text:
SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 62, Issue 5: 959505(2019) https://doi.org/10.1007/s11433-019-9394-x

## The radiation structure of PSR B2016$+$28 observed with FAST

JiGuang Lu1,2,*, Bo Peng1,2,*, Meng Yu1, Shi Dai1,4, Ye-Zhao Yu1,5, Lin Wang1,5,
• AcceptedMar 15, 2019
• PublishedMar 21, 2019
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### Abstract

With the largest dish Five-hundred-meter Aperture Spherical radio Telescope (FAST),both the mean and single pulses of PSR B2016$+$28, especially including the single-pulse structure, are investigated in detail in this study. The mean pulse profiles at different frequencies can be well fitted in a conal model, and the peak separation of intensity-dependent pulse profiles increases with intensity. The integrated pulses are obviously frequency dependent(pulse width decreases by $\sim$20$%$ as frequency increases from 300 to 750 MHz),but the structure of single pulses changes slightly (the corresponding correlation scale decreases by only $\sim$$1%$).This disparity between mean and single pulses provides independent evidence for the existence of the RS-type vacuum inner gap,indicating a strong bond between particles on the pulsar surface. Diffused drifting sub-pulses are analyzed. The results show thatthe modulation period along pulse series ($P_3$) is positively correlated to the separationbetween two adjacent sub-pulses ($P_2$). This correlation may hint a rough surface on the pulsar,eventually resulting in the irregular drift of sparks. All the observational results may have significant implicationsin the dynamics of pulsar magnetosphere and are discussed extensively in this paper.

### Acknowledgment

This work was supported by the National Key Rrm D Program of China (Grant Nos. 2018YFA0404703, and 2017YFA0402602), the National Natural Science Foundation of China (Grant Nos. 11673002, and 11225314), the Open Project Program of the Key Laboratory of FAST, National Astronomical Observatories, Chinese Academy of Sciences, and the project of Chinese Academy of Sciences (CAS) and the Max-Planck-Society (MPS) collaboration. This work made use of the data from the FAST telescope (Five-hundred-meter Aperture Spherical radio Telescope). FAST is a Chinese national mega-science facility, built and operated by the National Astronomical Observatories, Chinese Academy of Sciences. The FAST FELLOWSHIP was supported by the Special Funding for Advanced Users, budgeted and administrated by Center for Astronomical Mega-Science, Chinese Academy of Sciences (CAMS). YouLing Yue was supported by the National Key RrmD Program of China (Grant No. 2017YFA0402600), and Chinese Academy of Sciences “Light of West China” Program.

### References

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• Figure 1

(Color online) The narrow band profiles are fitted with two peaks model (a) and a conal beam function (b). The black curves are the observed pulse profiles (had been normalized) and the red curves are the fitting curves. The blue vertical line is 10 times of the rms (root-mean-square) of fitting residuals. Obviously, the conal beam function gets better fitting results.

• Figure 2

Best-fitting parameters of the conal beam model vs. frequency. From top to bottom, the parameters are the conal radius ($\theta_{\mu0}$), the cone wall thickness ($\sigma$), and the conal asymmetry ($k$).

• Figure 3

(Color online) Evolution of the conal beam center position. The ordinate is the time delay of conal beam center relative to that at 285 MHz. The evolution is fitted by a correction of DM, and it is shown by the black curve.

• Figure 4

(Color online) The statistics of single pulse SNR, and narrow bands with different frequencies are marked with different colors.

• Figure 5

(Color online) The mean cross-correlation coefficients of successive pulses are shown as blue dots, and they seems being composed of 3 components. It is tried to fit the coefficients with 3 square hyperbolic secant peaks, and the fitting result is plotted as red curve. The 3 green dashed curves are the 3 peaks, respectively, and the red dashed curve shows the fitting residuals. The centric position $D_i$ and width $\sigma_i$ of 3 peaks are also marked.

• Figure 6

(Color online) Part of single pulses are shown in (a), and the drifting sub-pulses are marked as red solid lines. The red dashed lines are fake drift tracks (both solid lines and dash lines corresponds to the red points in (b)). The flux variation at different drift rates is shown in (b), and each maximum point (red point) corresponds to a sub-pulse track.

• Figure 7

The drift rates of the extracted 622 sub-pulse tracks variation versus time (a) and the variation spectra of the drifting rate (b).

• Figure 8

(Color online) The statistics of the extracted 622 drift rates. The red dashed line marks the division point of the slower and faster drift sub-pulses for Figure 9.

• Figure 9

(Color online) The profiles of slower (red curves) and faster (blue curves) drift sub-pulses, and the division point is shown in Figure 8. The solid (dashed) curves represent the profiles of first (second) half of sub-pulses.

• Figure 10

(Color online) The total modulation spectra (a) and the flux modulation at different drift rates (b). The red points mark the maximum points along drift rate at different modulation frequency, and the black curve is the fitting result.

• Figure 11

The unfolded fluctuation spectra of time-domain data of pulses.

• Figure 12

(Color online) The intensity distribution with different $P_3$ (a) and the folded fluctuation spectra of time-domain data of pulses (b). In (b), three distinct areas are marked. In Area 1, the maximum points along vertical axis are marked as blue points and error bars, and the fitting curve is also plotted.

• Figure 13

(Color online) The best-fitting parameters $k_h$ and $b_h$ of eq. (8) versus frequency. It seems that $b_h$ shows a little increasing with frequency.

• Figure 14

(Color online) The red points in Figure 10, blue points in Figure 12and corresponding fitting curves are plotted as the form of $P_2$ and $P_3$. The best-fitting result of all data points is shown as black curve.

• Figure 15

The ratio of the intensity in Area 1 and Area 2 at different frequencies.

• Figure 16

(Color online) The corresponding phase difference $\phi_2-\phi_1$ between adjacent narrow bands at different phase $\phi_1$ is shown in (a). The obviously down trending of each curve shows the shrinking of the single pulse structure. The maximum linearly dependent coefficient at different phase is shown in (b).

• Figure 17

(Color online) The evolution of single pulse structure width (black markers) and mean pulse width (FWHM is denoted by blue markers and distance between components in two peaks fitting is denoted by red markers) with frequency is shown. (a) The magnified view of the part between two green dashed lines in (b).

• Figure 18

(Color online) The radiation altitude of every magnetic field line which passes polar cap region, and $\theta$ and $\phi$ are the zenith angle and position angle relative to magnetic axis. The black (red) curve denotes the intersection curve of pulsar surface and the last opening field lines (critical field lines).

• Figure 19

(Color online) As Figure 18, but for radiation pulse phase. Assuming the radiation concentrates in the field lines which pass the blue curve, and the cyan (orange) line is the line group which radiate high (low) frequency emission. Thus, the solid cyan (orange) line segment denotes the width of mean pulse profile at high (low) frequency. Given a bunch of magnetic field lines at the white disc generate a sub-pulse, the cyan (orange) point would be the center of this sub-pulse at high (low) frequency.

• Figure 20

(Color online) The simulated single pulse train with a same profile of PSR B2016+28 at 300 MHz (a), and the cross-correlation results (b) similar to Figure 5.

Citations

• #### 10

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text:
# Entire chapter as subsection

I have a document with 3 chapters. I would like the chapter 2 - Dolor, to appear as a section 1.1 in the table of contents, instead of chapter 2.

I have separate file for each of the chapter and it must stay as a seperate file. How can call chapter as a section from inside chapter 1?

MWE is :

\documentclass[british]{report}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage{subfiles}
\usepackage[backend=biber, style=numeric-comp, refsection=chapter]{biblatex}
\addbibresource{biblatex-examples.bib}

\begin{document}
\tableofcontents
\include{Lorem}
\include{Dolor}
\include{Sit}
\end{document}

The contents of chapter 1 (Lorem.tex) are:

\chapter{Lorem}
Ipsum \autocite{sigfridsson} dolor \autocite{geer,worman}
\section{Lorem Section 1}
To err is human
\printbibliography[heading=subbibliography]

The contents of chapter 2 (Dolor.tex) are:

\chapter{Dolor}
Lorem ipsum \autocite{sigfridsson} dolor \autocite{knuth:ct:a,pines}
\printbibliography[heading=subbibliography]

The contents of chapter 3 (Sit.tex) are:

\chapter{Sit}
Lorem ipsum \autocite{sigfridsson} dolor
\autocite{geer,cicero,companion}
\printbibliography[heading=subbibliography]

• Write \section{Dolor} instead of \chapter{Dolor}. – moewe Sep 29 '18 at 11:49
• But that will only help almost: The \include still causes the contents of Dolor to appear on a new page. If you don't want that you should probably use \input. Note that changing from \chapter to \section will also change the behaviour of the refsection. – moewe Sep 29 '18 at 11:56
• Not pretty, but \refstepcounter{section}\addcontentsline{toc}{section}{\protect\numberline{\thesection}Dolor} should do it. – moewe Sep 29 '18 at 12:12
• Where did you put the code? It should replace the \chapter{Dolor}. – moewe Sep 29 '18 at 12:22
• Aha. That would do to much. Just replace the \chapter{Dolor} in the .tex file for the second chapter with the suggested bit of code. That code just fakes the heading entry for the TOC. It does nothing more. – moewe Sep 29 '18 at 12:24

## 1 Answer

If you only want to have a section heading in the TOC, but not in the actual document you need to use a few more low-level commands.

Replace \chapter{Dolor} with \tocsection{Dolor} where \tocsection is defined as below

\documentclass[british]{report}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}

\newcommand*{\tocsection}[1]{%
\refstepcounter{section}%
\addcontentsline{toc}{section}{\protect\numberline{\thesection}#1}}

\begin{document}
\tableofcontents

\chapter{Lorem}
lorem ipsum

\section{Ipsum}
lorem ipsum dolor sit amet

\tocsection{Dolor}
sit amet
\end{document}

• hi @moewe, I have encountered a problem in this answer. I see by using this the page header does not get updated. It sticks to the global name (Lorem). However, I would like the page header to get updated to sub-section name (Dolor). Can you please help? – Rouge Dec 3 '18 at 8:57
• @Rouge Can you open a new question with a short example document that reproduces the issue along with a description of what you expect to see instead? – moewe Dec 3 '18 at 9:03
• @Rouge Maybe tex.stackexchange.com/q/35433/35864 can help you already, but the exact details will depend on your class and the setup of your headers/footers. – moewe Dec 3 '18 at 9:06

format: plain


text:
# The Sieve of Sundaram

The Sieve of Eratosthenes is probably the best known algorithm for generating primes. Together with wheel factorization and other optimization options, it can generate primes very quickly.

But a lesser well known algorithm for sieving primes is the Sieve of Sundaram. This algorithm was discovered in 1934 by Sundaram; like the sieve of Eratosthenes it finds all prime numbers up to a certain integer.

### The algorithm

A simplified version of the algorithm, using N as the limit to which we want to find primes to:

m =: Floor of N/2
L =: List of numbers from 1 to m
For every solution (i,j) to i + j + 2ij < m:
Remove i + j + 2ij from L

For each k remaining in L:
2k + 1 is prime.

In practice we can find solutions to $i + j + 2ij < m$ by using two nested for loops:

For i in 0 to m:
For j in i to m:
L[i + j + 2ij] =: False

Here i is always less than j, because the two are interchangeable and filtering it twice would be a waste.

We don’t actually need to loop j from 0 to m. From the inequality $i + j + 2ij < m$, we can solve for j: $j < \frac{m-i}{2i+1}$. The new algorithm:

m =: Floor of N/2
L =: Boolean array of length m
Fill L with true

For i in 0 to m:
For j in i to (m-i)/(2i+1):
L[i + j + 2ij] =: False

For each k remaining in L:
2k + 1 is prime.

### Why this algorithm works

In the algorithm, $2k+1$ is prime where k can be written as $i + j + 2ij$ where i and j are integers. We can rewrite this:

$\begin{array}{l} 2(i+j+2ij) + 1 \\ = 2i + 2j + 4ij + 1 \\ = (2i+1) (2j+1) \end{array}$

Both $2i+1$ and $2j+1$ are odd numbers, and any number that can be written as the product of two odd numbers are composite.

Of the odd numbers, those that cannot be written as the product of two odd numbers are prime. We’ve filtered everything that can be written as $(2i+1)(2j+1)$ so we are left with the odd prime numbers.

This algorithm only gets the odd prime numbers, but fortunately there is only one even prime number, 2.

### Benchmarks with the Sieve of Eratosthenes

Here’s an implementation of the Sieve of Sundaram:

#include <stdio.h>
#include <stdlib.h>

typedef unsigned long long ll;
int main() {
ll n = 100000000LL;
ll m = n/2;
char *sieve = malloc(m);

for(ll i=0; i<m; i++)
sieve[i] = 1;

for(ll i=1; i<m; i++)
for(ll j=i; j<=(m-i)/(2*i+1); j++)
sieve[i+j+2*i*j] = 0;

ll s=1;
for(ll i=1; i<m; i++)
if(sieve[i]) s++;

printf("%llu", s);
return 0;
}

This code counts the number of primes below 100 million, which should be 5761455. The above code runs in 9.725 seconds.

Here’s an alternative, an implementation of the more standard Sieve of Eratosthenes:

#include <stdio.h>
#include <stdlib.h>

typedef unsigned long long ll;
int main(){
ll lim = 100000000LL;
char *sieve = malloc(lim);

for(int i=0; i<lim; i++)
sieve[i] = 1;

int s=0;
for(int i=2; i<lim; i++){
if(sieve[i]){
s++;
for(int j=2; j<=lim/i; j++)
sieve[i*j] = 0;
}
}

printf("%d", s);
return 0;
}

I was surprised to find that the Sieve of Eratosthenes actually ran faster. It completed in 7.289 seconds.

I expected the Sieve of Sundaram to be faster because according to Wikipedia this algorithm uses $O(n \log(n))$ operations, while the Sieve of Eratosthenes uses $O(n \log(n) \log \log(n))$.


text:
Testing for differences in very small proportions

This is a somewhat typical a/b test setup. However the proportions that I'd like to test for differences are very small (< 1%). Consequently a 20% difference, which is meaningful, is 0.001. That's a small effect size!

A power test of the chi-squared test for differences in proportions (same sample size) using the pwr package in R yields

difference of proportion power calculation for binomial distribution
(arcsine transformation)

h = 0.001
n1 = 1e+05
n2 = 1e+05
sig.level = 0.05
power = 0.05574725
alternative = two.sided

So power grows very slowly. How can I get around this?

The group a proportion is lower than group b (which contains the treatment we're interested in). As expected the group b proportion is higher than group a. Say group bs proportion is 0.007.

Can I use an exact binomial test on group a with the alternative based on being greater than group bs proportion?

When I do this I get a p-value of 0.97, indicating that it's very unlikely that group a will increase in conversion to trump group bs current position.

I guess the question becomes one of power with this test? Any comments on the validity of this?


text:
# What are the requirements of a function so that the left Riemann sum equals the right Riemann sum?

My homework question in particular specifies over an interval of [0,1], the function is negative, and the function is decreasing.

• What is a "right" or "left" Riemann Sum?? – DonAntonio Jan 20 at 23:17
• @DonAntonio Presumably a Riemann sum in which one takes the value of the function at the right or left endpoints of the subintervals. – Math1000 Jan 21 at 0:22

Given: $$\Delta x = \frac{b - a}{n}$$, when no limits are involved we can expand the left and right Riemann sums as follows:

\begin{align*} R_L &= \sum_{k = 0}^{n -1} f(a + k\Delta x) \Delta x = f(a) +\sum_{k = 1}^{n -1} f(a + k\Delta x) \Delta x \\ R_R &= \sum_{k = 1}^{n} f(a + k\Delta x) \Delta x = f(a+ n \Delta x) + \sum_{k = 1}^{n - 1} f(a + k\Delta x) \Delta x \\ \end{align*}

If $$R_L = R_R$$, then their difference should be zero:

\begin{align*} R_L - R_R &= 0\\ \left(f(a) +\sum_{k = 1}^{n -1} f(a + k\Delta x) \Delta x\right) - \left( f(a+ n \Delta x) + \sum_{k = 1}^{n - 1} f(a + k\Delta x) \Delta x\right) &= 0 \\ f(a) - f(a+ n \Delta x) &= 0 \\ \end{align*}

Therefore, the left and right Riemann sums are the same, without limits, when the following holds true:

$$f(a) = f(a + n \Delta x)$$

When limits are involved, the left Riemann sum approaches the right Riemann sum, as $$n \to \infty$$.

\begin{align*} \lim_{n \to \infty} R_L &= \lim_{n \to \infty} R_R \\ \end{align*}

• Isn't the requirement for non-limit situations much looser, namely that the left and right ends must be equal? – Dan Uznanski Jan 25 at 9:51
• @DanUznanski I might be overlooking something. Can you explain what you mean by the left and right ends? – Gustav Jan 25 at 9:59
• $R_R - R_L = \sum_{k=1}^{n} df(a+kd) -\sum_{k=0}^{n-1} df(a+kd) = \sum_{k=1}^{n-1} df(a+kd) + df(a+nd) - (\sum_{k=1}^{n-1} df(a+kd) + df(a+0d) = d(f(a+nd)-f(a))$ so equality is when $f(a+nd)=f(a)$ – Dan Uznanski Jan 25 at 10:09
• @DanUznanski You are right. Do you want to submit this as an answer, or should I edit this into my answer? – Gustav Jan 25 at 11:33
• Think it belongs in yours – Dan Uznanski Jan 25 at 11:34


text:
Chang et al., ICLR, 2019

# Automatically Composing Representation Transformations as a Mean for Generalization

The authors focus on solving recursive tasks which can be decomposed into a sequence of simpler algorithmic procedures (e.g., arithmetic problems, geometric transformations). The main difficulties of this approach are (i) how to actually decompose the task into simpler blocks and (ii) how to extrapolate to more complex problems from learning on simpler individual tasks. The authors propose the compositional recursive learner (CRL) to learn at the same time both the structure of the task and its components.
• Pros (+): This problem is well motivated, and seems a very promising direction, for learning domain-agnostic components.
• Cons (-): The actual implementation description lacks crucial details and I am not sure how easy it would be to reimplement.

## Proposed model

### Problem definition

A problem $P_i$ is defined as a transformation $x_i : t_x \mapsto y_i : t_y$, where $t_x$ and $t_y$ are the respective types of $x$ and $y$. However since we only consider recursive problem here, then $t_x = t_y$. We define a family of problems $\mathcal P$ as a set of composite recursive problems that share regularities. The goal of CRL is to extrapolate to solve new compositions of these tasks, using knowledge from the limited subset of tasks it has seen during training.

### Implementation

In essence, the problem can be formulated as a sequence-decision making task via a meta-level MDP ($\mathcal X$, $\mathcal F$, $\mathcal P_{\mbox{meta}}$, r, $\gamma$), where $\mathcal X$ is the set of states, i.e., representations; $\mathcal F$ is a set of computations, i.e., istances of the transformations we consider, for instance as neural networks, and an additional special function HALT that stops the execution; $\mathcal P_{\mbox{meta}}: (x_t, f_t, x_{t + 1}) \mapsto c \in [0, 1]$ is the policy which assigns a probability to each possible transition. Finally $r$ is the reward function and $\gamma$ a decay factor.

More specifically, the CRL is implemented as a set of neural networks, $f_k \in \mathcal F$, and a controller $\pi(f\ |\ \mathbf{x}, t_y)$ which selects the best course of action given the current history of representations $\mathbf{x}$ and target type $t_y$. The loss is back-propagated through the functions $f$, and the controller is trained as a Reinforcement Learning (RL) agent with a sparse reward (it only knows the final target result). An additional important training scheme is the use of curriculum learning i.e., start by learning small transformations and then consider more complex compositions, increasing the state space little by little.

## Experiments

### Multilingual Arithmetic

The learner will aim to solve recursive arithmetic expressions across 6 languages: English, Numerals, PigLatin, Reversed-English, Spanish. The input is a tuple $(x^s, t_y)$, where $x$ is the arithmetic expression expressed in source language $s$, and $t_y$ is the output language.

• Training: The learner trains on a curriculum of a limited set of 2, 3, 4, 5-length expressions. During training, each source language is seen with four target languages (and one held out for testing) and each target language is seen with four source languages (and one held out for testing).

• Testing: The learner is asked to generalize to 5-length expressions (test set) and to extrapolate to 10-length expressions (extrapolation set) with unseen language pairs.

The authors consider two main types of functional units for this task: A reducer, which takes as input a window of three terms in the input expression and outputs a softmax distribution over the vocabulary. While a translator applies a function to every element of the input sequence and outputs a sequence of the same size.

The CRL is compared to a baseline RNN architecture that directly tries to map a variable length input sequence to the target output. On the test set, RNN and CRL yield similar accuracies although CRL usually requires less training samples and/or less training iterations. On the extrapolation set however, CRL more clearly outperforms RNN. Interestingly the CRL results usually have a much bigger variance which would be interesting to qualitatively analyze. Moreover, the use of curriculum learning significantly improves the model performance. Finally, qualitative results show that the reducers and translators are interpretable to some degree: e.g., it is possible to map some of the reducers to specific operations, however due to the unsupervised nature of the task, the mapping is not always straight-forward.

### Image Transformations

This time the functional units are composed of three specialized Spatial Transformer Networks [1] to learn rotation, scale and translation, and an identity function. Overall this setting does not yield very good quantitative results. More precisely, one of the main challenges, since we are acting on a visual domain, is to deduce the structure of the task from information which lacks clear structure (pixel matrices). Additionally the fact that all inputs and outputs have the same domain (images) and that only a sparse reward is available make it more difficult for the controller to distinguish between functionalities, i.e., it could collapse to using only one transformer.

## References

• [1] Spatial Transformer Networks, Jaderberg et al., NeurIPS 2016


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# Mathematical notes

Paris

Early works are unpolished notes from various textbooks, and later works cover algebraic topology and higher category theory


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MathSciNet bibliographic data MR2060128 60F15 Shixin, Gan Almost sure convergence for $\tilde\rho$$\tilde\rho$-mixing random variable sequences. Statist. Probab. Lett. 67 (2004), no. 4, 289–298. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


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# Reproducibility and Version Control¶

Reproducibility is one of the cornerstones of the scientific method and as computational science is increasingly becoming an alternative to costly experiments it is natural that the computational science community adopts the openness and full disclosure practices of experimental sciences, see for example this Science opinion piece. Other interesting reads are this piece and the sciencecodemanifesto.org

At the heart of reproducibility in computational sciences are the use of version control software (VCS). VCS allows you to keep track of the development of your software so that you can easily go back in the history of the software if needed. This can be highly useful in many situations. For example if you use your code to compute some results for a paper but realize a year later when you get the reviews back that you should have used 1.32 for some parameter, not 1.23. Most likely your code will have changed significantly in one year but if it is under version control it will be trivial to redo the computation!

Another example could be when you decide to add some new feature to your code but you don’t quite think through all the implications of the change until later. With version control you can just check out an old copy and start again.

Larger software projects with multiple developers are almost always under version control so that different developers can work simultaneously on different parts of the code. For larger projects it is also very important to have some kind of unit testing.

The most basic version control you can use is to simply make a new copy of a file every time you make a significant change. This works ok-ish if you are continuously working on the file, however if you work on some other project for a week it is not so easy to remember if it was file_a2.f90, file_b1.f90 or file_new.f90 that was the last version you used. Even harder is to remember what changes were made in between two versions. This is where VCS comes in. The typical VCS allows you to store all versions (or at least the differences between versions) of your file set along with user supplied information about what changed. In this course we will use GIT which is a distributed VCS. Other commonly used VCS are Subversion (or SVN), CVS and Mercurial.

The course information about GIT can be found in GIT.


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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01h702q8828
 Title: From Legislation to Installation: The Effects of State RPS Policies on Installed Solar Capacity Authors: Lynch, Madeline Advisors: Craft, Amy Department: Economics Class Year: 2016 Abstract: This past decade has seen an increase in interest and concern for the development of renewable sources of energy. This concern stems from increased attention to global warming and the impacts that fossil fuel energy sources may have on the environment. With gridlock at the federal level concerning which policy goals to pursue, state level incentives and renewable policies have appeared with increasing popularity. While these policies and incentives are still relatively new, enough years have passed with a significant level of state participation to discern preliminary results. As policies age and results are better understood, a national policy may one day be developed. This paper analyzes the relationship between the different existing state renewable energy policies, solar installation prices, and installed solar capacity within a state to determine whether or not these policies are having an impact. Also considered is the effectiveness of different aspects within individual renewable policies such as policy stringency, years until compliance, and monetary penalties for missing renewable capacity targets. Regression results have shown RPS policies within 5 years of compliance and the average price of solar installation to be statistically significant in their negative effect on state solar installation capacity. Other noteworthy results include the positive but statistically insignificant impact of an ACP, Solar Carve Out, and 10 year window until compliance of an RPS on state solar installation. A Renewable Portfolio Standard encompasses more renewable energy sources than solar, and reliance upon these sources rather than solar may have the potential to skew the results of this study, which focused solely on solar. The interplay between different renewable energy policies within a state was also outside the scope of this essay, but may have played a role in influencing the investment decision into solar. Extent: 71 pages URI: http://arks.princeton.edu/ark:/88435/dsp01h702q8828 Type of Material: Princeton University Senior Theses Language: en_US Appears in Collections: Economics, 1927-2016

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Archives

Strong law of large numbers for weighted sums of pairwise independent random variables
by SOO HAK SUNG
Vol. 27 No. 1 (1999)


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DOI
10.1139/facets-2017-0024

The not so over-the-counter status of emergency contraception in Ontario: A mixed methods study with pharmacists

Published Online
16 May 2017

Andréanne Chaumont

Faculty of Medicine, University of Ottawa, Ottawa, ON K1H 8M5, Canada

Contributions

• Conceived and designed the study
• Performed the experiments/collected the data
• Analyzed and interpreted the data
• Drafted or revised the manuscript

Angel M. Foster

Faculty of Health Sciences, University of Ottawa, Ottawa, ON K1N 6N5, Canada

Institute of Population Health, University of Ottawa, Ottawa, ON K1N 6N5, Canada

Contributions

• Conceived and designed the study
• Analyzed and interpreted the data
• Contributed resources
• Drafted or revised the manuscript

Abstract

Introduction: In Canada, the progestin-only dedicated pill is the most widely used method of emergency contraception (EC). This method gained over-the-counter status in Ontario in 2008. Our mixed methods study explored the progestin-only EC knowledge, attitudes, and provision practices of Ontario pharmacists.

Methods: From June 2015 to October 2015, we collected 198 mailed surveys from Ontarian pharmacy representatives and conducted 17 in-depth interviews with a subset of respondents. We analyzed these data using descriptive statistics and for content and themes.

Results: Results from our English/French bilingual survey indicate that respondents’ knowledge is generally accurate, but confusion persists about the mechanism of action and the number of times the drug can be used in one menstrual cycle. Nearly half (49%) of our survey respondents indicated that progestin-only EC pills are only available behind the counter. Interviewees strongly supported the introduction and promotion of more effective methods of EC in Ontario.

Conclusion: Continuing education focusing on both the regulatory status of progestin-only EC and information about the medication appears warranted. Health Canada’s recent approval of ulipristal acetate for use as a post-coital contraceptive may provide a window of opportunity for engaging with health service providers, including pharmacists, about all available modalities of EC in Canada.

Introduction

Emergency contraceptives are medications or devices that are used to prevent pregnancy after unprotected or under-protected sex. In Canada, the progestin-only dedicated pill, the Copper-T intrauterine device (IUD), and the Yupze method have long been available as methods of emergency contraception (EC). In addition, in 2015, Health Canada approved ulipristal acetate (UPA) for use as a post-coital contraceptive. However, for years the most widely used method of EC by Canadian women has been the progestin-only EC pill (Soon et al. 2005). A body of evidence shows that when used within 120 h of a sexual event, a single 1.5 mg dose of levonorgestrel can reduce the risk of pregnancy by up to 89% (Trussell 2012). Because the primary mechanism of action of progestin-only EC is to delay or inhibit ovulation, the medication is more effective when taken as soon after sex as possible (Trussell 2012).

In Ontario, progestin-only EC was first approved as a Schedule I drug requiring a prescription in 2000. In 2005, a regulatory change resulted in progestin-only EC moving to Schedule II status, such that a prescription was no longer required (Canadian Medical Association Journal 2005). This represented an important step in increasing timely access to the medication because women were then able to procure EC directly from pharmacists. However, a consultation with a pharmacist was still required. In 2008, the National Drug Scheduling Advisory Committee recommended the deregulation of progestin-only EC to a Schedule III drug, moving it from behind-the-counter (BTC) status to over-the-counter (OTC) status (Eggertson 2008). Thus, for almost a decade, women in Ontario have not been required to interact with a pharmacist to obtain progestin-only EC. As of 2016, three brands of progestin-only EC were available: Plan B® (the most widely used and well known) and two generic brands (NextChoice® and Option 2®). In response to recent studies suggesting that progestin-only EC may be less or not at all effective when used by heavier women (Glasier et al. 2011; Kapp et al. 2015; Gemzell-Danielsson et al. 2015), in 2014, Health Canada issued a warning stating that progestin-only EC may be less effective in women weighing 165 pounds or more and ineffective in women weighing over 176 pounds (Eggertson 2014). Health Canada subsequently requested that the labels for all progestin-only EC products in Canada incorporate this warning (Health Canada 2014).

As patient-oriented health care professionals, pharmacists are available and accessible to their communities and have long played a critical role in EC service delivery. However, the scientific literature on Canadian pharmacists’ EC knowledge and attitudes is limited. In addition, no study has been undertaken in Ontario since the last regulatory status change to determine current provision practices or since the weight advisory for progestin-only EC went into effect. Through a mixed methods study, we aimed to assess the knowledge, attitudes, and practice patterns of community pharmacists in Ontario with respect to all modalities of EC. In this paper, we focus on the findings that are specifically related to progestin-only EC pills.

Methods

Study design and data collection

Our study had two components: a mailed survey to Ontario pharmacists and in-depth interviews with a subset of survey respondents. With permission, we based our selection of pharmacies and the design of our survey instrument on a study conducted by Dunn et al. (2008) in the wake of the switch to BTC status.

We used a database from the Ontario College of Pharmacists to obtain our sample of community-based retail pharmacies, of which there were 4232 listed at the time of the study. We used a stratified random selection process to identify our sample and intentionally over-sampled independent pharmacies, pharmacies in rural areas, and pharmacies located in Franco-Ontarian communities. We initially sent surveys to 1428 pharmacies in June 2015; after accounting for closed pharmacies and inaccurate addresses, we ultimately surveyed 1396 pharmacies.

We contacted pharmacies four times over the course of the study period. The first contact included a bilingual (English/French) survey package with an instruction letter, the survey instrument, a stamped return envelope, a key informant interview response card, and a response card to participate in a draw for a $100 CAD gift card (one per 100 respondents). We sent non-respondents a reminder postcard after 1 month. Continued non-respondents received a second survey package and a final reminder postcard 3 and 4 months after the initial mailing, respectively. We included all surveys received before the end of calendar year 2015 in our analysis. Our questionnaire included four domains. The first section focused on demographic questions about the respondent, pharmacy, and catchment area. The second section contained a series of close-ended multiple choice and knowledge assessment questions related to different modalities of EC. The penultimate section asked the respondent a series of questions about current progestin-only EC provision practices. The final section explored respondents’ attitudes toward and interest in continuing education efforts and explored ways in which EC service delivery could be improved. We also provided participants with a free response space to comment on EC-related issues. Our cover letter asked participants not to consult resources or other members of the pharmacy team when completing the survey. We piloted the questionnaire with a convenience sample of 10 Anglophone and three Francophone pharmacists in May 2015; feedback from these early interactions allowed us to finalize the instrument and translation and demonstrated that completing the survey required about 20 min. We invited respondents to participate in a telephone/Skype follow-up interview to discuss issues related to service delivery in depth. A Master’s student (AC) in Health Sciences at the University of Ottawa conducted all English and French interviews, after receiving training from her supervisor (AMF), a medical doctor and medical anthropologist with extensive experience leading qualitative EC-related studies. We used an interview guide developed specifically for this study that explored the participant’s background, current practices, and reflections on the introduction of UPA and use of the IUD as EC. We concluded the interview with a discussion of avenues for improving EC access and engaging with pharmacists in Ontario. With permission, we audio recorded all interviews, which averaged about 30 min each, and offered all participants a$20 CAD gift certificate. AC took notes during and wrote formal memos immediately after each interaction.

Data analysis

We entered the survey responses into FluidSurveys and, after conducting an audit, exported our data to IBM SPSS 23.0 for statistical analysis. We analyzed our data using descriptive statistics, χ2 analysis, and Fisher’s exact text to detect regional differences and differences by pharmacy type. We analyzed open-ended questions for content and themes.

We used an iterative process to analyze our interviews for content and themes; this process began during data collection. AC or a study volunteer transcribed interviews verbatim, and we used ATLAS.ti (atlasti.com) to manage our data. We developed an initial codebook based on study questions and expected responses, and added codes and categories that emerged during the analytic process. Regular meetings between AC, the primary coder, and AMF guided our interpretation of the findings. In the final analytic phase, we combined the results of both components of the mixed methods study paying special attention to concordance and discordance.

Ethical considerations

We received ethics approval from the Research Ethics Boards at the University of Ottawa (File# H03-14-20 and File# 02-15-12). Throughout this manuscript, we have redacted or masked all personally identifying information about individual pharmacists and their pharmacies. We have translated all French-language responses from both the survey and the interview components to English.

Results

Description of participants and their pharmacies

We received 198 surveys (response rate of 14.2%); all but two respondents completed the survey in English. The majority of our survey respondents were from independent (39.1%) or chain (30.5%) pharmacies, and close to half of these pharmacies were located in the southern region of the province (46.6%). Nearly two thirds of respondent pharmacies were located in urban areas (65.0%) and all were open on weekdays; 82.3% of pharmacies were open on Sundays. One out of 10 respondents reported that the pharmacy was located more than 15 min drive from another pharmacy. We provide detailed information about the characteristics of these pharmacies in Table 1.

Table 1. Characteristics of the pharmacies reported on by survey respondents (n = 198).

n (%)
Type of pharmacy
Independent77 (39.1)
Chain60 (30.5)
Banner51 (25.9)
Other/no response10 (5.07)
Regional location of the pharmacy
East34 (17.4)
Central41 (21.0)
South91 (46.7)
North29 (14.9)
No response3 (1.51)
Area location of the pharmacy
Urban128 (65.0)
Rural69 (35.0)
No response1 (0.5)
Another pharmacy located within a 15 min drive
Yes180 (90.9)
No18 (8.6)
No response1 (0.5)
Store hoursa
Weekdays198 (100)
Saturdays189 (95.5)
Sundays163 (82.3)
Principal languages spoken by pharmacy staffa
English195 (98.5)
French34 (17.2)
Arabic28 (14.1)
Chinese27 (13.6)
Hindi12 (6.06)
Punjabi7 (3.53)
Spanish5 (2.52)
Other/no response34 (17.2)
Principal languages spoken by clientelea
English191 (97.0)
French37 (18.8)
Arabic17 (8.60)
Chinese23 (11.7)
Hindi18 (9.13)
Punjabi12 (6.09)
Spanish7 (3.55)
Other/no response27 (13.7)

aDoes not total 100% as respondents could select multiple responses.

We conducted 17 in-depth interviews with pharmacists practicing in Ontario; we completed 15 in English and two in French. Our interviewees worked in independent (n = 7), chain (n = 3), and banner (n = 7) pharmacies, and 12 self-identified as women.1 Almost all interviewees worked in pharmacies located in urban areas (n = 15) and in the central and south (n = 11) regions of the province.

1A banner pharmacy is independently owned and operated, but for a fee affiliates with a central office and uses a recognized name.

Ontario pharmacists’ knowledge of progestin-only EC

Overall, survey respondents demonstrated accurate knowledge of progestin-only EC. The majority of our participants (68.5%) correctly identified 1.5 mg of levonorgestrel taken as one dose as the evidence-based regimen and cited the most common side effects as nausea (96.9%), vomiting (76.4%), and inter-menstrual bleeding (53.3%). Three quarters of respondents reported that progestin-only EC must be taken within 72 h (n = 145, 75.1%) or within 120 h (n = 29, 15.0%), and 72.8% (n = 142) correctly indicated that efficacy decreases when the drug is taken more than 24 h after intercourse.

However, our survey results indicated that confusion persists surrounding the primary mechanism of action and how to manage side effects. Fully three quarters of our participants (n = 150, 77.7%) incorrectly indicated on a true/false question that progestin-only EC’s primary mechanism of action is to inhibit implantation, and nearly half (n = 91, 48.4%) reported that progestin-only EC should be taken in conjunction with a meal, a recommendation that is not evidence based. In addition, 26.5% (n = 50) of our respondents indicated that there is a limit to the number of times that a woman can take progestin-only EC in one menstrual cycle.

Consistent with Health Canada’s warning, 70.5% (n = 134) of our participants reported that the efficacy of progestin-only EC is lower in women weighing 75 kg or more. Several of our in-depth interview participants also discussed the weight efficacy issue and explained that they routinely inform patients of this risk. As explained by a Francophone pharmacist working at a pharmacy in the eastern region of the province:Guidelines and studies are not yet clear enough for me to decide whether I should provide [progestin-only EC] or not. If an 80 kg women does not want to become pregnant I do not want to be the cause [of an unwanted pregnancy]. There are few side effects, no down sides [to progestin-only EC]… we can still provide it but recommend women consult with a doctor later on. But this gives lots of women a false sense of security.

Progestin-only EC availability

Almost all survey respondents (n = 177, 93.2%) reported having progestin-only EC in stock at the time of the survey; Plan B®, Next Choice®, and Option 2® were carried by 97%, 26%, and 25% of these pharmacies, respectively. Of those pharmacies that carried a progestin-only EC product, the reported price ranged from $20 CAD to$60 CAD; consistent with drug pricing in general, the price of the brand product was generally higher than the price of generics. We did not detect statistically significant differences in price based on region or pharmacy type. Those pharmacies without progestin-only EC in stock related this to patient demographics, particularly elderly patient populations. However, most respondents (n = 179, 94.2%) indicated that the pharmacy receives requests for EC from patients, from less than 1 to more than 50 each month; the majority of respondents (n = 145, 83.8%) reported receiving 1–5 requests per month.

Despite the long-standing OTC regulatory status of progestin-only EC in Ontario, about half of our sample reported carrying at least one brand of progestin-only EC OTC (n = 91, 51.4%), and the other half reported carrying at least one progestin-only EC product BTC (n = 85, 48.6%). Eleven respondents (6.25%) reported having products on both the main shelf and behind the pharmaceutical counter. Among our interviewees, only 4 of 17 carried all progestin-only EC products OTC. There was no difference in the placement between regions and all chain pharmacies reported carrying at least one product BTC.

The interviews gave us insight into why pharmacists continue to keep the medication BTC. The majority of our interviewees (n = 12) kept progestin-only EC BTC to counsel patients and (or) create an opportunity for consultation. As explained by an Anglophone pharmacist working in an independent pharmacy in the southern region:I think there is pharmacist intervention needed. I always make sure that the patient present is the one that, like the female patient is presenting to the pharmacy to ask for it. And that there is [specific] advice and learning appropriate for the patient. All of that is not done when it’s over-the-counter. And there is a need to get patient details… I just want to make sure that this is going to be effective and safe for them.

Interviewees also indicated that concerns about theft, particularly of the more expensive branded product, and the absence of space factored into placement decision-making. Two of our interviewees kept the medication BTC because of a lack of understanding of the current regulations.

Progestin-only provision practices

In general, survey respondents reported that pharmacies provide a dedicated space for consultation (n = 178, 93.7%) and about a third (n = 70, 36.8%) sometimes use a screening or counseling tool during an EC-related consultation. Interview participants reported providing those seeking progestin-only EC with information and also asking a range of questions. Most of the EC information centered on side effects, regimen, future pregnancy prevention, and weight. Questions typically focused on the timing of intercourse, previous use of EC, and whether or not the woman wanted additional information. As noted by one Anglophone pharmacist working in the eastern region in a chain pharmacy:The most important [question] is when did it happen? You want to check if they’re eligible or not, sometimes they don’t know and they come and then you’re like “whoah don’t buy it,” so I always ask when for sure. Almost all of our interviewees (n = 16) felt that obtaining EC should include a mandatory standardized consultation with a pharmacist.

About a quarter of our survey participants (n = 45, 23.9%) reported that they had, at least on occasion, not provided progestin-only EC to someone who had requested it. Survey participants indicated their primary reasons as (1) not having the medication in stock (n = 16, 37.2%); (2) identifying that the unprotected intercourse occurred outside of the timeframe for use (n = 14, 32.6%); (3) confirming or suspecting a pregnancy (n = 13, 12.6%); (4) the patient not presenting in person (n = 10, 23.3%); or (5) the patient having contraindications or drug interactions (n = 7, 16.3%). None of the interviewees ever refused to provide the medication to a patient, but five had referred women to other reproductive health care providers. One of our Francophone participants from northern Ontario explained, “One of our patients was coming into the pharmacy almost once a month to get a Plan B®. So I referred her to [the] Health Unit for a birth control pill”.

Most survey respondents (n = 134, 70.9%) reported that their comfort in providing EC was on par with providing other medications; only 16.4% (n = 31) reported feeling less comfortable providing information about EC. Although most survey respondents reported having never obtained continuing education about EC, the overwhelming majority (n = 166, 86%) expressed interest in receiving information about EC in the future. Participants in our interviews were enthusiastic about the possibility of engaging in continuing education around EC. One interviewee working at a chain pharmacy in the southern region of Ontario highlighted:I think we did not cover [EC] well at all in school. As a recent grad, I remember exactly what happened. [EC] is something I’ve learned through practice and through different continuing events or word around the pharmacy community. I am sure that a lot of us would join [an EC continuing education course].

Discussion

General implications

A number of studies in North America have indicated that BTC status poses a barrier to timely access to progestin-only EC (Cohen et al. 2003; Erdman 2012; Wynn and Foster 2012). Furthermore, requiring a pharmacist consultation to obtain progestin-only EC subjects women to intrusive questions, raises privacy concerns, creates opportunities for pharmacists to deny women services, and increases costs (Eggertson and Sibbald 2005; Wynn et al. 2007; Eggertson 2008; Erdman 2012). Finally, keeping the product BTC creates a barrier for men who wish to purchase progestin-only EC on behalf of a friend or partner. These dynamics have shaped global and Canadian advocacy efforts to deregulate progestin-only EC (Erdman 2012; Foster and Wynn 2012).

Our results suggest that in stock availability of progestin-only EC remains comparable with the findings of Dunn et al. (2008). However, despite the regulatory change to OTC status that occurred subsequent to that study, nearly half of our survey participants reportedly carry at least one progestin-only product BTC. Circulating a reminder about progestin-only EC’s OTC status through a trusted source, such as the Canadian Pharmacist’s Letter, could address persistent confusion about the drug’s regulatory status and appears warranted.

However, Canadian pharmacists have been long-standing advocates of BTC status (Eggertson 2008; Erdman 2012). Indeed, our interviews highlighted that for many pharmacists, the decision to carry EC BTC is not based in misinformation about the regulatory status but rather in a belief that a consultation is necessary and valuable. The pharmacists interviewed for the study reported that these consultations benefitted women, especially with respect to determining eligibility for use; our interviewees did not express concern that these consultations might be perceived as intrusive or could create barriers to seeking care. Some pharmacists appear to be ignoring the regulatory status of progestin-only EC and effectively imposing BTC status on the drug, a dynamic that professional pharmacy associations may want to explore further.

Whether pharmacists in Ontario are requiring consultations or simply providing information about progestin-only EC when those who are procuring the drug have questions, it is essential that health service professionals provide evidence-based information. Yet our results demonstrate that pharmacists’ knowledge continues to be incorrect or incomplete with respect to the mechanism of action and the management of side effects. For example, routinely advising a patient to take EC in conjunction with an anti-emetic and (or) food is not evidence based (Raymond et al. 2000; Trussell 2012) and may increase the overall cost of treatment. Thus, developing continuing education resources for pharmacists, and educational resources that could be used by pharmacists in training, may address the existing gaps in knowledge.

As of the end of 2016, Canada was the only country in the world that had a formal warning about the association between weight and efficacy on the label of progestin-only EC products. Indeed, in 2014, the European Medicines Agency (EMA) retracted its original decision to include information about the weight efficacy issue from progestin-only EC product labels (EMA 2014). This has undoubtedly caused confusion among health care providers and anecdotal evidence suggests that provider practices in Canada are inconsistent (Eggertson 2014). Our findings further confirm that pharmacists have operationalized this label change in different ways. Black and Guilbert (2015) recently issued recommendations to address this issue, and our results suggest that the dissemination of evidence-based guidelines about the relationship between efficacy and weight, and a reminder to pharmacists that as an OTC product all people should be able to purchase the medication, is a priority.

Finally, the recent introduction of UPA into the Canadian health system for post-coital pregnancy prevention offers an opportunity to engage in discussion with both health service professionals and the public about all EC modalities. This is especially important given the different regulatory statuses that UPA (prescription required as of early 2017) and progestin-only EC (OTC) have and will likely continue to have in the immediate future. Developing Canada-specific educational resources for both providers and potential users could facilitate efforts to expand access to a full range of post-coital contraceptive methods.

Limitations

Despite four contacts, the response rate to our survey was low (less than 15%), and thus, our 198 respondent pharmacies represent less than 5% of retail pharmacies in Ontario. This necessarily limits the generalizability of our findings, which are best characterized as exploratory. Furthermore, we received very few responses from pharmacies in language minority communities. Future research that focuses specifically on this population should be prioritized. Although we instructed participants not to consult reference material when taking the survey, some participants may have looked up answers thus resulting in elevated levels of knowledge and a skew toward the best practices.

Conclusion

Health Canada’s recent approval of ulipristal acetate for use as a post-coital contraceptive may provide a window of opportunity for engaging with health service providers, including pharmacists, about all modalities of EC available in Canada. The findings from our study suggest that continuing education efforts that focus on both the regulatory status of progestin-only EC and information about the medication are warranted and would be welcomed by retail pharmacists in Ontario.

Acknowledgements

Andréanne Chaumont received a Queen Elizabeth II Graduate Scholarship in Science and Technology and several grants from the University of Ottawa to support this project. Dr. Foster’s 2011–2016 Endowed Chair in Women’s Health Research was funded by the Ontario Ministry of Health and Long-Term Care and the funding attached to her Chair covered the costs associated with this study. We are also grateful to the Society of Family Planning for its support of Dr. Foster’s mentorship activities. We would like to thank Drs. Raywat Deonandan and Karen Phillips for their feedback during various phases of this project and Dr. Sheila Dunn for providing us with her survey instrument. We are also grateful to the team of volunteers for their efforts. Both authors had full access to all the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis. The conclusions and opinions expressed in this paper are those of the authors and do not necessarily represent the views of the organizations with which the authors are affiliated or the funders.

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• European Medicines Agency. 2014. Levonorgestrel and ulipristal remain suitable emergency contraceptives for all women, regardless of bodyweight [online]: Available from: ema.europa.eu/ema/index.jsp?curl=pages/news_and_events/news/2014/07/news_detail_002145.jsp&mid=WC0b01ac058004d5c1.

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