Real Truth Matters - Visit us at realtruthmatters.com: RTM goes full time in less than three weeks!
RTM goes full time in less than three weeks!
As you have probably already heard, there are some exciting changes coming at Real Truth Matters. The ministry will officially be going full time on May 17, less than three weeks away. Details on how we reached this critical decision were outlined in our blog and a video now featured on our home page.
As the date rapidly approaches, we are excited about the work to come. Real Truth Matters exists to promote a return to New Testament Christianity by promoting the pursuit of Jesus Christ as the Gospel. So much of what we hear today is a man-centered theology based on what God can do for us. We believe that God is radically Christ-centered, and He points us to be as well. Yet in His amazing plan, when we are radically Christ-centered, we attain our greatest joy. This is what we pray Real Truth Matters will do: cause men and women to become so fascinated with all God is in Christ that they then live outside of themselves thus magnifying the worth of Christ by being completely satisfied in Him.
Some of our first tasks include producing a video series and teaching tools based on the core messages that came from our 2008 & 2009 conferences.
We are also continuing to improve and utilize the RTM website where we produce weekly teaching that cuts across many topics but always points listeners and viewers back to the pursuit of Christ.
We are also improving the magazine The Expositor while looking toward newer and broader venues in the world of magazine publishing.
In the ever growing area of online, social applications, we will be producing short films which can be easily shared that will drive home correct teaching in ways that will impact the viewer. We do this by utilizing sites such as Youtube and Facebook.
RTM also ministers directly to pastors and church leaders by providing them with networking and support, training, and ongoing encouragement and refreshing. In the future, we look forward to training men for new works in a more comprehensive, educational setting.
We will also work to support churches and other ministries in their endeavors to preach the gospel by assisting in audio/visual equipment set up/consultation/training, print design and layout for tracts and other printed materials, and website design.
Much of this work has already been taking place, but it has only trickled out due to our volunteer staff working only when time allows. With a full time staff, we will now have the time to dedicate to our full attention to our mission.
To accomplish this, we are relying on the same God who called us to this work to supply our needs. It takes money to support a staff, purchase and maintain equipment, and do the day to day work of RTM. We do not mention money and support of RTM ashamedly or with fear. Money is used by God to teach us many things as we see in the series Living Priorities – Living in Light of Eternity found under the Stewardship header on our topical index.
Both you and Real Truth Matters learn more about God and eternal values, and are brought closer to Him by learning what it truly means to be a steward. We do not take that lightly. God uses you and us together to accomplish this work. We do need your support as the Lord so leads.
We also want to hear from you! Let us know how RTM can serve you in your ministry. As believers, we are all ministers of Christ, and we want to serve you in the work in which He has called you.
Would You Uphold Us, Lord?


That we would find Marlowe's on our first trip to Memphis in search of barbecue art, was about as likely as Ponce De Leon landing his flagship in the Fountain of Youth. You're supposed to have to wait, to suffer, for that kind of payoff.
We had a short list of places to go, and Marlowe's was not on it. We must have been headed for A & R because we took the Elvis Presley exit. But we must have turned the wrong way because A&R is north of 55 and we were headed south.
We went a few blocks, eyes pealed for pigs, but came up with nothing but a couple of cowboy chickens. We saw it at the same time. We spent too much time gasping and gawking to stop. If there had been a car in front of us, my engine would have ended up in its trunk.
We pulled into the Krystal next door and parked in the back of the parking lot. Racing against time, we gathered our gear and ran from the car afraid that maybe it was a mirage, a hydraulic hyperbole that was in danger of evaporating at any moment.
And then we were there. Amy in front of the pig van staring at Spider Ham. Me face to face with Hogzilla.
Joe York: I am here with Melissa Coleman. It is the eleventh day of October, 2002. And we're here at Marlowe's Ribs and Restaurant. Well, you just said that you had been here since you were nine. So, your family started Marlowe's?
They opened the location here. Originally it was called White Haven Ranch House. It was the first salad bar concept in this area. It was the second in Memphis . The Danver's was what brought the salad bar here to Memphis . My father left the Marriott Corporation and started the Danver's chain here. And so this was going to be a Danver's. He decided not to and get out of the partnership, and opened it up on his own. And White Haven was booming, young, lots of money, and been here for a long time, and we went to Marlowe's, it's named after my sister, in 1982. So, we've been here since '73 until almost 2003, almost thirty years.
And your sister is Marlowe?
Yes, my sister is Marlowe.
No. He's Italian. Italians feel like they can cook anything. If you know many Italians, they're very boastful in their cooking. They think they're experts in everything. So, but we did hired the… Tops Bar-B-Q, was the first pit barbecue here in Memphis , and we contacted them and they built our pit for us. And we hired– and I wish I could remember the gentleman's name, but I cant… and we hired him for a short time to train us and he basically just led us through his techniques and we've been successful most of the time. Unsuccessful, burned a few over the years, but we've probably had fifteen Grand Champion placements in ten years. So, we've done very well, especially in whole hog competing because it's more of a… I don't want say it's a local level… but like a southeastern level of the United States.
Yeah. We've been very lucky.
What are your specialties as far as barbecue goes?
When we began Marlowe's in '82, our specialty was Italian being Italian-owned. We still do our homemade lasagna, but when we went to pork– We do whole hog and that's what we compete heavily on and very successful in competing, but we do mostly ribs. We do a thousand pounds of ribs a week. When it comes to pulled pork we do barbecue pizza, the barbecue nachos, not just the sandwiches, but we take the pulled pork and we do lots of different unique things with it.
Here at the restaurant we do have a spindle that we cook a whole hog on, but in competition it's more of a grill with heat that's cooked to the side. It's slow and low. And with this one we use electric heat. [She's referring to the glass-encased pit in the center of the dining room. On the spit above the electric pit is a plaster pig. Painted on the side of the pit are the words 'Love Me Tenderloin.'] But we use charcoal and hickory chips. But we do whole hog, and that is as much in the taste of the pork, but also it's presentation. When you open him up and you look at the pig he should be beautiful and brown and nice and have an absolutely gorgeous presentation to him along with the meat having not so much a pork flavor, but a very unique individual flavor. Because pork tastes like pork, but most everybody seasons it with garlic and apple juices and different types of marinade to give it a different kick or flavor. So, that's what we do with ours also.
Yes we have a blend as well as a marinade and we stuff him full of lots of garlic, but that's where our Italian roots kind of come in.
Well, how does that influence your barbecue? Because I would think that's a weird mix, going from Italian to barbecue.
It is a weird mix, but food is Italian. Period. Food is food. And Italians believe in eating, and eating well, and eating good food. So, we made the transition actually pretty easily. But we had to make the transition. No matter how much you like your own individual food, you could also be here by yourself. You have to change with the times and the times were dictating not so much heavy Italian, but the tourist-based industry was looking for Memphis barbecue. It has its own reputation, its own advertising base. So, we had to change with the times instead of sending everybody all over Memphis to find Memphis barbecue, we had to adapt and learn how to cook it to present to the millions of fans who come through Elvis Presley's place. We serve a lot of barbecue to them. We ship it all over the world. I have very loyal customers who will only have my ribs and barbecue and I do zero advertising when it comes to shipping.
Was that the main reason for [changing to a barbecue based business], your proximity to Graceland ?
Yes. Originally, back in 1973, it, Graceland … He was still alive. It was not the business that it is today. Like every community, the community has changed. There were already local businesses and homes, and this was a very viable, very wealthy part of Memphis . So, we didn't see tourists. That was not our initial trade. But over the last twenty-five years of Elvis' death, it has only grown and grown. Where you've lost a little more businesses, a lot more homes are going further and further out east. So, you're losing trade. And seventy-five percent of our night trade is out of the country, out of the state, Elvis fans.
So y'all get all kinds?
Oh, it's interesting. It's exciting. We're actually spoiled. We meet people from all over the world that are very nice, they're glad to be in Memphis . You give them a good meal, some southern hospitality, and they are so grateful. And they come in in a great mood. When you're out on vacation, aren't you smiling, relaxed. It's unlike the stresses of school and work and somebody sits down with you and tells you a little bit about the history of their family business, these people are so appreciative. We're very fortunate and very spoiled to have a relationship with so many out-of-towners.
And so y'all have the pink Cadillac service?
Yes. Well, we started out with the pig bus which caught your attention when you came by. It was an old school bus that we redid and Ruben Drewery had painted. And between my father, who has got the most creative mind. Coming from the Marriott Corporation, he could really think about future, not just now. And I'm a real now person. He can see what's going to happen two years from now and follow it and go with it gracefully. So, we noticed that the KOA Campground right down the street, right beside Elvis' place has lots of traffic. It's probably one of the biggest campgrounds in this area. A lot of them were older folks that were with big trailers that they didn't want to unhook. There wasn't really a restaurant that was close by. And with that campground we started picking up in this refurbished bus, this funny pig bus… You'd pull up and it was loud. It backfired. And they were having a blast. We were picking them up and bringing them back and forth. And the campground is the one that kind of initiated that. And then a customer came by and said, 'I've got an old Cadillac limousine. There's no trade for it. There's nobody looking for old limousines.' And my said, 'You know, we'll get one. Maybe upgrade a little and get them out of the pig bus.' We started out with one limousine and then we got to four. And then with my father's strange, creative mind, decided to paint them pink and make them stand out more, and part of Elvis. He did have a pink Cadillac at one time. People notice the pink Cadillacs. I have them call for weddings, to be picked up for weddings and brought back and forth. The chapel, Elvis' chapel. I've probably picked up this past year twenty brides and grooms and either brought them up here or to their hotel, Heartbreak Hotel. So, the pink was a great idea.
And how many of them do you have now?
Yes. And they're all running all the time. Of course, on the twenty-fifth four couldn't even keep up. With my father's really intuitive mind to the business, he noticed that out-of-towners, even if they have their own car, it's so much easier to have somebody call for a free ride… because it a completely free service. So, not driving around Memphis a little lost, not sure where to go. There are times that you'll look around on a Monday or Tuesday night and every one of the guests that are in here are people that we picked up. And that is so viable. What if you lost them between Point A and Point B and they turned off? We're filling up our own restaurant even if we have to go out and get them. And I don't know of any other restaurant in the world that will do that, go to your house, go to your hotel, and bring you back.
Well, we try to keep in this airport area and we do do all the hotels for safety, but there are probably ten thousand hotel guests in this area every night.
So they call and you say you'll be right there.
Yes. We have four drivers. Actually, my father's favorite position in the restaurant is being the limousine driver. He was the first official limousine driver we had. He knows everything about Memphis , everything about Graceland , and he'll talk to them and entertain them in between there and here. And it kind of completes their whole Elvis experience. Lots of pictures. People get their picture in front of the limousine. But Dad doesn't… He's not a very boastful person and the people don't realize that he is the owner driving them and he gets a real picture of what's going on. How was your meal? How was your service? And they think he's just the limousine driver, but actually he is the person that takes everything very seriously. So, if there is anything positive or negative we know very immediately. So, that's his favorite thing, is driving the car.
He is very smart. He loves this business. He was made for it. He'll never retire. He truly gets a lot of joy from the people. We make a good team. I'm very fortunate to have learned from such a master. But he was also the training manager for the Marriott Corporation. So, even when I was not even born they saw something in him.
Marlowe is my sister. She is two years younger than me. I'm the oldest of three sisters. And jokingly we've always said it's the middle child syndrome, you know, she never got anything as a younger child so we named the restaurant after her. She was with me for many years. She went to the University of Knoxville and got a marketing degree. Stayed here, worked with us, but had some growing pains. She was about thirty years old and wanted to try something and with my pushing her and wanting her to be more and successful, she is working in payroll services and is a top-notch female salesman in the city of Memphis . She is on the top of her trade and people know her and they even still know her from here, from the restaurant. Everybody knows Marlowe. She still comes in and eats for free, and visits, and will help me with anything. But when it comes to working she's actually outgrown me and I'm sad to see that.
Tell me more about the van. Because when I talked to Ruben, he basically said that most of the ideas for those different kinds of pigs came out of a late night around the bar in the back. Were you there?
Well, yes. And it's amazing how intelligent people are when they're sitting around the bar having a beer. A lot of my customers take this restaurant almost as their restaurant. They feel very close. We ask a lot of their opinions, what they think. We bring them in because some of them have a lot of great ideas. Some of them came up with… I guess Superman was big at the time. 'Why don't you paint a Superman with a pig face on it?!' And as the creative juices and beer got flowing it went from KISS pigs… There's the faces of the KISS band members with pig faces. And mayor pig. And we just all started having fun. There's probably thirty people's input on what should have painted on there along with a really creative artist with Ruben Drewery, that has been somebody we've known for twenty-five years and seen grow and develop into a fine artist.
There's a king pig on there which is kind of Elvis-like, but not quite. When we talked to Ruben a while back he was getting at the point that Graceland didn't want y'all to have an Elvis pig.
Right. We have to be real careful with the relationship with Graceland . You can't step on any toes. So, no you can't have Elvis' face or a picture or anything on that. So, yeah, it wasn't so much poking fun, because we're so grateful for Elvis. Today he's the reason for my children can go to private school. But in some ways it is poking fun. It's amazing at twenty-five years the amount of how such a king he is that people keep coming year after year. Thank goodness they do.
Obviously, it's kind of community here in the restaurant. Are there specific customers or people who y'all really like to see come through the door?
George Klein, doing the Elvis radio show, he very close personal friend of my mom and dad's. He did his deejay show from here for probably seven or eight years on Sunday night here. Of course, now he's down making the big times down at Horseshoe Casino and doing well for himself. I know Graceland employees call this place 'Elvis Presley South.' Before they opened up their restaurant, this is where they came for their meetings, for their runaways. Jack Soden brought Pricilla Presley in here when they were talking about the stamp. So, I feel so very much a part of Elvis' estate. There are so many people I've met. I was invited to go to the "Lilo and Stitch" premiere with Elvis employees. We meet people everyday that are famous that come in town, one, to perform, or two, to see Elvis' house. We've had the U2 group through here. Everyday we meet famous people, but we treat famous people the same as if they were family. We treat everybody the same way. So, we don't have this wall of pictures of people we've met.
Tell me about the 'Love Me Tenderloin' pig.
Who actually created that is Ruben Drewery. Ruben's behind that. Now, who's the creator of the cooker idea was my father. There are lots of restaurants that are very unique where they have their cooking or their grilling happening where the customers can see or participate in. He likes that idea. He likes customer involvement. So, he came up with this electric cooker, which is obviously not the most efficient way, but it was the only way to bring a cooker out here in the middle of the dining room. There's was no mold. There were no directions. He had friends that worked with steel, worked with… And he brought in everybody he knew that had some input and created this cooker. They had no blueprint. It is out of the mind of about three very intelligent people. And I can't tell you the excitement of kids when they see a whole hog come out on the spindle. I remember as a small child going to Shaky's Pizza and standing in the window and watching them throw the dough up, and just my faced glued, and I thought this is what I want to be when I grow up. And it was the entertainment. And along with the hog, you don't get nearly as much yield, but it is the fun, it's the presentation, it is something unique that you don't see anywhere you go, a whole hog cooking in front of you. To just kind of make a more fun, family atmosphere was our intention.
Now, something I forgot to ask you earlier, this bus with the pigs on it, that's the bus you used to pick the people up?
Yes, that's the original vehicle.
And it had the pigs on it then?
And that was after it became stationary?
My husband's best friend got married about five years ago and he came to me and said, 'I want to borrow the pig bus.' That's what we've always called it. I said, 'NO!' He said, 'I'm going to be the designated driver.' And they went to tittie clubs and they had more fun in the pig bus than the did in any of the bars. People laughing at them. They were laughing at themselves. Ten guys having a blast in this pig bus. It makes you laugh. It makes you smile. And it made the bachelor party something to be remembered versus just girls. It was this… Who else has been in a pig bus during their bachelor party?
And so it's full of trophies now?
Right now. I just ran out of room during Elvis Week to put all of my trophies. It's still drivable. It's still runs. But at this point now people are more pleased in being picked up in the pink limousine. When you tell them, 'There will be a pink limousine at the door to pick you up,' they're, 'Aw! A pink limousine!' And that's exciting. Now the pig bus, we do use it occasionally, but at this time we're just not because we've got four running limousines and it's just not necessary.
Is there anything that I haven't asked you that you want to say?
The only thing I can think of is that we've been fortunate to change with the times, and change with Elvis, and just be successful for thirty years, and we're really lucky.
I remembered another question I needed to ask. Where do you get your pigs from that you use when you cook whole hog?
We buy them from Fayette Packing. We get them straight from the slaughterhouse. We go down and pick them out. On this rod [the one currently occupied by the plaster pig] about a ninety-five pound pig is about all he could take without bending the rod. But when we do competition, which we're doing this weekend, we do about a hundred and fifteen, a hundred and twenty pound hog, and he has to be really pretty. So, you have to pick one out with pretty ears.
And you go in and it's just like picking produce?
Exactly. Straight from the slaughterhouse. They slaughter them there. So, it's as fresh as fresh can be.
So you walk through and they're all just sitting there?
We're just able to go in and you pick out the freshest… Even when you walk around the produce store, you move things around and pick the one you think is the prettiest. And it's the same thing with down there.
Right. Blazin' Bacon is the original team and we offshooted to City Hogs, which is the one we're competing under right now. They are in the top twenty nationally. They have not got a Grand Champion this year. They're a little disappointed, but they've gotten second place, which is still not perfect. But they're trying and they're competing this weekend hopefully to get a Grand Champion in whole hog. Tim Alread is a lieutenant for the White Haven Police Department and he is our team captain.
And how many people are on the team?
There are five and a lot of them are very sweet wives that work very hard for their husbands. But there are two main cookers and three helpers. I'm one of the helpers. I don't do too much of the cooking, but I enjoy it very much.
Do you cook it here and take it somewhere?
No. You have to cook it on site. It's inspected. The rules are here and we do Memphis In May sanctioned events. The meat is inspected before cooking. You're unable to marinate them or prior prep them. Everybody has the same amount of time to cook their meat, either whole hog, or ribs, or shoulders. But it's all up to you on the property. So, if you get the fire a little too hot and you burn him, you're done.
And how long does it take y'all to cook a whole hog?
It takes about twenty-two hours to cook a whole hog and about the same amount for shoulders. Ribs we run around ten hours. So, we're able to cook those within a day. We start those in the morning and by the evening we're able to pull those out for fresh serve to the dinner crowd that night.
Yes we do. Not nearly as often as we should. Sometimes you're just too busy, because it does have to be added afterwards. I like hickory. Not everybody likes it because it definitely gives the meat a real unique flavor. I have found that more time than not I've had people enjoy it maybe a little more than putting the hickory in it. But we do use hickory. The charcoal that we use also has hickory in it. So, it has a little bit of flakes in it.
We use the smoked ham from the pig for the Elvis Burger, the only Elvis Burger sanctioned by the Elvis Presley Enterprises.
An Elvis Burger is just a hamburger that we chargrill, but we use the smoked hog, you know, the smoked ham. We cook it on our pit and we use that for 'The Burger for the King Himself.' We use the ham, and bacon, and cheddar cheese.
So it's a hamburger with ham and bacon and cheese?
Yes, and that's is called our Elvis Burger with the rights from the Elvis Presley Estate that says it's an Elvis Burger, too.
Has anybody ever eaten more than one?
Unbelievably, yes. They're eight ounces each. And I have… I wish he was here. He worked at Federal Express. His name was Barry. Barry could sit down and eat two Elvis Burgers with only one order of fries, not two. And he was this little bitty… He was no bigger than you.
Did Elvis used to eat the same kind of thing?
Yes he did. That's how we came up with that. The toppings that are on the burger are the toppings that he liked. So, back when it was called White Haven Ranch House in the '70s, before he passed away in '73, that would be what he wanted on his burger. So, that's why Elvis Presley's estate was kind enough to allow us to name it after him, because it was something that he chose, and he chose to eat here a lot.
So it was White Haven Ranch House and then y'all bought it?
We owned it then. We opened it as White Haven Ranch House. In 1973, my father opened this. It was not a running restaurant at all and he opened as White Haven Ranch House. We served grilled hamburgers, the sliced roast beefs, the first salad bar in White Haven. Beautiful, cute girls in short blue jean skirts and cowboy boots and cowboy hats and they had a wonderful crowd. Lots of people, lots of fun. But in 1982 was when we went to Marlowes. By then, in that ten year span, the area had changed and we were going with the changes versus becoming just another fast food restaurant, which we were the first fast food restaurant in the area. And so we decided to be more of a finer dining, sit down service type of restaurant.


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\section{Principal components of genomics data}

Personalized medicine or precision medicine is a growing movement to tailor treatments of disease
to an individual's sensitivities to treatment, allergies, or other genetic
predispositions, using all available data about an individual~\cite{Desmond2012}.
Developers of personalized medical treatments are therefore interested in how an
individual's genome, both in isolation and within the context of the wider human
population, can be used to predict desired clinical outcomes (known as
comorbidities or phenotypes)~\cite[Ch. 8]{Laird2011}.
Genome-wide association studies (GWASs) are a new and popular technique for
studying the significance of human genome data, by studying the associate genotype
variation with phenotype variations in outcome variables e.g.\ the clinical
observation of a disease.

The genome data used in
GWASs are are often encoded in a matrix expressing the number of mutations
from a reference genome, which we will refer to as a \textit{genotype matrix}.
By convention, the genotype matrix is indexed by patients (or other test
subjects) on the rows and gene markers on the columns which represent some
coordinate or locus within the human genome. A common example of gene markers are
single nucleotide polymorphisms (SNPs), which represent gene positions with
pointwise mutations of interest that express variation in the genotype across
humans. Oftentimes, the explanatory data in a GWAS are simply called SNP data.
Since most human cells are at most diploid, i.e.\ have two sets of chromosomes,
the matrix elements can only be 0, 1, or 2 (or missing).

There are two major confounding sources of variation which are considered in
the analysis of human genome data, each of which have significance for the
spectral properties of the matrix:

\paragraph{Population stratification/admixing}
Population stratification is the phenomenon of common genetic variation within
mutually exclusive subpopulations defined along racial, ethnic or geographic
divisions~\cite{Pritchard1999,Cardon2003}. (Admixture models relax the mutual
exclusion constraint~\cite{Devlin1999,Sankararaman2008}.)
In linear algebraic terms, the genotype matrix will have a low rank component
with large singular values.

\paragraph{Cryptic relatedness}
Sometimes called kinship or inbreeding, cryptic relatedness is an increase in
sampling bias in the columns (human genomes) produced by having common ancestors,
thus increasing the nominally observed frequency of certain
mutations~\cite{Voight2005,Astle2009}. Relatedness is usually detected and removed in
a separate preprocessing step, but it is not always possible to remove
fully~\cite{PLINK}. Any remaining related samples will
result in (near) linear dependencies in the rows of the genotype matrix,
leading to the presence of several singular values that are very small or zero.

Principal component analysis (PCA) was historically first used as a dimensionality
reduction technique to summarize the variation in the human genes and study its
implications for human evolution in relation to other factors such as
geography and history~\cite{Menozzi1978,Cavalli1994,Novembre2008}.
However, we will focus on the more modern use of principal components (PCs) to
represent the confounding effects of population substructure in the statistical
modeling of GWASs~\cite{Chen2003,Patterson2006,Price2006,Zhu2002,Zhang2003}.

Genomics matrices form an interesting use case for the classical techniques of
numerical linear algebra, as the amount of sequenced genome data grows
exponentially~\cite{Stephens2015}. As the price of sequencing genome data declines
rapidly, genomics studies involving hundreds of thousands of individuals (columns)
are already commonplace today, with order of magnitude growth expected within the next year or two. Therefore, genomics researchers will require access to the best
available algorithms for parallel computing and numerical linear algebra to
handle the increasing demands of data processing and dimensionality reduction.

\subsection{The statistical significance of principal components}

The main statistical tool used in GWAS is regression, using some model that
associates genotype variation with phenotype variation.
While correlation does not imply causation in and of itself, the central dogma
of molecular biology states that causality flows from genetic data in DNA and RNA
to phenotype data in expressed proteins~\cite{Crick1970}. Consequently, correlations between genotypes and phenotypes could in theory have causal significance.
The \emph{linear} regression model is one the simplest useful models, and can be
motivated in several different ways. One way is in terms of least squares
minimization to find the coefficients that minimize the sum of squared distances
between a hyperplane and the observations. Another way to formulate the problem
as finding a projection of the vector of observations down onto the space
spanned by the vectors of explanatory variables.
One caveat in statistical studies is the assumption that the observations are
randomly sampled with replacement, and hence that the observations can be
assumed to be independent. In the context of statistical genomics, the
independence assumption is one of several bundled into the principle of
Hardy-Weinberg equilibrium~\cite{Hardy1908,Weinberg1908}, which is commonly
assumed in statistical genetics~\cite{Laird2011}. However, caution must be taken
to remove possible sampling bias due to the collection of genetic data from
patients from a single hospital or hospital network, on top of sampling bias
introduced by not treating the presence of population substructure.

\subsection{The linear regression model}

The statistical theory of regressing phenotypes against genotypes is best expressed
in terms from conditional expectations. If we for individual $i$ denote the genotype measurement by $x_i$ and the phenotype measurement by $y_i$, the conditional
expectation of interest can be written as $\E(y_i|x_i)=\beta_0 + \beta_1 x_i$.
A popular formulation of the this model is
\begin{equation*}
    y_i = \beta_0 + x_i \beta_1 + \varepsilon_i\quad i=1,\dots,n
\end{equation*}
where $n$ is the number of observations which in this case would be the number of individuals for which we have genotype data.
The variable $\varepsilon_i$ is called the error term and must satisfy $\E(\varepsilon_i|x_i)=0$.
More generally, $\varepsilon_i$ is the conditional distribution $y_i - \beta_0 - x_i\beta_1|x_i$.

The multivariate expression can be written conveniently in matrix form

\begin{equation}
\label{eq:linreg}
    y = X\beta + \varepsilon
\end{equation}
with
\begin{equation*}
    X = \begin{pmatrix}
        1 & x_1\\
        \vdots & \vdots \\
        1 & x_n
    \end{pmatrix}
\end{equation*}
and in this notation, the well-known least squares estimator for the coefficient
$\beta$ can be written as
\begin{equation}
\label{eq:ols}
    \hat{\beta} = (X^TX)^{-1}X^Ty.
\end{equation}

The conditional probability treatment demonstrates that when $(x_i,y_i)$ pairs
are considered to be random variables, then $\hat{\beta}$ is also a random
variable, with its mean and variance quantifying uncertainty about the least
squares solution.
First, notice that the least squares estimator \eqref{eq:ols} can be written
\begin{equation*}
    \hat{\beta} = \beta + (X^TX)^{-1}X^T\varepsilon
\end{equation*}
and the expected value of the estimator is
\begin{equation}
    \E(\hat{\beta}|X) = \E(\beta + (X^TX)^{-1}X^T\varepsilon|X) =
        \beta + (X^TX)^{-1}X^T\E(\varepsilon|X) = \beta
\end{equation}
which means that the estimator is \emph{unbiased}. Statisticians are interested in the variability of $\hat{\beta}$ under changes to the data that could be considered small errors. The most common measurement for the variability of an estimator is the (conditional) variance, i.e.
\begin{equation*}
    \Var(\hat{\beta}|X) = \Var(\beta + (X^TX)^{-1}X^T\varepsilon|X) =
        (X^TX)^{-1}X^T\Var(\varepsilon|X)X(X^TX)^{-1}.
\end{equation*}

This shows that variance of $\hat{\beta}$ depends on the (conditional) variance of $\varepsilon$, which has not been discussed yet. In classical treatments of the linear regression model it is typically assumed that, conditionally on $x_i$, the $y_i$s are independent and the have the same variance which is the same as $\Var(\varepsilon|X)=\sigma^2 I$ for some unknown scalar $\sigma^2$. Under this assumption, the variance of $\hat{\beta}$ reduces to $\sigma^2 (X^TX)^{-1}$. The magnitude of this quantity is unknown because $\sigma^2$ is an unknown parameter but $\sigma^2$ can be \emph{estimated} from the data. The usual estimator is
$\hat{\sigma}^2=\frac{1}{n} \|\hat{\varepsilon}\|^2$
where $\hat{\varepsilon} = y - X\hat{\beta}$.
This leads to the estimate of the (conditional) variance of the estimator $\widehat{\Var(\hat{\beta}|X)} = \hat{\sigma}^2(X^TX)^{-1}$.

The independence assumption is often used in statistics and can be justified from an assumption of random sampling with replacement. In studies where data is passively collected, this might not be a reasonable assumption as explained in the previous section. Non-random sampling might lead to correlation between the phenotypes even after conditioning on the genotypes. In consequence of that, $\Var(\varepsilon|X)$ will no longer be diagonal, but have some general positive definite structure $\Sigma$ and $\Var(\hat{\beta}|X)=(X^TX)^{-1}X^T\Sigma X(X^TX)^{-1}$. Since $\Sigma$ in general consists of $\frac{n(n+1)}{2}$ parameters, it cannot be estimated consistently.

In order to analyze the problem with correlated observations, it is convenient to decompose the error into a part that contains the cross-individual correlation and a part that is diagonal and therefore only describes the variance for each individual. This may be written as
\begin{equation*}
    y_i = \beta_0 + x_i\beta_1 + \eta_i + \xi_i
\end{equation*}
where is assumed that $\Var(\eta|X)=\Sigma_\eta$ and $\Var(\xi|X)=\sigma^2_\xi I$. Furthermore, it is assumes that the two error terms are independent.

\label{sec:regress-correction}
\subsubsection{Fixed effect estimation}

One way to produce a reliable estimate of the variance of $\hat{\beta}$ is to come up with a set of variables $z_1,\dots,z_k$ that proxies the correlation between the observations, i.e.\ $\eta=Z\gamma$. By simply including the variables $z_1,\dots,z_k$ in the regression model, it possible to remove the correlation which distorts the variance estimate for $\hat{\beta}$. For the regression $y|X,Z$, we get the least squares estimator
\begin{equation*}
    \begin{pmatrix}\hat{\beta} \\ \hat{\gamma}\end{pmatrix} =
    \begin{pmatrix}
        X^TX & X^TZ \\ Z^TX & Z^TZ
    \end{pmatrix}^{-1}\!\!
    \begin{pmatrix}
        X^T \\ Z^T
    \end{pmatrix}
    (X\beta + Z\gamma + \xi)=
    \theta +
            \begin{pmatrix}
        X^TX & X^TZ \\ Z^TX & Z^TZ
    \end{pmatrix}^{-1}\!\!
    \begin{pmatrix}
        X^T \\ Z^T
    \end{pmatrix}\xi,
\end{equation*}
which has variance
\begin{equation*}
    \Var\left(\begin{pmatrix}\hat{\beta} \\ \hat{\gamma}\end{pmatrix}|X,Z\right)=\sigma_\xi^2
        \begin{pmatrix} X^TX & X^TZ \\ Z^TX & Z^TZ \end{pmatrix}^{-1}.
\end{equation*}

In many applications, a few principal components of the covariance matrix of the complete SNP data set is used as a proxy for the correlation between individuals. Computing principal components is therefore often a first step in analyzing GWASs.

\subsection{Software for computing the principal components of genomics data}

The software stack for GWAS is generally based on command line tools written completely in C/C++. Not only is the core computational algorithm written in C/C++ but also much of the pre- and postprocessing of the data. The data sets can be large but and the computations at times heavy but it has been a surprise to learn the extend to which analyses are carried out directly from the command line instead of using higher level languages like MATLAB, R, or Python. This choice seems to limit the tools available to the analysts because, unless he is a C/C++ programmer, the programmer is restricted to the set of options included in the command line tool.

Two major packages exist for computing the PCA in the GWAS software stack. The package \emph{EIGENSOFT} accompanied~\cite{Patterson2006} which popularized the use of PCA in GWAS. In the original version of the package, the routine \texttt{smartpca} for computing the PCA of a SNP matrix was based on an eigenvalue solver from LAPACK. In consequence, all the eigenvalues and vectors of the SNP matrix were computed even though only a few of them were used as principal components. Computing the full decomposition is inefficient and as the number of available samples has grown over the year, this approach has become impractical.

More recently, \emph{FlashPCA}~\cite{abraham2014fast} has emerged as a potentially faster alternative to EIGENSOFT's \texttt{smartpca}. The PCA routine is based on a truncated SVD algorithm described in~\cite{halko2011finding}. More specifically, FlashPCA uses a subspace iteration scheme with either column-wise scaling (FlashPCA 1) or orthogonalization by QR (FlashPCA 2) in each iteration. The convergence criterion is based on the average of squared element-wise distance between the the bases for iteration $i-1$ and $i$. The QR orthogonalization step in the implementation of FlashPCA routine deviates from the algorithm in described~\cite{abraham2014fast} which only normalizes column-wise. Our conjecture was that this change was made to avoid loss of orthogonality in the subspace basis and the author of the package has confirmed this. In consequence, the timings in~\cite{abraham2014fast} do not correspond to the performance of the software run with default settings since the QR orthogonalization is much slower than the column-wise normalization. Furthermore, a degenerate basis might also converge much faster because it eventually converges to the single largest eigenvalue.

Table~\ref{tab:sw} lists some software packages providing eigenvalue or singular
value computations useful for PCA. It may surprise readers that well-established
packages in numerical linear algebra are rarely used in genomics, considering
that libraries like ARPACK and PROPACK have convenient wrapper libraries in both
R, Python, and \textsc{MATLAB}. This phenomenon might be explained by the pronounced use
of C/C++ in statistical genetics, where calling ARPACK and PROPACK are relatively
more demanding, combined with the fact that iterative methods are traditionally
not part of the curriculum in statistical genomics.

\begin{table}
    \centering
    \caption{List of software used for principal components analysis in statistical
    genomics. Notably, common packages known to numerical linear algebraists are
    rarely, if ever, used.
    $^*$: available in EIGENSOFT~\cite{Patterson2006}.
    $^\dagger$: uses dense LAPACK routines.
    \label{tab:sw}}
    \begin{tabular}{cccc}
       \hline
        Software         & Reference & Algorithm                              & Used in genomics \\ \hline
        smartpca$^{*\dagger}$ & \cite{Patterson2006} & Householder bidiagonalization & \cmark \\ FastPCA$^*$ & \cite{Galinsky2016} & Subspace iteration        & \cmark \\
        FlashPCA         & \cite{abraham2014fast} & Subspace iteration      & \cmark \\ \hline
        ARPACK           & \cite{Lehoucq1996} & Lanczos tridiagonalization  & \xmark \\
        PROPACK          & \cite{Larsen1998} & Lanczos bidiagonalization    & \xmark \\
        SLEPc            & \cite{Hernandez2008} & Lanczos bidiagonalization & \xmark \\
        Anasazi          & \cite{Baker2009} & Lanczos bidiagonalization     & \xmark \\ \hline
    \end{tabular}
\end{table}

\label{sec:model}
\section{A simple model for genomics data}

In this section we present a very simple random model which accurately mimics
the spectral features observed in real data matrices.
We hypothesize that the spectral properties of human patient genotype data can
be modeled the Julia code in Algorithm~\ref{code:model}, which captures the
confounding effects of population admixture and cryptic relatedness.
The former is modeled by setting randomly select subblocks to the same value,
whereas the latter is modeled by duplicating rows, thus purposely introducing
linear dependence into the row space. This model, while simplistic, can be
tuned to reproduce the scree plot observed in empirical data matrices and we
expect that such models may be of interest to researchers developing numerical
algorithms that lack access to actual data, which are often access-restricted
due to clinical privacy.

\begin{algorithm}
\caption{A simple model for human genotype data matrices in Julia
\label{code:model}}
\begin{lstlisting}
"""
Inputs:
- m: number of rows (gene markers)
- n: number of columns (patients)
- r: number of subblocks to model population admixing
- nsignal: number of entries to represent signal
- rkins: fraction of columns to duplicate

Output:
- A: a dense matrix of size m x n with matrix elements 0, 1 or 2
"""
function model(m, n, r, nsignal, rkins)
    A = zeros(m, n)
    #Model population admixing
    #by randomly setting a subblock to the same value, k
    for i=1:r
        k = rand(0:2)
        r1 = randrange(m)
        r2 = randrange(n)
        A[r1, r2] = k
    end

    #Model signal
    for i=1:nsignal
        A[rand(1:m), rand(1:n)] = rand(0:2)
    end

    #Model kinship by duplicating rows
    nkins = round(Int, rkins*m)
    for i=1:nkins
        A[rand(1:m), :] = A[rand(1:m), :]
    end
    return A
end

function randrange(n)
    i1 = rand(1:n)
    i2 = rand(1:n)
    if i1 > i2
        return i2:i1
    else
        return i1:i2
    end
end
\end{lstlisting}
\end{algorithm}

Algorithm~\ref{code:model} describes a \verb|model| function, which creates a
dense, synthetic data matrix of size $m\times n$. The synthetic data is
generated in three steps. First, randomly select $r$ rectangular submatrices
(which may overlap) and set the elements of each submatrix to the same value.
This process simulates crudely the effects of population admixture, where
each subpopulation has a common block of mutations that vary together, and the
possibility of overlap resembles the effect of mixing different subpopulations
together. (This step uses the auxiliary \verb|randrange| function, which returns
a valid Julia range that is a subinterval of the range \verb|1:n|.)
Second, model the genotype of interest by randomly setting $nsignal$ matrix
elements randomly to 0, 1 or 2.
Third, simulate the effects of kinship by choosing a fraction $rkins$ of the
rows to duplicate.

The model is clearly a very crude approximation to genotype data with the
confounding effects of population substructure. There is little overt control
over the admixture process, the precise distribution over matrix elements, and
all related patients are assumed to have identical genotypes. Nevertheless, the
model generates realistic distributions of singular values which mimic closely
what we have observed in that of real world genotype matrices.
Figure~\ref{fig:empirical-spectrum} shows the distribution of singular values
generated by our model with parameters $m=41505$, $n=81700$, $r=10$,
$nsignal=mn$, $rkins=0.017$.
There are a handful of ($\approx r$) large singular values,
while the rest follow a bulk distribution from random matrix theory known as the
Marchenko-Pastur law~\cite{Marchenko1967} with parameter $\rho = 1.86$.

\begin{figure}

\includegraphics[width=0.45\textwidth]{fig/synthetic/fig-empirical-density}
\includegraphics[width=0.45\textwidth]{fig/synthetic/fig-empirical-scree}

\caption{Left: Histogram of the singular values of a synthetic genomics data
matrix of size $41505\times81700$ (grey bars) generated with the code in
Algorithm~\ref{code:model}, overlaid with the
Marchenko-Pastur law \eqref{eq:mplaw-sv} for $\rho = 1.86$ (black line).
Light gray vertical lines show the
presence of 18 outlying singular values whose magnitudes exceed
$1.1\sigma_+ \approx 529.7$.
Right: Scree plot of the singular values of the same matrix
(black solid lines), showing the presence of a large, low rank portion
of approximately rank 10 (inset), and an asymptotic convergence to the same
Marchenko-Pastur law (red dotted line).
\label{fig:empirical-spectrum}
}
\end{figure}

The Marchenko-Pastur law describes the distribution of governs the eigenvalues
of a random covariance matrix $Y=XX^T$ formed from a data matrix $X$
of iid elements with mean 0 and finite variance $\sigma^2$.
Let $\rho$ be the ratio of the number of rows of $X$ to the number of columns of
$X$. Then, the nonzero eigenvalues follow the distribution
\begin{equation}
    \label{eq:mplaw-ev}
    p_e(\xi) = \frac {\sqrt{(\lambda_+-\xi)(\xi-\lambda_-)}} {2 \pi \sigma^2 \lambda x}
\end{equation}
where
$\lambda_+ = \sigma^2(1+\sqrt{\rho})^2$ and
$\lambda_- = \sigma^2(1-\sqrt{\rho})^2$.

When written in terms of the probability density of the singular values of $X$,
the law reads
\begin{equation}
    \label{eq:mplaw-sv}
    p_s(x) = \frac {\sqrt{(\sigma_+^2-x^2)(x^2-\sigma_-^2)}} {\pi \sigma^2 \min(1, \lambda) x}
\end{equation}
where
$\sigma_+ = \sqrt{\lambda_+} = \sigma(1+\sqrt{\rho})$ and
$\sigma_- = \sqrt{\lambda_-} = \sigma\vert1-\sqrt{\rho}\vert$.

Figure~\ref{fig:mplaw} shows typical density plots for random eigenvalues
and singular values for $\rho=1.5$.

\begin{figure}
\caption{Marchenko-Pastur law for $\rho=1.5$ (black lines) for the densities of
nonzero eigenvalues of a random covariance matrix ($XX^{T}$) and the singular
values of $X$ for iid matrix elements with mean 0 and variance 1
(black lines), corresponding to \eqref{eq:mplaw-ev} and \eqref{eq:mplaw-sv}
respectively.
Shown for comparison are corresponding histograms (grey
bars) of numerically sampled eigenvalues and singular vectors from
a numerically sampled random matrix $X$ of size $1000\times667$,
with iid Gaussian entries of mean 0 and variance 1.
\label{fig:mplaw}
}

\includegraphics[width=0.45\textwidth]{fig/mplaw/fig-mplaw-ev}
\includegraphics[width=0.45\textwidth]{fig/mplaw/fig-mplaw-sv}
\end{figure}

It is worth noting that random matrix theory had been previously introduced in
the theoretical analysis of principal components of genotype matrices.
\cite{Patterson2006} proposed a hypothesis test that computed principal components
should correspond to eigenvalues that were different from those expected from a
pure random covariance matrix,
and comparing in particular the largest eigenvalue against one randomly sampled
from the Tracy-Widom distribution~\cite{Tracy1993,Tracy1994}.
This analysis only shows that the matrix is not iid. In contrast, we show here
an explicit construction of a random matrix, whose elements are not iid, that
can generate a realistic spectrum of singular values that consists of several
large outliers and a bulk distribution that empirically satisfies the
Marchenko-Pastur law, albeit with a modified parameter $\rho = 1.86$ as opposed
to the value $81700/41505=1.97$ which would be expected from taking the ratio of
the number of rows to the number of columns.

\section{Algorithms for PCA}

The discussion in Section~\ref{sec:model} demonstrates that the
confounding effects of population substructure can and does produce a low
rank structure in the top singular vectors (i.e.\ singular triples
corresponding to the largest singular values), which can be captured even
in the very crude random matrix model of Algorithm~\ref{code:model}. The
top few principal components,
which by construction capture the largest components of the variability, are
good candidates for modeling the unwanted variation as described in
Section~\ref{sec:regress-correction} and have been used in the statistical
genetics community for this
purpose~\cite{Chen2003,Patterson2006,Price2006,Zhu2002,Zhang2003}.

Iterative eigenvalue (or singular value)
methods~\cite{Bai2000} are therefore computationally efficient choices for
determining these principal components, as only a handful of them are needed.
However, none of the classical methods known in numerical linear algebra
(apart from subspace iteration) is implemented in commonly used software packages
for PCAs in genomics, as shown in Table~\ref{tab:sw}.
Notably absent is any Lanczos-based bidiagonalization method.
We have therefore implemented the Golub-Kahan-Lanczos bidiagonalization~\cite{Golub1965}
method in pure Julia\cite{Bezanson2012,Bezanson2015}.
We have incorporated several of the best available numerical features, such as:

\paragraph{Thick restarting}
To control the memory usage and accumulation of
roundoff error, we also include an implementation of the thick restart
strategy~\cite{Wu2000,Stewart2001}, offering restarts using either
ordinary Ritz values~\cite{Wu2000} or harmonic Ritz
values~\cite{Baglama2005}. The thick restart variant is becoming
increasingly popular, being available not only in
SLEPc~\cite{Hernandez2008}, but also in R as the IRLBA
package~\cite{cran-irlba}, and has also become the new algorithm for
\verb|svds| in \textsc{MATLAB} R2016a (which also offers partial
reorthogonalization)~\cite{matlab-r2016a}. For the purposes of computing
the top principal components, it suffices to use thick restarts using
ordinary Ritz values.

\paragraph{Choice of reorthogonalization strategy}
We offer users the choice of partial
reorthogonalization~\cite{Simon1984,Larsen1998} or full
reorthogonalization using doubly reorthogonalized classical Gram-Schmidt.
By default, the implementation uses an adaptive threshold for determining
when the second reorthogonalization is necessary, based on the expected
number of digits lost to catastrophic
cancellation~\cite{Daniel1976,Bjorck2015}.
We also use the adaptive one-sided reorthogonalization strategy on either
the left or right singular vectors (whichever is smaller), unless our
estimate of the matrix norm is sufficiently large so that two-sided
reorthogonalization is necessary~\cite{Simon2000}.

\paragraph{Convergence criteria}
We use several different tests for determining when a Ritz value has
converged. At the beginning of the calculation when no other information
is known about the Ritz values, we use the crude estimate on the absolute
error bound on the singular values based on the residual norm computed
from a candidate Ritz value-vector pair~\cite[Ch. 3, \S 53, p.
70]{Wilkinson1965}. However, when the Ritz values become sufficiently
well-separated, more refined estimates can be derived from the
Rayleigh-Ritz properties of the Krylov process~\cite[Ch. 3, \S 54-55, p.
73]{Wilkinson1965}\cite{Yamamoto1980,Ortega1990}.
Experimental facilities are also provided to print and inspect further
convergence information, such as Yamamoto's eigenvector error
bounds~\cite{Yamamoto1980}, Geurt's formula for the componentwise backward
error~\cite{Geurts1982}, Deif's results for \textit{a posteriori} bounds
on eigenpairs and their backward error~\cite{Deif1989}. Interested users
and developers can easily modify the code to implement and inspect yet
other other proposed termination criteria~\cite{Bennani1994}.

The implementation of Lanczos bidiagonalization in Julia allows us to introspect
in great detail into the inner workings of the algorithm.
Figures~\ref{fig:conv-lanczos-tsvd} and \ref{fig:lanczos-tr} show two different
sets of running parameters for our code. The former is run with no restarting
and partial reorthogonalization with threshold $\omega = 10^{-8}$, whereas the
latter uses full reorthogonalization with thick restarting with a maximum
subspace size of 40.

\begin{figure}
\caption{Golub-Kahan-Lanczos bidiagonalization in Julia with no restarting and
partial reorthogonalization at a threshold of $\omega = 10^{-8}$, requesting
the top 20 singular values only. Orange vertical lines show when reorthogonalization
was triggered in the computation.
Left: Convergence behavior of the Ritz values.
Right: Computed errors in Ritz values from the residual norm criterion.}
\label{fig:conv-lanczos-tsvd}
\includegraphics[width=0.45\textwidth]{fig/tsvdconv}
\includegraphics[width=0.45\textwidth]{fig/tsvderror}
\end{figure}

\begin{figure}
\caption{Golub-Kahan-Lanczos bidiagonalization in Julia with thick restarting
every 40 microiterations and full reorthogonalization,
requesting the top 20 singular values only.
Gray vertical lines show when restarting was triggered in the computation.
\label{fig:lanczos-tr}
}

\includegraphics[width=0.45\textwidth]{fig/thickrestarted/fig-conv}
\end{figure}

\subsection{Convergence analysis of subspace iteration}

The software in Table~\ref{tab:sw} rely heavily on randomized block power
interactions, which are essentially equivalent to subspace iteration with a
randomized starting subspace.

FlashPCA also uses an unconventional convergence criterion, namely the matrix
norm of the difference between successive subspace basis vectors,
\begin{equation}
    \label{eq:flashpca-convergence}
    \Delta Y_n = \Vert Y_n - Y_{n-1} \Vert.
\end{equation}
A simple check of the condition number of $Y_n$ with block iteration $n$ shows
that the basis produced by the published version of FlashPCA (which does not
reorthogonalize the basis vectors) rapidly leads to a linearly dependent set of
vectors. As shown in Figure~\ref{fig:cond}, the loss of linear dependence occurs
essentially exponentially, with the inverse condition number reaching machine
epsilon after just five block iterations.
Therefore, we do not recommend the published version of the FlashPCA algorithm
for finding principal components, as it is practically guaranteed to not find
all the principal components requested. We note that the current version of
FlashPCA, which is newer than the published version, reorthogonalizes the
basis vectors by default. In this paper, we refer to the older and newer
versions as FlashPCA 1 and 2 respectively, to avoid ambiguity.

\begin{figure}
    \centering
    \begin{tikzpicture}
        \begin{semilogyaxis}[width=\textwidth, height=0.5\textwidth,
            xtick = {0,1,2,3,4,5}]
            \addplot[very thick, mark=*] file {data/condNumberNorm.txt};
        \end{semilogyaxis}
    \end{tikzpicture}
    \caption{Condition number of the matrix of subspace basis per iteration for
    the published version of FlashPCA~\cite{abraham2014fast}, which normalizes
    each vector but does not reorthogonalize them. Iteration zero is computed
    for the normalized basis after the initial range computation.
    \label{fig:cond}
    }
\end{figure}

\section{Performance and accuracy of Lanczos vs. subspace iteration}

We compared FlashPCA and our code on a machine with 230 GB of RAM and two
Intel(R) Xeon(R) CPU E5-2697 v2 @ 2.70GHz processors, each with 12 cores.
We used the FlashPCA v1.2 release binary for Linux.
Our Julia code was run on a pre-release v0.5 version of Julia,
built with Intel Composer XE 2016.0.109 Linux edition,
and linked against Intel's Math Kernel Library v11.3.

Table~\ref{tab:runtime} shows a breakdown of the execution time in FlashPCA
compared to our Lanczos implementation on our synthetic genotype matrix.
We observe a large difference in the run time between our Lanczos implementation
and subspace iteration.
The bulk of the difference comes from Lanczos taking much fewer iterations
(as measured by matrix-vector products) to converge. For FlashPCA, most of the
run time is spent in an initial matrix multiply, $XX^T$, and the subsequent
subspace iterations.

\begin{table}
    \caption{Run time in seconds for a synthetic genotype matrix of
    size $41505\times81700$ generated using Algorithm~\ref{code:model}.
    FlashPCA 1: the published version of the FlashPCA program
    algorithm~\cite{abraham2014fast}, which normalizes but does not reorthogonalizes
    the vectors. FlashPCA 2: the current version of the FlashPCA program,
    which now by default normalizes and reorthogonalizes the vectors using dense
    QR factorization. This work: Golub-Kahan-Lanczos bidiagonalization without
    restarting, employing partial reorthogonalization.
    \label{tab:runtime}
    }
    \centering
    \begin{tabular}{lrrr}
                                   & FlashPCA 1 & FlashPCA 2   & this work     \\ \hline
        Preprocessing              &   54        &   61        & 54            \\
        Forming $XX^T$             &  971        &  926        & N/A           \\
        Subspace/Lanczos iteration &   41        & 1935        & 37            \\
        Postprocessing             &    7        &   11        & 0             \\ \hline
        Total                      & 1073        & 2933        & 81  \\ \hline
    \end{tabular}
\end{table}

Forming the matrix $XX^T$ is the default option in FlashPCA; while advantageous
for very wide matrices $\rho \approx 0$, it is an expensive step for our matrix,
which has $\rho \approx 2$.
Furthermore, we observe a performance penalty in using the Eigen linear algebra
library (used by FlashPCA) relative to MKL.
Whereas the former took 926 seconds to compute $XX^T$, the latter took only
306 seconds on the same machine, using the same number of threads.
This discrepancy may be system dependent.

The subspace iterations form the bulk of the run time for FlashPCA 2. Even when
doing explicit reorthogonalization of the basis vectors, FlashPCA still performs
many more matrix-vector product-equivalents than our Lanczos implementation with
no restarting and partial reorthogonalization. Figure~\ref{fig:conv} contrasts
the convergence reported by FlashPCA 2 and our Lanczos implementation. Note that
the convergence criteria used by the two programs are very different---the former
uses the criterion \eqref{eq:flashpca-convergence}, which is very different from
the classical residual norm criteria commonly used by Lanczos-based
methods~\cite{Parlett1998}. Convergence of FlashPCA 2 is very slow,
being nearly stagnant for many iterations before improving dramatically
in the last iteration. In contrast, the Lanczos-based method shows essentially
logarithmic convergence in the residual norm after the first few iterations.

\begin{figure}
    \centering
    \begin{subfigure}{0.72\textwidth}
        \begin{tikzpicture}
            \begin{semilogyaxis}[width=9.5cm, height=5cm, xmin = 0, xmax = 169, ymin=10e-15, ymax=10e1]
                \addplot[very thick] file {data/FlashPCAQRconv.txt};
            \end{semilogyaxis}
        \end{tikzpicture}
        \caption{FlashPCA 2}
    \end{subfigure}
    \begin{subfigure}{0.23\textwidth}
        \begin{tikzpicture}
            \begin{semilogyaxis}[width=3cm, height=5cm, ymin=10e-15, ymax=10e1]
                \addplot[very thick] file {data/JuliaPCAconv.txt};
            \end{semilogyaxis}
        \end{tikzpicture}
        \caption{this work}
    \end{subfigure}
    \caption{Convergence of the FlashPCA 2 and Lanczos-based algorithms. The
    convergence criterion used in FlashPCA 2 is \eqref{eq:flashpca-convergence},
    which in principle can be very different from the residual norm criterion used
    in our Lanczos-based implementation. Convergence of FlashPCA 2 is very slow,
    being nearly stagnant for many iterations before improving dramatically
    in the last iteration. In contrast, the Lanczos-based method shows essentially
    logarithmic convergence in the residual norm after the first few iterations.
    \label{fig:conv}
    }
\end{figure}

Finally, we compare in Table~\ref{tab:shootout} the relative performance
and accuracy of the subspace iteration methods against our Lanczos
implementations as well as two other established libraries,
ARPACK~\cite{Lehoucq1996} and PROPACK~\cite{Larsen1998}. ARPACK, while not
originally designed for singular value computations, can be used to
compute eigenvalues of the augmented matrix $\begin{pmatrix}0 & X\\X^T &
0\end{pmatrix}$, whose eigenvalues are the same as the singular values of
$X$. To measure performance, we count the number of matrix-vector product
(mvps) as well as the wall time using the threaded BLAS implementation of
MKL on 24 threads. To measure accuracy, we provide both
$\Vert\Delta\theta\Vert_1 = \sum_{j=1}^k \beta_n \vert U^{(n)}_{mj}
\vert$, the sum of all estimated errors for the singular values, as well
as the relative error of the 10th singular value
as computed by LAPACK. Our results show that our implementation of Lanczos
bidiagonalization provides qualitatively better singular values that the
subspace iteration methods provided by FlashPCA, even with QR
reorthogonalization. Furthermore, our performance is significantly better
than the standard tools, ARPACK and PROPACK.

\begin{table}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
 & Algorithm & mvps & time (sec) & $\left\Vert \Delta\theta\right\Vert _{1}$ & rel. err. \tabularnewline
\hline
\hline
FlashPCA1 & Block power & 800 & 1073 & $2.55$ & $0.067$ \tabularnewline
\hline
FlashPCA2 & Block power & 33600 & 2933 & $0.0146$ & $1.88\cdot10^{-5}$ \tabularnewline
\hline
PROPACK & GKL (PRO, NR) & N/A & 120 & $5.2\cdot10^{-5}$ & $1.75\cdot10^{-11}$ \tabularnewline
\hline
ARPACK & GKL (FRO, IR) & 338 & 378 & $9.2\cdot10^{-6}$ & $8.34\cdot10^{-15}$ \tabularnewline
\hline
this work & GKL (FRO, TR) & 360 & 132 & $0.0037$ & $5.03\cdot10^{-8}$ \tabularnewline
\hline
this work & GKL (PRO, NR) & 190 & 81 & $2.5\cdot10^{-6}$ & $1.16\cdot10^{-14}$ \tabularnewline
\hline
\end{tabular}

\caption{Comparing various methods for computing the top 10 principal
components on a simulated genotype matrix of size $41505\times81700$.
Linear algebra kernels were run on MKL with 24 software threads except for
FlashPCA which ran on Eigen kernel.
Timings reported are wall times in seconds.
FlashPCA1 - FlashPCA with columnwise rescaling,
FlashPCA2 - FlashPCA with QR orthogonalization,
GKL - Golub--Kahan--Lanczos bidiagonalization,
PRO - partial reorthogonalization,
FRO - full reorthogonalization,
NR - no restart,
IR - implicit restart after 20 Lanczos vectors,
TR - thick restart after 20 Lanczos vectors,
mvps - number of matrix--vector products.
Termination criterion set to $\Vert \Delta Y\Vert = 10^{-8}$ for FlashPCA$n$,
and relative error in the 10th singular value compared with the value obtained from LAPACK.
\label{tab:shootout}
}
\end{table}

\section{Conclusions}

GWASs provide an exciting new data source for large scale matrix
computations, whose nominal dimensions are already on the order of $10^5
\times 10^5$ and will continue to grow rapidly in the near future.  The
statistical and computational demands of GWAS on genotype matrices
necessitate the best numerical algorithms and software.

We have implemented state of the art Lanczos bidiagonalization methods in
pure Julia, allowing us to compute the largest principal components of
genotype matrices more efficiently than any other tool currently being
used for genomics data analysis, and even outperforming some standard
packages for iterative eigenvalue and singular value computation such as
ARPACK and PROPACK. The implementation of these methods in the Julia
programming language provides a fast, practical software tool that permits
easy introspection into the inner workings of the Lanczos algorithms, as
well as experimentation into new methods with minimal fuss.

Further work may include generalizing the code to also handle block
Lanczos computations, which may further improve the performance of the
computation by making use of BLAS3 function calls. Imputation of missing
data will also become important in future data analysis, as nominal matrix
sizes grow and the number of incorrectly sequenced sites grows. We are
also implementing and studying into iterative methods for evaluating the
regression models used in GWASs.

\section*{Acknowledgments}

We thank the Julia development community for their contributions to free
and open source software. Julia is free software that can be downloaded
from \url{julialang.org/downloads}. The implementation of iterative SVD
described in this paper is available as the \verb|svdl| function in the
\href{https://github.com/JuliaLang/IterativeSolvers.jl}{IterativeSolvers.jl}
package. J.C. would also like to thank Jack Poulson (Stanford) and David
Silvester
(Manchester) for many insightful discussions.

redpajama_set_name: RedPajamaArXiv


text:
Q: MVC 4 Mocking HttpContext - how to mock DisplayModeProvider I was currently using Scott Hanselmans HTTP context mock for unit testing.  This worked well for MVC 3 and never looked back, I used it for testing calls for the following code.
public class PartialViewRenderer : IPartialViewRenderer
{
    public string Render(Controller controller, string viewName, object model)
    {
        if (string.IsNullOrEmpty(viewName))
            viewName = controller.ControllerContext.RouteData.GetRequiredString("action");

        controller.ViewData.Model = model;

        using (StringWriter sw = new StringWriter())
        {
            ViewEngineResult viewResult = ViewEngines.Engines.FindPartialView(controller.ControllerContext, viewName);
            ViewContext viewContext = new ViewContext(controller.ControllerContext, viewResult.View,
                                                      controller.ViewData, controller.TempData, sw);
            viewResult.View.Render(viewContext, sw);

            return sw.GetStringBuilder().ToString();
        }
    }
}

When I first converted my app to MVC 4 I ran into problems, it was getting runtime exceptions.  So I tried going through and fixing what needed fixing, which landed me on changing the following methods on Hanselmans MockHelpers: (I basically changed the HttpContext.Items to get returned since it was blowing an exception of "null")
 public static HttpContextBase FakeHttpContext()
    {
        var context = new Mock<HttpContextBase>();
        var request = new Mock<HttpRequestBase>();
        var response = new Mock<HttpResponseBase>();
        var session = new Mock<HttpSessionStateBase>();
        var server = new Mock<HttpServerUtilityBase>();
        var cookies = new HttpCookieCollection();
        var items = new ListDictionary();

        request.Setup(r => r.Cookies).Returns(cookies);
        response.Setup(r => r.Cookies).Returns(cookies);

        context.Setup(ctx => ctx.Items).Returns(items);

        context.SetupGet(ctx => ctx.Request).Returns(request.Object);
        context.SetupGet(ctx => ctx.Response).Returns(response.Object);
        context.SetupGet(ctx => ctx.Session).Returns(session.Object);
        context.SetupGet(ctx => ctx.Server).Returns(server.Object);

        return context.Object;
    }

 public static void SetFakeControllerContext(this Controller controller, RouteData route)
    {
        var httpContext = FakeHttpContext();

        ControllerContext context = new ControllerContext(new RequestContext(httpContext, route), controller);

        controller.ControllerContext = context;
    }

Here a very simple nUnit test I have to try and nail down what changes I need to make to this mock of http context (I havent even put in the asserts yet)
    [Test]
    public void test()
    {
        _contactsController = _container.Resolve<ContactsController>();

        var route = new RouteData();

        route.Values.Add("controller", "ContactsController");
        route.Values.Add("action", "GetEditContactDetailsDialog");

        _contactsController.SetFakeControllerContext(route);

        var result = _contactsController.GetEditContactDetailsDialog("1");
    }

Now when I run this test it bombs on the PartialViewRenderer.Render call on line ViewEngineResult viewResult = ViewEngines.Engines.FindPartialView(controller.ControllerContext, viewName);  Here is the following stacktrace.

at System.Web.WebPages.DisplayModeProvider.<.ctor>b__2(HttpContextBase context)
     at System.Web.WebPages.DefaultDisplayMode.CanHandleContext(HttpContextBase httpContext)
     at System.Web.WebPages.DisplayModeProvider.<>c__DisplayClass6.b__5(IDisplayMode mode)
     at System.Linq.Enumerable.WhereListIterator1.MoveNext()
     at System.Collections.Generic.List1..ctor(IEnumerable1 collection)
     at System.Linq.Enumerable.ToList[TSource](IEnumerable1 source)
     at System.Web.WebPages.DisplayModeProvider.GetAvailableDisplayModesForContext(HttpContextBase httpContext, IDisplayMode currentDisplayMode)
     at System.Web.Mvc.VirtualPathProviderViewEngine.GetPath(ControllerContext controllerContext, String[] locations, String[] areaLocations, String locationsPropertyName, String name, String controllerName, String cacheKeyPrefix, Boolean useCache, String[]& searchedLocations)

It seems I cant get in there and mock the DisplayModeProvider.  Per the MVC source Code Does anyone have a solution to this?  I havent been able to find a solution to this anywhere.

A: First, init mocks with MockBehavior.Strict like:
var context = new Mock<HttpContextBase>(MockBehavior.Strict);

Using this you can find dependency with DisplayMode.
Second, DisplayMode is new feature in asp.net mvc 4:
http://www.asp.net/whitepapers/mvc4-release-notes#_Toc303253810
So, it get Request.Browser params for determinate View which use. Add Mock for browser:
var browser = new Mock<HttpBrowserCapabilitiesBase>(MockBehavior.Strict);
var context = new Mock<HttpContextBase>(MockBehavior.Strict);
var request = new Mock<HttpRequestBase>(MockBehavior.Strict);
var response = new Mock<HttpResponseBase>(MockBehavior.Strict);
var session = new Mock<HttpSessionStateBase>(MockBehavior.Strict);
var server = new Mock<HttpServerUtilityBase>(MockBehavior.Strict);
var cookies = new HttpCookieCollection();
var items = new ListDictionary();

browser.Setup(b => b.IsMobileDevice).Returns(false);

request.Setup(r => r.Cookies).Returns(cookies);
request.Setup(r => r.ValidateInput());
request.Setup(r => r.UserAgent).Returns("Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.11 (KHTML, like Gecko) Chrome/23.0.1271.64 Safari/537.11");
response.Setup(r => r.Cookies).Returns(cookies);

request.Setup(r => r.Browser).Returns(browser.Object);
context.Setup(ctx => ctx.Items).Returns(items);

A: DisplayMode implements the interface IDisplayMode, so you should be able to (with Moq) create a mock to inject. DisplayModeProvider has a SetDisplayMode (protected) method you may be able to invoke via Reflection.

redpajama_set_name: RedPajamaStackExchange


text:
Astros fire A.J. Hinch, GM Jeff Luhnow after they get one-year suspensions for roles in sign-stealing scandal
By Bradford William Davis
The Astros fired GM Jeff Luhnow and manager A.J. Hinch on Monday after MLB gave them each one-year suspensions for their involvement in the team's illegal sign-stealing during the 2017 season. The 'Stros, who won the 2017 World Series and were runners-up in 2019, will also forfeit their first and second-round draft picks in 2020 and 2021 and pay a $5 million fine, the maximum legal amount.
After a months-long investigation, MLB found that the Astros connected a live feed from the centerfield camera — zoomed in on opposing catchers — to decipher sign sequences from the opposing catcher. While some Astros players monitored the feed, others would alert their teammate in the batter's box by banging a trash can from the dugout. MLB's investigation found that the Astros continued their illegal sign-stealing through the 2017 postseason, when they won the World Series.
"We need to move forward with a clean slate and the Astros will become a stronger organization because of this today," team owner Jim Crane said in a press conference. "You can be confident that we'll always do the right thing and will not have this happen on our watch." Crane said he had plans to install a "compliance program" to avoid future instances of cheating.
According to the report, Houston also experimented with clapping, yelling and whistling to relay pitch types to their teammates as they faced the opposing pitcher. Hinch called the whistling suggestion "ridiculous" during the 2019 ALCS, when they beat the Yankees.
If Luhnow or Hinch, now unemployed, are found to violate any more MLB rules upon continuing their baseball careers, they will be placed on the league's permanently ineligible list.
Hinch issued a statement to the decision on Monday night, expressing disappointment at the Astros' decision to part ways with him. And while he maintained he did not participate in the sign-stealing, he accepted fault for not stopping the players.
"As a leader and Major League Manager, it is my responsibility to lead players and staff with integrity the best possible way," Hinch said. "While the evidence consistently showed I didn't endorse or participate in the sign stealing practices, I failed to stop them and I am deeply sorry."
Statement from A.J. Hinch: pic.twitter.com/DtLMhySpgZ
— Daniel Gotera (@DTGoteraKHOU) January 13, 2020
Brandon Taubman was placed on MLB's ineligible list. The former assistant GM was fired for taunting three journalists about the team's 2018 acquisition of accused domestic abuser Roberto Osuna, then smearing their credibility in concert with the Astros' public relations team.
He can apply for reinstatement after the 2020 season.
Red Sox manager Alex Cora, who was Hinch's bench coach in 2017 and an architect of Houston's sign-stealing setup, has not been suspended — yet.
[More Sports] The Mets have no one but themselves to blame for this mess »
MLB is also undergoing an investigation of alleged sign-stealing by the 2018 Red Sox, which won the World Series in Cora's first year as manager.
No players were disciplined for their roles in the scandal, including Carlos Beltran, who was reported to help shape the system.
Beltran retired after the 2017 season and will manage the Mets in 2020.
The Yankees were eliminated by the Astros twice in the last three years, including in 2017′s closely-contested seven-game ALCS. Brian Cashman had strong words about the team's allegations back in November.
"You decide to play by the rules, or you don't," said Cashman shortly after The Athletic's initial report. "And if you don't, there's consequences. You're putting yourself at risk whether it's future employment, current employment, or sanctions."
[More Sports] Where do the Mets go from here? »
Luhnow said in a statement he accepted the league's ruling, but stressed that he was "not a cheater."
"Anybody who has worked closely with me during my 32-year career inside and outside baseball can attest to my integrity. I did not know rules were being broken," added Luhnow. "I am deeply upset that I wasn't informed of any misconduct because I would have stopped it.
However, according to commissioner Rob Manfred's report, Luhnow did receive at least two emails referencing the use of the replay review room staff's sign-stealing efforts.
In his statement, Manfred described the Astros' baseball operations department under Luhnow as "very problematic," an assessment Crane disagreed with during the team's presser.
Manfred wrote, "The baseball operations department's insular culture – one that valued and rewarded results over other considerations, combined with a staff of individuals who often lacked direction or sufficient oversight, led, at least in part, to the Brandon Taubman incident, the Club's admittedly inappropriate and inaccurate response to that incident, and finally, to an environment that allowed the conduct described in this report to have occurred."
Crane told reporters that he plans to oversee baseball operations and fill Crane and Luhnow's roles in time for spring training. Internal candidates will be interviewed for Luhnow's open position.

redpajama_set_name: RedPajamaCommonCrawl


text:
06/June/2017 01:12 PM
Foreign Ministry: 50 years of injustice and denial
RAMALLAH, June 6, 2017 (WAFA) – The Foreign Ministry said Tuesday that the Palestinian people mark this year the 50th anniversary for the Israeli occupation or 50 years of injustice and denial.
Marking this occasion, the Foreign Ministry issued the following statement:
"This week the Palestinian people mark fifty years since the beginning of the Israeli colonial occupation of the West Bank, including East Jerusalem, and the Gaza Strip. On this solemn occasion, the Palestinian people reflect on half a century of injustice and denial, which are an extension of an historical injustice that befell the Palestinian people nearly 100 years ago and remains without redress.
"The Israeli military occupation has established itself as a colonial regime founded and maintained by the policy of displacement and replacement. Israel's insatiable desire for territorial expansion and its insistence on denying the existence of the Palestinian people as well as its refusal to recognize the national, historic, and cultural rights of Palestinians to their homeland have made of this occupation a belligerent colonial regime that defies international law with impunity.
"Since 1967, the occupying Power has systematically carried out a colonization campaign throughout the Occupied Palestinian Territory, including, in particular, in and around Occupied East Jerusalem, aimed at the illegal, de facto annexation of the land as well as the displacement of the indigenous Palestinian population and their replacement by settlers. For five decades now, Israel has been incessantly confiscating Palestinian land and destroying Palestinian property for the purpose of constructing, expanding and entrenching its illegal colonial settlements regime, into which over half a million Israeli settlers have been illegally transferred. These illegal Israeli practices and measures are altering the demographic composition of and destroying the territorial contiguity, character and integrity of the Occupied Palestinian Territory, including East Jerusalem.
"The Israeli occupation of Palestine permeates all aspects of Palestinian life. It is a regime designed to oppress the Palestinian people, strip them of their land and natural resources, and deny them their basic human rights. This occupation is a cruel system of injustice predicated on the racist notion that one people's prosperity and strength must come from the subjugation and oppression of another people, whose rights, prosperity, and future are at the mercy of their occupier. The reality of Israel's occupation extends far beyond the parameters defined in international law, which regarded occupation as a temporary measure borne out of the circumstances of war yet subject to the rules of war and confined by the commitment to respect international law and the rights of protected persons. Indeed, the actions of successive Israeli governments expose Israel's unwillingness to end this occupation and hegemony over the land and people of Palestine.
"Over the past five decades, the international community has exerted various efforts and adopted a host of United Nations resolutions reiterating the need to put an end to this suffering and fulfill the rights of the Palestinian people in order to achieve a just and lasting peace. However, Israel's intransigence and its total disrespect and contempt for international law, including humanitarian and human rights law, have continuously derailed these efforts. Instead of complying with the law and pursuing peace, Israel, the Occupying Power, has acted with flagrant impunity, denying the rights of the Palestinian people and committing grave breaches, including war crimes, systematic human rights violations and acts of state terror against them. Israel has undermined or rejected all peace initiatives and violated all resolutions aimed at achieving a just and peaceful solution to the conflict on the basis of the rules of international law, the resolutions of international legitimacy and the principle of land for peace, because it has more invested in the colonial occupation than in the prospects of peace.
"The international community, including the United Nations, in particular the Security Council, has a standing legal and moral obligation to work towards ending this prolonged injustice and bring peace and security to the Palestinian and Israeli peoples. It should work to promote international law in accordance with its relevant resolutions, which form the foundations for the achievement of a just, lasting and comprehensive peace. In this regard, the international community must also honor its obligation to ensure that the principle of accountability is respected without exception. Israel continues to violate Palestinian rights, entrench its colonial occupation, and derail credible peace efforts because it has enjoyed immunity from accountability for over half a century. This destructive cycle of impunity and crimes must end in order for peace to have a chance."


Auditors and comptrollers play a vital role in the grant management process—ensuring financial information is accurately reported and risks are reduced. But, without accurate data that is easily accessible, their job can be hard to complete.
Below, we overview common auditor challenges, key benefits of grant software and specific features that may appeal to your auditor.
Poor data quality and/or lack of data consistency due to manual entry and processes at audited organizations.
Dishonesty of those submitting or reviewing financial expenses.
Lack of compliance with evolving federal regulations, such as OMB Uniform Grant Guidance and the DATA Act.
Insufficient internal controls at audited organizations to prevent waste, fraud or abuse of money.
Poorly constructed or missing grant performance management systems.
The above challenges can make it difficult for auditors to efficiently complete their job duties. With the right technology, though, these issues can be lessened.
Standardized internal grant management and expense tracking processes.
Identification of fund misuse or poorly performing programs for remediation.
Clear audit trail for traceability into how funds are used, managed and reported.
Improved compliance with grant agreements and federal regulations.
Better activity, spend and performance reporting.
Centralized grant data and documentation, leading to reduced audit findings and fewer questioned costs.
Organized data and processes make it easier for auditors to fact check spend and performance information, and pinpoint areas where waste, fraud or abuse may abound.
Audit logs document all activity within your grant software portal, including the action taken, who performed it and when. This way, if suspicious activity is detected, the auditor can pinpoint when and how things went awry.
Automated reporting of budget, performance, Time and Effort, grant portfolio analyses, OMB A-133 and outcome evaluations guarantees auditors have the data needed to properly assess spend, performance and compliance.
Centralized document management ensures vendor invoices, cancelled checks, travel logs, timesheets and other necessary documentation is easily accessible.
Timestamps allow auditors to see when specific tasks were performed.
User roles and permissions provide insight as to who has access to certain documents, data and grant management activities. This information can be helpful to auditors as they review your organization's internal controls.
The above features are just a few examples of how grant managers can use software to monitor the grants lifecycle, decrease time spent on audits, demonstrate effective budget and performance management, and better answer questions on how funds are spent. Make your auditor's job easier with more organized information and processes.
Learn how else your auditor can benefit from grant software. Schedule a demo today!


Play great traditional card games while strengthening your vocabulary!
A deck of 52 synonym cards, each with a point value.
The objective is to have the most points when the game ends.
The first dealer is chosen randomly, and the turn to deal alternates if there are two players, and rotates clockwise if there are more than two.
The dealer deals out seven cards to each player.
The dealer places the rest of the cards in a face down pile between the players. This pile is called the stock pile.
The dealer then places the top card from the stock pile face up on the table next to the stock pile to start the discard pile.
The players should organize the cards in their hands so that synonyms are grouped.
Starting with the person left of the dealer, the player either picks up one or more cards from the discard pile or picks up one card from the stock pile. If a player picks up more than one card from the discard pile, she must meld a group of synonyms containing the bottom-most card.
The player has the option of melding. Melding is taking a group of two or more synonyms from your hand, and placing it face up in front of you on the table, where it stays.
The player also has the option of laying off. Laying off is adding a card or cards from your hand to a meld already on the table. Laid off cards are placed in front of the player who laid them off.
The player finishes the turn by discarding a card.
The game ends when one player runs out of cards in his/her hand.
The player with the highest score wins the game. Scores are calculated by adding the point values of all the cards they have played (melded or laid off) and then subtracting the point values of the cards left in their hands.
The objective is to have the most cards when the game ends.
All 52 cards are laid face down in rows and columns on the table.
Starting with the youngest player, the player turns over two cards (one at a time so that all players can see them) and keeps them if they are synonyms. If they successfully match a pair of synonyms, that player takes another turn.
When a player turns over two cards that are not synonyms, those cards are turned face down again and the turn moves clockwise to the next player.
The game ends when all the cards have been taken.
The winner is the player with the most sets of cards.
The objective is to have the most complete sets of cards when the game ends.
The dealer deals out 7 cards to each player (5 cards if there are more than four players).
The dealer places the rest of the cards in a face down pile between the players.
Starting with the person left of the dealer, the player asks one other player for a specific synonym card. To ask for a card, the player must hold one of its synonyms. If the player gets the card asked for, he or she gets to ask again of the same player or a different player. If the player does not get the card asked for, the player draws one card from the top of the deck. If that card is the one asked for, the player gets to ask again. If not, the turn moves clockwise to the next player.
When a player gets a set of four synonyms, he or she must lay the set down on the table.
The objective is to be the first player to run out of cards.
Discard one card with the same rank / border color as the top card on the discard pile.
Discard two or more synonym cards. The bottommost card must have the same rank / border color as the top card on the discard pile.
Discard one or more cards that are synonyms of the top card on the discard pile.
If the player cannot play, he/she must draw cards from the stock pile until he/she can.
If the stock pile is exhausted, the discarded cards, except for the last card, are shuffled and placed face down to create a new stock.
The winner is the first player to run out of cards.


The College Porters are highly valued members of the College and are important people in College life. Most students will see more of them than of the other University officers and they provide all sorts of help cheerfully and informally. The College Porters keep the infamous 'incident book' covering everything from noise complaints to inter flat fall outs! If your actions warrant a mention 'in the book', expect a visit from the Deanery – you have been warned!
They can be contacted on 01524 593714.


Season 2 of Star Trek: Discovery has definitely focused less on the Klingons than the first season did, but members of everyone's favorite ridge-headed warrior race have popped up twice now for two glorious episodes.
The first was "Point of Light," which found High Chancellor L'Rell dealing with drama of Shakespearean proportions. The ramifications of that episode are still being felt, especially in the season's most recent episode (and second one to feature Klingons), "Through the Valley of Shadows." Chancellor L'Rell pays a visit to the U.S.S. Discovery just as the ship travels to the revered Klingon planet of Boreth.
For Trek fans, Boreth is a familiar location. The two-part Star Trek: The Next Generation episode "Rightful Heir" takes place there, Worf talks about visiting its monasteries many times after that, and according to Klingon legend, it is the planet where Kahless the Unforgettable promised to one day return.
SYFY WIRE caught up with Klingon High Chancellor L'Rell herself, Mary Chieffo, to discuss her character being further integrated into Trek canon, vulnerable conversations, parallels to Queen Elizabeth I, and even the (slight) possibility for a Klingon musical (based on "Point of Light") to be performed in Las Vegas.
When we last saw Chieffo's High Chancellor, she was not only giving up on the great love of her life (Ash Tyler/Voq, played by Shazad Latif), but also her son. Tyler joined Section 31, and her baby was sent to Boreth. As far as greater Klingon society was concerned, both Tyler and the baby were dead; L'Rell had to go along with the ruse to keep them both safe. In a monumental speech to the Klingon houses, L'Rell affirmed her power and told Klingon society that they may call her "mother." What has L'Rell been doing since that moment?
L'Rell has certainly been left in a vulnerable place, losing both her lover and her son, and both of her episodes this season make the viewer (at least this viewer) think of Queen Elizabeth I. A particular moment from Shekhar Kapur's film Elizabeth comes to mind, especially when Cate Blanchett's Elizabeth I is fully in power at the end, and tells a former adviser, "I am married…to England." L'Rell, it could be said, is similarly married to the Empire. Chieffo cited the former British monarch as having a big influence on her portrayal of L'Rell.
Chieffo mentioned that in the most recent episode, it's implied that she's been keeping the Empire in line for many months (no easy task), but that now when we meet her again, she's brought back to a place of extreme vulnerability. "You're seeing her interact with the man who is the center of her greatest heartbreak. You're getting to see the quieter moments. I love seeing strong powerful characters, male or female, but certainly female, that are embodying a certain persona externally, and getting to explore that inner life, because that's certainly how I feel," said Chieffo.
L'Rell's vulnerability underneath her immense strength has never been as clear, perhaps, as it was when she was reunited with Tyler. With insanely effective use of a pause (in the line, "I didn't expect to see you… ever again"), Chieffo makes us feel every bit of that vulnerability.
Perhaps a less heartbreaking (or tragic) aspect of this episode came with L'Rell cruising into the orbit of Boreth on a classic D7 Klingon vessel — both the location and the ship are huge in the lore of Trek. For Chieffo, the cementing of L'Rell within that lore (by the writers, not necessarily by Chieffo herself), has been "a huge theme" of the season.
In terms of new discoveries as far as Boreth itself is concerned, there were two big ones in the latest episode. The first is that the planet is home to time crystals, a very powerful resource that L'Rell herself remarks on, saying that their power is "the very reason we no longer exploit the crystals." Of course, this is a prequel series, and it would be impossible for Worf or any other Klingon Chancellor to have had this knowledge, but still — as one of the only trustworthy Chancellors that we've seen the Empire have, it makes sense that L'Rell would know about this secret, and keep it sacred. Gowron, for example, would probably not have used them to positive ends.
Mitchell, Chieffo, Latif are very close both on-set and off ("Being stuck in Klingon plots together for two years kind of binds you very intensely," Chieffo said), and the three of them discussed various possibilities for the older version of L'Rell and Voq's son once it was revealed that Mitchell would be playing him.
L'Rell may have (somewhat) come to a place of peace with Tyler, but Chieffo thinks there's more drama to be had from a scene between herself and Michael Burnham (Sonequa Martin-Green). "We are very aware of each other through Tyler, and Sonequa and I have certainly talked a lot about who the characters are, and what that relationship is for the both of us, but I've always been interested in what would happen if it wasn't Tyler and L'Rell in a room, or Tyler and Burnham in a room, what if it was just Burnham and L'Rell?" Chieffo said.
Would she like it if one (or both) of them appeared on Discovery? "I would love to see either of them doing anything on the show. I think it would be excellent," she said.


text:
Let's Find Out if You Follow Gordon Ramsay
Wolfgang Puck. Emeril Lagasse. Nigella Lawson. Rachael Ray. Bobby Flay. Jamie Oliver. Paula Deen. The list of chefs who have become celebrities beyond their restaurant kitchens is ever growing. Gordon Ramsay is another one of the well-known restaurateurs. He has 16 Michelin stars and exceedingly high standards. Furthermore, he backs those standards with profanity-laden blastings of his kitchen staff. But, the Scottish-born chef has also gained popularity as the host of numerous TV shows. These include shows such as Kitchen Nightmares and Masterchef. Whatever the reason you're drawn to this culinary star, this quiz will test your Gordon Ramsay know-how.
Do you like pizza swearing at you?
The Gordon Ramsay group has 14 restaurants in London and a total of 33 restaurants globally. The latest addition is a pizza joint on 10 Bread Street (really, the address would only be apter if it was Crust Street) in St. Paul's, London. For 15 pounds, roughly $20 US Dollars, customers can enjoy unlimited slices of artisanal pizzas — even a vegan option. "If there's one thing I believe it's that pizza doesn't need to be complicated," Ramsay said of the concept branded Gordon Ramsay's Street Pizza. "It's pizza without rules." Another unique element of the eatery? Thursday, Friday, and Saturday nights it will host a rotating roster of all-female DJs.


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The latest edition of Renault's celebrated hot hatch debuts in Paris with a turbocharger and dual clutches.
It's too bad the Renault brand isn't sold in the US because enthusiasts here are deprived of some of the best hot hatches in the world. The new Clio Renaultsport 200 Turbo, making its debut at the Paris Motor Show, is "an innovative response to the highly sophisticated expectation of the compact sports hatchback customer." European drivers are treated to a new direct-injection 1.6-liter turbo four with 200 horsepower at 6,000 rpm with 177 pound-feet of torque coming in as low as 1,750 rpm. That's practically idling.
That's mighty impressive for a car with a turbocharger that would otherwise struggle with turbo lag. Overcoming that - and widening the torque band - was clearly a priority for Renaultsport as it implemented forced induction for the first time in a model that was traditionally naturally aspirated. As such, this new engine is more powerful and more fuel efficient than its predecessor, augmented by a brake energy recovery system (not unlike the KERS it developed for the Red Bull and Lotus F1 teams) and variable valve timing. Shifting is handled exclusively by a six-speed dual-clutch gearbox - another first in a car that used to be manual.
As with previous models, buyers will be able to choose between Sport and Cup chassis, the latter being better suited to track day enthusiasts. Renault claims the new Clio RS 200 Turbo delivers excellent road handling, powerful braking, a user-friendly cabin layout, and high quality throughout. Throw in bucket seats, optional leather, touchscreen nav, Bluetooth, multimedia system and an extensive personalization program and you've got a hot hatch with premium features at an affordable price. Shame Americans can't have it.