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Excellent post! And I agree, the community aspect is one thing that makes "second wave" book blogs distinct from "literary" blogs and helps define it as having a different purpose, different place, and therefore a distinct legitimacy in its own right.
I think it all just boils down to the fact that blogs are, by their very nature, very fluid and flexible entities. Because blogging is open to all, blogs and the bloggers who write them will always be in a constant state of flux. In other words, being a blogger means living with a continually changing environment. We all know lots of people who are very resistant to change, so these types of arguments, like this one about professional vs. amateur bloggers, will always be around.
Take a look at Dooce: would you call her a personal blogger or a professional? She writes about her personal life, but she makes a full-time living with the ads she sells on her blog, and even appeared on Oprah.
Given the nature of blogs and blogging, these kinds of questions simply have no "right" answer. Your blog is simply whatever you want to make of it – that is the essence of what makes a blog a blog.
Fluid and flexible, that's a good reminder.
I think every blogger will end up having the kind of blog they want to have. I was really taken aback by this whole idea that I was supposed to be a professional! I have never thought of my blog in those terms, so I guess I "flaunt" my amateur status. Never really meant to it was just that I never thought of myself as a professional.
I love the many different voices and hope we can all see there is indeed space for them all.
I, too, enjoy the collective, and think there's certainly space for the many voices.
What GalleySmith had to say about target made sense to me. Define yourself and what you are setting out to accomplish. Don't let anyone else define you. As far as bridging gaps, I don't prevent anyone from interacting with me or my blog and I never felt that anyone else ever did that to me. I would hope that everyone would respect each other. Does that make sense? Maybe I'm missing something.
You and I got started at about the same time; and, I, too, was outside the book blogging community until 2008.
Yes, I agree, targeting our individual audiences does make sense.
About this: "I don't prevent anyone from interacting with me or my blog and I never felt that anyone else ever did that to me. I would hope that everyone would respect each other." Yes, it makes sense.
This is an interesting part of the debate between "side A" and "side B" — the "what if I don't fit into either" aspect of it all. The thing of it for me is that I don't really think there are sides so much as there are differences. More than two even. There are any number of different types of book/lit blogs and labeling things only polarizes people. Of course it's likely impossible for any discussion to take place without some sort of labeling system since it's how we are able to compartmentalize and distinguish this from that.
In the end, since I doubt that labeling will go away I think we are best served by self-identifying. That takes away the adversarial nature of finger pointing or the feeling of "name calling" when someone else does it for you. So I wouldn't dream of trying to comment on where you fit in because I think we all make that choice ourselves. All I know is that I enjoy reading your thoughts no matter if you are part of first wave, second wave, side A or B.
Great summary to the two sides! I actually posted a Sunday Salon today that talks about "Book Snobbery" because I was tired of the jabbing here and there. I think your approach here, discussing where we all fit, and the possible "whys" behind our choices is really well done! In the end, as non-paid (for the most part) book bloggers, we're not doing all of this for anything more than the satisfaction of sharing great books and making friends who feel the same!
Thanks for your overview and post!
Wow, somehow I have missed this debate – I saw some of it on Amy's site, and left a comment there, a while ago. I don't take it seriously, the lit bloggers making fun of 'non-professionals', partly because I don't care – I did my degree in English literature, and I know how pretentious that world can be. Anyone who says ideas and thoughts have to be couched in a certain form in order to be taken seriously, is a turn-off for me. I'm not interested in pleasing critics. When I started blogging, it was all new to me, and my purpose is to write and be honest about my feelings about books, and what I'm reading, and sometimes life.
I think the book-blogging community has so much to offer – not in terms of the latest literary theory and discussions on why some metaphor was used – but because it's like a gauge for authors and readers to know how books are really being received by the public. We're the readers that fuel the book industry, not the critics. So I'd much rather know what book bloggers, who blog for love of books, think about a book.
I hope this helps a bit. Very thought-provoking post, Wordlily!
I also have a journalism degree though I've never been paid to write a book review. I do try to main a certain level of professionalism to my blog in that I never write anything that I wouldn't want a potential employer (or my father) to read.
anks for discussing this and raising your questions. I find myself between two worlds as well. I'm a writer that started in the academic community, writing journal articles and academic reviews and then a series of YA non-fiction books. I started blogging about books and the writing life in 2005, independent of any community. Simply because of my background, the reviews I wrote for my blog were more cerebral/professional/authoritative/what have you; and though I have tons of lurkers, they tend not to comment on those posts. So I have started to shift the overall tone of my blog, learning to become more community-oriented, because I really do want to TALK with people about the books we're reading. I suspect that just being me is in itself a bridge between the two worlds. I'm not sure how my readers would classify my blog, but I agree with the other commenters here that all that's really important to me at this point is that 1) I am true to myself and my opinions about the books I read, and that 2) everyone feel welcome at all times to join the conversation at my site.
That is a really interesting post. I didn't realise that was the definition of a 'lit blog' I always assumed that 'lit blogs' reviewed literary fiction and therefore tended to have longer reviews that analysed the symbolism/writing structure of the book.
I thought I fell in the middle as I tend to review literary fiction, but in a 'book blogger' way. Now I know I'm definitely a book blogger and am proud to be one!


text:
takefootball
For those who take football too seriously
Snaps & Opinion
HomeEuropean LeaguesPSG confident of signing Di Maria in £46.5m…
PSG confident of signing Di Maria in £46.5m deal
July 26, 2015 July 28, 2015 paul meadows	Leave a comment 290 views
Laurent Blanc believes Paris Saint Germain are very close to concluding a transfer for Manchester United forward Angel Di Maria.
The Reds paid a club record £59.7million to take the Argentina international from Real Madrid last summer, at a time when financial fair play regulations made it impossible for PSG to compete. It was suggested at the time, although never confirmed, that the player would have preferred a move to France, but had to settle for a switch to Old Trafford instead.
Di Maria made a bright start to life in England, but his form badly trailed off as he had to deal with issues off the pitch when his house was burgled. He also suffered injury problems during his debut campaign in the Premier League, and he ended the season with 32 appearances to his name and four goals, but only Cesc Fabregas and Santi Cazorla made more than his 10 assists.
Louis van Gaal was hopeful that the 27-year-old would form part of his exciting side for the new campaign, but this is looking increasingly likely after the forward missed his flight to the United States to link up with his team-mates. This comes amidst reports that PSG have lodged a £46.5million bid for his signature, and one which Blanc appears confident of succeeding.
"I have no official news," said the PSG coach, a former player for United. "PSG are looking for an offensive player. Will it be Di Maria? I hope so. He plays for Manchester United at the moment and I hope that if that changes, it will be that he comes to us. We have to have patience a little longer. It's not easy, between two big clubs. The outcome is very close, in my opinion."
United, meanwhile, continued their impressive pre-season form with a 3-1 win against European champions Barcelona on Saturday evening. Wayne Rooney gave the Premier League side a half-time lead, with Jesse Lingard and Adnan Januzaj scoring the other goals. Pedro, who has been heavily linked with a move to Old Trafford, lined up for the Spaniards.
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text:
Knowledge Tree Pillars
People as Partners in Care
Transparency of progress, results and impact
Population health and wellbeing
Aligned payment systems
System wide governance and leadership
Shared values and vision
Resilient Communities & New Alliances
Workforce capacity and capability
Context search
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Conference search
People and organisations search
IJIC issues search
International Journal of Integrated Care – IJIC
Theories, Framework and Tools
Adolescent feedback on the Haemophilia Transition Programme between Our Lady's Children's Hospital and St. James's Hospital Dublin Ireland
Authors: Ruth Elizabeth Hunter Nolan , Eibhlin Mc Laughlin, Yvonne Duane, Ann O' Sullivan, Kevin Ryan, Niamh O' Connell, Beatrice Nolan
Abstract Introduction: Haemophilia is an X-linked congenital bleeding disorder caused by the absence or low level of particular proteins called clotting factors, specifically factor VIII or factor IX in the blood (1). The complexity of the condition be can be particularly challenging during adolesence, as the young adult assumes responsibility for managing their condition. In order to improve and standardise the transition pathway for young adults with haemophilia in Ireland, a Transition Programme was established in 2012 between the National Paediatric Coagulation Centre , Our Lady's Children's Hospital (OLCHC) and the National Coagulation Centre (NCC), St. James's Hospital, Ireland.Targeted population: To determine if the Transition Programme was addressing the needs and preferences of this patient group, a satisfaction survey was distributed to 83 patients in July 2016. The questionnaire comprised of 50 qualitative and quantitative questions and incorporated categories relating to the paediatric and adult service, knowledge of condition, self- management and general health. The questionnaire was approved by the NCC Patient Partnership Panel. The response rate was 23% (N=19)Highlights: 90% respondents reported that they felt prepared for their move from paediatric to adult services. Respondents expressed satisfaction with staff interactions, describing staff as helpful and pleasant.53% were not confident that they knew how to access the adult service after 5pm and 33% reported that they required additional information about the adult service. 26% of adolescents reported that they were not confident that they could recognise a bleeding episode. 21% of the adolescents surveyed were unsure about appropriate oral care. Five patients (26%) highlighted the need for access to personalised information about managing their condition and relevant services in the adult treatment centre. A shared action plan was developed as follows:Develop a Transition information leaflet.Develop a "Transition Pack" " containing information leaflets about the adult services, condition specific information and transition information.Facilitate group meetings for parents and adolescents.Distribute a parental satisfaction survey.Develop a shared electronic nursing care plan.Develop a patient portal where adolescents can access information about their treatment centre, condition, self-management and relevant education. This will also include an online transition education programme.Comments on Transferability: The questionnaire utilised can be adapted for evaluating other chronic disease transition programmes and the improvement initiatives could be adopted to develop transition programmes in haemophilia services internationally.Conclusions: Feedback on the Transition Programme between OLCHC and NCC revealed that the majority of young adults surveyed felt adequately prepared to transfer to the adult service. However; significant knowledge gaps about their condition and a lack of awareness regarding services available were also discovered. The multidisciplinary team in OLCHC and NCC have identified a number of initiatives that will improve adolescent satisfaction and develop the adolescent's condition knowledge and self-management skills.References:1- World Federation of Hemophilia. GUIDELINES FOR THE MANAGEMENT OF HEMOPHILIA 2nd edition. c2012. Available from: http://www1.wfh.org/publications/files/pdf-1472.pdf.
haemophilia, transition, patient feedback
Hunter Nolan RE, Mc Laughlin E, Duane Y, O' Sullivan A, Ryan K, O' Connell N, et al.. Adolescent feedback on the Haemophilia Transition Programme between Our Lady's Children's Hospital and St. James's Hospital Dublin Ireland. International Journal of Integrated Care. 2017;17(5):A569.
DOI: http://doi.org/10.5334/ijic.3889Published on 17th October 2017


2019 Goals: 1) Code more. 2) Eat like a vegan. 3) Build fun lamps as a hobby. 4) Publish progress of each on https://t.co/vS43kkV1wv at least monthly.
Let's break these out a bit more.
One of the big changes in 2018 was taking a new job as Principal Software Engineer at FM:Systems. In this role, much more than my previous job as Director of a consulting division, I get to write code. Lots of code. Every day code and more code. It's fantastic.
So Goal Achieved, right? Yes, but there's more. Returning to a full engineering role has reminded me that there is so much out there that code can do, but also so much that needs practice and coaching. Coding, like any skill, can have both a certain muscle-memory, as well as atrophy when not exercised. So the practical application of Code More is to really focus on depth of knowledge with .Net Core and C#, as well as best practices for architecture, unit testing, and new things like Infrastructure-as-Code.
This Goal is a bit hard to measure per se, so my metric will be blog posts for things I've learned, tried, continue to need practice in, and success stories.
For most of my life, I have dealt with a couple chronic health conditions, namely asthma and eczema. Over the past decade I've dabbled with a variety of what I'll call non-medical solutions, including acupuncture, cutting out or minimizing certain foods, and supplements of all kinds. In short, nothing has moved the needle.
This past week, my wife and I watched Eating you Alive, a movie promoting adoption of a Whole Food Plant Based diet. Participants in the documentary told story after story about how giving up meat, dairy, sugar, and oils had dramatic impacts on their health, including reversal of cardiovascular conditions, cancers, and obesity.
Thankfully, I am in generally good health. I have been blessed (cursed?) with an ectomorph body type. My weight has been unchanged for 20 years. I feel good when I work out (as well as any 40 something, right?) and I've been spared any major health incidences.
But I don't feel healthy. And clearly, as evidenced by my itchy red skin and wheezy congested lungs, there are some things, shall we say, out of whack!
Adopting a vegan diet is not going to make me happy. I have a real fondness for steak. I am probably addicted to sugar. But for at least a month at a time, I'm going to try. Here's to kale in 2019.
To track progress on this goal, I don't plan to write out my favorite recipes -but rather be an engineer about it. I'm working up a series of actual, measurable, health tracking values that I can monitor and report upon. Since redness in my face is my primary visible symptom, I've thought about taking pictures in a controlled location/environment, and using histogram data to track my actual appearance. More to come on that.
All my life I've been a builder. I am comfortable working with my hands, I have a full workshop of tools, and in 2017 I took on the significant project of finishing my basement. However, like coding, I wanted to define some parameters around building that allowed me to really practice my skills. To that end, I have decided to build lamps.
Lamps are simple objects. But they can take unlimited form. They can be made of wood, pipe, or found objects. They can be upcycled, recycled, made out of uni- bi- tri-cycles. They can be classic or modern, industrial or country. Basically, there is no wrong answer.
They don't know it yet, but my metric of this goal is to produce enough lamps during the course of the year to give as Christmas gifts to each of my family members. Parents + 2(siblings) + 2(inlaws) + wife + 4(children) = 10 creations. Roughly one per month.
I'll use this blog to post my designs, and where appropriate, talk about the challenges or discoveries I made along the way for each one.
So that's it! 2019 is planned and sized and ready for action. I'm excited to share my progress. Thanks in advance to those who might follow.
Good luck for your goals. Happy New Year!
It's good to see in 19′, that the light is being turned on! 🙂 Happy New Year to you & yours sir!


Image Title: Deer Proof Garden Fence Some Nice Photos From Chris In Raleigh NC Intended For Prepare 0. Post Title: Deer Proof Fence. Filename: deer-proof-garden-fence-some-nice-photos-from-chris-in-raleigh-nc-intended-for-prepare-0.jpg. Image Dimension: 1600 x 1200 pixels. Images Format: jpg/jpeg. Publisher/Author: Burley Schaden. Uploaded Date: Monday - October 01st. 2018 01:00:04 AM. Category: Architecture. Image Source: digsdigs.com. Garden Fence How Landscaping Ideas In Decor NC TOP Vegetable Exterior 2. Around 2018 Regarding Proof Panels Install Think For 13. To Remodel 20 Sunset Magazine Photos Co Regard From 8. Some Intended Nomadswe Yard Deer With Would Prepare Video Pertaining Like 3. Your A Fencing Designs 4. Outdoors Nodak Lowpricegolfaus Metal Or 18. Com Diamond Resistant Chris 0. Within 6. And Raleigh I Interior The 17. Nice 11.


text:
Judge Upholds "Affluenza" Teen's 2-Year Sentence
Texas Judge Wayne Salvant signed an order Wednesday.
NewsOne Staff
A Texas judge on Wednesday ruled that Ethan Couch, known as the "affluenza teen," must serve out his two-year jail sentence.
Couch's lawyers tried to argue that Judge Wayne Salvant exceeded the court's authority in April when he ordered their client to "spend 180 days in jail for each of the four people he killed in 2013 when he rammed a pickup truck into a crowd of people helping a motorist," reports the New York Daily News.
But Salvant upheld the order and canceled a May 16 hearing on the matter, the report says.
From CBS News:
The judge also set several conditions for Couch's probation when he does leave jail. Couch will not be allowed to drink, use drugs or drive, and he will be required to meet regularly with a community supervision officer.
In June 2013, at age 16, Ethan Couch was driving drunk and speeding when he crashed into a disabled SUV on the side of the road, killing four people and injuring nine others. Many of the victims had been helping the woman whose SUV had stalled, others were in Ethan Couch's pickup truck.
The 16-year-old's blood-alcohol level was three times the legal limit for an adult and there were traces of Valium in his system.
Couch and his mother fled to Mexico in December, a violation of his probation. He was extradited back to the U.S. in January, and his case was transferred from juvenile court to the adult legal system on April 11.
SOURCE: New York Daily News, CBS News | PHOTO CREDIT: Getty
Affluenza Teen Sentenced To 2 Years In Prison
Affluenza Teen Ethan Couch In U.S. Custody, Faces Hearing
Judge Upholds "Affluenza" Teen's 2-Year Sentence was originally published on newsone.com
Affluenza Teen Ethan Couch


Why the Craze For Likes?
These likes are just there to tell you whether people like what you posted or not. It doesn't go beyond that.
Whether you get 10 likes or 1000 likes on your picture. Likes are just likes. You don't have to judge yourself by number of likes.
You don't have to to almost go naked on social media just to get "likes" when it's not your thing. For Christ's sake, what are likes?
You don't have to pretend to support a particular group or ideology, just to get likes.
Are you gonna die without it? Does it give you money? Weren't you surviving before social media took over?
So why the heck are you crazed about getting likes?
Social Media platform is for networking and "genuinely" expressing ourselves and who we really are.
Always tailoring your posts to suit the public likes or sound politically correct is just plain stupid because we know that public approval does NOT ALWAYS mean that something is true.
Be true to yourself and don't lose your head to get likes on social media.
1 like or 1 billion likes, doesn't matter much. There's a reason Facebook allows you to like your own posts.


Hello Ga governor, BRIAN KEMP, i would like ask you why you allow illegal people driving without driving license.righ here in Norcross, gwinnett ga, 35% driving without driving license. They say isn't a crime. officers do not ticket them. i proof it. Other go to state of south Caroline to buy it. they pay under the table. corruption.? HOW MANY, HIT AND RUN, nobody kows who is who.


ISCB is seeking scholars interested in serving as the ISCB representative to the FASEB Editorial Board for the FASEB Journal (FJ). If you are interested, please submit the following information using our online system. If you have a colleague who may enjoy serving in this position for ISCB, please feel free to forward this information.
FASEB counts on these Society representatives to provide opinions to the Editors, review papers, suggest other reviewers as appropriate, and invite them to submit content to the Journal. The level of activity varies depending on the scientific area of submissions, but FJ has over 50 Editorial Board members (including the Society representatives) that collectively handle about 680 submissions per year after an initial query stage.
Editorial Board members are also invited to an annual FASEB Journal face-to-face meeting to discuss content, submissions, the peer-review process, misconduct, etc. The 2016 meeting will be March 22 in Crystal City, USA.
Applicants must be a member of ISCB and have a doctorate (or an equivalent degree), and significant publishing and reviewing experience. Due to the high volume of applications, only accepted applicants will be contacted via email.
Which journals do you currently serve (List of Journals)?


text:
\section{Introduction}
\label{sec:intro}

The disk-integrated flux of a spotted, rotating star often varies in a
non-sinusoidal and Quasi-Periodic (QP) manner, due to active regions on its
surface which rotate in and out of view.
Complicated surface spot patterns produce non-sinusoidal variations, and the
finite lifetimes of these active regions and differential rotation on the
stellar surface produce quasi-periodicity \citep{Dumusque2011}.
A strictly periodic sinusoid is therefore not necessarily a good model choice
for these time-series.
A physically realistic model of the stellar surface
would perfectly capture the complexity of shapes
within stellar light curves as well as the quasi-periodic nature, allowing for
extremely precise probabilistic period recovery when conditioned on the data.
However, such physical models require many free parameters in order to
accurately represent a stellar surface, and some of these parameters are
extremely degenerate \citep[{\it e.g.}][]{Russell1906, Jeffers2009, Kipping2012}.
In addition to global stellar parameters such as inclination and rotation
period, each spot or active region should have (at minimum) a longitude,
latitude, size, temperature and lifetime.
Considering that stars may have hundreds of spots, the number of free
parameters in such a model quickly becomes unwieldy, especially to explore its
posterior Probability Density Function (PDF).
Simplified spot models, such as the one described in \citet{Lanza2014} where
only two spots are modelled, have produced successful results; however, such
relatively inflexible models sacrifice precision.

Standard non-inference based methods to measure rotation periods include
detecting peaks in a Lomb-Scargle \citep{Lomb1976, Scargle1982} (LS)
periodogram \citep[{\it e.g.}][]{Reinhold2013}, Auto-Correlation Functions (ACFs),
\citep[{\it e.g.}][]{Mcquillan13b} and wavelet transforms \citep[{\it e.g.}][]{Garcia2014}.
The precisions of the LS periodogram and wavelet methods are limited by the
suitability of the model choice: a sinusoid for the LS periodogram, and a
choice of mother wavelet, assumed to describe the data over a range of
transpositions and scales \citep[see, {\it e.g.}][]{Carter2010}, for the wavelet
method.
In contrast, since it does not rely on a generative model, the ACF method is
much better suited to signals that are non-sinusoidal.
In fact, as long as the signal is approximately periodic the ACF will
display a peak at the rotation period, no matter its shape.
A drawback of the ACF method however, is that it requires data to be
evenly-spaced.
Most ground-based measurements, such as the future Large Synoptic Survey
Telescope ({\it LSST}), do not nearly satisfy this criterion, and even
light curves from the {\it Kepler}\ space telescope, which has provided the richest
stellar rotation data to date, can only be approximated as uniformly sampled.
An ACF is also an operation performed on the data rather than a generative
model of the data, and so is not inherently probabilistic.
This means that the effects of the observational uncertainties cannot be
formally propagated to constraints on the rotation period.

In this work, we test an {\it effective} model for rotationally modulated
stellar light curves which captures the salient behaviour but is not
physically motivated --- although some parameters may indeed be {\it
interpreted} as physical ones.
An ideal effective model should have a small number of non-degenerate
parameters and be flexible enough to perfectly capture non-sinusoidal and QP
behaviour.
A Gaussian process (GP) model fulfills these requirements. We thus use a GP
as the generative model at the core of a method to probabilistically
infer accurate and precise stellar rotation periods.
This enables us to estimate the posterior PDF of the rotation period, thereby
producing a justified estimate of its uncertainty.
\response{Using a quasi-periodic GP model to infer a rotation period is not a new
idea.
For example, we used this method in \citet{Vanderburg2015} to measure the
rotation period of an exoplanet host.
Previously to that, \citet{Haywood2014} used the quasi-periodic GP model
to disentangle the correlated noise produced by stellar activity and rotation
from the radial velocity signature of an exoplanet.
In addition, \citet{Littlefair2017} use a quasi-periodic GP to establish the
quasi-periodicity of variability in the light curves of brown dwarfs.
What we present here is a test of the GP method and a comparison with
alternative rotation period measurement methods.
We also provide code allowing others to easily apply this technique
themselves.}

GPs are commonly used in the machine learning community and increasingly
in other scientific fields such as biology, geophysics and cosmology.
More recently, GPs have been used in the stellar and exoplanet fields within
astronomy, to capture stellar variability or instrumental systematics
\citep[see {\it e.g.}][]{Gibson2012, Haywood2014, Dawson2014, Barclay2015,
Haywood2015, Evans2015, Rajpaul2015, Czekala2015, Vanderburg2015, Rajpaul2016,
Aigrain2016, Littlefair2017}.
They are useful in regression problems involving any stochastic process,
specifically when the probability distribution for the process is a
multi-variate Gaussian.
If the probability of obtaining a dataset is a Gaussian in $N$ dimensions,
where $N$ is the number of data points, a GP can describe that dataset.
An in-depth introduction to Gaussian processes is provided in
\citet{Rasmussen2005}.

GP models parameterise the covariance between data points by means of a
kernel function.
As a qualitative demonstration, we present the time-series in figure
\ref{fig:GP_example}: the \Kepler\ light curve of KIC 5809890.
This is a relatively active star that rotates once every $\sim$
30.5\ days, with stochastic variability typical of \Kepler\ FGK
stars.
Clearly, data points in this light curve are correlated.
Points close together in time are tightly correlated, and points more
widely separated are loosely correlated.
A GP models this variation in correlation as a function of the separation
between data points; that is, it models the {\it covariance structure} rather
than the data directly.
This lends GPs their flexibility---they can model any time
series with a similar covariance structure.
In addition, a very simple function can usually capture the covariance
structure of a light curve, whereas modelling the time series itself
might require much more complexity.
Figure \ref{fig:GP_example} demonstrates how a GP model fits the light curve of
KIC 5809890.

A range of covariance models, or kernel functions, can describe stellar
variability.
For example, the most commonly used kernel function, the `Squared
Exponential' (SE), defined as follows, could adequately fit the
KIC 5809890\ light curve:
\begin{equation}
\label{eq:SE}
k_{i,j} = A \exp \left(-\frac{(x_i - x_j)^2}{2l^2} \right).
\end{equation}
Here $A>0$ is the amplitude of covariance, $l$ is the length scale of
exponential decay, and $x_i-x_j$ is the separation between data points.
The SE kernel function has the advantage of being very simple, with
just two parameters, $A$ and $l$.
If $l$ is large, two data points far apart in $x$ will be tightly correlated,
and if small they will be loosely correlated.
Another property of the SE kernel function is that it produces functions that
are infinitely differentiable, making it possible to model a data set
and its derivatives simultaneously.
However, The SE kernel function does not well describe the covariance
in stellar light curves, nor is it {\it useful} for the problem of
rotation period inference because it does not capture periodic behaviour.
Inferring rotation periods thus requires a periodic kernel
function.
For this reason, we use the `Quasi-Periodic' kernel.
\citet{Rasmussen2005} model QP variability in CO$_2$ concentration on the
summit of the Mauna Loa volcano in Hawaii \citep[data from][]{Keeling2004}
using a kernel which is the product of a periodic and a SE kernel: the QP
kernel.
This kernel is defined as
\begin{equation}
\label{eq:QP}
k_{i,j} = A \exp \left[-\frac{(x_i - x_j)^2}{2l^2} -
    \Gamma^2 \sin^2\left(\frac{\pi(x_i - x_j)}{P}\right) \right] + \sigma^2
    \delta_{ij}.
\end{equation}
It is the product of the SE kernel function, which describes the overall
covariance decay, and an exponentiated, squared, sinusoidal kernel function
that describes the periodic covariance structure.
$P$ can be interpreted as the rotation period of the star, and $\Gamma$
controls the amplitude of the $\sin^2$ term.
If $\Gamma$ is very large, only points almost exactly one period away are
tightly correlated and points that are slightly more or less than one period
away are very loosely correlated.
If $\Gamma$ is small, points separated by one period are tightly
correlated, and points separated by slightly more or less are still highly
correlated, although less so.
In other words, large values of $\Gamma$ lead to periodic variations with
increasingly complex harmonic content.
This kernel function allows two data points that are separated in time by one
rotation period to be tightly correlated, while also allowing
points separated by half a period to be weakly correlated.
The additional parameter $\sigma$ captures white noise by adding
a term to the diagonal of the covariance matrix.
This can be interpreted to represent underestimation of observational
uncertainties~---~if the uncertainties reported on the data are too small, it
will be non-zero~---~or it can capture any remaining ``jitter,'' or residuals
not captured by the effective GP model.
We use this QP kernel function (Equation \ref{eq:QP}) to produce
the GP model that fits the {\it Kepler}\ light curve in figure
\ref{fig:GP_example}.

There are many ways to construct a QP kernel function, involving a range of
choices for both the periodic and aperiodic components of the model.
The kernel function presented above reproduces the behaviour of stellar light
curves, but other model choices can do so as well.
We do not attempt to test any other models in this paper, noting only that
this kernel function provides an adequate fit to the data.
We leave formal comparisons with other kernel function choices to a future
publication.

To infer a stellar rotation period $P$ from a light curve, we fit this
QP-kernel GP model to the data.  As with any model-fitting exercise, the
likelihood
of the model could be maximised to find the maximum-likelihood value for $P$.
In this study, however, we explore the full posterior PDFs using a Markov
Chain Monte Carlo (MCMC) procedure.  While
this approach comes at a computational cost, such posterior exploration
importantly provides a justified uncertainty estimate.

\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth, clip=true]{koi_lc_demo.pdf}
\caption[A light curve with a GP model.]
{Light curve of KIC 5809890, an active star with a rotation period of
$\sim$ 30.5\ days.
The blue line shows a fit to the data using a Gaussian process model with a QP
covariance kernel function.}
\label{fig:GP_example}
\end{center}
\end{figure}

\response{Performing inference with GPs is computationally expensive.
Is it worth spending the extra computation power to get slightly more
accurate, probabilistic rotation periods for a large number of stars?
A growing number of astronomers are interested in hierarchical probabilistic
modelling, particularly in the stellar and exoplanet communities.
These individuals are mindful of carefully inferring probabilistic parameters
wherever possible.
Probabilistic inference allows one to marginalise over nuisance
parameters while formally taking any uncertainty into account when
measuring the quantity of interest -- the star's rotation period, in
this case.
This becomes especially important as the signal-to-noise ratio
decreases and the rotation period is no longer tightly constrained,
and as the sampling becomes uneven.
Throughout the astronomical literature, hierarchical Bayesian
inference has been demonstrated to be a robust method of population
inference \citep[{\it e.g.}][]{Hogg2010, Foremanmackey2014, Wolfgang2015, Rogers2015}.
Probabilistic measurements with full, rigorous propagation of
uncertainties are a crucial ingredient for any hierarchical inference
where the target is the population level distribution.
Inferring the ages of stars in the galaxy via gyrochronology (age-rotation
relations) \citep[{\it e.g.}][]{Skumanich1972, Kawaler1989, Barnes2003, Barnes2007}
is an example of a hierarchical inference problem using stellar rotation.
Hierarchical inference allows you to marginalise over individual rotation
periods and infer age distribution parameters directly from the light curves.
Probabilistic rotation period inference is highly relevant to a large number
of galactic archaeology and exoplanet population studies which require
rotation period (or age) distributions.}

This paper is laid out as follows.
The GP method is described in \textsection \ref{sec:method}.
Its performance is demonstrated and compared with literature methods in
in \textsection \ref{sec:perf_and_comp}.
In \textsection \ref{sec:kepler} we apply the GP method to real \Kepler\ data,
and the results are discussed in \textsection \ref{sec:discussion}.

\section{GP Rotation Period Inference}
\label{sec:method}

In order to recover a stellar rotation period from a light curve using a
quasi-periodic Gaussian process (QP-GP), we sample the following posterior
PDF:
\begin{equation}
\label{eq:posterior}
p({\bm \theta}\,|\,y) \propto \mathcal L({\bm \theta}) p({\bm \theta}),
\end{equation}
where $y$ are the light curve flux data, $\bm \theta$ are the hyperparameters
of the kernel described in Equation \ref{eq:QP}, $\mathcal L$ is the
QP-GP likelihood function, and $p({\bm \theta})$ is the prior on the
hyperparameters.  Sampling this posterior presents several challenges:
\begin{itemize}
    \item The likelihood evaluation is computationally expensive;
    \item The GP model is very flexible, sometimes at the expense of
    reliable recovery of the period parameter; and
    \item The posterior may often be multimodal.
\end{itemize}
This Section discusses how we address these challenges through
the implementation details of the likelihood (Section \ref{sec:GP_lhood}), priors
(Section \ref{sec:GP_prior}), and sampling method (Section \ref{sec:sampling}).

\subsection{Likelihood}
\label{sec:GP_lhood}

The GP likelihood is similar to the simple Gaussian likelihood
function where the uncertainties are
Gaussian and uncorrelated. The latter can be written
\begin{equation}
    \ln \mathcal{L} = -\frac{1}{2}\sum_{n=1}^N\left[\frac{(y_n-\mu)^2}{\sigma_n^2}
    + \ln(2\pi\sigma_n^2)\right],
\end{equation}
\label{eq:chi2}
where $y_n$ are the data, $\mu$ is the mean model and $\sigma_n$ are the
Gaussian uncertainties on the data.
The equivalent equation in matrix notation is
\begin{equation}
    \ln \mathcal{L} = -\frac{1}{2}\bf{r}^T\bf{C}^{-1}\bf{r}-\frac{1}{2}\ln|\bf{C}|
    + \frac{N}{2}\log2\pi,
\end{equation}
\label{eq:lhf1}
where $\bf{r}$ is the vector of residuals and $\bf{C}$ is the covariance
matrix,
\begin{eqnarray}
    \mathbf{C} &=& \left (\begin{array}{cccc}
    \sigma^2_1 & \sigma_{2, 1} & \cdots & \sigma_{N, 1} \\
    \sigma_{1, 2} & \sigma^2_2 & \cdots & \sigma_{N, 2} \\
    && \vdots & \\
    \sigma_{1, N} & \sigma_{2, N} & \cdots & \sigma^2_N
\end{array}\right )
\end{eqnarray}
In the case where the uncertainties are uncorrelated, the noise is `white',
(an assumption frequently made by astronomers, sometimes justified)
and the off-diagonal elements of the covariance matrix are zero.
However, in the case where there is evidence for correlated
`noise'\footnote{In our case the `noise' is actually the model!  Incidentally, this approach is the reverse of the regression techniques
usually employed by astronomers.
In most problems in astronomy one tries to infer the parameters that describe
the mean model and, if correlated noise is present, to marginalise over that
noise.
Here, the parameters describing the correlated noise are what we are
interested in and the mean model is simply a straight line at $y=0$.}, as in the
case of {\it Kepler}\ light curves, those off-diagonal elements are non-zero.
With GP regression, a covariance matrix generated by the kernel function
${\bf K}$ replaces ${\bf C}$ in the above equation (for our purposes, the QP
kernel of Equation \ref{eq:QP} generates ${\bf K}$).

Evaluating this likelihood for a large number of points can be computationally
expensive.
For example, evaluating $\mathcal L$ for an entire {\it Kepler}\ lightcurve
($\sim$40,000 points) takes about $\sim$5\,s--- too slow to perform inference
on large numbers of light curves\footnote{All computational times cited in
this section are based on evaluations on a single core of a 2015 Macbook Pro,
3.1 GHz Intel Core i7.}.
The matrix operations necessary to evaluate the GP likelihood scale as
$N\ln(N)^2$, where $N$ is the number of data points in the light curve, using
the fast matrix solver HODLR \citep{Ambikasaran2014},
implemented in the {\tt george} \citep{George} python package.

We accelerate the likelihood calculation using two complementary strategies:
subsampling the data and splitting the light curve into independent sections.
To subsample {\it Kepler}\ data, for example,
we randomly select 1/30th of the points
in the full light curve (an average of $\sim$1.5 points per day).
This decreases the likelihood evaluation time by a factor of about 50, down to
about 100\,ms.
We then split the light curve into equal-sized chunks containing approximately
300 points per section (corresponding to about 200 days), and evaluate the
log-likelihood as the sum of the log-likelihoods of the individual sections
(all using the same parameters ${\bm \theta}$).
This reduces computation time because the section-based likelihood evaluation
scales as $mn\ln(n)^2$, where $n$ is the number of data points per section and
$m$ is the number of sections.
This method further reduces computation time for a typical light curve
(subsampled by a factor of 30) by about a factor of two, to about 50\,ms.

\subsection{Priors}
\label{sec:GP_prior}

\subsubsection{Non-period Hyperparameters}
\label{sec:nonperiod_prior}

The flexibility of this GP model allows for posterior multimodality and
``over-fitting''--like behavior.
For example, if $l$ is small, the non-periodic factor in the covariance
kernel may dominate, allowing for a good fit to the data without
requiring any periodic covariance structure---even if clear periodic
structure is present.
Additionally, for large values of $\Gamma$ the GP model becomes extremely
flexible and can fit the data without varying the period.
Managing this flexibility to reliably retrieve the period parameter requires
imposing informative priors on the non-period GP parameters.
In particular, we find it necessary to avoid large values of
$A$ and $\Gamma$, and small values of $l$; though the exact details of what
works well may differ among datasets.

\subsubsection{Period}
\label{sec:period_prior}

We use an informed period prior, based on the autocorrelation function (ACF)
of the light curve.
The ACF has proven to be very useful for measuring stellar rotation periods
\citep{Mcquillan2012, Mcquillan13b, Mcquillan2014}; however, the
method has several shortcomings,
most notably the inability to deliver uncertainties, but also
the necessity of several heuristic choices,
such as a timescale on which to smooth the ACF,
how to define a peak, whether the first or second peak
gets selected, and what constitutes a secure detection.
While this paper presents a rotation period inference method
that avoids these shortcomings,
it seems prudent to still use information available from the ACF.
We thus use the ACF to define a prior on period,
which can help the posterior sampling converge on the true period.

We do not attempt to decide which single
peak in the ACF best represents the true rotation period,
but rather we identify several \emph{candidate} periods and define
a weighting scheme in order to create a noncommital, though useful,
multimodal prior.  While this procedure does not avoid heuristic choices,
we soften the potential impact of these choices because we are simply
creating a \emph{prior} for probabilistically justified
inference rather attempting to identify a single correct period.

As another innovation beyond what ACF methods in the literature have
presented, we also bandpass filter the light curves (using a 5th order
Butterworth filter, as implemented in \texttt{SciPy}) before calculating the
autocorrelation.  This suppresses power on timescales shorter than a chosen
minimum period $P_{\rm min}$ and longer than a chosen maximum $P_{\rm max}$,
producing a cleaner autocorrelation signal than an unfiltered light curve.

We use the following procedure to construct a prior for rotation period
given a light curve:

\begin{enumerate}
\item{For each value of $P_i$, where $i = \{1, 2, 4, 8, 16, 32, 64, 128\}$\,d,
we apply a bandpass filter to the light curve using $P_{\rm min}=0.1$\,d
and $P_{\rm max} = P_i$.  We then calculate the ACF of the filtered
light curve out to a maximum lag of $2P_i$ and smooth it with a boxcar
filter of width $P_i/10$.}

\item{We identify the time lag corresponding to the
first peak of each of these ACFs, as well as the first peak's
trough-to-peak height, creating a set of candidate periods
$T_i$ and heights $h_i$.}

\item{We assign a quality metric $Q_i$ to each of these candidate
periods, as follows.  First, we model the ACF as a function of lag
time $t$ as a damped oscillator with fixed period $T_i$:
\begin{equation}
y = A e^{-t/\tau} \cos{\frac{2\pi t}{T_i} },
\end{equation}
and find the best-fitting parameters $A_i$ and $\tau_i$ by a non-linear
least squares minimization procedure--though enforcing a maximum
value of $\tau = 20 * P_i/T_i$ to avoid unreasonably
large solutions of $\tau$.
We then define the following heuristic quality metric:
\begin{equation}
\label{eq:quality}
Q_i = \left(\frac{\tau_i}{T_i}\right) \left(\frac{N_i h_i}{R_i}\right),
\end{equation}
where $h_i$ is the height of the ACF peak at $T_i$,
$N_i$ is the length of the lag vector in the ACF (directly proportional
to the maximum allowed period $P_i$),
and $R_i$ is the sum of squared residuals between the
damped oscillator model and the actual ACF data.  The idea behind this
quality metric is to give a candidate period a higher score if

    \begin{enumerate}[(a)]

    \item{it has many regular sinusoidal peaks, such that the decay
        time $\tau_i$ is long compared to the oscillation period $T_i$,}
    \item{the ACF peak height is high, and}
    \item{the damped oscillator model is a good fit (in a $\chi^2$
      sense) to the ACF, with extra bonus for being
      a good fit over more points (larger $N_i$, or longer $P_i$).}

    \end{enumerate}
}

\item{Given this set of candidate periods $T_i$ and quality metrics $Q_i$,
we finally construct a multimodal prior on the $P$ parameter of the GP
model as a weighted mixture of Gaussians:
\begin{multline}
\label{eq:mixture}
p(\ln P) = \\ \frac {\displaystyle \sum_i Q_i \left(0.9\mathcal N(\ln T_i, 0.2) +
                                          0.05\mathcal N(\ln (T_i/2), 0.2) +
                                          0.05\mathcal N(\ln (2 T_i), 0.2) \right)}
                {\sum_i Q_i}.
\end{multline}
That is, in addition to taking the candidate periods themselves as mixture
components, we also mix in twice and half each candidate period at a lower level,
which compensates for the possibility that the first peak in the ACF may actually
represent half or twice the actual rotation period.  The period width of 0.2 in
log space (corresponding to roughly 20\% uncertainty) is again a heuristic choice,
balancing a healthy specificity with the desire to not have the results of
the inference overly determined by the ACF prior.
}
\end{enumerate}

Incidentally, while we use the procedure described here to create a prior on
$P$ which we use while inferring the parameters of the quasi-periodic GP model,
this same procedure may also be used in the service of a
rotation-period estimating procedure all on its own, perhaps being even more
robust and accurate than the traditional ACF method.  We leave exploration of
this possibility to future work.

\subsection{Sampling}
\label{sec:sampling}

To sample the posterior in a way that is sensitive to potential multimodality,
we use the \texttt{emcee3}\footnote{\url{https://github.com/dfm/emcee3}} MCMC
sampler.
\texttt{emcee3} is the successor to the \texttt{emcee} project
\citep{Foreman-Mackey2013} that includes a suite of ensemble MCMC proposals
that can be combined to efficiently sample more distributions than the stretch
move \citep{Goodman2010} in \texttt{emcee}.
For this project, we use a weighted mixture of three proposals.
First, we include a proposal based on the \texttt{kombine}
package\footnote{\url{https://github.com/bfarr/kombine}} (Farr \& Farr, in
prep.) where a kernel density estimate (KDE) of the density represented by the
complementary ensemble is used as the proposal for the other walkers.
The other two proposals are a ``Differential Evolution (DE) MCMC'' proposal
\citep{terBraak2006, Nelson2014} and the ``snooker'' extension of DE
\citep{terBraak2008}.

We initialise 500 walkers with random samples from the prior and use a
weighted mixture of the KDE, DE, and snooker proposals with weights of 0.4,
0.4, and 0.2 respectively.
We run 50 steps of the sampler at a time, checking for convergence
after each iteration, up to a maximum of 50 iterations.
We declare convergence if the total effective chain length is at least
8$\times$ the maximum autocorrelation time.
When convergence is achieved, we discard the first two autocorrelation lengths
in the chain as a burn-in, and randomly choose 5000 samples as representative
of the posterior.
This fitting process takes several hours for a typical simulated light curve,
though in some cases it can take 12 hours or longer to converge.

\section{Performance and Comparison to Literature: Simulated Data}
\label{sec:perf_and_comp}

In order to test this new rotation period recovery method, we apply it to a
set of simulated light curves and compare to the performance of established
literature methods.
Section \ref{sec:simulations} describes the simulated data we use;
Section \ref{sec:performance} demonstrates the performance of the
QP-GP method; and Section \ref{sec:comparison} compares it to the performance
of the Lomb-Scargle periodogram and autocorrelation function methods.

\subsection{Simulated light curves}
\label{sec:simulations}

We take our test data set from the \citet{Aigrain2015} `hare and hounds'
rotation period recovery experiment.
These light curves result from placing dark, circular spots with slowly
evolving size on the surface of bright, rotating spheres, ignoring
limb-darkening effects.
\citet{Aigrain2015} simulated one thousand such light curves to test the
ability of participating teams to recover both stellar rotation periods
and rotational shear (the amplitude of surface differential rotation).
However, in this work, in order to focus on demonstrating reliable period recovery,
we select only the 333\ light curves without differential rotation,
as differential rotation may produce additional scatter in the
measured rotation periods.

Each of these light curve simulations uses a real {\it Kepler}\ long-cadence time array:
one data point every thirty minutes over a four year duration.
90\% of the rotation periods of the simulations come from a
log-uniform distribution between 10 and 50 days, and 10\% from a log-uniform
distribution between 1 and 10 days.
Figure \ref{fig:period_hist} shows the distribution of solid-body rotation periods.
The simulations also have a range of stellar inclination
angles, activity levels, spot lifetimes and more
(see Table \ref{tab:simulation_parameters}).
In order to preserve \Kepler\ noise properties,
\citet{Aigrain2015} add real \Kepler\ light curves with no obvious astrophysical
variability to the theoretical rotationally modulated light curves.
Figure \ref{fig:demo_lc} shows an example of a simulated light curve with a
period of 20.8 days.

\begin{table*}
\begin{center}
\caption{Ranges and distributions of parameters used to simulate light curves
in \citet{Aigrain2015}}
\begin{tabular}{lcc}
\hline\hline
    Parameter & Range & Distribution \\
    \hline
    Rotation period, $P_{rot}$ & 10 - 50 days (90\%) & log uniform \\
    & 1 - 10 days (10\%) & log uniform \\
    Activity cycle length & 1 - 10 years & log uniform \\
    Inclination & 0 - 90$^\circ$ & Uniform in $\sin^2i$ \\
    Decay timescale & (1 - 10) $\times P_{rot}$ & log uniform \\
\hline
\end{tabular}
\end{center}
\end{table*}
\label{tab:simulation_parameters}

\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth, clip=true]{period_hist.pdf}
\caption{A histogram of the rotation periods used to generate the 333\
simulated light curves in \citet{Aigrain2015}.}
\label{fig:period_hist}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth, clip=true]{demo_lc.pdf}
\caption[A simulated light curve.]
{An example simulated light curve. This `star' has a rotation period of
20.8\ days.}
\label{fig:demo_lc}
\end{center}
\end{figure}

\subsection{Method Performance}
\label{sec:performance}

We apply the QP-GP inference method described in Section \ref{sec:method}
to each of these 333 simulated light curves.  As discussed in Section
\ref{sec:nonperiod_prior}, reliable inference
requires defining a useful set of priors on the non-period
hyperparameters.
For this simulation dataset, we determined these by first running
the method using very broad priors on all the non-period parameters
(log-flat between -20 and 20)
and then inspecting the distribution of their posteriors for those cases
that successfully recovered the true period.
We also experimented with constraining the allowed ranges of the parameters
after discovering that some regions of parameter space (such as large values
of $A$ and $\Gamma$ and small values of $l$) tended to allow fits that ignored
the desired periodicity.
We list the final priors and bounds this process led us to adopt
in Table \ref{tab:priors}.
For the period prior, we tried two different methods: an uninformed (log-flat)
prior between 0.5\,d and 100\,d, and an ACF-informed prior
(Section \ref{sec:period_prior}).

Figures \ref{fig:compare_mcmc_acfprior} and \ref{fig:compare_mcmc_noprior}
summarise our results compared to the injected `true' stellar rotation
periods, for the uninformed and ACF-informed priors on period, respectively.
The periods inferred using the GP method show good agreement with the true
periods.
To assess the performance of the QP-GP and other period recovery methods, we
compute Median Absolute Deviations (MADs) of the results, relative to the
input periods.
We also compute the Median Relative Deviation (MRD), as a percentage and the
root-mean-squared (RMS).
These metrics are presented for the three different methods tested in this
paper in table \ref{tab:MADs}.
The informative and uninformative prior versions of the GP method have MRDs of
1.97 \% and 2.62 \% respectively.
The marginal posterior distributions of the QP kernel hyperparameters, for the
example simulated light curve in figure \ref{fig:demo_lc}, are shown in
figure \ref{fig:gp_posteriors}.

\begin{table*}
\begin{center}
\caption{Priors and bounds on the natural logarithms of the GP model
    parameters.}
\begin{tabular}{lcc}
Parameter & Prior & Bounds\\
    \hline
    $\ln A$ & $\mathcal N(-13, 5.7)$ & (-20, 0) \\
    $\ln l$ & $\mathcal N(7.2, 1.2)$ & (2, 20) \\
    $\ln \Gamma$ & $\mathcal N(-2.3, 1.4)$ & (-10, 3) \\
    $\ln \sigma$ & $\mathcal N(-17, 5)$ & (-20, 0) \\
    $\ln P $ & Uniform / ACF-based & ($\ln 0.5, \ln 100$) \\
\end{tabular}
\end{center}
\end{table*}
\label{tab:priors}

\begin{figure*}
\begin{center}
\includegraphics[width=6in, clip=true]{comparison_acfprior_03_10.pdf}
\caption{The `true' rotation periods used to generate 333\
simulated light curves vs the rotation periods measured using the GP
technique with an informed, ACF-based prior.
    Points are coloured by the peak-to-peak amplitude of the light curve, as
    defined in \citet{Aigrain2015}.
Since the posterior PDFs of rotation periods are often non-Gaussian,
    the points plotted here are maximum {\it a-posteriori} results.
The uncertainties are the 16th and 84th percentiles.
In many cases, the uncertainties are under-estimated.
The ACF-informed prior on rotation period used to generate these results is
    described in \textsection \ref{sec:GP_prior}.
    }
\label{fig:compare_mcmc_acfprior}
\end{center}
\end{figure*}

\begin{figure*}
\begin{center}
\includegraphics[width=6in, clip=true]{comparison_noprior_02_13.pdf}
\caption{The `true' rotation periods used to generate 333\
simulated light curves vs the rotation periods measured using the GP
technique with an uninformative prior.
    Points are coloured by the peak-to-peak amplitude of the light curve, as
    defined in \citet{Aigrain2015}.
Since the posterior PDFs of rotation periods are often non-Gaussian,
    the points plotted here are maximum {\it a-posteriori} results.
The uncertainties are the 16th and 84th percentiles.
In many cases, the uncertainties are under-estimated.
An uninformative prior, flat in the natural log of the rotation period between
    0.5 and 100 days was used to generate these results.
    }
\label{fig:compare_mcmc_noprior}
\end{center}
\end{figure*}

\begin{figure*}
\begin{center}
\includegraphics[width=6in, clip=true]{corner_plot.pdf}
\caption{Marginal posterior PDFs of the QP GP model parameters, fit to the
    simulated light curve in figure \ref{fig:demo_lc}.
    The blue line in the period panel shows the injected period.
    This figure was made using \texttt{corner.py} \citep{Corner}.}
\label{fig:gp_posteriors}
\end{center}
\end{figure*}

\subsection{Comparison with literature methods}
\label{sec:comparison}
\subsubsection{ACF}
\label{sec:acf}

\begin{figure}
\begin{center}
\includegraphics[width=\columnwidth, clip=true]{demo_ACF.pdf}
\caption[ACF of a simulated light curve.]
{An autocorrelation function of the simulated light curve shown in figure
\ref{fig:demo_lc}.
The vertical blue line shows the period measured using the ACF method (20.4
days) and the pink dashed line shows the period that was used to simulate the
light curve (20.8\ days).}
\label{fig:demo_acf}
\end{center}
\end{figure}

The ACF method has proven extremely useful for measuring rotation periods.
The catalogue of rotation periods of {\it Kepler}\ stars provided in
\citet{Mcquillan2013} has been widely used by the community and has provided
ground-breaking results for stellar and exoplanetary science.
The method also performed well in the \citet{Aigrain2015}
recovery experiment,
producing a large number of accurate rotation period measurements
(see, e.g., their figure 8).
Another advantage is its fast implementation speed.
However, because the ACF method is non-probabilistic, ACF-estimated rotation
period uncertainties are poorly defined~---~a clear disadvantage.
It also requires evenly-spaced data, therefore is not applicable to
ground-based light curves.
Figure \ref{fig:demo_acf} contains an example ACF of the light curve in
Figure \ref{fig:demo_lc}.

We compare our results to those of the Tel Aviv team in \citet{Aigrain2015}
who use the ACF method described in \citet{Mcquillan2014} and
\citet{Aigrain2015}.
\response{This method involves the calculation of an autocorrelation function, a
measure of the self-similarity of the light curve over a range of lags, which
is then smoothed with a Gaussian kernel.
Periodic variability in the light curve produces a peak in the ACF at the
period of the signal and a decaying sequence of peaks at integer multiples of
the period.
\citet{Mcquillan2014} first pre-processed the light curves by removing very
long-term variations.
They then calculated an ACF for each star and measured the positions of up to
the first four peaks in the ACF.
They fit a straight line to the periods of these peaks as a function of their
integer multiple and adopted the gradient of that line as the rotation
period.
The uncertainty on the ACF period is the uncertainty on the best-fit slope.
}
Figure \ref{fig:compare_acf} shows ACF-measured versus true rotation
periods, with the $2n$ and $\frac{1}{2}n$ harmonic lines as dashed lines.
The injected and recovered rotation periods generally agree well: the MRD of
their periods, relative to the true rotation periods, is 1.75\%
--- slightly smaller than the results produced by the GP method.
However, their results contain a larger number of extreme outliers --- they
predict periods that are significantly different from the true period in more
cases than the GP method.
This is revealed by comparing the RMS of the two sets of results since the RMS
is more sensitive to outliers.
The RMS of the Tel Aviv method results is 4.58\ days and the RMS of GP
method results is 0.25\ days.

\begin{figure*}
\begin{center}
\includegraphics[width=6in, clip=true]{compare_acf.pdf}
\caption[ACF results.]
{The `true' rotation periods used to generate 333\ simulated light
curves vs the rotation periods measured using the ACF technique.
    Points are coloured by the peak-to-peak amplitude of the light curve, as
    defined in \citet{Aigrain2015}.
    Several light curves have drastically over- and under-estimated rotation
    periods.

    }
\label{fig:compare_acf}
\end{center}
\end{figure*}

\subsubsection{LS periodogram}
\label{sec:ls}

The \citet{Aigrain2015} Tel Aviv team were the only group to report periods
for all 333\ simulated stars, and are therefore the only team with which
we compare results.
The other participating groups chose to report only the period measurements in
which they were confident and are likely to have omitted large outliers.
In order therefore to test our results against another commonly used
technique, we implemented a simple LS periodogram method.

\response{We first applied a high-pass filter to the light curves, removing
long-term trends that could produce large peaks at long periods in the
periodogram.
We used the 3rd order Butterworth filter in {\tt scipy} with a cut-off
of 35 days, attenuating signals with periods greater than this threshold.
This filter was applied in frequency space, rather than period space, and full
attenuation was attained at zero frequency.
In other words, the level of attenuation increased smoothly with period, for
periods above 35 days but no periods were fully suppressed.
Experimentally, we found the 35 day cut off removed the largest number of long
period outliers while preserving shorter period signals.
We also tried 50, 45, 40 and 30 day cut-offs but the 35 day cut-off value
minimised the RMS and MAD of the LS periodogram results.}
For each simulated light curve, we computed a LS periodogram\footnote{LS
periodograms were calculated using the gatspy Python module:
\url{https://github.com/astroML/gatspy/tree/master/gatspy/periodic}.} over a
grid of 10,000 periods, evenly spaced in frequency, between 1 and 100 days.
We adopted the period of the highest peak in the periodogram as the measured
rotation period.
\response{The uncertainties on the rotation periods were calculated using the
following equation for the standard deviation of the frequency
\citep{Horne1986, Kovacs1981}:
\begin{equation}
    \sigma_{\nu} = \frac{3\pi\sigma_N}{2N^{1/2}TA},
\end{equation}
where $A$ is the amplitude of the signal of highest power, $\sigma_N$ is the
variance of the time series, with the signal of highest power removed, $N$
is the number of observations and $T$ is the timespan of the data.
These formal uncertainties are only valid in the case that the noise is white,
the data are evenly sampled and there is only one signal present.
Since there are multiple signals present in these light curves, this formal
uncertainty is an underestimate of the true uncertainty.
}
Figure \ref{fig:pgram_compare} shows the resulting recovered rotation periods
as a function of true period.
\response{The MRD of the periodogram-recovered periods is 2.82\%,
slightly worse than the ACF and GP methods (see table \ref{tab:MADs} for
a side-by-side comparison with the other methods).
The filter suppresses signals with periods greater than 35 days but doesn't
eliminate them altogether, thus allowing high amplitude frequencies to be
detectable.
For this reason, some erroneous long periods are recovered by the periodogram
method.
These results still show a marked improvement in comparison to periodograms
calculated from unfiltered data.
Simply adopting the highest peak of a periodogram calculated from the {\it
unfiltered} simulated data resulted in an RMS of 18.98\ and relative
MAD of 4.70.}

\begin{figure*}
\begin{center}
\includegraphics[width=6in, clip=true]{compare_pgram_filtered_35.pdf}
\caption[LS periodogram results.]
{The `true' rotation periods used to generate 333\ simulated light
curves vs the rotation periods measured using a LS periodogram technique.
    Points are coloured by the peak-to-peak amplitude of the light curve, as
    defined in \citet{Aigrain2015}.
In many cases a large peak at a long period was present in the periodogram,
    producing a significant over-estimate of the period.
    }
\label{fig:pgram_compare}
\end{center}
\end{figure*}

\begin{table*}
\begin{center}
    \caption{Median absolute (MAD), median relative (MRD) deviations and
    root-mean-squared (RMS) for
    the LS periodogram, \citet{Mcquillan2013} ACF and GP period recovery
    methods.}
\begin{tabular}{lcccc}
    Method & MAD & MRD & RMS \\
    \hline
    GP (acf prior) & 0.40\ days & 1.97 \% & 0.25\ days \\
    GP (uninformative prior) & 0.48\ days & 2.62 \% &
    0.44\ days \\
    ACF & 0.37\ days & 1.75 \%
    & 4.58\ days \\
    LS periodogram & 0.52\ days & 2.82 \% & 1.04\ days\\
\end{tabular}
\end{center}
\end{table*}
\label{tab:MADs}

\section{Real \Kepler\ data}
\label{sec:kepler}

In order to test our rotation period inference method on real data,
we apply it to a set of 275\ {\it Kepler}\ Object of Interest (KOI)
host stars, that had rotation periods previously measured by
the ACF method by \citet{Mcquillan2013}.
We use the pipeline-corrected flux (\texttt{pdcsap\_flux} column in the
{\it Kepler}\ light curve table), median-normalized and unit-subtracted, and mask
out all known transiting planet candidate signals.
As with the simulated light curves, we randomly subsample each
light curve by a factor of 30 and split it into segments of about 300 points
for the purposes of evaluating the likelihood.
We also follow the same MCMC fitting procedure as with the simulated data,
using the ACF-based prior as before.

Initially, we also use the same priors on the hyperparameters for the KOIs
as for the simulated light curves (Table \ref{tab:priors}).
However, we found that $\ln l$ and $\ln \Gamma$ tended toward slightly
different values than the simulations.
We also found that the allowed hyperparameter range that we used for the
simulations was too large for the KOI population, as maybe $\sim$15\% of the
fits tended toward corners in the hyperparameter space, resulting in poor
period measurements.
As a result, after this initial test, we subsequently adjusted the priors and
re-fit all the KOIs.
The final priors and parameter ranges that we used are in Table
\ref{tab:koipriors}.
The posterior samples of the model parameters for the {\it Kepler}\ objects of
interest are available online:
\url{https://zenodo.org/record/292340\#.WKWpiBIrJE4}.

\begin{table*}
\begin{center}
\caption{Priors and bounds on the natural logarithms of the GP model parameters,
        for {\it Kepler}\ light curves}
\begin{tabular}{lcc}
Parameter & Prior & Bounds\\
    \hline
    $\ln A$ & $\mathcal N(-13, 5.7)$ & (-20, 0) \\
    $\ln l$ & $\mathcal N(5.0, 1.2)$ & (2, 8) \\
    $\ln \Gamma$ & $\mathcal N(1.9, 1.4)$ & (0, 3) \\
    $\ln \sigma$ & $\mathcal N(-17, 5)$ & (-20, 0) \\
    $\ln P $ & ACF-based & ($\ln 0.5, \ln 100$) \\
\end{tabular}
\end{center}
\end{table*}
\label{tab:koipriors}

Figure \ref{fig:mcquillan} compares the periods inferred with the GP method to
the ACF-based periods from \citet{Mcquillan2013} for the 275\ overlapping
KOIs.
This comparison shows generally very good agreement, demonstrating that this
method works not only on simulated data, but also on real data---with the
caveat that for any particular data set, some care is needed regarding the
setting the priors and ranges for the GP hyperparameters.
\response{The new GP rotation periods calculated for 1102\ KOIs are provided in an
online table accompanying this paper.
Samples of the rotation period posterior PDFs are available online:
\url{https://doi.org/10.5281/zenodo.804440}}

\begin{figure*}
\begin{center}
\includegraphics[width=6in, clip=true]{comparison_koi_01_23.pdf}
\caption[Comparison with McQuillan results.]
{A comparison of our GP rotation period measurements to those of
\citet{Mcquillan2013}.
The data points are coloured by the range of variability measured by
    \citet{Mcquillan2013}, defined as the interval between the 5th and 95th
    percentiles of normalised flux per period bin in millimagnitudes.}
\label{fig:mcquillan}
\end{center}
\end{figure*}

\section{Discussion}
\label{sec:discussion}

\response{The majority of long period outliers seen in the periodogram comparison
figure (figure \ref{fig:pgram_compare}) are produced when the rotation period
signal is highly non-sinusoidal.
This can be understood intuitively as the LS periodogram fits a series of sine
waves to the data; if the data are not sinusoidal, a sine wave will not
produce a good fit.
It is difficult to assess the reason for the ACF incorrect recoveries because
we do not have the individual ACFs computed by the \citet{Aigrain2015} Tel
Aviv team, however it seems that the ACF method is more sensitive than the LS
periodogram method to noise.
This particular implementation of the LS periodogram method is capable of
detecting periodic signals at lower amplitudes that the ACF.
We do not suggest that the LS periodogram method is better than the ACF method
in general.
It was made clear in \citet{Aigrain2015} that the performance of each of these
rotation period detection algorithms depends sensitively on the
implementation technique.
The exact steps performed in the pre-processing of the light curves and the
post-processing of the periodogram or ACF seem to affect the results strongly.
This is also true for the GP method.
Using a different MCMC sampler, different priors, different subsampling, or a
different kernel would all alter the results.
Clearly, none of these rotation period measurement methods is perfect and they
all require a lot of background engineering and tuning.
This is simply due to inherent difficulty of inferring periods, or any
parameter that produces a highly multimodal probability distribution, from
noisy data.}

The QP-GP inference method we test in this paper produces slightly more
accurate rotation periods than the ACF or periodogram methods.
Additionally, because it explores the posterior PDF with MCMC, the GP method
produces probabilistically justified uncertainties.
Unfortunately, these uncertainties still appear to be underestimated.
Of the rotation periods recovered from the simulated light curves using the
ACF-informed prior, only 25\% of the measured periods lie within 1$\sigma$ of
the true period, 50\% lie within 2$\sigma$, and 66\% within 3$\sigma$.
The largest outlier is 114$\sigma$ away from the true value.
The median uncertainty is underestimated by around a factor of two.
These numbers are similar for the uninformative prior results.
We attribute these underestimated uncertainties to the model choice.
Although more appropriate than a sinusoid, the QP-GP is still only an
 effective model.
A perfect physical model of the star would produce more accurate
uncertainties.

The QP kernel function represents a simple effective model of a stellar
light curve.
It can describe a wide range of quasi-periodic behavior and is
relatively simple, with only a few hyperparameters.
Nevertheless, it is still a somewhat arbitrary choice.
Another valid choice would be a squared cosine function multiplied by a
squared exponential, used by \citet{Brewer2009} to model asteroseismic
pulsations,
\begin{equation}
k_{i,j} = A \exp \left(-\frac{(x_i - x_j)^2}{2l^2}\right)
\cos\left(\frac{\pi(x_i - x_j)}{P}\right).
\end{equation}
\label{eq:cos_kernel}
This function produces a positive semi-definite matrix and has the $P$
parameter of interest, but differs qualitatively from the QP function
by allowing negative covariances.
Is it realistic to allow negative covariances?
In practice, the ACFs of {\it Kepler}\ light curves often go negative.
However, many stars have two active regions on opposite hemispheres that
produce two brightness dips per rotation, and it
may be difficult to model such stars with a kernel that forces
anti-correlation of points $\frac{1}{2}$ a period apart.
It would be worthwhile to test this assumption and this alternative
kernel function (and others) in the future.

Not all \Kepler\ light curves show evidence of stellar rotation.
In some cases a star may have few or no active regions, be rotating
pole-on, or be rotating so slowly that the \Kepler\ data detrending pipeline
removes any signal.
In other cases there may be another source of variability present in the light
curve, generating a false period detection.
These sources may be physical: {\it e.g.}\ binary star interactions, intra-pixel
contamination from other astrophysical objects, pulsating variable stars,
asteroseismic oscillations in giants and even stellar activity cycles.
Identifying many of these astrophysical false positives
falls outside the scope of this GP method
({\it e.g.}\ applying colour cuts to avoid giant contamination);
however, for some, such as variable stars, they may have distinctive
hyperparameters ({\it e.g.}\ long coherence timescales) that identify them.
Testing this may be an interesting follow-up study.
As well as astrophysical contamination, instrumental sources may contribute
to contaminating variability, {\it e.g.}\ temperature variations or pointing shifts
of the \Kepler\ spacecraft.
These are unlikely to be periodic and, again, may produce unusual combinations
of hyperparameters.
We also hope to test this in the future.

In addition, we are continuing to develop several other aspects of this GP
method:
\begin{itemize}
    \item{\response{To use an updated method for calculating the GP likelihood and
    drastically improve computational efficiency.
        {\tt celerite}, a new method for rapid computation of the `solve' and
        determinant calculations of covariance matrices necessary for GP
        inference has recently been developed \citep{Foremanmackey2017}.
        {\tt celerite} scales with the number of data points, $\mathcal{O}(N)$
        rather than the $N\log(N)^2$ scaling of the {\tt HODLR} algorithm used
        in this analysis.
        It requires a slightly different functional form for the kernel as the
        increased speed is obtained by using mathematical properties of
        exponential functions.
        Kernels must be written as the sums of exponentials in order to be
        implemented in {\tt celerite}, however a close approximation to the
        kernel function used here is demonstrated to recover rotation periods
        in \citet{Foremanmackey2017}.}}
\item{To investigate more physically motivated priors.
        In this paper we have only explored the physical interpretation of one
        parameter in the kernel function ($P$), which we related to stellar
        rotation periods, but others also warrant physically motivated priors.
        For example, the harmonic complexity parameter, $\Gamma$, defines the
        typical number of inflection points per function period; suitable
        priors may be informed by the typical properties of observed light
        curves.
        For the evolution time-scale, $l$,  it is sensible to enforce $l > P$,
        such that functions that have clear periodicity.
        Intuitively, if $l < P$, functions may evolve significantly over time
        scales shorter than one period, so a function $f(t+P)$ would look
        significantly different to $f(t)$, in which case any claims of
        periodicity become dubious.
        More stringent criteria may be suggested by stellar astrophysical
        considerations, e.g. knowledge of typical active region evolution
        time-scales or persistence lifetimes (e.g. $l\sim2P$).
        Finally, the amplitude hyper-parameter $A$ may be related to active
        region coverage.
        Unfortunately, because these hyper-parameters control the covariance
        structure of functions, their interpretation is not always
        straightforward; interpretation is further complicated by significant
        degeneracies between the hyperparameters.
        Therefore we defer such considerations, along with strategies for
        efficient optimization or marginalization of hyperparameters, to a
        separate paper (currently in prep.).}
\item{To build in a noise model for \Kepler\ data.
        Because it is a {\it generative} model of the data, the GP method
        models the rotation period at the same time as systematic noise
        features.  One can then marginalise over the parameters of the noise
        model.
        This approach would be extremely advantageous for \Kepler\ data since
        long-term trends are often removed by the \Kepler\ detrending
        pipeline.  Marginalising over the noise model at the same time as
        inferring the parameters of interest will insure that the periodic
        signal is preserved.}
\end{itemize}

\section{Conclusion}

We have attempted to recover the rotation periods of 333\ simulated
\Kepler-like light curves for solid-body rotators \citep{Aigrain2015} using
three different methods: a Gaussian process method,
an autocorrelation function method, and a Lomb-Scargle periodogram method.
We demonstrate that the GP method produces the most accurate rotation periods
of the three techniques.
Comparing our results with the results of the \citet{Aigrain2015} Tel Aviv
team who implement the ACF method of \citet{Mcquillan2013},
we find their results to be
slightly more precise in a median sense than the GP method results, but with
a larger number of significant outliers.
Additionally, we measure the rotation periods of 275\
\Kepler\ objects of interest
using the GP method, and find that these results compare well to those
measured previously by \citet{Mcquillan2013}.
The good agreement between these two sets of results demonstrates that the GP
method works well on real \Kepler\ data.
Samples of the full set of 1102\ KOI rotation period posterior PDFs can be
found at \url{https://doi.org/10.5281/zenodo.804440}.

Unlike the ACF and LS periodogram methods, the GP method provides posterior
PDF samples which can be used to estimate rotation periods uncertainties.
In general it provides more accurate rotation periods than either method and
produces significantly fewer outliers.
The GP method can also be applied to non-uniformly sampled light curves,
unlike the ACF method.

Although an improvement on competing methods, the uncertainties are still
underestimated by the GP method in many cases because it is an approximate
model.
A quasi-periodic Gaussian process is clearly a good model, as demonstrated
here, however it is still only an effective model, not an accurate physical
one.
It captures the posterior PDF of the periodic component of the covariance
matrix of a time series, not the actual rotation period of a physical star.
The marginalised posterior PDF does not therefore exactly reflect the
probability of a rotation period, given the data.
Similarly, the 16th and 84th percentile ranges calculated from the posterior
PDF of the QP-GP model, are not exactly the uncertainty of a physical
rotation period.
Although underestimated uncertainties are a drawback of this method, they are
at least well motivated and well defined which is not the case for
uncertainties calculated from the ACF and LS periodogram methods.

\response{Although GP inference is slow as it requires a `solve' and a matrix
determinant calculation at every step of an MCMC, a new GP solver, {\tt
celerite} \citep{Foremanmackey2017} shows promise for increasing the
computional speed of GP rotation period inference by several orders of
magnitude.
We intend to integrate {\tt celerite} into our code in the near future.
How much computational time is too much is a question that depends on the
available resources of each individual and their scientific priorities.
GP period inference is trivially parallelisable, so if one has access to
thousands of computer cores, one can infer rotation periods of thousands of
stars in a few hours (perhaps just a few minutes with {\tt celerite}).
For single stars GP rotation inference takes a reasonable amount of time and
has already been used on exoplanet hosts \citep[{\it e.g.}][]{Haywood2014,
Vanderburg2015}.}

The code used in this project is available at
\url{https://github.com/RuthAngus/GProtation/}.

This research was funded by the Simons Foundation and the Leverhulme Trust.
TDM is supported by NASA grant NNX14AE11G, and acknowledges the
hospitality of the Institute for Advanced Study,
where part of this work was completed.
VR thanks Merton College and the National Research Foundation of South Africa
for financial support.
We would like to thank the anonymous referee who's comments significantly
improved this paper.
Some of the data presented in this paper were obtained from the Mikulski
Archive for Space Telescopes (MAST).
STScI is operated by the Association of Universities for Research in
Astronomy, Inc., under NASA contract NAS5-26555.
Support for MAST for non-HST data is provided by the NASA Office of Space
Science via grant NNX09AF08G and by other grants and contracts.
This paper includes data collected by the Kepler mission. Funding for the
{\it Kepler}\ mission is provided by the NASA Science Mission directorate.

\bibliographystyle{plainnat}

redpajama_set_name: RedPajamaArXiv


I will limit myself only to matters relating to the Tamil United Liberation Front (TULF) and the TNA. I hope my efforts will be greatly appreciated, since the present generation knows little or nothing about our recent past and also because what I say is true. I am not a Historian to deal with all aspects of history.
But to deal with the history of the TULF, the TNA and about its leaders, I am one of the very few living today who can claim to be one of the founder members of the TULF and the TNA, knowing every leader and many youth leaders personally and about their worthy contributions and sacrifices made by them, in finding a solutions to the long standing ethnic problem.
I have a great sacred responsibility to show the world by whatever way possible, that the Ilankai Thamil Arasu Kadchi (ITAK) which is now functioning, has nothing to do with the Ilankai Thamil Arasu Kadchi (ITAK)founded by the great S.J.V.Chelvanayagam who left behind a new formation called the Tamil United Liberation Front, in place of the Federal Party 'ITAK' which he intended to wind up with the appointment of two other much respected Tamil leaders Hon.G.G.Ponnambalam Q.C leader of the All Ceylon Tamil Congress and Hon.S.Thondaman leader of the Ceylon Workers Congress to share with him the chair of the TULF.
The ITAK now formed was 26 years after the death of the founder and many others connected with it. The legal successor of the original ITAK 'Federal Party' is only the TULF. If I remain silent even now, all their sacrifices and the hard work they did risking their lives and some losing their lives as well, will remain buried with their bones.
The adoption of the New Republican Constitution in 1972 precipitated a constitutional crisis and at the request of Hon. S.J.V.Chelvanayagam, Hon.G.G.Ponnambalam agreed to merge his party with that of the ITAK to form a new party called the Tamil United Front which later adopted a new name as Tamil United Liberation Front (TULF) at a subsequent convention of the Party. Office bearers for the new Party were selected from both groups.
Hon.S.J.V.Chelvanayagam became President. Mr.A.Amirthalingam of the ITAK and Mr.M.Sivasithambaram of the ACTC became Joint Secretaries and Mr.V.Anandasangaree of the ACTC and Mr.M.Aalalasundaram of the ITAK became joint Propaganda Secretaries and Mr.T.Thirunavukarasu of the ACTC and Mr.V.Dharmalingam of the ITAK became Joint Treasurers. There were very senior lawyers from both parties like Ex-Senator S.R.Kanaganayagam, M/s T.Sangarapillai, R.Vishvanathan, V.Yogeswaran. K.Selvarajah, S.Rajanayagam, S.Nadarajah and many such other prominent citizens. Mr.S.C.Chandrahasan functioned as legal secretary.
Many were interested only in getting nominated to fill the vacancy in Parliament. It was I who presided over and proposed Mr.Mavai Senathiraja's name at the meeting held on 16th September,1989 to fill the vacancy. Much later only I came to know that Mr.Mavai Senathiraja wanted to be both the leader of the party and also the nominated membership of Parliament. All members of Mr.A.Amirthalingam's family were aware of it, because this request was made to Mrs.Mankayarkarasi Amirthalingam. There were several others who participated at that meeting thinking that their names also will be considered. Mr.R.Sampanthan came all the way from India with this idea and Dr. Neelan Thiruchelvam wanted a postponement when Mr.Senathiraja's name was considered for appointment as nominated MP. Accordingly at a subsequent meeting held on the 05th of October,1989 also, it was I who proposed Mr.Senathiraja's name and had him nominated to fill the seat occupied by Mr.A.Amirthalingam in Parliament. I hope Mr.Senathiraja and Mr.Sampanthan will remember the difficulty we had in persuading the Commissioner of Elections to accept Mr. Senathiraja's nomination, because according to the records available with the Commissioner of Elections Mr.A.Amirthalingam's name was there as the Secretary General of the TULF. I am sure Mr.Senathiraja will agree and Mr.R.Sampanthan will confirm that if not for the declaration made by three of us as members of the politburo, Mr.Senathiraja would not have got it even in his dreams. In any case only very small number of people attended this meeting, most of whom were not members of the party, only supporters.
Mr.Mavai Senathiraja was aware about it. Following Mr..A.Amirthalingam's assassination even important members of the party avoided visiting the office in Colombo for years. Two people who attended the meeting were shot dead one of whom was Mr.Nadesu, a District Council member.
The next General Election took place on 08th of August, 1994. At that Election due to the dominance of the armed groups the TULF could not win any seat in the North but won four seats in the East totaling five including the one National list seat. Mr.Senathiraja who contested Digamadulla and Mr.R.Sampanthan who contested in Trincomalee lost at the Elections. The only National list seat was justifiably given to Dr.Neelan Thiruchelvam when Mr.M.Sivasithambaram the President of the party was living. Although there were several defeated candidates including me, only Mr.R.Sampanthan and Mr.Mavai Senathiraja were demanding the National seat for themselves.
But the party could not give in. In the mean time Hon A.Thangathurai who won the Trincomalee seat was assassinated and that vacancy automatically got filled by Mr.R.Sampanthan who was next in the list. Up to now except me no one had asked for a Presidential Commission to inquire this case also. Mr.Senathiraja and his constituents continued to agitate to get the National list seat inspite of the fact that National list vacancy had already been given to Dr.Neelan Thiruchelvam. They were repeatedly sending deputations from Digamadulla Electorate to pressurize the party. Since Mr.M.Sivasithambaram, the President of the party who was ill in India, I had to take a decision in this matter.
On the 31st of May 1999, I wrote a lengthy letter running to five pages to Dr.Neelan Thiruchelvam explain the situation and asking him to resign his seat and nominate Mr.Mavai Senathiraja in his place, since the Ampara people were harassing me. Their claim was that they had given a substantial number of votes to Mr.Mavai Senathiraja. Since I had to go to Germany to take up the issue of the asylum seekers with the German officials, I wrote another letter briefly on the 05th of July,1999 asking Dr.Neelan to resign the seat and give it to Mr.Mavai Senathiraja without waiting for my arrival. Unfortunately Dr.Neelan Thiruchelvam was assassinated and I had to rush back to Colombo to attend the funeral. A couple of days later Mr. R.Sampanthan as Secretary General of the party convened a meeting which M/s R.Sampanthan, Joseph Pararajasingam, P.Selvarajah,S.Thurairajasingam all of whom were Members of Parliament, Mr.Mavai Senathiraja Mr.S.Thiyagaraja and myself attended. When Mr.R.Sampanthan asked as to who we should nominate, I promptly told him what I wrote to Dr.Neelan before leaving for Germany and expressed my support for his nomination, hearing which Mr.Mavai Senathiraja appeared to be very happy.
Accordingly Mr.Mavai Senathiraja was nominated and he was happy that he was qualifying for Parliamentary pension. Those present at the meeting were shocked at my decision and some of them even found fault with me subsequently for offering the National list membership to the same person a second time. As far as I was concerned it was a scarifies on my part to keep the party united. Had I indicated my willingness I would have got it easily. Now I realize my mistake because some of our party members were angry with me for not considering them for the appointment, if I did not want it. If another person had been appointed to this office he would have helped the Party, which was financially poor. Furthermore the embarrassment I suffered due to this appointment cannot be described in words. I earned a number of enemies unnecessarily, all of whom are still angry with me, even more than 25 years after Mr.Mavai Senathiraja was nominated as M.P twice on the initiative taken by me.
At that Election out of the candidates nominated he selected two strong candidates and canvassed support for the three of them which act was condemned by everybody as unethical and also as a selfish act. At this Election he polled about 33,000 votes while I polled 36,000 votes. This is the time Mr. Mavai Senathiraja started showing his true colors and led the party to total destruction.
The TULF is a Political Party based on non-violence and founded by the late Hon.S.J.V.Chelvanayagam who was affectionately referred to as Gandhi of Eelam. Gradually the conduct of Mr.Mavai Senathiraja became very shocking. Although he was appointed as nominated M.P twice on my initiative and gave all help to contest to enter Parliament a third time on the TULF ticket. His trying to revive the Federal Party was an outright betrayal of the trust the leaders like Hon. S.J.V.Chelvanayagam, Mr.A.Amirthalingam and such others had on him. The following report in the media raised serious doubt in the minds of the people about the genuineness of this M.P. Mrs.M.Amirthalingam in a statement had said "My husband preserved the registration of the Federal Party for the sole purpose that no undesirable elements could misuse its symbol and the name. He never wanted to revive the Federal Party" She further said "Thus I categorically make it clear to all that I have neither approved nor blessed the revival of the Federal Party but instead condemned it, as this act is a ploy to destroy the TULF which was formed by our great leaders" .
The Government that should have taken remedial measures did not take any action. The Members so elected, should have been either removed or expelled from Parliament. They did not resign their seats on their own or any legal action taken again them. Instead all these 22 Members, who were 10% of the total Membership of Parliament, which was 225, continued to serve their full term of six years uninterruptedly. They also contested the next election with their legal disability and won 14 seats by obtaining only 10% of the total votes. The TULF was not merely defeated at the poll. The TULF a moderate political party committed to non-violence that had 18 members in Parliament once, was virtually got rid of forever, by illegal means and without any action taken by the Government to have it reinstated. The irony is some who lost the Election in the morning surprisingly won in the evening.
Furthermore for the assassinations of M/s Kingsly Rasanayagam, N.Raviraj, T.Maheswaran, Laxman Kathirgamar, Rajan Sathiyamoorthy and for the killings of over five hundred innocent people and injuring over 1500 others are commitments for which M/s R.Sampanthan and Mavai Senathiraja, should be held responsible for misleading the TNA and for all crimes committed till the end of the war. The irony is that some of the authors of this master plan, who got defeated at the 2004 General Elections in the morning and later in the day, won the election mysteriously. The truth is that the Election was conducted by the LTTE and these gentlemen owe their victory to the LTTE. These are the great leaders now wanting the LTTE to be tried for War Crimes, having encouraged them as Sole Representative of the Tamil people and indirectly appreciated and encouraged all their activities.