circle of ideas that are just too easy to believe one understands when one actually does not. These are ideas that, whether or not they appear simple, have the peculiar ability to lure us into a completely unfounded confidence in our understanding of them. Clearly this circle contains virtually all public political discourse, for example, but it also contains some surprises: Robert Frost’s “Stopping by Woods on a Snowy Evening,” the dangers of quicksand, leprosy, and the inventor of peanut butter, to name a few. You think you know, but google it.

Frightening is the overlapping intersection of these three circles. Here are challenging ideas that are important for human society that we often get wrong while confidently believing we understand. Bayes’ Theorem is one of these ideas.

## The Basics of Bayes’ Theorem

It’s not that Bayes’ Theorem is widely known—it does have “theorem” in its name, after all. But when it is known, it is often misinterpreted or misapplied. Despite mathematical notation that makes it look like an alien language, Bayes’ Theorem is actually quite short and simple:

$\displaystyle P(A\mid B) = \frac{P(B \mid A) \times P(A)}{P(B)}$.

This formula expresses a relationship between four probabilities. It’s best explained with a concrete example, and the subject of this article, testing for disease, is a classic. If we test somebody for, say, COVID-19, then there are four possible scenarios:

Person actually has COVID-19 Person does not have COVID-19
Test result is positive true positive false positive
Test result is negative false negative true negative

A word of warning: It is very easy to mix up these terms. Just keep referring back to this table whenever you need to.

The first thing to understand is this: The probability of having COVID-19 given that you already know the test came out positive, which we will denote by $P(cov\mid pos)$, is a different probability from the probability of the test coming out positive given you have COVID-19, which we likewise denote by $P(pos\mid cov)$. The difference, of course, is what information you already know. The question, “If an animal is in the chicken coup, what’s the probability that it is a chicken?,” $P(chicken \mid coup)$ in our notation, is a different question from, “If the animal is a chicken, what is the probability that it is in the coup?,” $P(coup\mid chicken)$. It could be that my chickens are indoor chickens that never leave the coup, so $P(coup \mid chicken)=100\%$, but I also keep an equal number of turkeys in the coup, so $P(chicken \mid coup) = 50\%$.2

You are now fluent in the alien language that makes up the mathematical notation of Bayes’ Theorem. The power of Bayes’ Theorem is that we can convert from $P(chicken \mid coup)$ into $P(coup\mid chicken)$ using the unconditional probabilities of an animal being a chicken regardless of location, $P(chicken)$, and the probability of an animal being in the coup regardless of species, $P(coup)$. With COVID-19 testing, we can compute the probability that you are infected with COVID-19 given that your test result is positive using knowledge of the probability that you will test positive given that you really are infected:

$\displaystyle P(cov\mid pos) = \frac{P(pos \mid cov) \times P(pos)}{P(cov)}$.

This mathematical trick allows us to determine the relationships between the four scenarios in the table above.

## The Importance of Bayes’ Theorem

It should be obvious that understanding the performance of tests for disease and of drugs with which to treat them is paramount for the prevention and treatment of disease from the individual level to the level of worldwide populations.

As we form policies about testing people for COVID-19, we need to answer these questions: How should the knowledge we get out of Bayes’ Theorem influence our testing strategy for monitoring the population for COVID-19? What policies would be the best use of our limited resources?

## The Paradox of Bayes’ Theorem

What could be so subtle about a simple formula with just four quantities and two arithmetic operations? In short, interpretation. Here is a classic homework problem described by mathematician Chris Wiggins3:

A patient goes to see a doctor. The doctor performs a test with 99 percent reliability—that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only one percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?

The intuitive answer is 99 percent, but the correct answer is 50 percent….

Even with “good” tests, testing positive does not necessarily mean you “probably” have the disease! For this example, the surprising result is because the disease is very rare in the population. When it comes to testing for diseases, the punchline is: There is a higher proportion of false positives relative to true positives when the prevalence of a disease is very low.

## The Deadly Misunderstanding of Bayes’ Theorem

### False Positives

That last sentence is worth repeating:

There is a higher proportion of false positives relative to true positives when the prevalence of a disease is very low.

False positives come with “costs”. If people who test positive but are in reality not infected have to self-quarantine, they could experience a major disruption to their lives, including to their financial and mental health. Citing Bayes’ Theorem, many experts conclude that because COVID-19 is such a low-incidence disease, the cost of whole population testing outweighs the benefits. A logician might structure this argument as follows:

1. The prevalence of COVID-19 is low, perhaps less than 1% in the United States.
2. Since the prevalence of the disease is very low, the proportion of false positives to true positives will be high for any given test.
3. The social and economic cost of false positives is high.
4. Therefore, the cost of large scale testing swamps any possible benefit.

This is a dangerously incorrect mathematical interpretation.

Consider a 99% reliable test as in the classic example above. Suppose we test a town with a population of 10,000 people. If 0.1% of people in town (that’s 1 in 1000) are infected, then 10 people have COVID-19, and our test detects all 10 of them 99 times out of 100 (on average). Meanwhile, the test incorrectly labels 1% of the 9990 remaining people (again, on average), which is about 100 people, as positive.

Will we get significantly fewer false positives if the infection rate is higher, as some experts suggest? Let’s instead suppose that 1% of the people are actually infected—that’s 100 infected people, 10 times more than we thought. Then the test correctly labels 99 of the 100 infected people on average. Of the remaining 9900 covid-free people, 99 people are incorrectly labeled as positive by the test. There are fewer false positives, yes, but fewer only by one person.

The mistake is to think that the quality of testing depends on the prevalence of disease. It doesn’t. The test will be exactly the same regardless of prevalence, because its false positive rate is not affected by prevalence. The test could not possibly be influenced by the state of the population outside of the testing lab.

On the other hand, our testing policies must be informed by the state of the population. A significantly lower prevalence does not result in significantly more false positives as some experts have claimed, and so we shouldn’t care at all that 50% versus 9% of the people who tested positive are actually infected—the “cost” we pay as a population for those false positives is virtually the same as it would be with a much higher rate of infection. Yet the benefit is exponential: We catch infections much sooner, before they have a chance to take root.

We want nobody in the population to be infected, and if nobody is infected, then the only way for a test to turn out positive is if the test is wrong—a false positive. In other words, we want every positive test result to be a false positive—and to keep it that way. Choosing not to test the population at large because the prevalence of disease is low is the equivalent of deciding that you don’t need to take your medication anymore because it is working. The reason you are healthy is because it is working! Many public health specialists are advising schools and employers based on exactly this backwards reasoning.

### False Negatives

Some have argued that we should be concerned instead about false negatives. Suppose, for example, that a test is only capable of identifying an infected sample 50% of the time. That means roughly that every time the population is tested, half of the infected individuals are identified and removed (via quarantine). If removing half of all infected individuals from a college campus sounds like an obviously good idea to you, that’s is because it is. Simple arithmetic shows whole population testing — especially repeated whole population testing — reduces the number of infected individuals in the population. (Sophisticated models do as well: See Larremore et al.; Dawoud, RSAP.)

And yet some health experts like Dr. Tom Jeanne, the deputy epidemiologist for Oregon, justifies his guidance to not employ whole population testing based on the rate of false negatives: “A negative result does not meaningfully increase confidence that a person is not infected,” Jeanne said. “And just as importantly, a negative result does not mean that a person has any period of protection when they are not or cannot be infected” (Murakami, InsideHigherEd). But our inability to certify an individual as disease free with a high degree of confidence is immaterial. Our goal, rather, is to reduce the rate of infection to zero or near zero and then keep it that way.

The discussion so far is based on the premise that tests for COVID-19 have a nonzero false positive rate. Current tests for COVID-19 use a diagnostic technique called qPCR to detect the presence of three distinct genes, a control and two carried by the coronavirus that causes COVID-19.4 In essence, the test makes copies of these genes, if they are present, “amplifies” their presence in the sample, and quantifies the amount of the original gene by measuring this amplification. For this discussion, our only interest is in the presence or absence of the gene. The probability of detecting these genes in people that are notor were not infected by nCOV-SARS-2 is virtually zero. Thus, if the gene is detectable after amplification, it must have been present in the original sample, and the person that sample came from must therefore be infected by the virus. If a gene were somehow constructed by cosmic coincidence, it is possible that the gene would be amplified and detected by the test. But remember, two distinct genes are detected, so a false positive requires not one but two separate cosmic coincidences to occur simultaneously. It is exceedingly rare to have a false positive with the PCR methods developed for this virus. None of the FDA approved tests have false positives. (FDA)

On the other hand, false negatives are possible. For qPCR methods, a false negative occurs when the viral load, that is, the number of viruses in the sample, starts out too low to be amplified sufficiently to be detected (Prinzi, ASM). In the course of a COVID-19 infection, there are two time periods during which the viral load is very low: when the infection has only barely begun, and when the virus has been almost completely wiped out by the body’s immune system. Early in the infection (Kucirka et al, AIM) is the period with the highest likelihood that an infected person will transmit the virus to others. This is also the easiest point in the progression of infection to detect the virus. Thus, false negative rates are tied to infection potential: the higher the potential for spreading the infection, the lower the false negative rate, and vice versa. This situation is exactly why testing populations repeatedly are worthy causes.

What does Dr. Jeanne conclude from this? That because false negative rates are high, the results likely will be wrong, and thus it doesn’t make sense to use tests on asymptomatic people (Murakami, InsideHigherEd). This is not what a high false negative rate means. A test with a high false negative rate might also have an extremely high true positive rate, which is precisely the situation with qPCR tests for COVID-19. Indeed, if almost nobody has a disease, then a test that always gives a negative result no matter what would be correct the vast majority of the time. It simply is not the appropriate measure by which to judge a test in this context.

## The Deadly Misapplication of Bayes’ Theorem

Moreover, when we say the false negative rate is high, we implicitly mean that it is high relative to some other thing and for a specific purpose. If a person is tested every 3 days, and the false negative rate is 70%, then the probability that the person will test positive before or on day nine is 76%. Now, a false negative rate of 70% is very high relative to other tests for other diseases, and for the purpose of testing a person a single time to certify that person as free of disease, the test would be all but useless. But in the context of whole population testing, even a false negative rate as “bad” as 70% is actually pretty good.

This misinterpretation of the significance of Bayes’ Theorem and of false positives and false negatives in particular is not isolated to just one or two public health specialists. I have collected in the table below just a small sampling of different public health authorities that are making this same mistake.

Public health professionals arguing against mass scale testing.

Person / Group Reason for not deploying population scale testing.
Dr. Tom Jeanne, the deputy epidemiologist for Oregon “’A negative result does not meaningfully increase confidence that a person is not infected,’ Jeanne said. ’And just as importantly, a negative result does not mean that a person has any period of protection when they are not or cannot be infected.’"And because the state has only so many tests, he said it doesn’t make sense to use them on asymptomatic people when the results likely will be wrong.”
Michael T. Osterholm, PhD, MPH of University of Minnesota, CIDRAP “Universal testing in hospital settings (not recommended). Universal testing of all patients at the time of admission is of limited value in areas with low prevalence of infection (particularly in the absence of a known exposure) because of the high likelihood of false-positive tests. The lower predictive value of a positive test in this setting makes interpretation of the test result difficult.”

“Workplace testing (not recommended except in certain circumstances). In most situations, workplace testing will not be of value… Owing to uncertainties in test performance in asymptomatic individuals because of low prevalence of infection in the population, the meaning of a positive or negative test result in this situation is not clear.”

“Widespread community-based testing (not recommended). Again, in low-prevalence settings, widespread community testing does not offer a public health benefit because of the varying positive and negative predictive value of the test results.”
American College Health Association “The overall prevalence of COVID in a healthy young adult population is likely to be very low, and probably less than 1%. At this prevalence level, the positive and negative predictive values of most screening tests would be unreliable unless the test used has both extremely high sensitivity and specificity. Many tests available today do not meet that standard.”
“Screening large numbers (thousands) of students will likely produce no substantial public health benefit, and at very high cost.”
Response to our email expressing concern about their approach: “Thank you for reaching out and providing your thoughts. Our brief aligns with current CDC testing recommendations.”
Rhode Island School of Design “Based on our research, as well as consultation with Keeling and Associates, we recommend that RISD focus on the use of diagnostic testing, initiated by symptomatology and/or contact tracing, supported by strict use of quarantine and isolation. Mass testing of asymptomatic people has been proposed by several schools, however we have found that such testing does not have high scientific value, because it provides only a quick snapshot of a current condition, which could change within hours. We also do not recommend surveillance testing, which samples the population to track the presence of the virus, because the rates of false negative/positive results for low-prevalence groups may approach the population disease incidence (~1%).”

## The Mathematician’s Stone

Some widespread claims about population testing are likely to be true. For example, several scientists and public health specialists have pointed out that random population sampling is unlikely to make a significant impact on public health. This claim is backed by strong scientific evidence. There is also near universal agreement that serology (antibody) tests, or any other tests currently available for past or present nCOV-SARS-2 infection, should not be used to clear someone as healthy and therefore safe to join a group. Since these conversations necessarily use a lot of technical language—serology tests, random sampling—it is all too easy for nonspecialists to hear one thing and understand another. It matters a great deal how scientists talk about these technical topics. Scientists need to anticipate sources of confusion, like the difference between sensitivity and specificity, or false positives and false negatives, or random sampling and whole population testing.

It is possible that I am grossly misinformed regarding the characteristics of qPCR testing for COVID-19, or that I am wrong in thinking most people have significant misconceptions about leprosy. But with mathematics, nobody needs to trust what I say is true on my authority as a mathematician. Anyone with sufficient mathematical training can see for themselves. To make it easier for nonscientists to do this kind of verification, I have built an online tool that anyone can use to compute outcomes of interest based on estimates of a test’s performance characteristics that can be adjusted with a slider. The source code is also available on GitHub so that anyone who finds a mistake in the code can report the error or even submit a fix.

I want to be very clear about what I am criticizing in the work of the scientists I have pointed out by name or description. In the case of Oregon’s deputy epidemiology Dr. Tom Jeanne, for instance, it may be the case that Dr. Jeane is right that wide-scale testing is not the right thing for Oregon at this time. There are many factors to consider in making that determination, including test kit availability, test processing capacity, and funding, and it is likely that Dr. Jeane has carefully weighed all of these factors. However, his claim that a high false negative rate means that test results will likely be incorrect or that they make wide-scale testing of little use is wrong as a matter of arithmetic.

## But What If…?

A variety of justifications have been proposed for not implementing whole-population testing. Suppose that the only tests we have access to are not as good as the qPCR methods have been described above.

Problem Remedy
The sensitivity (true positive rate) of the test is low, resulting in many false negatives Test often and reduce the dilution of the samples at collection.
The specificity (true negative rate) of the test is low, resulting in many false positives. Re-test samples that test positive, preferably with a more accurate test. If the population is tested frequently at regular intervals, say, every three days, a person who tests positive might only be asked to quarantine until the next test returns negative. Since the entire population is regularly tested, contact tracing may not be necessary. In some limited circumstances, it might be reasonable only to ask someone who tests positive to follow more aggressive prevention and social distancing practices instead of absolute quarantine until they can be retested.
The prevalence (infection rate) of the disease is extremely low or zero. This is the goal and is not a problem. Keep testing to keep it this way.
We do not have the test processing capacity or number of tests or financial resources necessary to test everybody in the population. Several reports have demonstrated sample pooling as effective in the context of population monitoring for COVID-19. Sample pooling can increase testing capacity by an order of magnitude and reduce costs.
Quarantining and contact tracing are too disruptive or costly or distressing to implement for someone who is a false positive (healthy but tests positive). If you are regularly testing the entire population, there is less need to do contact tracing, because you are already testing the contacts regularly. Reduce false positives by retesting samples that test positive, preferably with a more accurate test. People who test positive can also be tested again after a few days, increasing confidence in the test result.People that are isolated because of contacts with positive people can be tested negative and return to their lives rather than sitting in isolation for two weeks.
Even with mitigation strategies, the test processing capacity is not sufficient to test everyone. Test as many people as you have capacity for on a schedule that will eventually test everyone given enough time. Prioritize the processing of tests of clinical importance, skipping them to the front of the line.

Among the greatest concerns of public health officials regarding whole population testing are the availability and cost of tests and the available capacity to process the tests. At the same time, the benefit of whole population testing is enormous. Resource usage may be a limiting factor in some regions, but sample pooling can potentially magnify the capacity of those resources by an order of magnitude. Performing and processing 2,500 tests a day might be out of reach for a single institution, but 300 or fewer tests required by sample pooling might be feasible, allowing the institution to test everyone on a regular schedule. Over time, test processing capacity is likely to increase (MA High Technology Council, The War on COVID-19: Reducing Rt Deep Dives).

## When not to use whole population testing, and when to stop testing

Despite the mathematical case for whole population testing, there are still valid reasons not to employ wide scale testing of asymptomatic people. There is still an acute shortage of test kits in many regions. Similarly, test processing capacity needs to be ramped up to support large-scale testing. Some institutions might not have sufficient funding for whole population testing in communities that feel the need to accept the risk of reopening without ideal precautions. Some communities may have so much contact with their ambient population that testing the entire community would be futile.

For communities that are good candidates for whole population testing, the argument we are making may sound too aggressive, as if the argument does not allow for the end of testing. The purpose of testing the population is to reduce the prevalence of the disease to zero despite the nonzero prevalence of the disease in the ambient region. Testing can stop

1. when the prevalence of the disease in the region off-campus drops low enough to no longer be a threat to the health and lives of the campus community;
2. when a vaccine is widely available to the campus community;
3. when the region reaches herd immunity.

What should Colleges and Communities do? There is no one-size-fits-all solution. What does seem clear is that unless campuses are willing to take dramatic measures that will be hard for colleges and universities to swallow, the outcome is likely to be grim. We have no choice but to pay a steep price while we wait for the endgame of this pandemic. We can choose to pay the financial costs of investing in the infrastructure and resources for wide-scale testing, or we can save our money and pay instead with the human lives of those that will succumb to the disease we choose not to test for.

Background image credit: Governor Tom Wolf
1. This paradox is more popularly—and more boringly—called the Raven Paradox. Unfortunately, we are no closer to understanding why a raven is like a writing desk.

2. This does not constitute animal husbandry advice.

3. From Chris Wiggins, “What is Bayes’s theorem, and how can it be used to assign probabilities to questions such as the existence of God? What scientific value does it have?” Scientific American, Dec. 2005. Online: https://www.scientificamerican.com/article/what-is-bayess-theorem-an/

4. The technique also detects an additional “control” gene inserted artificially as a baseline comparison for quantitative measurements. For the purposes of the present discussion, we care only about detecting the presence of the virus, not about quantifying viral load.

#### Robert Jacobson

R&D-oriented computer scientist, mathematician, and software engineer with broad experience. I have particular interests in compilers, programming languages, and virtual machines; computer vision and machine learning; and algorithm design and mathematical programming.


text:
Alice led the discussion again this week.  At the end of the session we realised that this will be the last study group for the year due to various people going away for holidays/conferences/meetings in the lead up to christmas and of course the school’s christmas party. We will resume sometime early in the new year.

We first began by discussing the comments on the post on last week’s study group.

Recall from last week how given a building with apartments isomorphic to the Coxeter complex $(W,S)$, we can define the W-distance on chambers. We look again at the chamber system we obtain from the Fano plane.

Let $s_1$ denote differ by a point and $s_2$ denote differ by a line. Let x be the chamber whose line is the orange line and point is the bottom left hand corner of the diagram and y be the chamber whose line is the red line and point is the top of the diagram. Then $\delta(x,y)=s_1s_2=w$. There are four chambers which are neighbours of y. These are $z_1$, which has line the red line and point the point in the middle of the line, $z_2$ which has line the pink line and point the top point,  $z_3$ which has line the orange line and point the top point, and $z_4$ which has line the red line and point the bottom right hand corner.  Then $\delta(y,z_1)=s_1$ and $\delta(x,z_1)=s_1s_2s_1=ws_1$. Also $\delta(y,z_2)=\delta(y,z_3)=s_2$ and $\delta(x,z_3)=s_1=ws_2$ while $\delta(x,z_2)=s_1s_2=w$.  Moroever, $\delta(x,z_4)=ws_1$. Thus we have the property that if $z$ is a chamber such that $\delta(y,z)=s\in S$ then $\delta(x,z)\in\{w,ws\}$ and if $\ell(ws)=\ell(w)+1$,  (where $\ell(g)$ is the length of a reduced expression for g in terms of elements of S), then $\delta(x,z)=ws$.

This motivates the following definition of a building: A building of type $(W,S)$ is a pair $(C,\delta)$ with C a set (whose elements are called chambers) and $\delta:C\times C\rightarrow W$, such that for $x,y\in C$ with $\delta(x,y)=w$ the following hold:

• $w=1$ if and only if $x=y$
• If $z$ is a chamber such that $\delta(y,z)=s\in S$ then $\delta(x,z)\in\{w,ws\}$ and if $\ell(ws)=\ell(w)+1$, then $\delta(x,z)=ws$.
• If $s\in S$ then there exists $z\in C$ such that $\delta(y,z)=s$ and $\delta(x,z)=ws$.

This alternative definition of a building yields a chamber system such that the relations are defined by $x\sim_s y$ if and only if $\delta(x,y)\in\langle s\rangle$.

Alice says that this definition is what she uses in her papers on buildings as this is usually easier to work with than the other two definitions.

Given a subset J of S, the residue of type J, denoted $R_J(c)$, is (using the chamber system definition) the connected component containing c when only taking colours in J. Using the distance W-distance definition, it is the set $\{x\in C\mid\delta(x,c)\in W_J\}$ where $W_J=\langle s\mid s\in J\rangle$.

The usual graph distance between x and y is equal to $\ell(\delta(x,y))$.

Using this definition we have the Gate property: Given $x\in C$ and R a residue, there exists a unique $c\in R$ such that $\ell(x,c)\leq \ell(x,y)$ for all $y\in R$.  Moreover, $\delta(x,y)=\delta(x,c)\delta(c,y)$ and $\ell(x,y)=\ell(x,c)+\ell(c,y)$.  That is there is a  shortest path from x to any $y\in R$ which goes through c. The element c is called the projection of x onto R.

Let $\mathcal{B}$ be a thick building with apartment set $\mathcal{A}$ and let $G\leqslant \mathrm{Aut}(\mathcal{B})$ act strongly transitively on $\mathcal{B}$, that is acts transitively on $\{(A,c)\mid c\in A, A\in \mathcal{A}\}$. Pick one of these pairs $(A_o,c_0)$. Let $B=G_{c_0}$,$N=G_{A_0}$ and $T=B\cap N=G_{A_0,c_0}$, which fixes $A_0$ chamberwise. Then $N/T=G_{A_0}^{A_0}\cong W$. Moreover, $s\in S$ is the reflection of $A_0$ mapping $c_0$ onto its s-neighbour in $A_0$.

Now given $s\in S$ we have $s=nT=Tn$. Moreover, if $nT=n'T$ then $nB=n'B$. Thus $sB$ makes sense and we can also refer to $sBs$, $BsB$ and $BwB$ for any $w\in W$.

Now $G, B, N, S$ have the following properties:

1. $G=\langle B,N\rangle$
2. $T=B\cap N\vartriangleleft N$ and $W=N/T$ admits a set of generators $S$ such that $(W,S)$ is a Coxeter system.
3. $sBs^{-1}\not\subseteq B$ for all $s\in S$, that is, the stabiliser of $c_o^s$ does not stabilise $s_0$. This follows from the thickness of the building.
4. $G=\bigsqcup_{w\in W} BwB$, this is called the Bruhat decomposition of G. Proof: Let $g\in G$. Then there exists an apartment A containing $c_0$ and $c_0^g$. By the strong-transitivity, there exists $b\in B$ mapping $(A,c_0)$ to $(A_0,c_0)$. Let $w=\delta(c_0,c_0^{gb})=\delta(c_0,c_0^g)$. Also $c_0^w=c_0^{gb}$ and so $c_0=c_0^{gbw^{-1}}$, that is $gbw^{-1}\in B$. Hence $gb\in Bw$ and so $g\in BwB$.
5. $P_J$,  the stabiliser of the J-residue, is equal to $\bigsqcup_{w\in W_J} BwB$. Such subgroups are called special subgroups.
6. $BwB BsB=BwsB$ if $\ell(ws)=\ell(w)+1$ and $BwBBsB=BwB\cup BwsB$ if $\ell(ws)=\ell(w)-1$.

Now any group G with subgroups B, N satisfying the above 6 properties (where $P_J$ in 5 is defined as the union instead of as the stabiliser of the J-residue), is called a group with a BN-pair. Equivalently we call $(G,B,N,S)$ a Tits system.

In fact, these 6 axioms are not independent and later it was realised that a group with a BN-pair could be defined by the following:

1. $G=\langle B,N\rangle$
2. $T=B\cap N\vartriangleleft N$ and $W=N/T$ admits a set of generators $S$ such that $sBs^{-1}\not\subseteq B$ for all $s\in S$.
3. $BwBBsB\subseteq BwB\cup BwsB$.

BN-pairs are not unique for a given group G. I suppose an example would be $G=PSp(4,3)=PSU(4,2)$, where the two different interpretations of G as a classical group would give two different buildings for G and so two different BN-pairs. Hopefully Alice can confirm this.

Now starting with a group G with a BN-pair, we can let C be the set of right cosets of B in G.  Then we can define $Bg\sim_s Bg'$ if and only if $P_sg=P_sg'$ where $P_s=B\cup BsB$. (It turns out that the axioms imply that the elements of S are involutions.) This gives a building where one apartment is $A_0=\{Bw\mid w\in W\}$ and the whole set of apartments is $\mathcal{A}=A_0^G$.

Axioms 2 and 3 above imply that $S$ consists only of involutions. Let $s\in S$. First substitute $w=s^{-1}$ in (3). Then $(Bs^{-1}B)(BsB)\subseteq (Bs^{-1}B)\cup B$. Now we can use (2) to see that $(Bs^{-1}B)(BsB)\ne B$ (see what happens otherwise!) and so
$(Bs^{-1}B)(BsB)=(Bs^{-1}B)\amalg B$ (the disjoint union). But we can take inverses of both sides, and we only change the right-hand side:
$(Bs^{-1}B)(BsB)=(BsB)\amalg B$
$Bs^{-1}B=BsB$ and $(BsB)(BsB)=BsB\amalg B$.
Now substitute $w=s$ in (3) and see what happens. Then you end up with
$(BsB)(BsB)=Bs^2B\amalg BsB$. and hence $Bs^2B=B$. Since $BsB\ne B$, it follows that $s$ has order 2 in $W$.