text:
Article Text

Reported awareness of tobacco advertising and promotion in China compared to Thailand, Australia and the USA
1. L Li1,
2. H-H Yong1,
3. R Borland1,
4. G T Fong2,3,
5. M E Thompson4,
6. Y Jiang5,
7. Y Yang5,
8. B Sirirassamee6,
9. G Hastings7,
10. F Harris8
1. 1
VicHealth Centre for Tobacco Control, The Cancer Council Victoria, Melbourne, Victoria, Australia
2. 2
Department of Psychology, University of Waterloo, Waterloo, Ontario, Canada
3. 3
Ontario Institute for Cancer Research, Toronto, Ontario, Canada
4. 4
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada
5. 5
Center for Chronic and Non-communicable Disease Control and Prevention, Chinese Center for Disease Control and Prevention, Beijing, China
6. 6
Institute for Population and Social Research, Mahidol University, Bangkok, Thailand
7. 7
Institute for Social Marketing, University of Stirling, Stirling, UK
8. 8
The Open University Business School, Milton Keynes, UK
1. Dr L Li, VicHealth Centre for Tobacco Control, The Cancer Council Victoria, 100 Drummond Street, Carlton, Victoria 3053, Australia; Lin.Li{at}cancervic.org.au

## Abstract

Background: China currently does not have comprehensive laws or regulations on tobacco advertising and promotion, although it ratified the World Health Organization (WHO) Framework Convention on Tobacco Control (FCTC) in October 2005 and promised to ban all tobacco advertising by January 2011. Much effort is needed to monitor the current situation of tobacco advertising and promotion in China.

Objective: This study aims to examine levels of awareness of tobacco advertising and promotion among smokers in China as compared to other countries with different levels of restrictions.

Methods: One developing country (Thailand) and two developed countries (Australia and the USA) were selected for comparison. All four countries are part of the International Tobacco Control (ITC) Policy Evaluation Survey project. Between 2005 and 2006, parallel ITC surveys were conducted among adult smokers (at least smoked weekly) in China (n = 4763), Thailand (n = 2000), Australia (n = 1767) and the USA (n = 1780). Unprompted and prompted recall of noticing tobacco advertising and promotion were measured.

Results: Chinese respondents reported noticing tobacco advertisements in a range of channels and venues, with highest exposure levels on television (34.5%), billboards (33.4%) and in stores (29.2%). A quarter of respondents noticed tobacco sponsorships, and a high level of awareness of promotion was reported. Cross-country comparison reveals that overall reported awareness was significantly higher in China than in Thailand (particularly) and Australia, but lower than in the USA.

Conclusions: There is a big gap between China and the better-performing countries such as Thailand and Australia regarding tobacco promotion restrictions. China needs to do more, including enhanced policy and more robust enforcement.

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## Statistics from Altmetric.com

Banning tobacco advertising and promotion is an important part of the effort to curb the tobacco epidemic. Comprehensive advertising bans reduce tobacco consumption whereas partial bans have little or no effect.15 Article 13 of the World Health Organization (WHO) Framework Convention on Tobacco Control (FCTC) states that each party to the convention shall “undertake a comprehensive ban or,… restrict tobacco advertising, promotion and sponsorship on radio, television, print media and, as appropriate, other media, such as the internet”.6 Some countries have enacted comprehensive advertising bans and positive impacts have been reported.1 710

The aim of this study was to compare smokers’ awareness of tobacco advertising and promotion in China with levels in Thailand and Australia (countries with strong policies) and with the USA (which has weak policies). This provides an indication of China’s relative progress towards eliminating this activity.

China ratified the WHO FCTC in October 2005, promising to ban all tobacco advertising by January 2011. Like China, Thailand and Australia have ratified the FCTC. The US has yet to ratify the FCTC.

In Thailand substantial tobacco control efforts have been made over the years, including laws and regulations designed to limit access to tobacco products, placing bans on displaying cigarettes and on various advertising, and enhancing pictorial health warnings on cigarette packets.1 8 9 15 16 The Tobacco Products Control Act 1992 comprehensively banned advertising and promotion and made most forms of promotional activities illegal. These restrictions on tobacco marketing have been reasonably well enforced, despite a reported increase in point-of-sale advertising and indirect marketing since 1997.8 9 15

Australia has a well known record on tobacco control, although smoking prevalence is still high among the Aboriginal population.10 17 Considerable progress in banning advertising has been achieved since federal legislation banning direct cigarette advertising on television and radio came into effect with the Australian Broadcasting and Television Act Amendment ACT 1976. Advertising was banned in print media in 1993 and outdoors in 1996. Several states have banned point-of-sale advertising and have considerably limited the number of packs permitted to be displayed.10 1719 Sponsorships of sport and arts were also banned by 1996,19 but exemptions were allowed until 2006 for internationally significant events, most notably Formula 1 Grand Prix motor racing.

The US has fewer restrictions compared to Thailand and Australia. In response to the first Surgeon General’s Report on Smoking and Health, Congress enacted the Cigarette Labelling and Advertising Act in 1965, which required health warnings on all cigarette packages. The 1969 Federal Public Health Cigarette Smoking Act banned advertising of tobacco from television and radio. The 1998 Tobacco Master Settlement Agreement has restricted marketing to some extent.20 21 However, the restrictions were not comprehensive, with many marketing channels open. As a result, the tobacco industry has taken advantage of this and expanded their marketing in areas where it is allowed. In 1999 the overall tobacco advertising expenditures in the US was $8.24 billion, an increase of 22.3% compared with 1998; spending in newspapers increased by 73%, magazines by 34.2% and direct mail by 63.8%.21 22 According to the Federal Trade Commission, total cigarette advertising and promotional expenditures remained as high as$14.15 billion in 2004 and \$13.11 billion in 2005.23

## METHODS

### Sampling design and procedures

The International Tobacco Control (ITC) China Survey is a prospective face to face cohort survey of adult smokers (at least weekly use) and non-smokers conducted between April and August 2006 in 6 cities (800 smokers and 200 non-smokers in each city: Beijing, Shenyang, Shanghai, Changsha, Guangzhou and Yinchuan). These cities were selected based on geographical representations and levels of economic development. Within each city there was a random sample selected using a stratified multistage design. In each of the 6 cities, 10 Jie Dao (street districts) were randomly selected at the first stage, with probability of selection proportional to the population size of the Jie Dao. Within each selected Jie Dao, two Ju Wei Hui (residential blocks) were selected, again using probability proportional to the population size. Within each selected Ju Wei Hui, a complete list of addresses of households was first compiled, and then a sample of 300 households were drawn from the list by simple random sampling without replacement. The enumerated 300 households were then randomly ordered and approached accordingly until 40 smokers and 10 non-smokers were surveyed. Because of low smoking prevalence among women, one male smoker and one female smoker from every selected household were surveyed whenever possible to increase the sample size for women. At most one non-smoker was interviewed per household. Where there was more than one person in a sampling category to choose from in a household, the next birthday method was used to select the individual to be interviewed.

The survey interviewers were trained by staff from local Centers for Disease Control. The average time to complete a survey was about 30 min for smokers and 10 min for non-smokers. Up to four visits to a household were made in order to interview the target person. The wave 1 cooperation rates range from 80% in Beijing and Guangzhou to 95% in Changsha. The response rates range from 39% in Yinchuan to 66% in Guangzhou. A total of 4763 smokers and 1259 non-smokers were included in the analysis. Additional information about the ITC China survey methodology and sampling is available at http://www.itcproject.org.

Thai participants came from the first wave of the ITC Southeast Asia (ITC-SEA) survey, which was conducted in January to February 2005. Respondents were selected based on a multistage cluster sampling procedure. The primary strata consisted of regions. Respondents were selected from Bangkok and two provinces in each of Thailand’s four regions. There was a secondary stratification into rural and urban regions within each province. Subdistricts and communities were selected within urban and rural districts, with probability proportional to population size, for a total of 125 sampling clusters of about 300 households in the whole country. Households were selected within each cluster using simple random sampling until the respondent quota (16 adult smokers) in each cluster was filled. In households with more than one eligible respondent per quota cell, respondents were randomly selected by using a Kish Grid. A total of 2000 smokers were surveyed through face to face interview. A more detailed description of the ITC-SEA study can be found in Yong et al 2008.9

Australia and the USA are part of the ITC Four Country Survey, which has been running annually since 2002. Participants used here were 1767 Australians and 1780 US smokers surveyed in wave 5, conducted from September to December 2006. They were interviewed over the telephone and were recruited by probability sampling methods (random digit dialling methods from list-assisted phone numbers). A detailed description of the ITC conceptual framework, methodology and survey rates has been reported by Fong et al (2006) and Thompson et al (2006),24 25 and more detail is available at http://www.itcproject.org.

### Data analyses

The analyses were conducted on weighted data using SPSS V. 14.0 (SPSS, Chicago, Illinois, USA). Differences between samples were assessed using Pearson χ2 tests and logistic regression models (for categorical variables) and Kruskal–Wallis test for count variables. An α level of p<0.05 was used for all statistical tests.

## RESULTS

### Demographic and smoking related characteristics

Nearly all the Chinese sample (95.2%) were of Han ethnicity. Other sample characteristics are shown in table 1. The respondents were overwhelmingly male, and smoked only factory-made cigarettes (93.8%).

Table 1 Demographic and smoking-related characteristics of the smokers, by country

As in China, the vast majority of the Thai sample were men, while the proportion of male smokers was about 54% in Australia and the US, reflecting the low smoking prevalence among women in China and Thailand. Young people aged 18–24 were notably under-represented in the Chinese and the Thai samples. The age compositions of the Australian and American samples were comparable. Due to the differences in economic development and educational systems across the four countries, only relative levels of income and education were used. The Thai sample had more roll your own smokers especially compared to China and the USA, and the Thais also smoked fewer cigarettes per day.

### Reported awareness of advertising and promotional activities

Without prompting, overall 40.3% of Chinese smokers reported noticing things that were designed to encourage smoking at least once in a while in the last 6 months (table 2). This was significantly higher than that in Thailand (20.2%), Australia (18.9%) and the US (35.5%) (p<0.001). Unprompted recall was higher than for non-smokers (table 3).

Table 2 Awareness of tobacco marketing activities among Chinese smokers (n = 4763), by age
Table 3 Unprompted recall of noticing things that encourage smoking in the last 6 months among Chinese smokers and non-smokers*

For prompted recall, total noticing advertising, sponsorship and promotion in any channel among Chinese smokers was 75.6% with an average of 3.4 (SEM 0.05, table 2) channels noticed, the most common being television (34.5%), billboards (33.4%) and at points of sale (29.2% in stores and 20.3% around street vendors).

Overall, the younger Chinese smokers were more likely to have noticed various marketing activities with the exception of radio where the aged 60 and older were just as likely to notice such activities as the 18–29-year-old group (table 2).

Compared to the other three countries in table 4, the total prompted recall proportion in China (73.4%) was significantly lower than that in the US (95.3%, adjusted odds ratios (AOR) = 9.32, 95% CI 7.19 to 12.07, p<0.001) but much higher than that in Thailand (22.4%, AOR = 0.10, 95% CI 0.09 to 0.12, p<0.001) and somewhat higher than Australia (60.3%, AOR = 0.63, 95% CI 0.54 to 0,73, p<0.001). A similar pattern was evident when using mean number of venues noticing advertisements: highest in the US (89.6%, mean 1.90), followed by China (58.9%, mean 1.34), then Australia (40.2%, mean 0.60) and the least among the Thai (14.5%, mean 0.22). However, when “noticed advertisements in stores” was examined, Australian respondents were more likely to notice advertisement inside the stores than their Chinese counterparts (33.0% vs 29.2%, AOR = 1.18, p<0.05), although still far less than US smokers (p<0.001).

Table 4 Comparison of awareness of tobacco marketing activities, by country

Awareness of sponsorship followed a similar pattern, about a quarter of Chinese smokers reported noticing sport sponsorship and 8.4% reported noticing arts sponsorship, similar levels to Australia (AOR = 1.01, p = 0.89), more than Thailand (AOR = 0.12, p<0.001), while American respondents were more likely to report sponsorship (AOR = 1.27, p<0.01), although not by as much as for other promotional forms.

Overall, 38.5% of Chinese smokers reported noticing any of the five types of promotion, with just over a fifth reported noticing free gifts or special discount offers on other products, and 13.8% reported noticing free samples of cigarettes (table 2). Again, American smokers were the most likely to be exposed to special price offers for cigarettes (71.4%, table 4), followed by respondents in Australia (23%), then Chinese (12.9%) and the least in Thailand (2.5%). For other forms of promotion, a similar pattern was found: US smokers were the most likely to be exposed (82%), with much lower proportions among the Chinese and Australian respondents (36.6% and 31.0%, respectively) and the least among the Thai sample (9.5%).

### Opinions regarding tobacco companies’ advertising and promotion

Figure 1 presents smokers’ attitudes towards tobacco companies’ advertising and promotional activities. Overall, only 18.2% of the Chinese smokers agreed or strongly agreed that tobacco companies should be allowed to advertise and promote cigarettes as they please. The endorsement rates were considerably lower among smokers in Thailand and Australia (5.3% and 13.7% respectively), but markedly higher among smokers in the US (31.5%).

Figure 1

Proportion of smokers agreeing to allow tobacco companies to advertise and promote cigarettes as they please.

## DISCUSSION

This is the first study of which we are aware to assess the extent of tobacco advertising and promotion in China. The results show that most Chinese smokers in the six selected cities frequently reported noticing tobacco marketing activities in various forms and channels, particularly in the media and at points of sale. In addition, there were considerable levels of reported exposure in some other venues, such as on public transport vehicles and at workplaces.

• This paper is the first paper to document Chinese smokers’ reported awareness of tobacco advertising and promotion. It has identified a big gap between China (at least in the six selected cities) and the better-performing countries such as Thailand and Australia regarding effective tobacco promotion restrictions.

• This paper demonstrates the need for China to implement its promise to ban all tobacco advertising by 2011 and suggests that if it is to be maximally effective, it should eliminate existing loopholes and be accompanied by robust monitoring and enforcement.

The main limitation of this study is the use of respondent reports to provide information on exposure to marketing activities. Reported awareness is a function of the presence of the promotional activity, the respondent paying sufficient attention to it to remember it, and being able to retrieve it from memory when asked. While such measures are indirect and imprecise, they have some validity as it has been shown that at least some of these measures are sensitive to changes in policies within countries.7 The recall period is also notional, as most memories of advertisements do not come “time stamped” in memory, so timing will often be guessed. For example, more salient events may be recalled from before the given time window. Similarly, there is likely to be some misremembering of venues or media in which advertisements or other activity was reported. These measures should not be considered to be absolute levels of recall,9 let alone of actual promotional activity, merely as one that should provide reasonable ranking of exposure levels. If there is a systematic bias, it is more likely to be over-reporting in countries where the target advertisements are rare, as those that appear may have increased salience, and underreported where advertisements are common, as they will be more likely to be taken for granted. If this speculation is correct, then the real differences in promotional activities may be even greater than our data suggest.

Other problems are less likely to have had large effects. Since the methods used were not identical in all four countries, it remains possible that some of the differences found are at least partly due to such differences, but we think large effects are unlikely. In China the sample was not a nationally representative sample, unlike the three comparison countries, being restricted to six cities. Also, like Thailand, it under-represented young people. An urban only sample is likely to have higher awareness of forms of promotion that occur most often in towns and cities,9 while the under-representation of young people is likely to reduce estimate sizes as they were more likely to report promotions in most areas. It is also possible that there are effects as a function of mode of surveying (phone versus face to face), but we can think of no strong rationale for any large effect in either direction. Further, this cannot explain any of the differences with Thailand. Any net effect of these differences is likely to be small relative to the large country differences we typically found. That said, care should be taken in interpreting small significant effects, as these could be artefacts of these complex of factors. Particular care should be taken in interpreting demographic difference, where sensitivity to exposure could produce effects independent of actual exposure. We suspect that lower level of interest in tobacco promotions is probably why non-smokers report lower awareness.

It is possible that some of the age effects on noticing promotions are also a function of younger people being more likely to pay attention to, or remember things in their environments, rather than of any selective targeting of them. However, some of the differences found almost certainly reflect real differences in exposure, as the areas where the age differences were greatest (eg, internet, discos) are places where young people are more likely to be exposed. Further, there is evidence that the tobacco industry selectively targets youth in other countries,1 13 20 so it is credible that this also happens in China. While this study is not focusing on young people vulnerable to uptake, it is likely that they will also be reached through promotions in youth-focused venues, suggesting they might be a priority area for tightening restrictions. Point of sale was another area where younger smokers were much more likely to notice things. Here the explanation is less likely to be greater opportunity, but a greater interest in such material. Regardless of the explanation, it is of concern, as young people are priority group to protect from smoking. Comprehensive laws need to reach all these kinds of places.

Compared to the USA, where there are constitutional barriers to fully constraining tobacco promotion, China is doing well, but the comparisons with Australia and particularly Thailand show that there is great potential for improvement. Thai respondents consistently reported very low levels of exposure, either to advertising, sponsorship or to promotion, suggesting well enforced restrictions, as has been reported previously.3 8 9 Australian respondents also reported low awareness, but with higher than desirable levels in stores, sports sponsorship, as well as special price offers for cigarettes. This is consistent with earlier findings of Harris et al7 using the same survey tool 3 years earlier, and reflects gaps that have not yet been closed or, in the case of sponsorship, closed too recently for the memories to have dissipated. Sponsorship of the high profile Formula 1 Grand Prix ended only months before our survey in Australia. It is apparent that where promotion is allowed, or there are opportunities to get around existing laws, the tobacco companies will take advantage of it.

The Chinese government (and other governments) should be reassured by the high levels of support in all countries for restricting advertising. Presumably, smokers realise that smoking is dangerous and don’t want tobacco companies making it harder for them to quit. A recent review of the literature concluded that tobacco promotions encouraged smoking among non-users and increased consumption among tobacco users.26

China can learn a lot from the experiences of other countries, especially those with strong controls on tobacco promotion. What China should be aiming to achieve is a genuine comprehensive ban. Achieving it will require new policies that address the areas that are not covered by the existing laws and regulations, such as outdoor and internet tobacco advertisements, and advertising and promotional activities at workplaces and other public places. It also needs to focus on point of sale. At the same time, China needs to reinforce enforcement of all existing laws and regulations regarding tobacco advertising and promotion, as there are still disturbingly high levels of reported promotions from many of these areas.

In conclusion, there is no doubt that Chinese smokers report higher levels of tobacco promotion in their environments than Australian or particularly Thai smokers. China needs to do more to comprehensively eliminate tobacco promotion to fulfil its FCTC obligations. Models exist, especially in Thailand, of how to do this.

## Acknowledgments

We would like to acknowledge the assistance of Dr Changbao Wu, Dr Anne CK Quah and the other members of the ITC team. We are grateful to the anongmous reviewers who provided useful suggestions on an earlier draft of this paper.

View Abstract

## Footnotes

• LL conducted the literature review, performed the data analysis, wrote most of the initial draft and coordinated input from other authors. H-HY helped to design the analytic strategy, provided input into the initial draft and edited subsequent drafts. RB conceived of the paper and articulated the broad framework for analysis. RB reviewed the data analysis strategy and provided comment on all drafts. GTF helped to design the study, was involved in instigating the study in all jurisdictions and provided detailed edits. MT helped to design the study, provided analytical suggestions and edited the manuscript. YJ and YY helped to design the ITC China survey, supervised the collection and management of the Chinese data and provided comments on drafts as well as ensuring the accuracy of the descriptions of the situation in China. BS supervised collection and management of the Thai data and provided input into the description of the Thai context. GH and FH provided overviews and detail on the arguments about the role of advertising and its measurement and comments on drafts.

• Funding: The research reported in this paper was supported by grants P50 CA111236 and R01 CA100362 (Roswell Park Transdisciplinary Tobacco Use Research Center) from the US National Cancer Institute, Robert Wood Johnson Foundation (045734), Canadian Institutes for Health Research (57897 and 79551), National Health and Medical Research Council of Australia (265903 and 450110), Cancer Research UK (C312/A3726), Canadian Tobacco Control Research Initiative (014578), Center for Behavioural Research and Program Evaluation, National Cancer Institute of Canada/Canadian Cancer Society and Thai Health Promotion Foundation.

• Competing interests: None.

• Ethics approval: Ethical clearance for ITC study has been obtained for all ITC countries. In particular, there was clearance from the institutional review or research ethics boards from the University of Waterloo (Canada), Roswell Park Cancer Institute (USA), University of Strathclyde (UK), the Cancer Council Victoria (Australia), Mahidol University (Thailand) and the Chinese Center for Disease Control and Prevention.

• This is an open-access article distributed under the terms of the Creative Commons Attribution Non-commercial License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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# Could arc reactors eventually be real?

Could arc reactors eventually be real? I have wondered about this, there is not much about it online. If they could how would they work?

-

There are efforts to build small nuclear reactors which we can use in our homes. The effort is to use LENR technology. As for whether arc reactors can eventually be real, then we could wait for engineering innovations and scientific discoveries under the condition that

“All we really need is that one bit of irrefutable, reproducible proof that we have a system that works,” Zawodny said.

The short answer is We don't know yet.

format: plain


text:
Do electrons move in a conductor when it is connected to only one pole of a power supply?

If I were to get a conductor e.g. a piece of copper wire or aluminium and connect it to one pole of a battery (let's take the positive pole for example), will electrons be removed from the conductor forming Cu or Al ions? Or does the flow only start when the circuit is completed?

I think as soon as a pole is connected, some physical change takes place. Let's say you connect both poles, there needs to be a potential difference, and I would think that difference would need to be "felt" by the other side for the electrons to flow. But if the second pole was only connected later, there needs to be a potential difference, so the metal would be charged (or I believe, ionised). Am I right in saying this?

Also, if electrons are flowing through a wire, can you say the wire is ionised, or am I getting this wrong?

• It's impossible. I mean how the current can flow if you are not applying any kind of potential difference along the circuit. The motive of using a battery in a circuit is to maintain a potential difference along it which result in flow of electron and the flow of current. It's not possible to form an ionised metal piece by this method. – Saharsh Jun 6 '14 at 17:46

Let's start from the main question

Do electrons move when only one end/pole of the battery is connected ?

They do! Let's say that you attach a wire to the positive terminal of the battery and this terminal is at "conventional" +5V. Imagine a lot of positively charged particles accumulated there, now electrons would move as near them as possible, creating the same +5V potential throughout the wire.

A very similar effect takes place in the charging of a capacitor by DC source, in that case too the circuit is never completed but we know that charges flow because that's how the capacitor charges.

I could only understand the other question as

Does attaching conductors to battery or other sources of electrical energy ionize them?

It would be wrong to say that something like this happens, because when atoms get ionized they have quite a bit of freedom of movement for example $\text{Na}^+$ and $\text{Cl}^-$ in water are ionized and move freely similarly ions in hot plasma move about freely. While in conductors the concept of free electrons is accepted because electrons rather than completely leaving the atom, get into contact with several atoms and even though they leave a charged specie behind, that specie does not have freedom of movement and hence cannot be called ionized.

• Thanks! About the ion part - I believe I got a little confused about the metallic bonding part. One more Q, are all the electrons of the metal atoms in a metallic bond part of the electron "sea", flowing randomly, or do they still form something similar to shells around the nucleus of the atoms? – baharini Jun 6 '14 at 22:35
• Normally only the outermost electrons participate. I personally have never heard of a case in which "all" electrons of an atom have been involved. – Rijul Gupta Jun 6 '14 at 22:40
• Ok, that certainly makes better sense to me. – baharini Jun 6 '14 at 22:45


text:
# fspl

Free space path loss

## Syntax

`L = fspl(R,lambda)`

## Description

`L = fspl(R,lambda)` returns the free space path loss in decibels for a waveform with wavelength `lambda` propagated over a distance of `R` meters. The minimum value of `L` is 0, indicating no path loss.

## Input Arguments

 `R` Propagation distance in meters `lambda` Wavelength in meters. The wavelength in meters is the speed of propagation divided by the frequency in hertz.

## Output Arguments

 `L` Path loss in decibels. `L` is a nonnegative number. The minimum value of `L` is 0, indicating no path loss.

## Examples

Calculate free space path loss in decibels incurred by a 10 gigahertz wave over a distance of 10 kilometers.

```lambda = physconst('LightSpeed')/10e9; R = 10e3; L = fspl(R,lambda);```

collapse all

### Free Space Path Loss

The free-space path loss, L, in decibels is:

$L=20{\mathrm{log}}_{10}\left(\frac{4\pi R}{\lambda }\right)$

This formula assumes that the target is in the far-field of the transmitting element or array. In the near-field, the free-space path loss formula is not valid and can result in a loss smaller than 0 dB, equivalent to a signal gain. For this reason, the loss is set to 0 dB for range values R ≤ λ/4π.

## References

[1] Proakis, J. Digital Communications. New York: McGraw-Hill, 2001.


text:
Free Version
Easy

# Snake Eyes

COMBIN-PE4C1L

Roll two standard 6-sided dice simultaneously.

What is the probability that we roll two 1's (snake eyes)?

A

$\cfrac{1}{2^6}$

B

$\cfrac{1}{6!}$

C

$\cfrac{2}{6!}$

D

$\cfrac{1}{6^2}$

E

$\cfrac{6}{6^2}$


text:
I’ve made a few violin bows and a couple cello bows. I’m very much a novice bow maker, but I’m learning. As I’m an engineer, I’m naturally trying to apply engineering principles to bow making, which isn’t necessarily easy since violin bows are actually very complex, despite looking quite simple.

The stiffness of a bow affects what the player is able to do with it. If a bow is too stiff, it becomes nearly unplayable; if it’s too soft, they player can’t apply much force to the string before the stick bottoms out and contacts the string (normally the hair of the bow contacts the string). The stiffness affects how much camber the bow maker must add to the stick. The wrong combination of stiffness and camber can lead to a torsional-bending buckling mode, which will make the bow unplayable. The mass and mass distribution of the bow has a large effect on playability. Plus, the aesthetics of the bow are of importance. As I said, a bow is quite complex.

The “standard” wood for making violin bows has been pernambuco for the past 250 years. However, the tree that produces this wood is endangered and hence this wood is difficult to obtain. I’ve been making bows out of other types of wood — mostly ipe and snakewood. In order for a bow made from ipe to have the same stiffness as a bow made from pernambuco, the dimensions need to be altered. Hence, having a good understanding between the taper of the stick and the resulting stiffness is important.

# Taper

Henry Saint-George provides a procedure for calculating the taper of a bow based on measurements of Tourte bows ( SaintGeorge (1896) ). In this procedure, the bow is divided into 12 (unequal) segments. Referring to the figure below (reproduced from Saint-George’s book), line AC is constructed perpendicular to the bow with a length of 110 mm. A second line BD is constructed perpendicular to the stick at the other end. Saint-George indicates that the line BD is 22 mm when the total length (AB) is 700 mm. A compass is used to draw the arc Ce. A line perpendicular to the stick is then constructed starting from point e and terminating at the line CD. The compass is re-set to draw the arc fg and the process is repeated. The points A, e, g, i, k, etc. are the points at which the diameter of the bow is set. At points A and e, the diameter are set equal to one another. At points y and B, they are equal to another fixed value. The diameter at the remaining points are each decremented by a fixed value. But, since those points are not uniformly spaced, the taper is not linear, but instead accelerates along the length of the stick.

This procedure seems quite complicated. However, the keen reader might recognize that the points along the stick form a geometric series. The keen reader may also recognize that the values 22 mm and 700 mm cannot both be taken as fixed: if you change the length of the bow (which affects the slope of the line CD), you also need to change the length of line BD, otherwise the procedure described above will not produce the correct overall length.

The sum of each of these segments is given by:

$$L = \sum_{k=0}^{12} C r^k = C\left(\frac{r^{12}-1}{r-1}\right)$$

Here, the value C is selected as 110 mm and the value of $$r$$ needs to be found based on the value of $$L$$ chosen. This can be done numerically in Python. The following code does that, then computes the points and the diameters of the bow:

import scipy.optimize

length = 700.
length_constant = 110.
d_butt = 8.6

r = scipy.optimize.root(
lambda r: length_constant * (r**12 - 1) / (r - 1) - length,
22
).x[0]
print(f"Found r = {r}\n")

x_points = [0.] * 13
d_points = [0.] * 13

for i in range(13):
if i == 0:
d_points[i] = d_butt
else:
x_points[i] = length_constant * (r**i - 1) / (r - 1)
d_points[i] = d_butt + (d_head - d_butt) * (i - 1.) / 10.
if i == 12:

print(f"x = {x_points[i]:.1f}, d = {d_points[i]:.2f}")

Found r = 0.8741349707251251

x = 0.0, d = 8.60
x = 110.0, d = 8.60
x = 206.2, d = 8.30
x = 290.2, d = 8.00
x = 363.7, d = 7.70
x = 427.9, d = 7.40
x = 484.0, d = 7.10
x = 533.1, d = 6.80
x = 576.0, d = 6.50
x = 613.5, d = 6.20
x = 646.3, d = 5.90
x = 675.0, d = 5.60
x = 700.0, d = 5.60

We can plot the diameter of the stick:

import matplotlib.pyplot as plt

plt.plot(x_points, d_points)
plt.title("Bow Diameter")
plt.xlabel("x")
plt.show()

# Stiffness

## Section Properties

Bows are either (approximately) round or octagonal in cross-section. The area moment of inertia of each of these are as follows ( Oberg et al. (2000) ):

Shape Area Moment of Inertia
Circle $$\frac{\pi d^4}{64} = 0.0490874 d^4$$
Octagon $$\frac{2 d^2 \tan\frac{\pi}{8}}{12}\left[\frac{d^2 \left(1 + 2 \cos^2\frac{\pi}{8}\right)}{4\cos^2\frac{\pi}{8}}\right] = 0.0547379 d^4$$

Of course, when determining the stiffness of the bow, the modulus of elasticity also needs to be known. From my research, the modulus of elasticity of pernambuco is about 30 GPa. From my measurements, the modulus of elasticity of ipe is about 20 GPa.

## Finite Element Method

In order to determine the stiffness of the stick, we’ll use the finite element method with tapered beam elements. This analysis will be done in two dimensions. We’ll define a node at each of the x points found in the previous calculation of bow taper with a tapered beam element connecting adjacent nodes. The diameter (or width across flats in the case of an octagonal cross-section) is known at each of the nodes. Our model will assume that the variation in the diameter is linear between nodes.

The following derivation is based on Chapter 3 from Cook et al. (2001) , but differs since the elements are tapered beams instead of constant section beams.

Each node will have two degrees of freedom: a transverse displacement and a rotation. The degrees of freedom associated with a single element (which connects two nodes) is thus:

$$[d] = \left[ \matrix{ \nu_1 & \theta_1 & \nu_2 & \theta_2 } \right]$$

Some of the algebra that we’ll use in the following derivation gets a bit tedious, so we’ll use the symbolic mathematics package sympy to help us:

import sympy

# Due to the way that my blogging platform works, we need to
# define a new function for printing symbolic math:
def sym_print(x):
print('$${}$$'.format(sympy.printing.latex(x)))

The shape function for our element is a function of the element length $$L$$ and the position along the element $$x$$ and is given by:

L = sympy.var("L")
x = sympy.var("x")

B = sympy.Matrix([[
-6 / L**2 + 12 * x / L**3,
-4 / L + 6 * x / L**2,
6 / L**2 - 12 * x / L**3,
-2 / L + 6 * x / L**2
]])
sym_print(B)

$$\left[\begin{matrix}- \frac{6}{L^{2}} + \frac{12 x}{L^{3}} & - \frac{4}{L} + \frac{6 x}{L^{2}} & \frac{6}{L^{2}} - \frac{12 x}{L^{3}} & - \frac{2}{L} + \frac{6 x}{L^{2}}\end{matrix}\right]$$

For the purpose of stiffness calculations, we’re idealizing the taper of the bow so that within each element the taper is linear. This means that the diameter of the stick at the point $$x$$ is given by the following. Note that in this section, $$x$$ and $$L$$ refer to the distance along the length of the element dn the length of the element, respectively, rather than the dimensions of the bow.

$$d = d_1 + \frac{x}{L}\left(d_2 - d_1\right)$$

where $$d_1$$ and $$d_2$$ are the diameters at nodes 1 and 2, respectively. So that we don’t have to carry around so many variables, we’ll define the variable $$\beta$$ such that:

$$d = d_1 + \beta x$$

As we found earlier, for both circular sections and octagonal sections, the moment of inertia ($$I$$) is a function of $$d^4$$. We’ll define a new variable $$\alpha$$ such that:

$$EI = \alpha d^4$$

Combining the previous two equations and entering this into sympy, we get:

alpha = sympy.var("\\alpha")
d1 = sympy.var("d_1")
beta = sympy.var("\\beta")
EI = alpha * (d1 + beta * x)**4
sym_print(EI)

$$\alpha \left(\beta x + d_{1}\right)^{4}$$

The stiffness matrix for the element is given by:

$$[k] = \int_0^L \left[B\right]^T EI \left[B\right] dx$$

Solving and simplifying this using sympy, we get the following. The stiffness matrix is a 4x4 matrix that is quite complex, so we’ll show one column at a time in this post:

k = sympy.simplify(
sympy.integrate(B.T * EI * B, (x, 0, L))
)

# The first column
sym_print(k[:,0])

$$\left[\begin{matrix}\frac{12 \alpha \left(11 L^{4} \beta^{4} + 49 L^{3} \beta^{3} d_{1} + 84 L^{2} \beta^{2} d_{1}^{2} + 70 L \beta d_{1}^{3} + 35 d_{1}^{4}\right)}{35 L^{3}}\\\frac{2 \alpha \left(19 L^{4} \beta^{4} + 84 L^{3} \beta^{3} d_{1} + 147 L^{2} \beta^{2} d_{1}^{2} + 140 L \beta d_{1}^{3} + 105 d_{1}^{4}\right)}{35 L^{2}}\\\frac{12 \alpha \left(- 11 L^{4} \beta^{4} - 49 L^{3} \beta^{3} d_{1} - 84 L^{2} \beta^{2} d_{1}^{2} - 70 L \beta d_{1}^{3} - 35 d_{1}^{4}\right)}{35 L^{3}}\\\frac{2 \alpha \left(47 L^{4} \beta^{4} + 210 L^{3} \beta^{3} d_{1} + 357 L^{2} \beta^{2} d_{1}^{2} + 280 L \beta d_{1}^{3} + 105 d_{1}^{4}\right)}{35 L^{2}}\end{matrix}\right]$$
# The second column
sym_print(k[:,1])

$$\left[\begin{matrix}\frac{2 \alpha \left(19 L^{4} \beta^{4} + 84 L^{3} \beta^{3} d_{1} + 147 L^{2} \beta^{2} d_{1}^{2} + 140 L \beta d_{1}^{3} + 105 d_{1}^{4}\right)}{35 L^{2}}\\\frac{4 \alpha \left(3 L^{4} \beta^{4} + 14 L^{3} \beta^{3} d_{1} + 28 L^{2} \beta^{2} d_{1}^{2} + 35 L \beta d_{1}^{3} + 35 d_{1}^{4}\right)}{35 L}\\\frac{2 \alpha \left(- 19 L^{4} \beta^{4} - 84 L^{3} \beta^{3} d_{1} - 147 L^{2} \beta^{2} d_{1}^{2} - 140 L \beta d_{1}^{3} - 105 d_{1}^{4}\right)}{35 L^{2}}\\\frac{2 \alpha \left(13 L^{4} \beta^{4} + 56 L^{3} \beta^{3} d_{1} + 91 L^{2} \beta^{2} d_{1}^{2} + 70 L \beta d_{1}^{3} + 35 d_{1}^{4}\right)}{35 L}\end{matrix}\right]$$
# The third column
sym_print(k[:,2])

$$\left[\begin{matrix}\frac{12 \alpha \left(- 11 L^{4} \beta^{4} - 49 L^{3} \beta^{3} d_{1} - 84 L^{2} \beta^{2} d_{1}^{2} - 70 L \beta d_{1}^{3} - 35 d_{1}^{4}\right)}{35 L^{3}}\\\frac{2 \alpha \left(- 19 L^{4} \beta^{4} - 84 L^{3} \beta^{3} d_{1} - 147 L^{2} \beta^{2} d_{1}^{2} - 140 L \beta d_{1}^{3} - 105 d_{1}^{4}\right)}{35 L^{2}}\\\frac{12 \alpha \left(11 L^{4} \beta^{4} + 49 L^{3} \beta^{3} d_{1} + 84 L^{2} \beta^{2} d_{1}^{2} + 70 L \beta d_{1}^{3} + 35 d_{1}^{4}\right)}{35 L^{3}}\\\frac{2 \alpha \left(- 47 L^{4} \beta^{4} - 210 L^{3} \beta^{3} d_{1} - 357 L^{2} \beta^{2} d_{1}^{2} - 280 L \beta d_{1}^{3} - 105 d_{1}^{4}\right)}{35 L^{2}}\end{matrix}\right]$$
# The fourth column
sym_print(k[:,3])

$$\left[\begin{matrix}\frac{2 \alpha \left(47 L^{4} \beta^{4} + 210 L^{3} \beta^{3} d_{1} + 357 L^{2} \beta^{2} d_{1}^{2} + 280 L \beta d_{1}^{3} + 105 d_{1}^{4}\right)}{35 L^{2}}\\\frac{2 \alpha \left(13 L^{4} \beta^{4} + 56 L^{3} \beta^{3} d_{1} + 91 L^{2} \beta^{2} d_{1}^{2} + 70 L \beta d_{1}^{3} + 35 d_{1}^{4}\right)}{35 L}\\\frac{2 \alpha \left(- 47 L^{4} \beta^{4} - 210 L^{3} \beta^{3} d_{1} - 357 L^{2} \beta^{2} d_{1}^{2} - 280 L \beta d_{1}^{3} - 105 d_{1}^{4}\right)}{35 L^{2}}\\\frac{4 \alpha \left(17 L^{4} \beta^{4} + 77 L^{3} \beta^{3} d_{1} + 133 L^{2} \beta^{2} d_{1}^{2} + 105 L \beta d_{1}^{3} + 35 d_{1}^{4}\right)}{35 L}\end{matrix}\right]$$

We can now write a function that outputs the stiffness matrix for a tapered beam element:

import numpy as np

def elm_k(L, d1, d2, alpha):
b = (d2 - d1) / L
return 2 * alpha / (35*L**3) * np.array(
[
[
6*(11*L**4*b**4 + 49*L**3*b**3*d1 + 84*L**2*b**2*d1**2 + 70*L*b*d1**3 + 35*d1**4),
L*(19*L**4*b**4 + 84*L**3*b**3*d1 + 147*L**2*b**2*d1**2 + 140*L*b*d1**3 + 105*d1**4),
6*(-11*L**4*b**4 - 49*L**3*b**3*d1 - 84*L**2*b**2*d1**2 - 70*L*b*d1**3 - 35*d1**4),
L*(47*L**4*b**4 + 210*L**3*b**3*d1 + 357*L**2*b**2*d1**2 + 280*L*b*d1**3 + 105*d1**4)
],
[
L*(19*L**4*b**4 + 84*L**3*b**3*d1 + 147*L**2*b**2*d1**2 + 140*L*b*d1**3 + 105*d1**4),
2*L**2*(3*L**4*b**4 + 14*L**3*b**3*d1 + 28*L**2*b**2*d1**2 + 35*L*b*d1**3 + 35*d1**4),
L*(-19*L**4*b**4 - 84*L**3*b**3*d1 - 147*L**2*b**2*d1**2 - 140*L*b*d1**3 - 105*d1**4),
L**2*(13*L**4*b**4 + 56*L**3*b**3*d1 + 91*L**2*b**2*d1**2 + 70*L*b*d1**3 + 35*d1**4)
],
[
6*(-11*L**4*b**4 - 49*L**3*b**3*d1 - 84*L**2*b**2*d1**2 - 70*L*b*d1**3 - 35*d1**4),
L*(-19*L**4*b**4 - 84*L**3*b**3*d1 - 147*L**2*b**2*d1**2 - 140*L*b*d1**3 - 105*d1**4),
6*(11*L**4*b**4 + 49*L**3*b**3*d1 + 84*L**2*b**2*d1**2 + 70*L*b*d1**3 + 35*d1**4),
L*(-47*L**4*b**4 - 210*L**3*b**3*d1 - 357*L**2*b**2*d1**2 - 280*L*b*d1**3 - 105*d1**4)
],
[
L*(47*L**4*b**4 + 210*L**3*b**3*d1 + 357*L**2*b**2*d1**2 + 280*L*b*d1**3 + 105*d1**4),
L**2*(13*L**4*b**4 + 56*L**3*b**3*d1 + 91*L**2*b**2*d1**2 + 70*L*b*d1**3 + 35*d1**4),
L*(-47*L**4*b**4 - 210*L**3*b**3*d1 - 357*L**2*b**2*d1**2 - 280*L*b*d1**3 - 105*d1**4),
2*L**2*(17*L**4*b**4 + 77*L**3*b**3*d1 + 133*L**2*b**2*d1**2 + 105*L*b*d1**3 + 35*d1**4)
]
]
)

## Stroup Test

The Stroup Test is a way of testing the stiffness of the stick of a bow. In this test, the bow is mounted in a jig that supports the stick on two rollers that are 575 mm apart. A transverse force of 2 lb is applied mid-way between the two rollers and the deflection at the force application point is measured. From what I can tell, there were a small number of people advocating this test some time ago, but it has since become quite uncommon — most makers will assess the stiffness of a stick by feel. However, the Stroup Test can be easily implemented using the finite element method for the purpose of assessing relative stiffness of sticks made from different materials with different dimensions.

## Implementing the Stroup Test

We already have a list of nodal locations. We’ll choose one of these nodes as the location of one of the supports (we’ll use the second last node for this). We’ll need to ensure that there are two other nodes for the load application point and the other support in the correct location. We’ll likely need to create these nodes and sub-divide the existing elements. We can do this in Python as follows:

x_nodes = []
d_nodes = []

x_s2 = x_points[11]
x_s1 = x_s2 - 575
x_l = x_s2 - 575 / 2

nid_s1 = -1  # storage for node ID of support #1
nid_s2 = -1  # storage for node ID of support #2
nid_l = -1   # storage for node ID of load application

tol = lambda xa, xb: abs(xa - xb) < 1e-3
inside = lambda x, xa, xb: (x - xa) * (x - xb) < 0

for x1, x2, d1, d2 in zip(
x_points, x_points[1:], d_points, d_points[1:]):
x_nodes.append(x1)
d_nodes.append(d1)

if tol(x_s1, x1):
nid_s1 = len(x_nodes) - 1
elif inside(x_s1, x1, x2):
x_nodes.append(x_s1)
d_nodes.append(d1 + (x_s1 - x1) / (x2 - x1) * (d2 - d1))
nid_s1 = len(x_nodes) - 1

if tol(x_s2, x1):
nid_s2 = len(x_nodes) - 1
elif inside(x_s2, x1, x2):
x_nodes.append(x_s2)
d_nodes.append(d1 + (x_s2 - x1) / (x2 - x1) * (d2 - d1))
nid_s2 = len(x_nodes) - 1

if tol(x_l, x1):
nid_l = len(x_nodes) - 1
elif inside(x_l, x1, x2):
x_nodes.append(x_l)
d_nodes.append(d1 + (x_l - x1) / (x2 - x1) * (d2 - d1))
nid_l = len(x_nodes) - 1

x_nodes.append(x_points[-1])
d_nodes.append(d_points[-1])

We can now build a stiffness matrix for the model. There are now 15 nodes and each node has 2 DOF, so the matrix will be 30 x 30. We’ll use a sparse matrix. We’ll assume that all elements are round and the material has a modulus of 30 GPa.

k_model= np.zeros((2 * len(x_nodes), 2 * len(x_nodes)))

for i, (x1, x2, d1, d2) in enumerate(
zip(x_nodes, x_nodes[1:], d_nodes, d_nodes[1:])):
# Each element connects the two adjacent nodes
k_elm = elm_k(
L = x2 - x1,
d1 = d1,
d2 = d2,
alpha = 0.0490874 * 30e3
)
for ii in range(4):
for jj in range(4):
k_model[i * 2 + ii, i * 2 + jj] += k_elm[ii,jj]

We can visualize the stiffness matrix. As expected, all of the elements are near the diagonal.

plt.matshow(k_model)
plt.title("Visualization of Stiffness Matrix")

Text(0.5, 1.0, 'Visualization of Stiffness Matrix')

Next, we will create the load vector. This vector will have all elements set to zero except for the entry corresponding to the first DOF of the loading node.

p_model = np.zeros(2 * len(x_nodes))
p_model[nid_l * 2] = -8.9075  # 2 lb in N

Next, we’ll take away the constrained DOFs from the stiffness matrix and the load vector. In our case, those DOFs are the transverse displacement of the constrained nodes.

mask = [i for i, _ in enumerate(p_model)
if i != nid_s1 * 2 and i != nid_s2 * 2]

Now, we can solve for the deflections:

import scipy.linalg
d_const = scipy.linalg.solve(k_const, p_const)

Now, we can add back in the constrained DOFs into the displacement solution. These will be zero because these DOFs were constrained.

d_model = np.zeros(2 * len(x_nodes))

Now, we can plot the results:

plt.plot(x_nodes, d_model[0::2])
plt.grid()
plt.title("Deflection")
plt.xlabel("x")
plt.ylabel("Vertical Deflection")
plt.show()

Stroup values are normally given in thousandths of an inch, which we can calculate as follows:

-d_model[nid_l * 2] / 25.4 * 1000

301.20020904559294

# Conclusion

This blog post describes a way of numerically finding the relationship between the stiffness of a violin bow and its taper. We used the finite element method to do so. I’m planning on developing an online calculator for performing this computation. I plan to use an early version of py-script to do so, but since I’ve never used py-script, it’s possible that it will take a while to figure it out.

### Citations

1. Henry Saint-George. The bow, its history, manufacture & use. “The Strad” Office, 1896. 1
2. Erik Oberg, Franklin Jones, Holbrook Horton, and Henry Ryffel. Machinery's Handbook. Industrial Press, 26th edition edition, 2000. 1
3. Robert Cook, David Malkus, Michael Plesha, and Robert Witt. Concepts and applications of finite element analysis. John Wiley & Sons, fourth edition edition, 2001. 1


text:
# How to calculate $\lim_{x\to \infty} \frac{x+2}{\sqrt{9x^2+1}}$

$$\lim_{x\to \infty} \frac{x+2}{\sqrt{9x^2+1}}$$

What I tried to do was to divide every term my $$x^2$$:

$$\frac{\frac{1}{x} + \frac{2}{x^2}}{\sqrt{9+\frac{1}{x^2}}}$$

Then I calculated the limits of the numerator and denominator separately, which gave:

$$\frac{0}{3}$$

For some reason though, it appears that the right answer is $$\frac{1}{3}$$? Can someone explain me what's wrong with my solution?

• You divided the numerator by $x^2$, but you really divided the denominator by $x^4$. Do you see why? – user296602 Dec 3 '18 at 0:00
• @T.Bongers not really, care to explain? – Trey Dec 3 '18 at 0:01
• What is $\sqrt{x^2}$? – user296602 Dec 3 '18 at 0:03
• (1) It is positive for lage $x$. (2) The limit of the square is easy to compute. – GEdgar Dec 3 '18 at 0:11

Your mistake is that when $$1/x^2$$ passes through a square root it becomes $$\sqrt{1/x^4}$$. You should instead have hit numerator and denominator with $$1/x$$, not $$1/x^2$$.

However, only leading terms matter. As a shortcut, it is perfectly fine (and much quicker) to reason as follows:

$$\lim_{x\to\infty}\frac{x+2}{\sqrt{9x^2+1}}=\lim_{x\to\infty}\frac{x}{\sqrt{9x^2}}=\frac{1}{3}$$

• Although you're right in principle, I think it's worth noting that many of the people who are grading student work at this level would disagree that this is "perfectly fine" without more justification. – user296602 Dec 3 '18 at 0:08
• That's a nice suggestion even if not completely rigorous, in that case I would prefer use the following notation $$\frac{x+2}{\sqrt{9x^2+1}} \sim \frac{x}{\sqrt{9x^2}}\to \frac{1}{3}$$ – gimusi Dec 3 '18 at 0:09
• That notation is fine and I use it myself sometimes. However, I do not believe my suggestion is any less rigorous than any other. It simply presses into service different theorems than that $\lim1/x^n=0$. – Ben W Dec 3 '18 at 0:11
• I suppose you are appling that as equivalents but sometimes equivalents can induce to some mistakes. We need to be careful with that. Of course one expert user csn handle that without problem but a newbie must pat great attention with that. – gimusi Dec 3 '18 at 0:27
• What I was applying was this fact: Let's say that a function $f(x)$ is polynomial-like if it has the form $f(x)=\sum_{i=0}^na_i^{(f)}x^{b_i^{(f)}}$ for real coefficients $a_i^{(f)}$ and an increasing sequence $(b_i^{(f)})_{i=0}^n$ of nonnegative real numbers. Let $r$ and $s$ be positive real numbers, and let $g$ be another polynomial-like function. Then $\lim_{x\to\infty}\frac{[f(x)]^r}{[g(x)]^s}=\lim_{x\to\infty}\frac{[a_n^{(f)}x^{b_n^{(f)}]^r}{[a_n^{(g)}x^{b_n^{(g)}]^s}$. – Ben W Dec 3 '18 at 0:34

HINT

We have

$$\lim_{x\to \infty} \frac{x+2}{\sqrt{9x^2+1}}=\lim_{x\to \infty} \frac x{\sqrt{x^2}}\frac{1+2/x}{\sqrt{9+1/x^2}}$$


text:
## 5.5 Quality of equate groups

Figure 5.4 shows how the passing percentage depends on the child’s D-score as calculated under four models. All models include the same 1339 milestones, but differ in the number of active equates. The grey curve corresponds to the estimate made under the assumption that milestones are equally difficult. Good milestones for bridging instruments will have a tight bundle of curves. For example, equate EXP26 has tight bundles especially in models 1339_11 and 1339_33. By comparison, the curves of the two extreme models vary considerably: the model without any bridges (1339_0) or the model with all bridges (1339_184) are thus less than ideal. The shallow grey curve of model 1339_184 indicates a poorer overall fit.

Outfit and infit statistics measure the residual deviation of the items to the grey curve. High values (e.g. above 1.4) are undesirable and indicate lack of fit to the model. For example, the fit statistics for EXP26 in model 1339_184 (1.70 and 1.25) indicate a mediocre fit, whereas EXP26 in models 1339_33 and 1339_11 fits well. Sometimes the individual item curves are steeper than the grey curve. This indicates that these milestones are more discriminative than the combined item. Model 1339_0 lacks a grey curve and has no fit statistics for equate groups, because in that model, the combined item is not activated.

The probability curves provide a quick visual method for spotting promising and problematic equate groups. Examples of promising equate groups include COG36, FM31, GM26 and GM42. A little more weak are FM26 (has more variability), FM52 (looks promising, but has a problem with the item grigcd402 from the GCDG_JAM_STUNTED cohort), and GM35 (does not align cohort GCDG-ZAF). In such cases, one may wish to move an item out of an equate group, combine equate groups, or inactivate troublesome links.

Until now we only looked at models that include all 1339 items. In practice, we may improve upon the model by selecting the subset of milestones that fit the Rasch model. The next section looks in this modelling step in more detail.


text:
# Sorted list of symbolic eigenvalues (and corresponding eigenvectors)

Is there a way to obtain a sorted list of eigenvalues when they are computed symbolically (in SR). Particularly knowing that in specific points, they can switch order.

So far, what I have is (assuming $R^3$):

def sorted_eval(m, x, y, z, order=0):
_ev = m.eigenvalues()
_ev = numpy.array(ev.subs(x=x, y=y, z=z))
_ev.sort()
return _ev[order]

But then if I want to perform a contour plot:

x, y, z = var('x y z')
p = vector([x,y,z])
f = p * p
h = f.hessian()
contour(lambda x, y: sorted_eval(h, x, y, 0, 0), (x, -1.5, 1.5), (y, -1.5, 1.5))

It takes a long time Thanks D

edit retag close merge delete

Also, in this particular case h is 2 times the identity matrix... and what is ev (maybe from numpy?) and you didn't import numpy... Given the number of other typos, I suspect you had a slightly more complicated setup in mind. Feel free to edit with the *exact* code you used, and we'll give it another shot! :-)


text:
# Expected Goals And Exponential Decay

## Introduction

In my last article on expected goals I showed how to incorporate the distance from goal along the Y axis into the expected goal model using Pythagoras' Thereom.

This all worked pretty well, giving us an r squared value of 0.95. However, while the r squared value was good there was still a flaw in the model we need to fix.

## Better than Ronaldo

Eagle-eyed readers will have noticed that the fit of the curve broke down for very short distances, meaning the probability of scoring from zero metres was actually slightly above one. And as reader Benjamin Lindqvist commented, not even Ronaldo will score more than 100% of the time, not even from the goal line. Benjamin also had a good suggestion to improve this, adding an exponential decay function into the model to make it behave better around zero

## Exponential Decay

If you aren’t familiar with exponential decay it basically means that a value decreases at a rate proportional to its current value. It’s a phenomenon that crops up fairly frequently in science and the natural world. For example, air pressure decays exponentially as you go higher up into the Earth’s atmosphere and radioactivity decreases exponentially over time.

A general equation for exponential decay is shown in Figure 1, where Y(t) is the value at time t, a is the starting value, k is the decay constant and t is time.

$$y(t)=ae^{kt}$$

Figure 1: Exponential Decay

So how do we apply this to football? Well, the first thing to do is replace time with metres and assume that the probability of scoring a goal decreases exponentially based upon the distance from goal the shot is taken from.

Next we need to find the correct value for the decay constant as this controls the shape of the curve. Rather than doing this manually through trial and error, we can use something such as R’s optim function to find it for us. We can also tweak the equation to add in a multiplier for the independent variable and an intercept as found in a traditional regression model giving us the fit shown in Figure 2.

Figure 2: Shots Versus Distance From Goal

Notice how the orange line now hits the Y axis just below 1.0? This fixes the problem we had before where it was possible to score more than one goal from a single shot. In fact, if you’re standing on the goal line the model now predicts around 0.96 expected goals, so very likely to score but with a small chance of screwing up (yes Edin Džeko I’m looking at you).

The new curve fit also pushes the r squared value up to 0.9883, meaning 98.83% of the variance for the probability of scoring from a shot can be accounted for using just distance from goal along the X and Y axes.

The final equation (Figure 3) is slightly more complicated now but it’s still pretty simple to use.

$$expg=e^{-d/4.79}*0.921985+0.036212$$

Figure 3: Expected Goals Equation Incorporating Exponential Decay

where:

$$d=sqrt(dx^2+dy^2)$$

Figure 4: Equation for d

and dx, dy are the difference between the x coordinates and y coordinates in metres for the shot location and the goal location.

As ever, let me know what you think!

OI - April 24, 2014

Two Questions:

-Did you use two different samples for this article and the last one about the y-axis? Some points seem to be relocated from Figure 3 in the last piece to Figure 2 here. For example, there is hardly a difference in scoring probability between 5 and 6 metres distance in the other diagramm, whereas in this diagramm the difference is approximately 5%!

-Are blocked shots included in your calculations?-

Martin Eastwood - April 24, 2014

Yes, in between those articles I increased the number of shots in my database by nearly 25% so hopefully some of the noise for distances where I didn’t have many shots should be smoothed out. Everything categorised as a shot by Squawka is included in the calculation except for penalties and own goals.

Benjamin Lindqvist - April 24, 2014

Hi Martin,

Glad to have been of help. If you’re interested in hearning more negativity, I think your function is now probably overfitted :)

If you have Skype, feel free to add me (benjaminlindqvist). Not all topics regarding football and numbers are suited to the public!

Martin Eastwood - April 25, 2014

Ah the perennial conflict between optimising and over-fitting :)

It’s certainly a risk considering the number of data points I have but I’m not too concerned at the moment as it’s a fairly simple curve rather than some high-order polynomial weaving between the data points. Plus, even though the exponential decay certainly improved the fit the actual expected goal values predicted haven’t really change too much, so in the grand scheme of things any over-fitting probably isn’t having that much of an impact at the moment. It’s certainly something to bear in mind though!

I’ve added you to Skype, would be good to have a chat sometime if you’re free :)

PeP - April 28, 2014

Hi Martin,

I’m very intrigued by your expected goals model and I’m very impressed with the accuracy. Would it be possible to include the Z-axis into your model or is the lack of data holding you back on this.

Martin Eastwood - April 28, 2014

By z axis do you mean location in the goal? If so, then there is no reason it couldn’t be incorporated into the model I just don’t have the data available yet.

PeP - April 28, 2014

I meant at what height the ball is struck from off the pitch. For example if the xy coordinates were kept the same then was the ball struck from off the ground , was the ball struck on the volley or was it an overhead kick.

Benjamin Lindqvist - May 5, 2014

I highly doubt that would be a convex realtionship so that would be hard to fit into this particular model.

Max - May 20, 2014

This is amazing… How did you the power curve? Did you find it by trial and error?

Martin Eastwood - May 20, 2014

No, it was created using mathematical optimisation techniques rather than trial and error as they can do a better job than me!

EV - July 21, 2014

This is an amazing piece of work Martin. And thank you very much for sharing it with us. The effort of gathering the data must have been enormous. I have some questions that will probably be interesting for you:

I assume you group the shot distances into 1m intervals, and got the probability of a goal inside each interval as number of goals / number of shots inside that interval? Then you used some max likehood to fit the curve? However, the number of shots inside each distance interval is different, I’m gussing there were far more shots around 12m than shots around 3m, and probably no shots at 0m, but you would fit a point at (0m,P(goal)=1) for common sense anyway. Does this introduce a bias where some shots are given more weight than others in fitting the curve? So when predicting the total number of goals for a season, this model will be predicting significantly under the actual number of goals? (Because decay constant is too fast due to the heavier weight given to shorter distances)

Is it possible to fit a curve that gives equal weight to each shot? I imagine such a curve is likely to significantly under estimate the probability of scoring from short distances, but will predict season totals more accurately. But the real question is, which curve would predict individual teams’ or even individual matches’ goals more accurately?

Martin Eastwood - July 21, 2014

Hi EV,

Yes the shots are binned by distance so there will be different numbers of shots per game. One way to investigate whether this causes any biases could be to bin by percentiles instead to normalize the bin sizes. Hopefully the fit of the curve will be stable enough that it wouldn’t really affect the results too much but there is only one way to find out…

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# How do you divide  (1-2i) / (6-8i)  in trigonometric form?

Jan 10, 2016

First of all we have to convert these two numbers into trigonometric forms.
If $\left(a + i b\right)$ is a complex number, $u$ is its magnitude and $\alpha$ is its angle then $\left(a + i b\right)$ in trigonometric form is written as $u \left(\cos \alpha + i \sin \alpha\right)$.
Magnitude of a complex number $\left(a + i b\right)$ is given by$\sqrt{{a}^{2} + {b}^{2}}$ and its angle is given by ${\tan}^{-} 1 \left(\frac{b}{a}\right)$

Let $r$ be the magnitude of $\left(1 - 2 i\right)$ and $\theta$ be its angle.
Magnitude of $\left(1 - 2 i\right) = \sqrt{{1}^{2} + {\left(- 2\right)}^{2}} = \sqrt{1 + 4} = \sqrt{5} = r$
Angle of $\left(1 - 2 i\right) = T a {n}^{-} 1 \left(\frac{- 2}{1}\right) = {\tan}^{-} 1 \left(- 2\right) = \theta$

$\implies \left(1 - 2 i\right) = r \left(C o s \theta + i \sin \theta\right)$

Let $s$ be the magnitude of $\left(6 - 8 i\right)$ and $\phi$ be its angle.
Magnitude of $\left(6 - 8 i\right) = \sqrt{{6}^{2} + {\left(- 8\right)}^{2}} = \sqrt{36 + 64} = \sqrt{100} = 10 = s$
Angle of $\left(6 - 8 i\right) = T a {n}^{-} 1 \left(\frac{- 8}{6}\right) = T a {n}^{-} 1 \left(- \frac{4}{3}\right) = \phi$

$\implies \left(6 - 8 i\right) = s \left(C o s \phi + i \sin \phi\right)$

Now,
$\frac{1 - 2 i}{6 - 8 i}$

$= \frac{r \left(C o s \theta + i \sin \theta\right)}{s \left(C o s \phi + i \sin \phi\right)}$

=r/s*(Costheta+isintheta)/(Cosphi+isinphi)*(Cosphi-isinphi)/(Cosphi-isinphi

$= \frac{r}{s} \cdot \frac{\cos \theta \cos \phi + i \sin \theta \cos \phi - i \cos \theta \sin \phi - {i}^{2} \sin \theta \sin \phi}{{\cos}^{2} \phi - {i}^{2} {\sin}^{2} \phi}$

$= \frac{r}{s} \cdot \frac{\left(\cos \theta \cos \phi + \sin \theta \sin \phi\right) + i \left(\sin \theta \cos \phi - \cos \theta \sin \phi\right)}{{\cos}^{2} \phi + {\sin}^{2} \phi}$

$= \frac{r}{s} \cdot \frac{\cos \left(\theta - \phi\right) + i \sin \left(\theta - \phi\right)}{1}$

$= \frac{r}{s} \left(\cos \left(\theta - \phi\right) + i \sin \left(\theta - \phi\right)\right)$

Here we have every thing present but if here directly substitute the values the word would be messy for find $\theta - \phi$ so let's first find out $\theta - \phi$.

$\theta - \phi = {\tan}^{-} 1 \left(- 2\right) - {\tan}^{-} 1 \left(- \frac{4}{3}\right)$
We know that:
${\tan}^{-} 1 \left(a\right) - {\tan}^{-} 1 \left(b\right) = {\tan}^{-} 1 \left(\frac{a - b}{1 + a b}\right)$

$\implies {\tan}^{-} 1 \left(- 2\right) - {\tan}^{-} 1 \left(- \frac{4}{3}\right) = {\tan}^{-} 1 \left(\frac{\left(- 2\right) - \left(- \frac{4}{3}\right)}{1 + \left(- 2\right) \left(- \frac{4}{3}\right)}\right)$

$= {\tan}^{-} 1 \left(\frac{- 6 + 4}{3 + 8}\right) = {\tan}^{-} 1 \left(- \frac{2}{11}\right)$

$\implies \theta - \phi = {\tan}^{-} 1 \left(- \frac{2}{11}\right)$

$\frac{r}{s} \left(\cos \left(\theta - \phi\right) + i \sin \left(\theta - \phi\right)\right)$

$= \frac{\sqrt{5}}{10} \left(\cos \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right)\right)$

$= \sqrt{\frac{5}{100}} \left(\cos \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right)\right)$

$= \sqrt{\frac{1}{20}} \left(\cos \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right)\right)$

$= \frac{1}{2 \sqrt{5}} \left(\cos \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right)\right)$

You can also do it by another method.
By firstly dividing the complex numbers and then changing it to trigonometric form, which is much easier than this.

First of all let's simplify the given number
$\frac{1 - 2 i}{6 - 8 i}$.

Multiply and divide by the conjugate of the complex number present in the denominator i.e $6 + 8 i$.

$\frac{1 - 2 i}{6 - 8 i} = \frac{\left(1 - 2 i\right) \left(6 + 8 i\right)}{\left(6 - 8 i\right) \left(6 + 8 i\right)} = \frac{6 + 8 i - 12 i - 16 {i}^{2}}{{6}^{2} - {\left(8 i\right)}^{2}}$
$= \frac{6 - 4 i + 16}{36 - \left(- 64\right)} = \frac{22 - 4 i}{36 + 64} = \frac{22 - 4 i}{100} = \frac{22}{100} - \frac{4 i}{100} = \frac{11}{50} - \frac{i}{25}$

$\frac{1 - 2 i}{6 - 8 i} = \frac{11}{50} - \frac{i}{25}$

Let $t$ be the magnitude of $\left(\frac{11}{50} - \frac{i}{25}\right)$ and $\beta$ be its angle.

Magnitude of $\left(\frac{11}{50} - \frac{i}{25}\right) = \sqrt{{\left(\frac{11}{50}\right)}^{2} + {\left(- \frac{1}{25}\right)}^{2}} = \sqrt{\frac{121}{2500} + \frac{1}{625}} = \sqrt{\frac{121 + 4}{2500}} = \sqrt{\frac{125}{2500}} = \sqrt{\frac{1}{20}} = \frac{1}{2 \sqrt{5}} = t$
Angle of $\left(\frac{11}{50} - \frac{i}{25}\right) = T a {n}^{-} 1 \left(\frac{- \frac{1}{25}}{\frac{11}{50}}\right) = {\tan}^{-} 1 \left(- \frac{2}{11}\right) = \beta$

$\implies \left(\frac{11}{50} - \frac{i}{25}\right) = t \left(C o s \beta + i \sin \beta\right)$

$\implies \left(\frac{11}{50} - \frac{i}{25}\right) = \frac{1}{2 \sqrt{5}} \left(C o s \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right) + i \sin \left({\tan}^{-} 1 \left(- \frac{2}{11}\right)\right)\right)$.


text:
# Paper Summary - Explainable Reinforcement Learning Through a Causal Lens by Madumal et. al. (2020)

Madumal, P., Miller, T., Sonenberg, L., & Vetere, F. (2020, April). Explainable reinforcement learning through a causal lens. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 34, No. 03, pp. 2493-2500).

## My Objectives

To learn about a specific approach which generates explanations for decisions made by RL agents and use it for my own project.

## Paper Summary

This paper tries to develop an algorithm to generate explanations for decisions made by RL models. It introduces a new model based on structural causal equations which can be trained alongside the original RL model. This model approximates the policy of the original model. The paper presents algorithms to train this model and use it to generate explanations and perform task prediction. The authors evaluate the task prediction accuracy of this model. The authors perform a human subject study to evaluate the explanations generate by their model. They evaluate explanation satisfaction, accuracy of task prediction by the test subjects, and trust in the agent.

## Methodology

The paper introduces a new model to approximate the policy of a model-free RL agent called an action influence model. This model is inspired by structural causal equations and is designed to represent causal relationships between state variables in terms of actions i.e., how do actions influence the environment. This is basically equivalent to having an environment model, although the paper acknowledges this and mentions that the objective is to merely learn an approximation good enough for explanations. The environment model is necessary to provide counterfactual explanations - answering “Why not action B?” instead of just “Why action A?”. The authors claim this makes for better explanations for humans.

I will intentionally try to be less formal and not use mathematical formalisms to describe the concepts presented in the paper.

### Action Influence Model

The action influence model can be visualized as a DAG with nodes as the state variables and edges as the structural equation associated with an action. This structure represents how the state variables are causally related to each other. The sink nodes represent state variables which directly contribute to the agent’s utility function. The source nodes, I believe, are what the authors call exogenous variables - representing external factors, but I’m not sure what a concrete example of this would be. The edges are labelled by an action and represent the set of structural equations which govern how the variable at the edge head changes under the influence of the variable at the edge tail when the action in the edge label is applied. More formally, if we have an edge $(X) \xrightarrow[]{A_s}(Y)$, then we will have a structural equation of the form $Y = f_{A_s}(X)$. This equation is learned using traditional function approximators like linear regression, decision trees and MLPs.

To make this description more concrete, I will try to explain it in terms of Figure 1 from the paper. The figure represents an action influence model learned in a StarCraft II domain. We can see the DAG of the state variables represented. The sink nodes $D_u$ and $D_b$ directly contribute to the agent’s utility function. The edge labelled $A_s$ connects node $W$ to node $B$ and would contain a set of equations which describe how $B$ changes w.r.t $W$ when the action $A_s$ is taken.

It is important to note that the structure of the DAG is not learned but is created by hand. I think this has some important implications for how generalizable this technique is. The authors do not describe the design challenges of coming up with a useful DAG.

### Learning Structural Equations

The structural equations are learned from a dataset of experience frames. During the training of the original agent (for whose decisions the action influence model will provide explanations), we must generate records of the form $(s_t, a, r, s_{t+1})$, where $s_t$ is the state at time $t$, $a$ is the action taken by the agent, $r$ is the rewards obtained and $s_{t+1}$ is the successor state. This dataset can be generated during training (as in experience replay) or presumably post-training as well by executing the agent in an environment.

Given this dataset and the action influence model DAG, we use any function approximator to learn, for every edge $(X) \xrightarrow[]{A_s}(Y)$, the function $Y = f_{A_s}(X)$. The paper does this in minibatches drawn uniformly from the dataset. It uses as function approximators regression learners, decision trees and MLPs.

### Explanation Generation

This model generates local explanations i.e., explanations for a single decision taken by the agent (as opposed to global explanations which explain the overall policy of the agent). Given an action influence model $M$ and an agent action $a$ (and given instantiations of the state variables), we locate all edges in $M$ which are labelled with $a$ and find their head nodes. Starting here, we follow the causal chain till we reach the sink nodes. An explanation as defined in the paper is the set of ancestors of the reached sink nodes, and the set of head nodes. This is basically the immediate reason for doing an action and the immediate causes of rewards. This serves to heuristically simplify an explanation instead of providing the entire causal chain.

Perhaps a model of the explainee could serve to guide how to present the causal chain as an explanation.

It seems the explanation is only defined in terms of the causal DAG, which has to be hand-designed. The structural causal equations serve only to quantify how much an action influences a causal relationship between two state variables, and this information is not used in the explanation. I wonder if adding this information would improve the explanation. As it stands, all informtion used in the explanation comes from the hand-written causal DAG alone. Every action can be assumed to have some influence i.e. we can label an edge in the causal DAG with every possible action, and learn separate sets of structural causal equations for each of them.

### Counterfactual Explanation Generation

A counterfactual explanation is the explanation of “Why not B?” given a decision A taken by the agent. A counterfactual explanation as defined in the paper is, given a model $M$, an action $a$ and a counterfactual action $b$, the difference between the causal paths taken from the head nodes of edges labelled $a$ and $b$. Basically, we follow the process of generating explanations for $a$ and $b$ using $M$ and return their difference.

This model can perform task prediction i.e., the task of predicting the action that would be selected by an agent given the current state $s_t$. To do this, it uses every structural equation that applies to an action in order to predict the successor state. Recall that a structural equation $Y = f_{A_s}(X)$ gives us the change in $Y$ in terms of $X$ when an action $A_s$ is applied. We are in fact getting the value of $Y_{t+1}$ from $X_t$. If we obtain the changes in all state variables using all the structural equations that apply to $A_s$, we can obtain a complete description of the successor state $s_{t+1}$. Of course, this will be a prediction made by the model. We need to use this prediction to also predict the action that would have been taken by the original model.

It does so by computing the delta between the predicted successor state and the actual successor state. It selects the action whose structural equation has the highest difference between the predicted state variable value and the actual value i.e., it selects $\underset{A_s}{\operatorname{arg max}} f_{A_s}(X_{t+1}) - Y_{t+1}$ where $f$ represents the set of all structural equations in the action influence model.

This way of doing task prediction seems incorrect for two reasons -

1. Task prediction takes as input only the current state. Its output is a prediction of what the action the original model selects would be. This algorithm requires the actual successor state as input, which should be hidden from the algorithm.
2. Selecting the action which has the maximum difference between predicted successor state variable and actual successor state variable seems like selecting the worst possible action. Wouldn’t a better way of doing this be to predict an entire successor state, obtain a measure of the delta between the predicted and actual successor, and select the action with minimum delta? The explanation for this method in the paper seems unconvincing -

This is informed by the reasoning that the agent will try to follow the optimal policy, and the action with the biggest impact to correct the policy will be executed. The impact is measured by the above mentioned difference. This is itself an approximation, but is a useful guide for task prediction.

### Computational Evaluation

The paper presents a computational evaluation of the action influence model using task prediction for several RL benchmarks. It calculates the model’s accuracy and runtime. It performs reasonably well, although these metrics are not too valuable for its purpose. The benchmarks also have small action spaces, which might misrepresent the capabilities of the algorithm.

## Experimental Setup

The paper hypothesizes two things -

1. Causal-model-based explanations build better mental models of the agent leading to a better understanding of its strategies.
2. Better understanding of an agent’s strategies promotes trust in the agent.

The authors use StarCraft II as their testbed. They use a reduced version of it with smaller action and state spaces. To test $H_1$, they use task prediction. They use a 5-point Likert scale to measure explanation satisfaction and trust ($H_2$).

The human subject study uses a 22 min. gameplay video of the RL agents (including baselines) playing against the in-game bot. The participants were sourced from Amazon Mechanical Turk. The study consists of 4 phases -

1. Collecting demographic information and training the participants to differentiate the agents’ actions. Demographic information included sex, age self-rated gaming and StarCraft 2 experience.

The authors did not run a Chi-squared test for independence of each demographic variable, as in Lage et. al. (2019). As I didn’t understand why it was done in that paper, I cannot judge whether it should have been done here.

1. Gathering data for the explanation satisfaction survey by allowing subjects to query for “Why/Why not?” explanations from 5 different 15 sec. gameplay clips.
2. Gathering data for task prediction. The tasks being predicted are divided evenly between tasks which are similar to those the subjects were trained with, and novel tasks (in terms of the causal chain involved). Scores were given for correct, incorrect and “I don’t know” responses and tallied.
3. Gathering data for the trust survey.

The authors describe how they avoided noise in the dataset and controlled for language by only recruiting participants from the US.

The independent variables of the experiment are the techniques used to generate explanations, including one prior work. The four different models are -

1. No explanation (N)
2. template 1 of Khan, Poupart, and Black (2009, p.3) (R)
3. action influence model with detailed explanations (using atomic actions in the causal graph) (D)

1. (presumably) the original action influence model (C)

It is unclear how Phase 2 of the study would work for subjects assigned to explanation techniques other than action influence models.

## Results & Analysis

The null hypothesis was $\mu_C = \mu_R = \mu_D = \mu_N$. The alternative hypotheses were -
$H_1$: $\mu_C \geq \mu_R$
$H_2$: $\mu_C \geq \mu_D$
$H_3$: $\mu_C \geq \mu_N$

Basically, the proposed model was expected to outperform the other models when it came to task prediction scores obtained when the subjects used its explanations. A one-way ANOVA was conducted, and a significant p-value was obtained. Tukey multiple pairwise comparisons was used to obtain significances of differences between groups, and the obtained p-values were significant.

Correlation between the number of questions and the score was not significant.

Differences between the groups remained significant when accounting for only correct answers, only incorrect answers, and only “I don’t know answers”.

I’m not sure how exactly this division was accounted for.

Pearson’s Chi-Square was done as a non-parametric test on task prediction scores, and it showed significant results.

I’m not sure what the purpose of this test is here.

The explanation quality data is analysed using a pairwise ANOVA, and the model outperforms the other on all metrics except “Understand”.

The metrics are not sufficiently explained in terms of how the questions were presented to the subjects. How were explanations of the ‘No explanation’ model presented? Lastly, Table 3 does not report the differences with the detailed action influence model explanations (D).

The data on trust was similarly analysed using the metrics confident, reliable, predictable and safe. These were not statistically significant.

Here, too, it isn’t clear in what sense these metrics are presented. What is being measured when a subject is asked to rate the safety or reliability of an agent? Are the subjects’ notions of these terms consistent?

A Pearson’s correlation test was run to check for correlation between self-reported StarCraft II experience and task prediction scores. No significant correlation was found. The authors hypothesize that it could be because the reduced version of StarCraft II used as a testbed is sufficiently different that external experience couldn’t influence the results.

The authors acknowledge the strong linearity assumption made for StarCraft II allowing linear regression to learn SCMs.

## Discussion

The authors reiterate the paper’s contributions and briefly acknowledge the limitation that the causal model must be provided beforehand. They mention using explainee models to target explanations and adapting their model for continuous state variables (the ones in the StarCraft II domain were discrete).

## Impressions

This is an interesting paper and has a nice attempt at explanation generation for RL agents. I believe the issue of requiring a causal model is significant, and it deserved more explanation in the paper. How do we design a causal model for a different domain? It requires some amount of expert knowledge, which is precisely what model-based RL agents try to learn themselves. Perhaps this technique could be adapted to model-based RL agents: namely approximating their model using an action influence model and using the latter to generate explanations. I’m not sure why the paper restricted itself to model-free agents.

The action influence model also seems limited in its ability to represent the causal structure of a domain. It uses a DAG, which does not account for cyclic dependencies in domains (could one exist?). The authors acknowledge that the use of linear regression does not account for non-linear relationships between state variables, but I believe that could be solved by using a non-linear function approximator.

Lastly, the usage of satisfaction and trust metrics to measure explanation quality seems to incentivize explanations which sound good to humans but may not give them a good idea of how the agent works. Task prediction accuracy is a better metric, but then that constrains the model to be simulatable by a human, which is a big limitation. Perhaps a compromise would be accepting a certain score threshold.

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# 7.9 *extended topic* microscopy enhanced by the wave characteristics

 Page 1 / 8
• Discuss the different types of microscopes.

Physics research underpins the advancement of developments in microscopy. As we gain knowledge of the wave nature of electromagnetic waves and methods to analyze and interpret signals, new microscopes that enable us to “see” more are being developed. It is the evolution and newer generation of microscopes that are described in this section.

The use of microscopes (microscopy) to observe small details is limited by the wave nature of light. Owing to the fact that light diffracts significantly around small objects, it becomes impossible to observe details significantly smaller than the wavelength of light. One rule of thumb has it that all details smaller than about $\lambda$ are difficult to observe. Radar, for example, can detect the size of an aircraft, but not its individual rivets, since the wavelength of most radar is several centimeters or greater. Similarly, visible light cannot detect individual atoms, since atoms are about 0.1 nm in size and visible wavelengths range from 380 to 760 nm. Ironically, special techniques used to obtain the best possible resolution with microscopes take advantage of the same wave characteristics of light that ultimately limit the detail.

## Making connections: waves

All attempts to observe the size and shape of objects are limited by the wavelength of the probe. Sonar and medical ultrasound are limited by the wavelength of sound they employ. We shall see that this is also true in electron microscopy, since electrons have a wavelength. Heisenberg’s uncertainty principle asserts that this limit is fundamental and inescapable, as we shall see in quantum mechanics.

The most obvious method of obtaining better detail is to utilize shorter wavelengths. Ultraviolet (UV) microscopes have been constructed with special lenses that transmit UV rays and utilize photographic or electronic techniques to record images. The shorter UV wavelengths allow somewhat greater detail to be observed, but drawbacks, such as the hazard of UV to living tissue and the need for special detection devices and lenses (which tend to be dispersive in the UV), severely limit the use of UV microscopes. Elsewhere, we will explore practical uses of very short wavelength EM waves, such as x rays, and other short-wavelength probes, such as electrons in electron microscopes, to detect small details.

Another difficulty in microscopy is the fact that many microscopic objects do not absorb much of the light passing through them. The lack of contrast makes image interpretation very difficult. Contrast is the difference in intensity between objects and the background on which they are observed. Stains (such as dyes, fluorophores, etc.) are commonly employed to enhance contrast, but these tend to be application specific. More general wave interference techniques can be used to produce contrast. [link] shows the passage of light through a sample. Since the indices of refraction differ, the number of wavelengths in the paths differs. Light emerging from the object is thus out of phase with light from the background and will interfere differently, producing enhanced contrast, especially if the light is coherent and monochromatic—as in laser light.

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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• ### Spectroscopic binaries in the Solar Twin Planet Search program: from substellar-mass to M dwarf companions(1708.07465)

Aug. 24, 2017 astro-ph.SR, astro-ph.EP
Previous studies on the rotation of Sun-like stars revealed that the rotational rates of young stars converge towards a well-defined evolution that follows a power-law decay. It seems, however, that some binary stars do not obey this relation, often by displaying enhanced rotational rates and activity. In the Solar Twin Planet Search program we observed several solar twin binaries, and found a multiplicity fraction of $42\% \pm 6\%$ in the whole sample; moreover, at least three of these binaries (HIP 19911, HIP 67620 and HIP 103983) clearly exhibit the aforementioned anomalies. We investigated the configuration of the binaries in the program, and discovered new companions for HIP 6407, HIP 54582, HIP 62039 and HIP 30037, of which the latter is orbited by a $0.06$ M$_\odot$ brown dwarf in a 1-month long orbit. We report the orbital parameters of the systems with well-sampled orbits and, in addition, the lower limits of parameters for the companions that only display a curvature in their radial velocities. For the linear trend binaries, we report an estimate of the masses of their companions when their observed separation is available, and a minimum mass otherwise. We conclude that solar twin binaries with low-mass stellar companions at moderate orbital periods do not display signs of a distinct rotational evolution when compared to single stars. We confirm that the three peculiar stars are double-lined binaries, and that their companions are polluting their spectra, which explains the observed anomalies.
• The Astropy Project (http://astropy.org) is, in its own words, "a community effort to develop a single core package for Astronomy in Python and foster interoperability between Python astronomy packages." For five years this project has been managed, written, and operated as a grassroots, self-organized, almost entirely volunteer effort while the software is used by the majority of the astronomical community. Despite this, the project has always been and remains to this day effectively unfunded. Further, contributors receive little or no formal recognition for creating and supporting what is now critical software. This paper explores the problem in detail, outlines possible solutions to correct this, and presents a few suggestions on how to address the sustainability of general purpose astronomical software.
• ### The Solar Twin Planet Search: IV. The Sun as a typical rotator and evidence for a new rotational braking law for Sun-like stars(1606.06214)

June 20, 2016 astro-ph.SR
It is still unclear how common the Sun is when compared to other similar stars in regards to some of its physical properties, such as rotation. Considering that gyrochronology relations are widely used today to estimate ages of stars in the main sequence, and that the Sun is used to calibrate it, it is crucial to assess if these procedures are acceptable. We analyze the rotational velocities -- limited by the unknown rotation axis inclination angle -- of an unprecedented large sample of solar twins in order to study the rotational evolution of Sun-like stars, and assess if the Sun is a typical rotator. We use high-resolution ($R = 115000$) spectra obtained with the HARPS spectrograph and ESO's 3.6 m telescope at La Silla Observatory. The projected rotational velocities for 82 solar twins are estimated by line profile fitting with synthetic spectra. Macroturbulence velocities are inferred from a prescription that accurately reflects their dependence with effective temperature and luminosity of the stars. Our sample of solar twins include some spectroscopic binaries with enhanced rotational velocities, and we do not find any non-spectroscopic binaries with unusually high rotation velocities. We verified that the Sun does not have a peculiar rotation, but the solar twins exhibit rotational velocities that depart from the Skumanich relation. The Sun is a regular rotator when compared to solar twins with a similar age. Additionally, we obtain a rotational braking law that better describes the stars in our sample ($v \propto t^{-0.6}$) in contrast to previous, often-used scalings.