text:
## on Pitman closeness

I came by happenstance upon this talk, “Some Pitman Closeness Properties Pertinent to Symmetric Populations”, given by Mohammad Jozania, at the University of Manitoba next week, and it rescinded my former (if negative) interest in Pitman nearness (or closeness). This criterion, which originated in a 1937 paper of E.J.G. Pitman, compares two estimators in the light of the probability of one being closer (to the “truth”) than the other,

$\text{Pr}_\theta(|\hat\theta_1(X)-\theta|<|\hat\theta_2(X)-\theta|)$

and there was a brief interest in the method at the end of the 1980’s, culminating with Keating and Mason’s book on the topic.

In a 1993 JASA paper I wrote with Gene Hwang and Bill Strawderman, entitled “Is Pitman Closeness a Reasonable Criterion?“, we demonstrated that, in many respects, this criterion was not appropriate for comparing estimators. For instance, the comparison was not transitive, two estimators with the same marginal distribution could sometimes be ranked, a Bayes estimator could not be properly derived, some counter-intuitive orderings could be exhibited, &tc… This was an exciting (and fun) paper to  write as it was only made of (counter)examples. (Hence our answer to the above question was  definitive no.) Judging from the abstract to the talk,

In this talk, we focus on Pitman closeness probabilities when the estimators are symmetrically distributed about the unknown parameter θ. We first consider two symmetric estimators θ¹ and θ² and obtain necessary and sufficient conditions for θ¹ to be Pitman closer to the common median θ than θ². We then establish some properties in the context of estimation under Pitman closeness criterion. We define a Pitman closeness probability which measures the frequency with which an individual order statistic is Pitman closer to θ than some symmetric estimator. We show that, for symmetric populations, the sample median is Pitman closer to the population median than any other symmetrically distributed estimator of θ. Finally, we discuss the use of Pitman closeness probabilities in the determination of an optimal ranked set sampling scheme (denoted by RSS) for the estimation of the population median when the underlying distribution is symmetric. We show that the best RSS scheme from symmetric populations in the sense of Pitman closeness is the median and randomized median RSS for the cases of odd and even sample sizes, respectively.

it sounds like the authors have relaunched research in this area, hence that our 1993 definitive conclusion against the use of the criterion was not definitive for everyone…  (I could not find a trace of the corresponding paper through google, but I would be interested in reading the recent research on the topic! Even though the result about the “optimality” of the sample median reminds me of earlier results, with the related drawback that this optimality is incompatible with the sufficiency principle.)

### 5 Responses to “on Pitman closeness”

1. William Volterman Says:

Having done some work with Pitman Closeness myself, I have of course read your paper. It was quite an interesting read.

And while I agree with many points raised, I don’t think that any definitive statements regarding Pitman Closeness can be made based on your article. In fact I believe there were strong points made on both sides. (Though it is my opinion that all sides had their minds made up definitively before reading the others arguments anyways.)

You will find many papers now on Pitman Closeness, primarily with ordered data. (For where transitivity often follows.)

That said, I’m sure you’ve already made up your mind, so I will not trouble you further, but it couldn’t hurt to look up a few new papers on PC.

2. Hi

I just notified by a friend of mine that you have made a comment on my recent talk that I gave in our weekly seminars.

My main research area is in decision theory and I have recently begun to do research in the area of ranked set sampling as well.
As you may know, ranked set sampling (RSS) is an efficient method for data collecting which can be used to obtain better estimators of the population mean when there are some cheap and easy to use auxiliary information that can be used for ranking the sampling units before the actual measurement. There are many variations of RSS and recently(??) in a paper at the Biometrical Journal it is shown that the median ranked set sampling works very good in estimating the median for symmetric populations. After one of our weekly seminars given by a colleague of mine who is working mostly on PC, I became interested to see what would be the best ranked set type sampling design for estimating the median for symmetric populations using the PC as the criterion of performance. It turns out that here also the median RSS or its randomized version would be the best RSS design to follow.

In addition, let d1 nd d2 be two independent and symmetrically distributed estimators about the parameter \theta. Among other results, we show that a sufficient condition for d1 to be PC to \theta than d2 is that the distribution og d1 to be more peaked about \theta than d2.

Anyway, the seminar that I gave talks about both pros and cons of the PC as a criterion. In this work, we also obtain some results in the same spirit as the one you have in the JASA paper which can be used to show some of the deficiencies of PC. The whole point is that as an statistician when we are making inference we should not base all of our inference solely using one criterion and we should try to see the performance of the estimators using other criteria of performance.

I have seen your JASA paper, I also read its comments and discussions. It seems to me that, those who are not agreeing with you about not using PC are having their own reasoning as well. It is obvious that PC suffers from some problems (and disabilities) but I think this does not mean we should ignore it totally. PC is born (whether we like or not) with all of its pros and cons and it is now part of our life as statisticians. Imagine what will happen if we decide not to use any criteria which suffers from some deficiencies and disabilities. Like people (no matter black or white, etc.) I think different criteria and methods have the right to exist in the statistics world.

By the way, I can send you a copy of my talk if you are interested and thanks again for your comments.

Regards

• Sure, I’d be interested in the talk (and the papers if any are available). I (and others) however remain unconvinced by the pros of Pitman closeness, but don’t take it personally!

3. Hi,

But what kind of criterions would you recomend for comparison of estimators, since you disagree with the use of Pitman closeness criterion?
In your book “The Bayesian choice” you mentioned that integrated risk can served as measure for ordering of estimators, but it requires integration over sample space (and steps into the land of frequentists) and not very friendly when it comes to its values calculation in complex problem.


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Software Open Access

# Linear Optimal Low-Rank Projection

Eric W Bridgeford; Minh Tang; Jason Yim; Joshua T Vogelstein

### Dublin Core Export

<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:creator>Eric W Bridgeford</dc:creator>
<dc:creator>Minh Tang</dc:creator>
<dc:creator>Jason Yim</dc:creator>
<dc:creator>Joshua T Vogelstein</dc:creator>
<dc:date>2018-05-15</dc:date>
<dc:description>Supervised learning techniques designed for the situation when the dimensionality exceeds the sample size have a tendency to overfit as the dimensionality of the data increases. To remedy this High dimensionality; low sample size (HDLSS) situation, we attempt to learn a lower-dimensional representation of the data before learning a classifier. That is, we project the data to a situation where the dimensionality is more manageable, and then are able to better apply standard classification or clustering techniques since we will have fewer dimensions to overfit. A number of previous works have focused on how to strategically reduce dimensionality in the unsupervised case, yet in the supervised HDLSS regime, few works have attempted to devise dimensionality reduction techniques that leverage the labels associated with the data. In this package, we provide several methods for feature extraction, some utilizing labels and some not, along with easily extensible utilities to simplify cross-validative efforts to identify the best feature extraction method. Additionally, we include a series of adaptable benchmark simulations to serve as a standard for future investigative efforts into supervised HDLSS. Finally, we produce a comprehensive comparison of the included algorithms across a range of benchmark simulations and real data applications.</dc:description>
<dc:identifier>https://zenodo.org/record/1246979</dc:identifier>
<dc:identifier>10.5281/zenodo.1246979</dc:identifier>
<dc:identifier>oai:zenodo.org:1246979</dc:identifier>
<dc:relation>url:https://github.com/neurodata/lol/tree/v2.2.0</dc:relation>
<dc:relation>doi:10.5281/zenodo.1246978</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:title>Linear Optimal Low-Rank Projection</dc:title>
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71
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format: plain


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## Friday, February 09, 2018

### A simple Dow Jones targeting monetary policy

For some two years, the world's stock markets have enjoyed a calm era with a seemingly healthy growth. The volatility was almost zero and the positive returns looked as safe as if you buy the Bitcoin. Needless to say, aside from the fact that the companies have some intrinsic value which is why investors know that the prices shouldn't drop too low, the emotional part of the price swings is completely analogous in the case of the stocks and the Bitcoin. A difference is that emotions decide about some 30% of the stock prices but about 100% of the cryptocurrency prices.

OK, this calm era ended abruptly when the stock market indices saw a terrible week, with at least two days of 4-5 percent drops per day. The main reason that is cited is the U.S. investors' realization that the interest rates will go up.

Now, unfortunately, I couldn't predict the precise timing but I did predict all these events qualitatively. For some 5-10 years, we saw the era of extremely low interest rates combined with low inflation. Well, the interest rates were really zero in many countries while some countries started experiments with negative interest rates.

Negative interest rates look like a borderline contradiction. Why would someone lend his money for a negative return? Isn't it better to keep the money at zero interest rate, e.g. in the basement? Needless to say, whether this is a real contradiction depends on "who is the someone". Some institutions don't really look for profit or may be regulated so that "they're not allowed to do certain things" which is why negative interest rates may be enforced there.

But yes, I think it would be paradoxical and market-wrecking if true negative interest rates made it to the real economy involving regular people.

Nevertheless, why did we go through this long era of vanishing interest rates and what was the future? Some people were predicting that those would be here forever. I knew it was complete nonsense. The vanishing interest rates were inevitably a temporary anomaly and an eventual growth of the inflation rate and the interest rates – possibly a speed growth – was an unavoidable outcome at some moment. Czechia was among the first ones that saw this return of the inflation and the interest rate hikes that reacted to the resuscitated inflation pressures. Our inflation exceeded 2% for more than a year.

Why was it inevitable? Because when the interest rates are too low, the money is simply piling. It's just too easy for the people to borrow the money even if they don't really need it. Some of it is used to buy products, some of it is invested. These processes unavoidably exert a positive pressure on prices of products, prices of assets, and indirectly on wages, and the return of the inflation simply cannot be prevented.

So the stock markets have grown more quickly than rationally roughly since the election of Donald Trump (who has a higher approval rate than Obama had 8 years ago exactly in the same stage of the presidency, by the way: so much for all the hysteria about the most catastrophic U.S. president). Some of the growth of the U.S. stocks seems absolutely sensible – especially because of the approved lower corporate taxes, some 20% uptick of the stock prices is justifiable. But the growth was even faster than that.

And now this excessive growth entered a correction. Well, everyone who has enough stocks hopes that this will be called a correction in the future.

Over the years, I've spent a nonzero amount of time by trying to develop more efficient, stable, productive, safe rules for a monetary policy and/or methods to collect taxes and tax revenue and other things. I think that I can design rules that need vastly less paperwork and that are much more resilient to shocks.

These days, central banks typically regulate the interest rates to achieve their approximately 2% inflation rate. The U.S. Federal Reserve is actually considering a clear transition to this regime, too. That's what we were told yesterday. I think it would be progress. Instead of the targeting of the inflation rate, a better system is the targeting of the actual integrated inflation rate – the price of the actual inflation basket. This would do a better job in counting episodes in which the inflation is overshot or undershot.

You may define the inflation basket in various ways – I think that the expenses that the poorest people have to pay should still be the most important component of such a basket if one exists at all (because those people are most sensitive to changes of the price level of the products they need). However, you may replace the inflation basket by the GDP or GNP. Instead of targeting inflation, you may target the nominal GNP which may be required to grow at a 5% annual rate. Sweden has tried it, I think.

On top of that, I think that corporate taxes should be replaced by the government's ownership of some 20% of the companies – so that it would simply get a part of the dividends like everyone else. Those could be non-voting stocks (you don't want communism in which the government officials influence the commercial sector much) although I suppose that left-wing government would try to change it. But the unification of corporate taxes and dividends – the government is just another stockholder and companies don't pay extra taxes – would simplify things and it would also create a better "mood" concerning the role of the government. The government isn't some ultimate dictator above everybody; it is a minority shareholder and it may want to behave accordingly.

There are mood swings in the market and they lead to oscillations in the inflation rate and other things. And the central banks are effectively trying to counteract these swings and regulate the inflation rate. You might say that by their changes to the interest rates (and sometimes by exceptional policies such as the quantitative easing), the central banks are indirectly trying to regulate the mood itself – the exuberance vs fear – to achieve stable conditions. It's the emotions, exuberance and fear, that seem to matter fundamentally. And they use things like the inflation rate to measure the mood.

Well, if you accept this picture that the central banks regulate the psychology – excessive exuberance or excessive fear – then your next question should be: Aren't there better ways to measure it than to look at the inflation rate? The inflation rate is confusing and delayed etc. Of course there are better ways. And I think that the stock market indices are actually some of the best simple indicators.
The stock market drops are not only a great indicator of a negative mood swing that will lead to deflationary pressures; stock market drops are also the most important causes of recessions and depressions. That was the case in 1929 and 2008, too. And it makes sense to fight against the primary causes, not just symptoms, of recessions, which is why it's a good idea to discourage big stock market drops.
When the Dow Jones drops some 10%, as in a recent week, it isn't just some arbitrary isolated figure. It's also a very strong sign that the mood has deteriorated and people and companies will be less willing to spend and invest. So already this drop of the stock market could be a good reason to revise the plans for the interest rate hikes in the downward direction. Well, because the drop of the stock market is driven by the realization that the interest rates will go up, the rule that the "interest rates won't go up too fast because the stock market has dropped" would decelerate or stop the stock market drop which could be a good thing.

Some of my proposed recipes for an optimal monetary policy involved some rather complicated formulae etc. Instead, one could demand that the monetary policy rules should be extremely simple so that everyone may quickly understand it and sort of figure out what the consequences are. In the past, I was proposing "Dow Jones money", a money unit linked to the Dow Jones index, which would have many advantages. (The Dow Jones index would become a strictly predictable, smoothly increasing function of time, when expressed in these money units.) But the transition to that new regime could be controversial (but doable).

What about the following simple rule that has "similar" outcomes?

Just define the target for the Dow Jones index. It is meant to be 22,000 on January 1st, 2017 – near the beginning of the Trump presidency – and increase 6% a year. So it's expected to be 23,320 on January 1st, 2018, respectively (sorry, in this way, one would expect further drops now LOL, maybe we should increase the base so that no drop is expected now). And you may calculate the expected value of the targeted Dow Jones index for every day by interpolation – by the smooth exponential function.

Now, the role of the Federal Reserve during the monetary meeting would be simple. If the Dow Jones on that day is equal to the targeted one within e.g. 10%, then the Feds do nothing. When the Dow Jones is lower than the target by more than 10%, they lower the interest rates by 0.25%, When it's higher than the target by more than 10%, they increase the interest rates by 0.25%. There could be special rules that ignite changes of the interest rates that are higher than 0.25% in either direction, too.

In this way, everyone would know that if the stocks go too low, the Fed will help. If they get too high, the Fed will discourage the companies by higher interest rates. One would automatically get some reasons to believe in the relative stability – and the stability would be imprinted to the real world as a self-fulfilling prophesy. Investors would be less likely to join massive mood swings together. On top of that, the price level would also be relatively stabilized because the long-term, averaged over years ratio of the Dow Jones and the price level is relatively constant.

I do believe that the excessive short-term and medium-term mood swings – the the heavy swings of the overall stock indices (and sometimes even restricted stock market indices that only measure one sector of the economy) etc. – play no useful role in the markets. They're a net negative, basically negative consequences of an imperfect choice of the money and/or monetary policy, and these oscillations should be suppressed to achieve a more optimal system.

Three paragraphs above, I wrote about the "plus minus 10% tolerance" for the Dow Jones. But even the changes of interest rates by 0.25% aren't ground-breaking so one could expect that the Dow Jones would "rather often" oscillate away from the target by more than 10%. So it wouldn't be a completely safe investment with a 6% return. But it would be safer than today and I think it should be safer. One of consequences would be that a greater number of people would have savings in stocks because those would be somewhat safer than they are today. Because the promised higher stability would make stocks more attractive, people would probably go to stocks as soon as the new policy is announced, which would lead to a higher Dow Jones, and according to my rules, an increase of the interest rates to make the cash more attractive again. I think there's nothing wrong about this expected evolution.

The Dow Jones index is a collection of selected companies. One would have to impose rules so that its percentage as a part of the economy and/or the total capitalization of everything doesn't change too much with time.


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# 7.4.5.11 Qto_ElectricMotorBaseQuantities

## 7.4.5.11.1 Semantic definition

Base quantities that are common to the definition of all occurrences of electric motor.


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# Homework Help: Conservation of Energy in Conjunction With Momentum

1. Oct 5, 2013

### Bashyboy

1. The problem statement, all variables and given/known data
Consider an elastic collision between two bodies of equal mass, one of which is initially at rest. Let their velocities be $\vec{v_1}$ and $\vec{v_2} = \vec{0}$ before the collision, and $\vec{v_1 '}$ and $\vec{v_2 '}$ after the collision. Write down the vector equation representing conservation of momentum and the scalar equation which expresses that the collision is elastic. Use these to prove that $\vec{v_1 '}$ and $\vec{v_2 '}$ are orthogonal.

2. Relevant equations

3. The attempt at a solution

If the collision is elastic, then KE = KE'.

m1 = m2 = m

$\vec{p} = \vec{p'}$

If the two velocity vectors are orthogonal, then $\vec{v_1 '} \cdot \vec{v_2 '} = 0$.

Conservation of energy:

$\frac{1}{2} mv_1^2 = \frac{1}{2} m v_1^{'2} + \frac{1}{2} m v_2^{'2}$

$v_1^2 = v_1^{'2} + v_2^{'2}$, which can be written as $| \vec{v_1} |^2 =| \vec{v_1 '} |^2 + | \vec{v_2 '} |^2$, although I am not sure of how helpful this will be.

Conservation of momentum:

$m \vec{v_1} + \vec{0} = m \vec{v_1 '} + m \vec{v_2 '}$

$\vec{v_1} = \vec{v_1 '} + \vec{v_2 '}$

Taking the magnitude, $| \vec{v_1} | = | \vec{v_1 '} |+ | \vec{v_2 '} |$; again, I am not certain of how helpful this will be.

______________________________________________________

Up to this point, I am not sure as to how to proceed. Could someone provide me with a hint?

2. Oct 5, 2013

### Saitama

Hi Bashyboy!

Nooo.

$|\vec{v_1}|=| \vec{v_1 '} + \vec{v_2 '} | ≠ | \vec{v_1 '} |+ | \vec{v_2 '} |$.

3. Oct 5, 2013

### Bashyboy

Yes, of course. I actually have the correct expression on my paper, but somehow I failed to properly type it up.

4. Oct 5, 2013

### Saitama

Well...$|\vec{v_1'}+\vec{v_2'}|$ means the magnitude of resultant of $\vec{v_1'}$ and $\vec{v_2'}$. Can you proceed further?

5. Oct 5, 2013

### Bashyboy

Well, I now have that $| \vec{v_1} | = | \vec{v_r '} |$, and I also have that $|\vec{v_1}|^2 = | \vec{v_1 '} |^2 + | \vec{v_2 '}|^2$. I am to make some sort of substitution?

6. Oct 5, 2013

### Saitama

If two vectors, $\vec{A}$ and $\vec{B}$ make an angle $\theta$ with each other, what is the magnitude of resultant of the two vectors?

7. Oct 5, 2013

### Bashyboy

I don't quite follow. I have never seen the sum of two vectors in terms of their angle.

8. Oct 5, 2013

### Saitama

I don't know how it is at your place but that's something taught at the very beginning here.

Okay, if you haven't seen it, you can use cosine rule to derive it. Draw a vector diagram.

9. Oct 5, 2013

### Bashyboy

10. Oct 5, 2013

### Saitama

Apply cosine rule to the triangle shown in the attachment.

#### Attached Files:

• ###### vector.png
File size:
3 KB
Views:
200
11. Oct 5, 2013

### Bashyboy

When you say cosine rule, do you also mean the law of cosines? The law of cosines for vectors is simply the dot product, is it not?

12. Oct 5, 2013

### Saitama

Yes, very sorry, it is the law of cosines. I am used to calling it the "cosine rule".

13. Oct 5, 2013

### Bashyboy

So, you are suggesting that by solving the law of cosines for theta, it will equal 90 deg.?

14. Oct 5, 2013

### Saitama

You can see it yourself. Apply the law of cosines. Show your work.

15. Oct 5, 2013

### Bashyboy

Sorry it took awhile to reply. Well, after applying the Law of Cosines, the problem became rather trivial: it's all a matter of memorizing those tricks and formulas of mathematics. At any rate, Pranav-Arora, I thank you very much for time.

16. Oct 5, 2013


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# Knowledge International says its new scheme will support

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Knowledge International says its new scheme will support [#permalink]  24 Nov 2010, 22:05
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Knowledge International says its new scheme will support federal objectives on investments for meeting the future economy needs, and encouraged mature students to participate

A. will support federal objectives on investments for meeting the economy needs, and encouraged mature students to participate

B. can support federal objectives regarding the investments in meeting economy's future needs, and encourage older students for participation.

C. has supported federal objectives regarding investments in meeting the economy’s future needs and encouraged older students participation.

D. would support federal objectives regarding investment to meet the economy's future needs, and would encourage mature students to participate

E. could support federal objectives regarding investments to meet the economy's future needs and encourages older students to participate

"to meet the economy's future needs" is an adverbial modifier and requires a verb .The only present D and E is "would / could support ). Therefore the meaning is changed
In C, the scheme is new, then how could it already have supported?
In A, there is tense mismatch between "says" and encouraged"
In B "can" shows ability and there is no definite article before "economy's"
In D, would shows hypothetical.
In E , could indicates possibility
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Last edited by Zatarra on 25 Nov 2010, 01:52, edited 1 time in total.
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Re: Knowledge International [#permalink]  24 Nov 2010, 23:30
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I Choose D over E...Would support is better than could support according to me, but this is just my opinion...
I would select D.
IMO D
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Re: Knowledge International [#permalink]  25 Nov 2010, 00:46
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Expert's post
Between D and E, E misses parallelism by using the present tense -encourages - while the modal - would encourage - will make the construction a lot better. In addition, the use of - older - in E is badly chosen because intellectual matters such as participation in schemes is not age based. D is my choice
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Re: Knowledge International [#permalink]  25 Nov 2010, 01:13
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mundasingh123 wrote:
Knowledge International says its new scheme will support federal objectives on investments for meeting the future economy needs, and encouraged mature students to participate

A. will support federal objectives on investments for meeting the economy needs, and encouraged mature students to participate

B. can support federal objectives regarding the investments in meeting economy's future needs, and encourage older students for participation.

C. has supported federal objectives regarding investments in meeting the economy’s future needs and encouraged older students participation.

D. would support federal objectives regarding investment to meet the economy's future needs, and would encourage mature students to participate

E. could support federal objectives regarding investments to meet the economy's future needs and encourages older students to participate

"to meet the economy's future needs" is an adverbial modifier and requires a verb .The only present D and E is "would / could support ). Therefore the meaning is changed
In C, the scheme is new, then how could it already have supported?
In A, there is tense mismatch between "says" and encouraged"
In B "can" shows ability and there is no definite article before "economy's"

I'd Go for B with this - As per the intent the sentence has to be in present tense . and B is the only choice which does that well .
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Re: Knowledge International [#permalink]  25 Nov 2010, 01:49
daagh wrote:
Between D and E, E misses parallelism by using the present tense -encourages - while the modal - would encourage - will make the construction a lot better. In addition, the use of - older - in E is badly chosen because intellectual matters such as participation in schemes is not age based. D is my choice

I agree with you on the use of older.
But E does maintain parallelism because the subject is knowledge international and agrees with the word "encourages ".Isnt "would reserved for hypothetic events.
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Re: Knowledge International [#permalink]  25 Nov 2010, 02:11
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yes - one use of "would" is for hypos --- this is a hypo --- the "new scheme" is going to do something, so it is unreal in that sense

in E there is no comma before "and" - you need a comma before an "and" if it is joining two separate clauses.
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Re: Knowledge International [#permalink]  25 Nov 2010, 02:18
gmat1011 wrote:
yes - one use of "would" is for hypos --- this is a hypo --- the "new scheme" is going to do something, so it is unreal in that sense

in E there is no comma before "and" - you need a comma before an "and" if it is joining two separate clauses.

What abt D?
Nones commenting on "investment/investments to verb/in verbing
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Re: Knowledge International [#permalink]  25 Nov 2010, 02:25
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"Investment" can be used that way... investment to meet... needs seems fine to me

The broad agenda for the Prime Minister's emergency meeting was related to foreign investment in the country.

You don't have to say foreign "investments" though it is pretty unlikely that it will just be one 'investment'
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Re: Knowledge International [#permalink]  25 Nov 2010, 02:31
gmat1011 wrote:
"Investment" can be used that way... investment to meet... needs seems fine to me

The broad agenda for the Prime Minister's emergency meeting was related to foreign investment in the country.

You don't have to say foreign "investments" though it is pretty unlikely that it will just be one 'investment'

to verb is an adverbial modifier and needs a verb to modify.In D and E the only verb is support
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Re: Knowledge International [#permalink]  25 Nov 2010, 02:47
so what is your conclusion? support X.... to meet Y is a valid formulation. Just googled and found this on a Canadian government website:

We therefore recommend that dedicated funding be made available to support organizations to meet AODA compliance standards.
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Re: Knowledge International [#permalink]  25 Nov 2010, 03:07
gmat1011 wrote:
so what is your conclusion? support X.... to meet Y is a valid formulation. Just googled and found this on a Canadian government website:

We therefore recommend that dedicated funding be made available to support organizations to meet AODA compliance standards.

To meet economy's needs is an infinitive and modifies a verb."to support" modifies made available and to meet modifies to support.
I think Dand E are wrong because of misplaced modifier also.Need expert to corroborate
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Re: Knowledge International [#permalink]  25 Nov 2010, 09:14
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what is OA? I am chose ans:D...it was between D/E. E throws this older people statement into the sentence.
does investments need to be plural or singular?
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Re: Knowledge International [#permalink]  25 Nov 2010, 18:40
I also think it is D, but i am not sure about the use of needs.
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Re: Knowledge International [#permalink]  26 Nov 2010, 17:22
daagh wrote:
Between D and E, E misses parallelism by using the present tense -encourages - while the modal - would encourage - will make the construction a lot better. In addition, the use of - older - in E is badly chosen because intellectual matters such as participation in schemes is not age based. D is my choice

Can you clarify one two points

1) why B is wrong here

B. can support federal objectives regarding the investments in meeting economy's future needs, and encourage older students for participation.

2) In the option b, do we require to repeat to be - can after comma and 'and' conjunction or can we take placement of 'can' implied before the verb encourage ? because if the repition is necessary then the same sentence has two different tenses within
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Re: Knowledge International [#permalink]  26 Nov 2010, 22:00
hirendhanak wrote:

1) why B is wrong here

B is not correct on multiple counts:

1. B uses encourage. We can interpret this in two ways:

a. …its new scheme will support X and (its new scheme) encourage Y. This is not correct construction, since you would expect the verb to be encourages (since scheme is singular).

b. …its new scheme can support X and (can) encourage Y. The issue here is more of logic. When Knowledge International (or anyone else for that matter) says something about its (own) scheme, can comes out as too in-definitive and non-committal a statement (think about it: Fed says its measures can improve US economy).

2. Changes the meaning of the original sentence, since older is not the same as mature.

p.s. I would strongly encourage test takers to not interpret would as hypothetical usage. For example, I will become a pilot is a correct usage, though at this point of time, it is still hypothetical (whether I finally end up becoming a pilot or not).

The best way to interpret would is when one talks about future from past perspective. In this case, Knowledge International said in the past (sentence, due to its typical construction, uses says, but this act of saying clearly occurred sometime in the past) something about future (that its scheme in future will do X and Y). Hence, would is the most appropriate usage here.
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Re: Knowledge International [#permalink]  29 Nov 2010, 11:01
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Hey guys,

Thank you for the invitation to chime in! I'll throw my support for choice D here, as well. A few big-picture problems with some of the choices include:

-The use of "encouraged" in A and C - this "new scheme" doesn't call for a past-tense verb. At its most retroactive, you'd use the present perfect "has encouraged" to indicate that it's still ongoing, but a straight past-tense verb isn't correct here.

-"investments in meeting" or "investments for meeting" in choices A, B, and C are poorly phrased - that present-tense verb isn't really anything you can invest in, so in order to use a verb you really need to use the "to meet" infinitive form.

-"could" and "can" (E and B) aren't really good uses of business writing. As far as meaning goes, they're not something that a company like Knowledge Int'l would ever make an official statement on. "Will" and "Would" are better - they predict that something will happen instead of saying "maybe" or "it might". It's a subtle thing but I've seen the "nobody knows" forms of "can", "could", "maybe" come up and in contexts like these I haven't ever seen them be correct.

-Between D and E, E isn't really a pure parallelism error, as you could reverse the two verbs and it would be okay: "the program encourages older students and could support federal objectives". In that case, one thing is definitely true ("encourages") and the other is potentially true ("could support"), so the meaning is correct. But in the reverse order, as E is written, the conditional comes first making an awkward meaning "could support...and encourages" - the "could" really should control both verbs, and in this case that makes the second half illogical (you can't have "could" with an indicative form like "encourages").

I hope that helps...

One other point - I don't think that the GMAT would use "mature" vs. "older" in an official question as this question does...that seems to be a word-choice smokescreen that I haven't really seen them do. And 'investments" vs. "investment" - they're two different meanings but I think that both are appropriate here. "Investments" refers to specific levels or quantities of investments (e.g. "the government wants investments totaling $500 million"), whereas "investment" is the overall entity or idea. I don't think either is particularly wrong or right here. _________________ Brian Save$100 on live Veritas Prep GMAT Courses and Admissions Consulting

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Re: Knowledge International [#permalink]  01 Dec 2010, 11:02
it is d and in b the idiom encourage for is wrong
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Re: Knowledge International says its new scheme will support [#permalink]  05 Jul 2012, 11:30
I have a question here, if in the option A if the answer choice did not make the parallelism error and did have will support...and [will] encourage.. would it then be correct?

In case yes, then what makes us select would/will or the vice versa?
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Re: Knowledge International says its new scheme will support [#permalink]  11 Jul 2012, 09:43
Can anybody tell me when to use "could" and when to use "would" with examples ? It's really confusing me
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Re: Knowledge International says its new scheme will support [#permalink]  02 Jun 2015, 15:09
Hello from the GMAT Club VerbalBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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# TubuleJ

TubuleJ has been developed has a plugin to the multi-platform ImageJ software to facilitate analysis of microtubule images obtained by cryo-electron microscopy. The basic principles of TubuleJ were originally described in (Blestel et al., 2009). The current version has been updated with new routines, and incorporates TomoJ (Messaoudi et al., 2007) to perform fast 3D reconstructions of microtubules.


text:
## Introduction

Retinoblastoma (RB) is a childhood cancer that forms in the developing retina of babies and toddlers. Malignant tumors can form in one or both eyes. Without treatment RB is life threatening; even with treatment there is a high chance of losing the eye if cancer does not respond to therapy1,2. Although the majority of RB cases are initiated by biallelic inactivating mutations of the RB1 tumor suppressor gene3, ~13% of non-hereditary RB have RB1 promotor methylation and silencing4,5,6. In addition, epigenetic deregulation of tumor-promoting pathways has been shown to be important for RB tumorigenesis and disease progression beyond RB1 inactivation7,8,9. Due to the fundamental role epigenetics plays in this malignancy, a mechanism to assay epigenetic tumor profiles in vivo from eyes undergoing salvage therapy would be highly relevant.

While tumor biopsy is the diagnostic norm for most malignancies, direct tissue biopsy is contraindicated for RB due to the risk of provoking extraocular tumor spread. Until recently, this contraindication meant that no molecular tumor information was available unless the eye was enucleated (surgically removed). However, in 2017 we demonstrated that the aqueous humor (AH), the clear fluid in front of the eye, is an enriched source of tumor-derived cell-free DNA (cfDNA) for RB10,11, that facilitates analysis of tumor-derived cfDNA in the absence of tumor tissue. Molecular genomic profiling of AH cfDNA opens the door to apply decades of knowledge about RB genomics in an impactful in vivo clinical application10,12,13,14. The addition of epigenetic assays enables a better understanding of the role of methylation in orchestrating gene expression in disease initiation and progression. This includes the identification of tumors initiated by DNA hypermethylation of the RB1 or other gene promoters that may help stratify patients for epigenetic treatment regimens. Thus, epigenetic analysis of AH cfDNA is a highly desired aspect of an integrated, multi-modal liquid biopsy platform.

In this study, we performed genome-scale DNA methylation profiling of paired AH cfDNA and primary RB tumors and integrated the results with existing RB tumor DNA methylation profiles. The methylation profiles of AH cfDNA and primary tumors show high concordance, demonstrating that the AH profiling is a reliable mechanism to evaluate the methylation status of the tumor. We further performed enriched pathway analysis to identify aberrantly methylated genes directly involved in RB tumorigenesis. Finally, we demonstrated the ability to identify RB1 promoter DNA hypermethylation, a known cause of sporadic, non-heritable RB, as well as DNA methylation profiles that may predict an aggressive tumor subtype less likely to respond to medical therapy. Our findings support accessible approaches of molecular-based RB diagnosis, and potential future clinical implications of epigenetic dysregulation in RB using this liquid biopsy.

## Results

### Validation of DNA methylation profiles in RB specimens

Genome-scale DNA methylation profiling of AH cfDNA and RB tumors was investigated to characterize RB epigenetic changes in vivo. DNA methylation profiles of four paired primary RB tumors and AH cfDNAs (CHLA 1–4) were measured using the Illumina MethylationEPIC (EPIC) DNA methylation BeadArray system. An additional 11 AH cfDNA (CHLA 5–15) samples collected at diagnosis or at the time of enucleation (i.e., surgical removal of the eye) were similarly analyzed (Table 1). DNA methylation datasets were filtered as per standard to remove data from probes that are: (1) linked to known polymorphisms, (2) located on the X- and Y-chromosomes, and (3) related to aging (Fig. S1). Publicly available DNA methylation data (Illumina Infinium HumanMethylation450, HM450) for primary RB tumors (RB_SR) (n = 57) and tumor-adjacent retinas (n = 12) as controls (GSE57362)9 were integrated for validation. By overlapping our EPIC array data with the published HM450 data, a total of 363,579 probes remained for downstream analysis. After filtering for RB tumor purity, 34 primary RB (RB_SR_1–30 and RB_CHLA_1–4) and 15 AH cfDNA (AH_CHLA_1–15) samples were retained for further analysis.

We sought to identify RB tumor-specific DNA methylation changes. Welch’s t-test was applied on the filtered 363,579 probe set to identify differentially methylated probes across the four primary RB samples from CHLA and the 30 tumors and 12 retinas from a publicly available dataset. With average β value difference >0.3 and p < 0.05, 15,483 probes were identified that are significantly differentially methylated between retina and RB samples. DNA methylation changes were identified in 31 of the 34 RB tumors with three exceptions (RB SR_18, 21, and 29) that displayed DNA methylation profiles similar to the normal retina (Fig. 1A). Approximately 19% of the probes showed strong DNA hypermethylation in RB samples, while 81% displayed DNA hypomethylation, consistent with the previous reporting8.

Similarly, multidimensional scaling (MDS) of the DNA methylation data revealed that RB tumors mainly clustered separately from normal retina, aside from the three aforementioned tumors (RB_SR_18, 21, and 29) that may represent uninvolved retina (Fig. 1B). The MDS analysis also revealed greater DNA methylation heterogeneity in RB tumors versus the normal retina (Fig. 1A, B).

DNA hyper- or hypomethylation occurs in promoters, gene bodies, enhancer elements, and other as inter-genetic region. However, in the RB-specific group of 15,483 probes, DNA hypermethylated loci were mostly enriched within gene bodies and DNA hypomethylation was most prevalent in gene promoter regions (Fig. 1C). These findings are suggestive of gene expression alterations, as promoter DNA hypomethylation and gene body DNA hypermethylation are correlated with gene activation15,16. In addition, DNA methylation in intergenic regions may correlate with chromatin instability and regulation of functional elements, such as enhancers17,18. The distribution of RB-specific DNA methylation alterations across various genic regions may provide clues regarding potential gene activity.

### DNA methylation profiles in cfDNA of aqueous humor (AH) are reliably assayed and highly concordant to primary RB tumors

The AH cfDNA, like that of other body fluids, is highly fragmented19. The Illumina Infinium EPIC DNA Methylation BeadChip is a widely used genome-scale DNA methylation assay20, however, applying this technology for DNA methylation profiling of highly degraded, low input DNA samples, such as FFPE-DNA or cfDNA with less than the recommended input DNA amounts (250 ng), presented a challenge.

We evaluated the lower limits of fragmented DNAs on the EPIC DNA methylation array using short DNA fragments. Genomic DNA extracted from the human HCT116 colon cancer cell line was first sonicated to 200–300 bp to match AH cfDNA fragments and then 1, 5, 10, and 20 ng of the fragmentized DNA were subjected to the Illumina Restoration Kit after bisulfite conversion which is recommended for repairing FFPE-DNA samples prior to hybridization to Illumina EPIC DNA methylation arrays. 200 ng DNA was used as a control for bulk DNA amounts commonly evaluated on the EPIC DNA methylation array platform.

DNA methylation β values for 1, 5, 10, and 20 ng of the repaired DNA were plotted versus the 200 ng DNA sample (Fig. 2A). The 1 ng input DNA sample showed some DNA methylation β value skewing compared to the bulk sample, but still showed a high correlation (r2 = 0.899) to the bulk 200 ng DNA sample (Fig. 2B). The scatterplots and associated correlation coefficients show a strong and reliable association of the 5, 10, 20 ng input DNA samples vs. the bulk 200 ng control sample (r2 = 0.97–0.98) (Fig. 2B). These findings suggested that Illumina EPIC DNA Methylation assay is applicable for measuring DNA methylation of cfDNA samples with >1 ng input DNA and as such can be applied to the lower amount of cfDNA in the AH.

DNA methylation data on AH cfDNA samples with 1–10 ng input was successfully generated. DNA methylation profiles of four pairs of RB tumors and AHs (CHLA 1–4) demonstrated highly concordant DNA methylation profiles for each tumor-AH pair and distinct separation between different tumor-AH pairs (Fig. 2C). Unsupervised clustering of the most variably methylated probes across all four tumor-AH pairs also highlighted differential DNA methylation among these four patients and highly concordant DNA methylation profiles between each RB tumor and its corresponding paired AH (Fig. 2D); this demonstrates that the AH could be used in the absence of tumor (e.g., from eyes that have not been surgically removed) to accurately assay the methylation signature of the tumor in vivo. Copy number analysis of the EPIC DNA methylation data set18,21 also showed high concordance between each primary RB tumor and its paired AH cfDNA specimen (Supplementary Fig. 3A).

An additional set of 11 AH samples from CHLA were included for further comparison, such that a total of n = 15 AH cfDNA specimens were analyzed. All 15 AH_CHLA samples showed the RB-specific DNA methylation pattern by unsupervised clustering (Fig. 3A) and MDS (Fig. 3B) analyses. The RB-specific DNA methylation profiles were not detected in cfDNA isolated from blood plasma in two RB patients but rather clustered with white blood cell DNA isolated from RB patients (Fig. S4) as expected since the disease was confined to the eye without high tumor fraction in the blood12,22.

Analyses of gene-level DNA methylation in Fig. 3A revealed RB1 promoter DNA hypermethylation in five samples (RB_CHLA_3, AH_CHLA_3, RB_SR_16, RB_SR_24, and RB_SR_30) consistent with RB1 inactivation via epigenetic silencing; a known mechanism of non-heritable RB1 inactivation. Previously this could only be determined with access to tumor tissue, however identical RB1 promoter DNA hypermethylation was detected in cfDNA of AH and from tumor DNA from the same enucleated eye (RB_CHLA_3 and AH_CHLA_3) further demonstrating that RB1 promoter DNA hypermethylation can be reliably detected via ocular AH liquid biopsy in the absence of tumor tissue (Fig. 3C).

Overexpression and/or amplification of MYCN and SYK have been demonstrated to highly correlated to RB tumorigenesis and considered as potential therapeutic targets23,24,25. In our cohort, the majority of RB tumors demonstrated MYCN and SYK promoter DNA hypomethylation (associated with gene activation); this profile was similarly identified in all AH samples as compared to apparently normal retinal tissues (Fig. 3C), suggesting that these targets can be detected via AH methylation profiling.

### Characterization of genes with RB-associated DNA methylation profiles and their involvement in RB tumorigenesis

While most cancer-specific DNA methylation alterations do not result in altered gene expression16,26,27, promoter DNA methylation is negatively correlated with gene expression and gene body DNA methylation is positively associated with gene expression15,28. To characterize the extent to which promoter and gene body DNA methylation affect gene expression, we used publicly available RNA sequencing (RNA-seq) data (GSE125903 and GSE111168)29,30 due to the limited availability of our primary RB samples.

First, we identified DNA methylation probes exhibiting RB-specific DNA methylation changes (delta β value > 0.3) in promoter or gene body regions by comparing normal retina and primary RB samples (Fig. 1). In total, we identified promoter DNA hypermethylation (978 probes), promoter DNA hypomethylation (4949 probes), gene body DNA hypermethylation (1178 probes) and gene body DNA hypomethylation (3856 probes) (Fig. 4A). In addition, we uncovered upregulation of 889 and downregulation of 382 genes in RB. After integrating the RB-specific promoter and gene body DNA methylation (Fig. 4A) with differential gene expression data, we identified 294 genes that show potential gene regulation by aberrant DNA methylation directly in RB (Fig. 4B). These genes include those upregulated and correlated with promoter DNA hypomethylation (n = 172) or gene body DNA hypermethylation (n = 37), as well as those downregulated and correlated with promoter DNA hypermethylation (n = 67) or gene body DNA hypomethylation (n = 18) (Fig. 4B and Supplementary Data 1). Although Illumina-based DNA methylation data are reliable and have been validated using pyrosequencing and targeted bisulfite sequencing27,31, we confirmed the EPIC DNA methylation array data by performing targeted bisulfite sequencing of four gene regions (TFF1 and HOXC4 promoters and MNX1 and CELSR3 gene bodies) on 10 additional primary RB tumors and one apparently healthy retina (Supplementary Data 3 and Supplementary Fig. 5). The EPIC array and targeted bisulfite sequencing DNA methylation data are highly consistent at these four loci.

The potential roles of epigenetic-directed gene expression during RB tumorigenesis remain unclear. Core analysis in Ingenuity Pathway Analysis (IPA, Qiagen) was performed on the set of 294 differentially expressed genes to understand their potential functional profiles for RB tumorigenesis (Fig. 4B, C). The Graphical Summary algorithm predicted down-regulation of tumor suppressor pathways involving p53, RB1, CDKN2A/p16, and CDKN1A/p21, and activation of oncogenic pathways involving E2F1, E2F2, E2F3, and MYC (Fig. 4C). Furthermore, we used TRANSFAC analysis to identify transcription factors (TFs) involved in the regulation of these pathways or genes32. The top over-represented transcription factors binding sites included oncogenic regulators involved in ER (Estrogen receptor), Ras (RREB-1, Ras responsive element binding protein 1), E2F, MYC (MAZ, MYC associated zinc finger protein), NF-kB, and EGR1 (Early growth response protein 1) signaling pathways (Supplementary Fig. 6).

These pathways are known to be involved in RB tumorigenesis and contribute to upregulation of aryl hydrocarbon receptor (AhR) signaling, estrogen-mediated S-phase entry for cancer cell proliferation, and others33,34,35. These findings suggest that in addition to genetic alterations such as pathogenic RB1 variants, DNA methylation-regulated genes related to cancer aggressiveness can be involved in the downregulation of tumor suppressor pathways as well as upregulation of oncogenic pathways that contribute to RB tumorigenesis. Further detailed analysis of Estrogen-mediated S-phase pathway elements revealed several key downstream signaling genes that are upregulated in association with promoter DNA hypomethylation in RB tumors, including CCNA1 and CCNA2 for Cyclin A, CCNE1 and CCNE2 for Cyclin E, as well as E2F1, E2F2, and CDC2 (Fig. 4D). Interestingly, our data also showed that these genes, especially in downstream of RB1 such as Cyclin A, Cyclin E, and CDC2, can be upregulated by promoter DNA hypomethylation independent of germline RB1 mutation status (Fig. 4E).

### AH cfDNA methylation profiles are associated with RB tumor aggressiveness

To explore the potential of epigenomic prognostic biomarkers to predict eye salvage via AH, we analyzed EPIC DNA methylation data from 12 AHs from eyes with different clinical outcomes, including four eyes salvaged with therapy (SV) with at least 1 ng AH cfDNA (AH_CHLA_6 removed), four primarily enucleated eyes (PE) without initial medical intervention and four secondary enucleations (SE) in which the eye failed attempted treatment. Three AH samples with low data quality were excluded. Specifically, AH cfDNA methylation profiles between salvage (AH_CHLA_5, 8, 9, and 10), primary enucleation (AH_CHLA_1, 2, 3, and 4) and secondary enucleation (AH_CHLA_11, 12, 13, and 14) cases were analyzed using heatmap representation after unsupervised clustering. In total, 1092 probes were identified that are significantly differentially methylated ($$\triangle$$β > 0.4, p < 0.01) between the salvage (n = 4) and enucleation groups (n = 4 PE and n = 4 SE) (Fig. 5A). As expected, based on our previous work12 and that of Liu et al.36, salvaged eyes had fewer copy number alterations than enucleated eyes, especially for gain of 1q, 6p and loss of 16q in current dataset (Supplementary Fig. 3B).

To determine if these same probes could be used to distinguish primary tumors, DNA methylation data for this set of 1092 differentially methylated probes was further applied to the above-described 30 primary RB tumors (RB_SR, GSE57362). Interestingly, in the larger data set there remained differential methylation between the salvaged group and the enucleated tumors (Fig. 5B). For further validation, this comparison was repeated with a second DNA methylation data set of 67 primary RB tumor samples (RB_NC, GSE58783)36 using unsupervised clustering (Fig. 5C). The distinguishable pattern (Fig. 5A) between salvaged samples and enucleation samples in DNA from primary tumors or AH liquid biopsy (Fig. 5B, C) suggests that DNA methylation analyses of AH cfDNA samples from RB eyes may be used to predict eye salvage.

To further investigate if the AH cfDNA methylation signature discriminates distinct tumor subgroups, we performed unsupervised clustering of the merged datasets: 4 AH cfDNAs collected at diagnosis from eyes that were salvaged, 8 AH cfDNAs from eyes that were eventually enucleated, and 97 (30 + 67) enucleated samples from primary RB tumors (Fig. 5D). While the heatmap representation after unsupervised clustering (a) and MDS analyses (b) demonstrate the variability of methylation signatures in RB tumors, there were two unique patterns on the edges of the spectrum. We identified a subset of tumors that had a similar methylation signature to CHLA salvaged tumors (Cluster A) and an opposite signature more typical of the tumors enucleated at CHLA, either primarily or secondarily (Cluster B). The distribution of salvaged tumors on one arm and subsequently enucleated tumors on the other arm was significant (p < 0.01). We further identified 320 significantly differentially methylated probes ($$\triangle$$ β > 0.4, p < 0.01) spanning 185 unique genes between the Cluster A and Cluster B (Supplementary Data 2) that were well separated using MDS analysis in (c) of Fig. 5D.

To better understand the characteristics of Cluster A and Cluster B tumors, we further investigated the data (GSE58783) from Liu et al.36, who identified two RB tumor subtypes (Subtype 1 and Subtype 2) based on DNA methylation, copy number variation and gene expression profiles from 67 enucleated RB samples with DNA methylation data. Subtype 1 RB tumors maintained a differentiated state, while Subtype 2 RB tumors displayed more aggressive disease that is associated with dedifferentiation, stemness features, and expression of neuronal markers36. We applied the Subtype assignments with our Cluster A and B subgrouping, which were distinguished by 320 differentially methylated probes in AH cfDNA (Fig. 6A, B) and compared our assignments with theirs. Cluster A tumors (n = 19) fully overlapped with differentiated Subtype 1 (n = 27) cases while Cluster B tumors (n = 24) also fully overlapped with de-differentiated Subtype 2 (n = 37) cases as described by unsupervised clustering and Venn diagram (Fig. 6A, B), suggesting our classifier for treatment outcome prediction is consistent with their classifier for disease aggressiveness. Taken together, these data suggested that a more aggressive RB tumor subtype could be predicted by cfDNA methylation profiles of AH liquid biopsies.

We performed a literature search to identify known oncogenesis genes that display the greatest extent of differential DNA methylation from the identified 185 genes (Supplementary Data 2) based on 320 differentially methylated probes between Clusters A and B. The examples of those genes that had either DNA hypomethylation in Cluster B tumors as compared to Cluster A tumors (Fig. 6C), or DNA hypermethylation in Cluster B tumors as compared to Cluster A tumors are shown in Fig. 6D. Unexpectedly, by including normal retina DNA methylation as a control (bright green), we determined that the majority (7/8) of the hypermethylated genes in Cluster A are similarly hyper methylated in normal retina, while these genes remain unmethylated in Cluster B tumors (Fig. 6C). However, the FZR1 promoter displayed similar and moderate DNA methylation levels in normal retina and Cluster B tumors, but DNA hypermethylation in Cluster A tumors. Concurrently, most (5/8) hypermethylated genes in Cluster B were similar to the normal retina, while these genes are unmethylated in Cluster A tumors thus it is the hypomethylation that is aberrant (compared to the retina) (Fig. 6D). However, it should be noted that SORBS2 promoter and DDC and MPP7 gene bodies showed little to moderate DNA methylation in normal retina and Cluster A tumors, but DNA hypermethylation in Cluster B tumors (Fig. 6D).

Most of the genes identified are known to be involved in tumor aggressiveness (Fig. 6C, D) and may directly contribute to an RB phenotype that is more likely to fail treatment (or require more aggressive intervention to salvage the eye). TFF1 overexpression is associated with aggressive disease and correlated with dedifferentiation with stemness features and a higher risk of metastasis in RB36,37, while GSTA4 overexpression plays a key role for resistance of cisplatin-chemotherapy38,39,40. AXIN2 expression is driven by MYC and overexpressed in multiple human cancers critical to maintain cancer cell aggressiveness via regulation of the beta catenin/wnt pathway41. STK19 is an NRAS-activating kinase and the over-expression of which leads to cancer invasion and is a potential therapeutic target42. FRGR1 is involved in cancer cell proliferation and metastasis43, and IL1R2 promotes cancer cell proliferation and invasion and IL1R2 blockade suppresses tumor progression44 (Fig. 6C).

FZR1 has been described as both a tumor suppressor and oncoprotein. FZR1 promoter DNA hypermethylation in Cluster B tumors may correlate with FZR1 loss that results in increased sensitivity to DNA damage and resistance to chemotherapy45. In addition, SORBS2 and CAB39L have been suggested as potential tumor suppressors46,47, and silencing of these genes by promoter DNA hypermethylation in Cluster B RBs may contribute to tumor aggressiveness (Fig. 6D). Taken together, these genes not only serve as prognostic biomarkers to predict eye salvage, tumor aggressiveness and likely response to treatment, but opens the door to future applications of predictive medicine by facilitating an in vivo evaluation of potential therapeutic targets for patients with RB, particularly those with more aggressive disease (Fig. 6 and Supplementary Data 2).

## Discussion

There exists a significant body of research into the genetic, genomic and epigenomic alterations of RB. However, this research was done on tumor tissue from surgically removed (enucleated) eyes. Due to the discernable risk of tumor dissemination after tumor biopsy48,49, obtaining RB tissue DNA has been challenging aside from enucleated specimens. Thus, any application of molecular diagnostic or prognostic biomarkers, or use of these biomarkers for personalized medicine, was limited by the lack of tumor tissue at diagnosis or during therapy. Thus, utilization of a liquid biopsy approach may address this concern for RB and other malignancies in which tumor biopsy is not readily accessible.

Research into the AH liquid biopsy has demonstrated that this biofluid is an enriched source of tumor-derived DNA. In our previous work, we have identified a prognostic genomic biomarker in the AH cfDNA, gain of chr6p, which could predict eye salvage better than currently used clinical classification schemes10,13,14. However, this molecular prognostication analysis relies on the presence of somatic copy number alterations in Rb genomes, which not all tumors harbor. In addition, based on the previous investigations6, ~13% of Rb tumors are initiated by RB1 promoter hypermethylation. The other genes involved in aggressive RB tumorigenesis, and more importantly, whether they differ between more and less aggressive RB phenotypes, remains an area of active investigation36.

Aberrant DNA methylation is a common event in most malignancies and a reliable tumor marker for diagnosis and prognosis, however most of the defined alterations appear to be passenger events that do not actually lead to gene expression changes27,50,51,52. The ability to identify RB-derived molecular aberrations in cfDNA isolated from the aqueous humor provides an opportunity to characterize genetic and epigenetic features of eye tumors in vivo while RB patients are actively undergoing therapy12,13,14.

In this study, we compared the DNA methylation profiles of primary RB specimens, cfDNA from AH of RB patients, and normal retina tissues, which are available in public databanks. Our analyses revealed that DNA methylation profiles from the tumor-derived cfDNA in the AH is representative of RB tumor tissue9, thus demonstrating the AH is a reliable biofluid for methylation profiling of the tumor. In this subset we were able to demonstrate a patient with hypermethylation of the promotor, a known mechanism of tumorigenesis. Previously this could only have been identified from tumor tissue in enucleated eyes; however, the work herein demonstrates the ability to detect this from the aqueous humor (alongside methylation signatures of multiple other genes including SYK, MYCN, and others). This opens a multi-omics approach to AH analysis, enabling us to characterize the global methylation pattern of RB tumors in vivo at diagnosis and during therapy, thus obviating the need for tumor tissue. Moreover, unlike genetic alterations, RB1 epigenetic silencing is reversible and may be a therapeutic target of DNA methylation inhibitors. These have not been used for the treatment of RB, but have been used for treatment of several cancer types in clinical trials28,53.

By integrating DNA methylation and gene expression data from primary RB tumors, 294 genes were identified that are directly regulated by promoter or gene body DNA methylation. The established correlation between DNA methylation and gene expression in these genes suggests that these DNA methylation markers can be used in place of RNA- or protein-based gene expression profiling. For example, the key therapeutic target genes of RB1, SYK, MYCN, E2Fs expression status can be predicted by their DNA methylation status. As expected, RB1 was also identified as the potential top upstream regulator of genes involved in Estrogen-mediated S-phase entry, and downregulation of downstream of these genes mimic decreased RB1 activity54,55. Notably, the expression changes of these downstream genes controlled by DNA methylation may directly alter the estrogen-mediated S-phase entry independent of RB1 mutation status, suggesting that DNA methylation is an independent driving force for RB tumorigenesis. Interestingly, these genes also are directly regulated by oncogenic regulators, such as ER, Ras, E2F, MYC, NF-kB, and EGR1 signaling.

Potential prognostic methylation markers for tumor aggressiveness were identified from RB eyes in vivo via an AH liquid biopsy taken at diagnosis or during active treatment. This liquid biopsy approach enabled assay of tumor-derived cfDNA in the absence of tumor tissue. Using the AH, we identified a clear differential methylation signature between eyes that were salvaged with therapy (Cluster A) and eyes that failed therapy and were enucleated (Cluster B). This AH methylation signature is highly concordant with previous genomic and epigenetic analyses of RB tumors36. While these results need to be validated in a larger multi-center cohort with various treatment schemes, this work builds upon the important work from Liu et al.36, suggesting molecular subtypes of RB. Our work allows for detection of these subtypes from the AH in vivo. Once validated prospectively, this has potential for direct impact to these young patients with RB by allowing the clinician to understand the state of the tumor, and combined with clinical features, the likelihood of salvage with various therapies.

Although we did not have the ability to perform gene expression profiling to identify genes whose expression is modulated by DNA methylation in current study, TFF1, GSTA4, AXIN2, IL1R2, STK19, and FRGR1 promoter DNA hypomethylation in aggressive RBs (Cluster B) identified in this study may result in gene overexpression, thereby leading to tumor dedifferentiation with stemness features36, resistance to cisplatin-chemotherapy39,40, maintained cancer cell aggressiveness by protecting the tumor from oxidation stress and ensuring MYC-driven transcription41,56, cancer invasion42,43, and T-cell suppression44,57. Furthermore, silencing of FZR1 due to promoter DNA hypermethylation in Cluster B cases may decrease sensitivity to chemotherapy45 and suppress antitumor immunity44,57. Interestingly, promoter DNA methylation of tumor suppressor genes SORBS2 and CAB39L may also contribute to tumor aggressiveness characteristic of Cluster B cases46,47.

DNA methylation is a stable epigenetic modification that is routinely assayed by several technologies58. Isolating cfDNA from AH is now a well-established procedure12,59, and therefore can easily be applied to RB patients in the clinical setting. Characterizing RB-specific DNA methylation markers in AH cfDNA provides a foundation for future applications in the clinical diagnosis and prognostication of RB and as well as potential for precision medicine-based treatment approaches.

Although our analyses identified regions of interest that may help RB patients in the clinic, these findings are limited by small sample size from a single center. A prospective, multi-center collaborative effort with a large sample size of AH cfDNA from salvaged eyes of RB patients is needed to validate these findings regarding Cluster A and B and assess their clinical relevance with multiple therapeutic options. In addition, future studies could evaluate methylation signatures of cones as an improved control over retina60.

In conclusion, this study characterizes tumor methylation profiles of RB tumors in vivo using AH liquid biopsy, establishes that the AH methylation signature is highly representative of matched RB tumors, and identifies a cohort of differentially methylated genes with significant potential prognostic utility.

## Methods

### Ethics approval and consent to participate

All human subjects research conducted under this retrospective study was reviewed and approved by the institutional review board at the Children’s Hospital Los Angeles (CHLA-17-00248) and following written informed consent from all patients’ parents. These experimental methods comply with Helsinki Declaration.

### Consent for publication

Written information consent for publication was obtained from the parents of patients at enrollment.

### Sample collection

Tumor and AH specimens were collected from patients with retinoblastoma at Children’s Hospital Los Angeles (CHLA). AH collection was performed at diagnosis or at the time of secondary enucleation and at specified clinical intervals throughout therapy; the methods for AH specimen collection and storage have been previously published10. No statistical method was used to predetermine the sample size. For all participants, treatments were performed per routine CHLA protocol. Treatment regimens were unique for each child and only some children had disease recurrence or enucleation. Therefore, a range of biosamples (0–10 AH samples) were collected for each child depending on the clinical course, and blood was drawn alongside AH. HCT116 (CCL-247) human colon cancer cell line was purchased from ATCC with ATCC Cell Line Authentication Service. The growth and passages of cell line was under mycoplasma monitoring.

### DNA extraction from AH, blood plasma, primary tumor samples, and cultured cells

cfDNAs were extracted from AH or blood plasma using the QIAgen QIAamp Circulating Nucleic Acid kit (Qiagen, Valencia, CA USA) as described by the manufacturer. Formalin-fixed, paraffin embedded (FFPE) tumor sections were obtained from the CHLA Pathology Laboratory, and FFPE-DNAs were extracted using the QIAgen QIAamp FFPE DNA Extraction Mini kit as recommended by the manufacturer. cfDNA and FFPE-DNA concentrations were measured using the Qubit dsDNA High Sensitivity Assay system (ThermoFisher, Waltham, MA USA). For analytical validation purpose, 1 μg genomic DNA from HCT116 (CCL-247) human colon cancer cells in 100 μl ddH2O was sonicated 200–300 bp fragment sizes that were verified by agarose gel electrophoresis.

### Bisulfite conversion and restoration

cfDNA and FFPE-DNA samples were subject to bisulfite conversion using the Zymo EZ DNA methylation kit (Zymo Research, Irvine, CA USA) as specified by the manufacturer. AH cfDNA sample input ranged from 1 to 2 ng, while FFPE-DNA sample input ranged from 160 to 240 ng. The amount of bisulfite-converted DNA as well as the completeness of bisulfite conversion for each sample are assessed using a panel of MethyLight-based real-time PCR quality control assays61. Bisulfite-converted DNAs are then subjected to the Illumina EPIC BeadArrays, as recommended by the manufacturer and described by Moran et al.62.

### Targeted bisulfite sequencing

Bisulfite-converted DNA was amplified by PCR using the following primers (5′ to 3′) targeting: (1) TFF1 promoter (forward: GGG AAA GAG GGA TTT TTT GAA TT, REVERSE: AAC TAC CAA AAC TAA CTA TAA CCC CAC AA), (2) HOXC4 promoter (forward: ATT TAT TTA AGT GTT AAT TAG GTT GGG T; reverse: AAT TTA AAA TCA TAA CTT ACC AAA ACT CAA), (3) MNX1 gene body (forward: GGG ATT TGA GGG ATA GTG ATT T, REVERSE: CAA AAT TCA AAT TTC AAC CCC CTA A) and (4) CELSR3 gene body (forward: AGT ATT GGG AGT TAT TTT TGA GGT T, REVERSE: CAA TCC TCT CCT AAA AAC CAA A). PCR products were then sequenced using Amplicon-EZ service (Genewiz). Sequencing data were analyzed using the EPIC TABSAT tool63.

### EPIC DNA methylation data production

DNA methylation was evaluated using the Illumina Infinium MethylationEPIC (EPIC) BeadArray at the USC Norris Molecular Genomics Core Facility. Specifically, each bisulfite converted sample was whole genome amplified (WGA) and then enzymatically fragmented. Samples were then hybridized overnight to an 8-sample EPIC BeadArray, in which the amplified DNA molecules anneal to locus-specific DNA oligomers linked to individual bead types. The oligomer probe designs follow the Infinium I and II chemistries, in which cy3/cy5-labeled nucleotide base extension follows hybridization to a locus-specific oligomer. After the chemistry steps, BeadArrays were scanned using the Illumina iScan system to generate the *.IDAT files in both red and green channels. Raw signal intensities were extracted from the *.IDAT files using the ‘noob’ function in the minfi 1.40.1 R package and the B5 version of the probe manifest. The ‘noob’ function corrects for background fluorescence intensities and red-green dye-bias developedby Triche et al.21. The beta (β) value represents the DNA methylation score for each data point and is calculated as (M/(M + U)), in which M and U refer to the mean methylated and unmethylated probe signal intensities, respectively. β values range from 0 to 1, with zero indicating an unmethylated locus and one indicating a fully methylated locus. Measurements in which the fluorescent intensity is not statistically significantly above background signal (detection p value > 0.05) as well as non-specific probes and those on the X- and Y-chromosomes were removed from the data set.

### Data analysis

DNA methylation data of normal retina and RB tumors were obtained from the Gene Expression Omnibus (GEO, GSE57362 and GSE58783)9,36. Sample purity was assessed using the LUMP (leukocytes unmethylation for purity) assay64 and 27 samples with LUMP values <0.5 (<50% purity) were removed from further analysis (Fig. S2). Probes related to gender and age, and as well as those overlapping known polymorphisms were also excluded from further analysis20,65. Differentially methylated probes were selected using absolute mean β-value difference > 0.3 between normal retina and RB tumor samples from GSE58783. Two-sided Welch’s t-test (R package matrixTests) was used to identify statistical significance (p value <  0.05). The top 10,000 probes with the greatest β-value standard deviation (SD) across the four pairs of matched RB primary tumors and AH samples (RB_CHLA_1–4 and AH_CHLA_1–4) were also selected for DNA methylation comparisons. Heatmaps were generated using the R package ComplexHeatmap66, and multidimensional scaling (MDS) plots were generated using ‘plotMDS’ function in the edgeR package67.

### Probe annotations

Probe annotations were obtained from the B5 version of the Infinium MethylationEPIC probe manifest (hg19, illumina.com). We defined “Promoter” probes as those located at the transcription start site (TSS200 or TSS1500), 5’ untranslated regions (UTR) and the first exon. In addition, we classified “Gene Body” probes as those located within gene bodies and 3’UTRs. The remaining probes were classified as “Other” probes as those not included in Promoter or Gene Body categories.

### Differentially expressed genes

Gene expression array data (GSE125903 and GSE111168)29,30 were used to identify differentially expressed genes between apparently normal retina and RB tumors. The processed expression data were downloaded from BaseSpace correlation engine68. The upregulated genes and down-regulated genes (fold change > 2 or <−2) overlapped from both datasets were used for further analysis.

### Pathway and TF binding motif analyses

Pathway analyses for genes regulated by DNA methylation were performed using Ingenuity Pathway Analysis (QIAGEN) (https://digitalinsights.qiagen.com/products-overview/discovery-insights-portfolio/analysis-and-visualization/qiagen-ipa/). The transcription factor (TF) binding motif prediction was performed using F-match analysis from the TRANSFAC 2.0 database (genexplain, Germany)32.

### Copy number variation analysis

Copy number variation was detected using the R package SeSAMe21,69. The stored normal data (EPIC.5.SigDF.normal) from sesameData was used for normalization.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.