text:
Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 Jul 2016, 02:02

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Iridium, a hard, whitish metal similar to platinum, is

Author Message
TAGS:

### Hide Tags

Manager
Status: 700 (q47,v40); AWA 6.0
Joined: 16 Mar 2011
Posts: 82
GMAT 1: 700 Q47 V40
Followers: 1

Kudos [?]: 84 [4] , given: 3

Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

22 May 2011, 12:33
4
KUDOS
14
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

25% (02:32) correct 75% (01:37) wrong based on 1204 sessions

### HideShow timer Statistics

Iridium, a hard, whitish metal similar to platinum, is extremely rare on Earth. Extremely high concentrations of iridium on Earth result
from only two scenarios: massive volcanic eruptions that release iridium from deep within the Earth and meteorites that shower down on Earth from space. When scientists found concentrations of iridium 30 times higher than normal in rock stratum from 65 million years
ago, they concluded that a massive meteor or comet hit the Earth and caused the massive extinction of the dinosaurs.

Which of the following, if true, most strongly supports the scientist’s conclusion?

A. Volcanoes massive enough to generate high concentrations of iridium are very rare.
B. Massive volcanic eruptions occurred frequently 80 million years ago.
C. Most scientists support the hypothesis that a cosmic impact wiped out the dinosaurs.
D. The massive extinction that occurred 70 million years ago killed not only the dinosaurs but also 70 percent of all life on Earth.
E. A comet struck the earth some 120 million years ago, but no widespread extinction occurred.

I think that C supports the conclusion better than B, which is the right answer. I am placing the question before this forum for moot so that I can learn flaws in my thought, if any.

Source: TMH's verbal workbook.

Regards
Rahul.
[Reveal] Spoiler: OA

_________________

Regards
Rahul

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 156

Kudos [?]: 1527 [1] , given: 376

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

22 May 2011, 13:44
1
KUDOS
retro wrote:
Iridium, a hard, whitish metal similar to platinum, is extremely rare on Earth. Extremely high concentrations of iridium on Earth result
from only two scenarios: massive volcanic eruptions that release iridium from deep within the Earth and meteorites that shower down on Earth from space. When scientists found concentrations of iridium 30 times higher than normal in rock stratum from 65 million years
ago, they concluded that a massive meteor or comet hit the Earth and caused the massive extinction of the dinosaurs.

Which of the following, if true, most strongly supports the scientist’s conclusion?

A. Volcanoes massive enough to generate high concentrations of iridium are very rare.
B. Massive volcanic eruptions occurred frequently 80 million years ago.
C. Most scientists support the hypothesis that a cosmic impact wiped out the dinosaurs.
D. The massive extinction that occurred 70 million years ago killed not only the dinosaurs but also 70 percent of all life on Earth.
E. A comet struck the earth some 120 million years ago, but no widespread extinction occurred.

I think that C supports the conclusion better than B, which is the right answer. I am placing the question before this forum for moot so that I can learn flaws in my thought, if any.

Source: TMH's verbal workbook.

Regards
Rahul.

I thought it should be "A".

Conclusion:
The meteorite shower is the cause of the dinosaurs' extinction.

The scientists associated high concentration with meteorite shower and meteorite shower with extinction. But, there is no guarantee that high concentration of iridium was indeed due to meteorite shower and not volcanic eruptions.

A- clears the confusion that such high concentration can't be created by eruptions leaving us with only one choice for iridium concentration i.e. meteorite shower.

C- can be another possibility but using the word "cosmic impact" is too broad. Who knows if other scientists hypothesized that the extinction was due to ultraviolet rays(just in case there was no ozone then). Thus, a pure hypothesis by other scientists won't make this argument too strong.

Ans: "A"

But, on a second thought; the word "rare" in A is not too strong. Rare doesn't mean non-existential. Thus, the extinction may have been caused by volcanic eruption.

C becomes the strongest support.

Ans: "C"

"B" actually weakens the argument in a sense and is strict no-no.
_________________
Manager
Status: 700 (q47,v40); AWA 6.0
Joined: 16 Mar 2011
Posts: 82
GMAT 1: 700 Q47 V40
Followers: 1

Kudos [?]: 84 [0], given: 3

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

22 May 2011, 13:54
Fluke,

I could not get your final conclusion. What exactly are you converging on? A, B, C, D or E?

Rgds
Rahul
_________________

Regards
Rahul

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 156

Kudos [?]: 1527 [0], given: 376

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

22 May 2011, 13:58
retro wrote:
Fluke,

I could not get your final conclusion. What exactly are you converging on? A, B, C, D or E?

Rgds
Rahul

"C"
_________________
Manager
Joined: 21 Aug 2010
Posts: 58
Location: United Kingdom
GMAT Date: 06-28-2014
Followers: 2

Kudos [?]: 6 [0], given: 2

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

22 May 2011, 15:49
Somewhere i also feel it should be C...
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 16

Kudos [?]: 209 [0], given: 10

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

22 May 2011, 20:47
There is a slight reasoning gap in the argument. It is between the two methods mentioned and the scientist picking up one of the methods for the conclusion.

Hence a supporter answer choice is required here that fills the gap in the reasoning.

A defender answer choice eliminating the 2nd method. Not an answer option.

B This is a sense can neither be related to the argument nor it supports the conclusion. It in fact weakens the conclusion. POE.

C gives a reason filling the gap in the reasoning mentioned above in the analysis. Crystal choice.

D and E are out of scope and hyperbole answer choices. POE.

C is clean here.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Status: 700 (q47,v40); AWA 6.0
Joined: 16 Mar 2011
Posts: 82
GMAT 1: 700 Q47 V40
Followers: 1

Kudos [?]: 84 [19] , given: 3

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

22 May 2011, 22:08
19
KUDOS
3
This post was
BOOKMARKED
Here is the explanation provided by the guide:

Answer: B. This is a strengthen question. Its conclusion and premises are:
Premises: (1) Extremely high concentrations of iridium on Earth result from only two scenarios: massive volcanic eruptions that release iridium from deep within the Earth and meteorites that shower down on Earth from space. (2) Scientists found concentrations of iridium 30 times higher than normal in rock stratum from 65 million years ago.
Conclusion: A massive meteor or comet hit the Earth and caused the mass extinction of the dinosaurs.

According to the premises, there are two possible causes of high iridium levels. But the conclusion states that one of the causes—a meteor— was definitely the culprit. So the assumption must be that there was not a volcanic eruption that caused the extinction. Once again, you have a causal argument, but now you are going to strengthen it. In order to do so, you should look for answers that rule out other possible causes. Choice B strengthens the argument by showing that volcanic eruptions occurred frequently before the extinction, but the dinosaurs continued to live. Thus, it is unlikely that the extinction was caused by a volcano and more likely that a meteor caused it. Choice A doesn’t go far enough. Even if the volcanoes are rare, the extinction could have been caused by just one eruption. Choice C doesn’t strengthen the argument. Other scientists’ support of the hypothesis doesn’t address the connection between the conclusion and the premise. Choice D has nothing to do with the argument, while choice E weakens the argument by indicating that a previous comet strike did not lead to an extinction.

_________________

Regards
Rahul

Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 247
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Followers: 5

Kudos [?]: 69 [0], given: 46

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

24 May 2011, 10:49
retro wrote:
Here is the explanation provided by the guide:

Answer: B. This is a strengthen question. Its conclusion and premises are:
Premises: (1) Extremely high concentrations of iridium on Earth result from only two scenarios: massive volcanic eruptions that release iridium from deep within the Earth and meteorites that shower down on Earth from space. (2) Scientists found concentrations of iridium 30 times higher than normal in rock stratum from 65 million years ago.
Conclusion: A massive meteor or comet hit the Earth and caused the mass extinction of the dinosaurs.

According to the premises, there are two possible causes of high iridium levels. But the conclusion states that one of the causes—a meteor— was definitely the culprit. So the assumption must be that there was not a volcanic eruption that caused the extinction. Once again, you have a causal argument, but now you are going to strengthen it. In order to do so, you should look for answers that rule out other possible causes. Choice B strengthens the argument by showing that volcanic eruptions occurred frequently before the extinction, but the dinosaurs continued to live. Thus, it is unlikely that the extinction was caused by a volcano and more likely that a meteor caused it. Choice A doesn’t go far enough. Even if the volcanoes are rare, the extinction could have been caused by just one eruption. Choice C doesn’t strengthen the argument. Other scientists’ support of the hypothesis doesn’t address the connection between the conclusion and the premise. Choice D has nothing to do with the argument, while choice E weakens the argument by indicating that a previous comet strike did not lead to an extinction.

dear retro
even I couldn't get it how come the author is supporting the answer.........
may be fluke can help us......
I am sure that if this question would have appear on GMAT
i would have ruined my score further...
_________________

WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post.

Manager
Status: 700 (q47,v40); AWA 6.0
Joined: 16 Mar 2011
Posts: 82
GMAT 1: 700 Q47 V40
Followers: 1

Kudos [?]: 84 [0], given: 3

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

24 May 2011, 21:39
Quote:
dear retro
even I couldn't get it how come the author is supporting the answer.........
may be fluke can help us......
I am sure that if this question would have appear on GMAT
i would have ruined my score further...

Hehe.. we are in the same boat, bloke.

Regards
Rahul/retro
_________________

Regards
Rahul

Manager
Joined: 03 Aug 2010
Posts: 106
GMAT Date: 08-08-2011
Followers: 1

Kudos [?]: 51 [0], given: 63

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

05 Aug 2011, 20:33
What's the source?

I, too, am going with $$A$$. $$B$$ does not strengthen the conclusion. $$A$$ leads us to believe that it probably wasn't the volcano eruption and more likely a massive meteor or comet that caused the increased iridium that coincides with the massive extinction of the dinosaurs.
Intern
Joined: 06 Jul 2011
Posts: 25
Followers: 1

Kudos [?]: 7 [0], given: 0

Re: Iridium from meteors and comets: Need help [#permalink]

### Show Tags

06 Aug 2011, 15:02
Notice that in the conclusion, the author has introduced another effect, 'extinction of dinosaurs'. Why?
Know this' why', and 50% job is done. The only reason from the context seems to be introduction of a layer of ambiguity to make the stimulus complex.
The other 50% is the elimination of this ambiguity. Choice 'b' shores up the implication that only the meteorite could have caused this extinction, and hence it is sufficient to remove the ambiguity.

meteorite -> extinction <-volcanic eruption
Choice 'c' is a close one. It does increases the weight of the causal link, 'meteorite -> extinction', but doesn't eliminate 'volcanic eruption ->extinction' link, the very cause of ambiguity.
_________________

squeakvm

Senior Manager
Joined: 12 Oct 2011
Posts: 272
Followers: 0

Kudos [?]: 38 [0], given: 110

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

26 Dec 2011, 07:20
I think this is too far a leap to be taken to reach the conclusion. Is this a regular GMAT-like question?

Even I thought the answer would be either A or C. B was totally unexpected.
_________________

Consider KUDOS if you feel the effort's worth it

Manager
Joined: 07 Aug 2011
Posts: 186
Location: United States
GMAT 1: 690 Q48 V37
Followers: 3

Kudos [?]: 22 [0], given: 6

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

26 Dec 2011, 11:36
We need to conclude that only meteor shower can bring that much of iridium 65 million year ago and not volcanic eruption.
And due to that dinosaurs got extinct
A does not prove this theory
B ok volcanic eruption was there 80 million back but no point in discussing for activity happened 65 million year ago
C possible yes they agree that cosmic activity was there
D and E has nothing to do with the point.

So C or B
B as no volcano happened in 65th year so it must be meteor shower
Manager
Joined: 25 Sep 2010
Posts: 85
Schools: HBS, LBS, Wharton, Kelloggs, Booth
Followers: 0

Kudos [?]: 5 [0], given: 15

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

24 Jan 2012, 23:12
IMO A. But i'm utterly confused.
The explanation provided by the guide seems to give more weight to the cause of extinction of dinosaurs than to the cause of high iridium levels.
B. Massive volcanic eruptions occurred frequently 80 million years ago. the massive volcanic eruptions may have caused high iridium levels, but the explanation doesn't seem to care about that. It says, if massive eruption were frequent enough(80m years ago) and the dinosaurs were still not extinct(65m years ago), then the eruptions would not have caused the extinction.
Not sure which to give more importance to: the high levels of iridium or the extinction of dinosaurs
Manager
Joined: 10 Jan 2010
Posts: 192
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GMAT 1: Q V
GPA: 3
WE: Consulting (Telecommunications)
Followers: 2

Kudos [?]: 27 [0], given: 7

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

25 Jan 2012, 01:48
IMO C, but after reading the explaination it does make sense to go with B. Even though i would have never considered it before.
Manager
Joined: 12 Nov 2011
Posts: 143
Followers: 0

Kudos [?]: 17 [0], given: 24

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

25 Jan 2012, 05:23
C
Senior Manager
Joined: 15 Sep 2009
Posts: 271
GMAT 1: 750 Q V
Followers: 10

Kudos [?]: 66 [1] , given: 6

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

24 Apr 2012, 09:22
1
KUDOS
Not a well-framed question but decent practice nonetheless.

Worth noting that even the hardest actual GMAC questions leave you somehow satisfied after reading the explanations/rationale for the correct answer--this particular question doesn't.

Posted from my mobile device
_________________

+1 Kudos me - I'm half Irish, half Prussian.

Current Student
Joined: 03 Aug 2012
Posts: 915
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 21

Kudos [?]: 576 [0], given: 322

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

28 Feb 2013, 20:21
P1: Two causes

1. Volcanoes
2. Meteorites/Comets = > Iridium

P2: -65 million yrs , iridium was 30 times the normal

C: M/C => Dinosaurs extinction

Now B Says ,Massive volcanic eruptions occurred frequently 80 million years ago.Moreover,nowhere it is mentioned that they were infrequent (-65) million years.

A. Volcanoes massive enough to generate high concentrations of iridium are very rare.
B. Massive volcanic eruptions occurred frequently 80 million years ago.
C. Most scientists support the hypothesis that a cosmic impact wiped out the dinosaurs.
D. The massive extinction that occurred 70 million years ago killed not only the dinosaurs but also 70 percent of all life on Earth.
E. A comet struck the earth some 120 million years ago, but no widespread extinction occurred.

Poorly framed question

_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6765
Location: Pune, India
Followers: 1878

Kudos [?]: 11576 [2] , given: 219

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

28 Feb 2013, 21:41
2
KUDOS
Expert's post
targetgmatchotu wrote:
P1: Two causes

1. Volcanoes
2. Meteorites/Comets = > Iridium

P2: -65 million yrs , iridium was 30 times the normal

C: M/C => Dinosaurs extinction

Now B Says ,Massive volcanic eruptions occurred frequently 80 million years ago.Moreover,nowhere it is mentioned that they were infrequent (-65) million years.

A. Volcanoes massive enough to generate high concentrations of iridium are very rare.
B. Massive volcanic eruptions occurred frequently 80 million years ago.
C. Most scientists support the hypothesis that a cosmic impact wiped out the dinosaurs.
D. The massive extinction that occurred 70 million years ago killed not only the dinosaurs but also 70 percent of all life on Earth.
E. A comet struck the earth some 120 million years ago, but no widespread extinction occurred.

Poorly framed question

The OA is a little debatable but not very much.
(C) is certainly not in the running. Just because other people say it, something doesn't become true. You need facts. Most scientists supporting the hypothesis is not a fact that will help me believe the hypothesis. The reason why most scientists support it, might.
(D) and (E) are irrelevant.

So it comes down to:
A. Volcanoes massive enough to generate high concentrations of iridium are very rare.
B. Massive volcanic eruptions occurred frequently 80 million years ago.

Both support the conclusion to an extent.
In (A), volcanoes massive enough to generate high concentrations of iridium are rare, not impossible. There could have been one 65 million yrs ago. Hence, it doesn't strengthen our belief in a comet/meteor much.
In (B), massive volcanic eruptions occuring frequently through Earth's history while dinosaurs lived doesn't imply that there couldn't have been an especially huge one which wiped out the dinosaurs. But it does make comet/meteor theory more probable.

Look at the argument again - two things cause concentration of iridium - volcanoes and meteors
Volcanoes occured frequently while dinosaurs lived on Earth. Chances are that an activity which was not usual wiped out dinosaurs. Since dinosaurs were wiped out 65 million yrs ago and there was iridium concentration in rocks which are from 65 million yrs ago, it makes it more likely that a meteor wiped out dinosaurs.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Verbal Forum Moderator
Status: Getting strong now, I'm so strong now!!!
Affiliations: National Institute of Technology, Durgapur
Joined: 04 Jun 2013
Posts: 634
Location: India
GPA: 3.32
WE: Information Technology (Computer Software)
Followers: 93

Kudos [?]: 458 [1] , given: 78

Re: Iridium, a hard, whitish metal similar to platinum, is [#permalink]

### Show Tags

27 Oct 2013, 11:44
1
KUDOS
Karishma,

Option B comes somewhat closer, but B has flaws:
1. Do we know when for how long dinosaurs existed?
2. 80m years ago meteoric showers were frequent but is that anyhow supports dinosaurs to be killed?
_________________

Regards,

S

Consider +1 KUDOS if you find this post useful

Re: Iridium, a hard, whitish metal similar to platinum, is   [#permalink] 27 Oct 2013, 11:44

Go to page    1   2    Next  [ 29 posts ]

Similar topics Replies Last post
Similar
Topics:
5 #Top150 CR: Iridium, a hard, whitish metal similar to platinum 2 10 Oct 2015, 22:06
3 A scrap metal recycling plant processes the excess metals 13 25 Jul 2010, 00:44
1 Many people feel that gold and platinum are the most 2 20 Jun 2009, 03:56
Similar Reasoning. 1 14 May 2009, 21:53
Similar Reasoning. 7 14 May 2009, 21:52
Display posts from previous: Sort by


text:
## How to define a new floating environment

### Foreword

We all know the two floating environments table and figure which almost all document classes provide. Every once in a while there is the need for another floating environment. For example chemists often need something like a scheme environment. Although the latter is easily obtained using the chemmacros package and its scheme module I want to show the several methods I know for defining new floats. Continue reading “How to define a new floating environment”

## a new chemmacros – but how?

I have written earlier about a new concept for chemmacros and about the current development of chemmacros. I really want to go along with e idea of modularity. In fact so much that I already have a draft completed (without manual and probably a number of bugs but still…). The big question is, though: How do I procede without annoying all the users of chemmacros? If I am consequent with the modularity then there need to be breaking changes.
Continue reading “a new chemmacros – but how?”

## Name change and other changes

Yesterday I’ve changed the name of this blog. The reason is that I’d like to change the focus of this blog away from chemistry in LaTeX.

More precisely I want LaTeX in general to be the topic. That doesn’t mean I won’t be writing about chemistry in LaTeX any more – of course I still will. But there are so much more topics worth writing about! Certainly one main focus will be news about the development of my packages (one reason for not focussing on the chemistry part: I have a number of packages not related to chemistry at all!). Continue reading “Name change and other changes”

## new package: elements

While working on chemmacros I found I wanted to use some functionality which is currently provided by the package bohr. But since I only wanted part of the functionality I realised that the same was true for bohr: it needed the functionality but wasn’t originally designed to provide it. It made sense to extract said functionality into a package of its own, extended with further functioniality. Long story short: there’s a new package called elements which will be sent to CTAN once bohr is updated to use the new package.

June 24th, 2015: elements has been sent to CTAN, bohr has been updated to v1.0.

## modular chemmacros

OK, it’s been a while since I’ve posted anything. But now it’s time to discuss a few ideas I have about chemmacros. As you are probably aware if you are a user of the package: it provides lots of different stuff. At least in my experience it is rarely the case that you need all of its features. Continue reading “modular chemmacros”

## Carbohydrates

Since a few weeks I’m working on a package using chemfig as a backend that allows a simple yet flexible input syntax for typesetting carbohydrates. My draft at this point allows the following:

\documentclass{scrartcl}
\usepackage{carbohydrates}
\begin{document}

format: plain


text:
# How is the image in a mirror created? Are there infinitely many light rays?

How is the image in a mirror created? Are there infinitely many light rays?

My motivation for the question is from image processing. We work with images as discrete 2D functions, as matrices. Spatial sampling is done, and also quantization. Then I thought, well that is far from perfect, I wonder how does God create images? And then I thought of a real example, well, the mirror! The 3D world is projected on a 2D plane, the mirror. So how many rays arrive on the mirror? Infinitely many? Does God do spatial sampling or is the image in the mirror continuous?

• By "God" do you happen to happen to mean "image sensors" or "retina"?
– user12029
Apr 2 '14 at 0:57

The approximate number of photons which strike a mirror and enter your eye over the period of a couple seconds is a massive quantity (in Mathematica):

<< PhysicalConstants
Convert[(1 Milli Joule 600 Nano Meter)/(PlanckConstant SpeedOfLight), 1]
`

Output:

3.02047*10^15

Since this is in the quadrillions, for all practical intents and purposes, the number of individual rays that the photons striking a mirror in your living room/bathroom and enter your eye is enough to consider it a continuum of rays forming an image.

However, despite this large number, our bodies are imperfect, and there are limits on the resolution imposed by the optical properties of our body. In image processing language, there is a point spread function associated with our eye's ability to resolve objects in our field of view; the image we see is the actual image convolved with the point spread function of our vision.

So even though there are a gigantic number of rays being traced, we're still limited by our body's ability to spatially resolve them.

Nothing in the universe is continuous. Matter and light are made up of particles, and physicists have strong reason to believe that even space is quantised.

As for the mirror, photons travel from the lightsource to the object. There they are either absorbed or reflected, depending on their wavelength and the properties of the object at the point of interaction. The reflected photons leave the object, and some of them will hit the mirror, which reflects most of them (and absorbs the rest).

The number of photons hitting us is not infinite (nothing is, except perhaps the universe/multiverse, but the answer to that is not in yet), but we are struck by a huge number of them. The sun emits enough photons so that approximately $3.6*10^{21}$ photons strike each square metre of the earth every second.

If the object reflects 50% of the photons and the mirror 99%, that still leaves $1.78*10^{21}$ photons per square meter per second - close enough to infinity for me.


text:
liu.seSearch for publications in DiVA
Change search

On the formation of cyclobutane pyrimidine dimers in UV-irradiated DNA: why are thymines more reactive?
Uppsala University, Sweden.
Uppsala University, Sweden.
2003 (English)In: Photochemistry and Photobiology, ISSN 0031-8655, E-ISSN 1751-1097, Vol. 78, no 2, 159-167 p.Article in journal (Refereed) Published
##### Abstract [en]

The reaction pathways for thermal and photochemical formation of cyclobutane pyrimidine dimers in DNA are explored using density functional theory techniques. Although it is found that the thermal [2+2] cycloadditions of thymine + thymine (T + T $\rightarrow$ T<>T), cytosine +  cytosine (C + C $\rightarrow$ C<>C) and cytosine + thymine (C + T $\rightarrow$ C<>T) all are similarly unfavorable in terms of energy barriers and reaction energies, the excited-state energy curves associated with the corresponding photochemical cycloadditions display differences that – in line with experimental findings – unanimously point to the predominance of T<>T in UV-irradiated DNA. It is shown that the photocycloaddition of thymines is facilitated by the fact that the S1 state of the corresponding reactant complex lies comparatively high in energy. Moreover, at a nuclear configuration coinciding with the ground-state transition structure, the excited-state energy curve displays an absolute minimum only for the T + T system. Finally, the T + T system is also associated with the most favorable excited-state energy barriers and has the smallest S2–S0 energy gap at the ground-state transition structure.

##### Place, publisher, year, edition, pages
John Wiley & Sons, 2003. Vol. 78, no 2, 159-167 p.
Natural Sciences
##### Identifiers
OAI: oai:DiVA.org:liu-96780DiVA: diva2:643329
Available from: 2013-08-27 Created: 2013-08-27 Last updated: 2013-09-04Bibliographically approved

#### Open Access in DiVA

No full text

Publisher's full text

#### Search in DiVA

Durbeej, Bo
##### In the same journal
Photochemistry and Photobiology
Natural Sciences


text:
Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Google Trends can improve surveillance of Type 2 diabetes

## Abstract

Recent studies demonstrate that people are increasingly looking online to assess their health, with reasons varying from personal preferences and beliefs to inability to book a timely appointment with their local medical practice. Records of these activities represent a new source of data about the health of populations, but which is currently unaccounted for by disease surveillance models. This could potentially be useful as evidence of individuals’ perception of bodily changes and self-diagnosis of early symptoms of an emerging disease. We make use of the Experian geodemographic Mosaic dataset in order to extract Type 2 diabetes candidate risk variables and compare their temporal relationships with the search keywords, used to describe early symptoms of the disease on Google. Our results demonstrate that Google Trends can detect early signs of diabetes by monitoring combinations of keywords, associated with searches for hypertension treatment and poor living conditions; Combined search semantics, related to obesity, how to quit smoking and improve living conditions (deprivation) can be also employed, however, may lead to less accurate results.

## Introduction

Recent research demonstrates1 that more people in Britain are turning to Google to diagnose their ailments rather than going to see their doctor. Thus, according to Google UK1, 2, since 2008 there has been a surge in the number of people searching for information related to health, with 21.8 per cent of people in 2015 choosing to self-diagnose via search engines, rather than consulting their family, friends or even a professional GP.

It is reported that one of the main reasons why people are self-diagnosing online is they find it harder to get access to medical professionals2. According to a recent UK Digital Health Report3, which conducted research on 61 million Google searches and a survey of 1013 adults, 11 per cent of respondents prefer to self-diagnose online because they cannot get help from their doctor, while another 10.8 per cent said Google was the best option because their doctor was not available quickly enough4.

No consensus exists at the moment among medical practitioners in regards to the value of self-diagnosis. Thus, the British Medical Association recognizes that about one in five people are self-diagnosing online today and they are generally supportive of bona fide web resources like NHS Direct5. The Australian Patients Association, on the other hand, expresses concerns that more people tend to self-diagnose without seeking professional advice in the first instance and they advise against that very strongly because online information is often not to be relied upon6.

Although it is largely impossible to uncover the exact motives behind self-diagnosing online, researchers increasingly recognize that cases of cyberhondria (self-diagnosis by search engine) are predominantly based on the signs of real illness, leading people to fear the worst and seek remedies using easily accessible online channels7. Previous studies identified that such behaviours can be influenced by social, situational or psychological factors, including personal theories and beliefs8, 9 and vary with the availability of instruments for self-diagnosing, which may comprise online calculators and personal monitoring devices10, 11.

Despite wide media coverage and an increased recognition by health professionals of this trend towards self-diagnosis, there is currently a lack of understanding of how such personal disease detection information can be used to advance research towards accounting for the significance of self-diagnosis pathways on proactive health behaviours. In this paper, we use Type 2 diabetes as an example to investigate this phenomenon and its relationship with formal disease diagnosis mechanisms.

Type 2 diabetes is a growing public health problem associated with significant rates of mortality, morbidity and long-term financial healthcare costs12. This non-communicable disease, accounting for over 95% of diabetes cases worldwide13, is a result of complex gene-environment interactions; the role of several risks factors, including age, sex, ethnicity, family history, obesity, and hypertension is well documented in the research literature14,15,16,17. The precise interaction of these and other risk factors is complex, and varies both within and across populations18.

In order to identify diabetes risk with the highest degree of certainty, a number of complex diagnostic tests are required to be completed under clinical conditions. Such tests include physical examination, a urine sugar test, a urine ketones test, an oral glucose tolerance test, blood glucose tests (fasting plasma glucose and random plasma glucose), a C-peptide blood test or insulin level blood test19. Before a formal examination is scheduled, Diabetes UK recommends that the patient look for such symptoms as increased thirst, hunger or night-time urination, general fatigue, weight loss, blurred vision or sores that do not heal20.

As the early stages of Type 2 Diabetes do not usually exhibit signs or symptoms, the use of models for predicting risk of developing chronic disease have become more common in the last decade21. A recent systematic literature review revealed around 150 such models developed by epidemiologists and statisticians13, each designed to provide health information in an easily accessible format in order to enable planning, monitoring and coordination of clinical and public health interventions. Simple clinical models using readily available data can offer similar discrimination to more complex models using laboratory data or biomarkers, and clinical models that do not need clinical measurements may have a further utility in settings where clinical measurements are not available or are too costly to collect12, 22. The simplicity of the structure of these weighted models, which can comprise up to ten risk factors, including age, sex, ethnicity, smoking habits, hypertensive symptoms and obesity, has also enabled their widespread publication on the Internet, as online calculators and risk modeling tools. These include, amongst others, Diabetes Risk Calculator23, ARIC Diabetes Risk Calculator24, QDiabetes25, UKPDS Risk Engine26, etc.

In this study, we make use of currently adopted risk factors as background information against which the relationships between medically diagnosed diabetes and self-diagnosis are established: we hypothesize that false positive and negative components of self-diagnosis can fine-tune the performance of broadly defined risk factors in contemporary models by introducing specific behavioural preferences of the populations considered at risk. The latter can be also regarded as more temporally dynamic risk factors, currently unaccounted for in Type 2 diabetes models and, which, as a consequence, have been the cause of long-standing skepticism towards contemporary surveillance programs for chronic conditions27. In this study we assume that self-diagnosis is a quantifiable category, derived predominantly from traces of online human activity, while bearing in mind that not all self-diagnosing behaviour will be captured through digital records.

## Results

Worldwide, around 150 models are currently in use for Type 2 diabetes surveillance, and whilst broad areas of risk have been outlined (e.g., Gender, Age, Ethnicity, Deprivation, etc.), no definite consensus currently exists on the final inventory of the candidate risk variables21. It has been already recognized28, 29 that using new or alternative data sources for monitoring or in supporting public health decision-making often necessitates an understanding of the complex connections between time varying public health problems and the time varying signal of new data streams. The research literature demonstrates that such connections can be highly situational and depend on user behaviour or the influence of external forces on user behaviour30. In the context of this data-driven experiment we therefore proposed an evaluation of two model scenarios, one with and one without a self-diagnosis variable, on the matter of co-occurrence of their associated regressors with the public interest in the topic of diabetes on the web. This idea is linked to the so-called post-GFT (Google Flu Trends) syndrome, where several authors have argued for the need to [quantitatively] account for the reasons behind changing user behaviour when exploiting new data sources in the design of risk surveillance systems for anomalous events31,32,33,34. To take this idea further, in our study we aim to test the hypothesis that self-diagnosis, as a risk variable reflecting the dynamic nature of public interest in the topic, is significant for revealing additional behavioural and lifestyle risk factors, which are currently not accounted for in design of the digital disease detection tools.

In search of the most integrative social bulk records to date, we decided to make use of a single geodemographic and lifestyle segmentation dataset, the Experian Mosaic Public Sector database (the detailed structure of the original components of the database is presented in the Supplementary Materials). This consists of UK postcode area aggregated records of traditional demographic indicators (such as gender and age) and various lifestyle choices (such as smoking, drinking, medical records or preferred communication channels) (Fig. 1). For this study, we selected records for the Central London geographical area, which is known to suffer the highest risk of diabetes as compared to the UK national average. An illustration of the distributions of both medically- and self-diagnosed populations across Central London is presented in (Fig. 2).

In order to extract the variables for modeling scenarios, we used a combined inventory of risk factors from two main UK models: Cambridge Diabetes Risk Score12 and QDScore22. Risk prediction models used by healthcare professionals are calculated from cohorts of non-diabetic individuals who are followed over time until some have developed diabetes and an ensuing assessment made based on risk factor measurements as to which were significant for those who developed the disease. The risk factors considered are: age, gender, ethnicity, Townsend score of deprivation, family history of diabetes, history of cardiovascular disease, smoking status, treated hypertension, use of corticosteroids and BMI. Variables, selected from Experian Mosaic datasets covered all the above risk categories, apart from family history of diabetes (genetic determinants of the disease). As the BMI risk factor was not available from the dataset, we used a selection of proxy variables instead: ‘Rarely Diet, ‘Sometimes Diet’ and ‘Often Diet’, ‘Use of Slimming Products’, ‘Trying to Lose Weight’, ‘Self-diagnosed obesity’ and ‘Felt Overweight Last Year’. The complete inventory of the candidate risk variables is presented in (Fig. 3), which also demonstrates strength and direction of their correlation with both medically- and self-diagnosed diabetes variables.

We applied both MLR and SMR regression methods for model scenarios, one of which comprised a ‘Self-diagnosed diabetes’ variable. Results of these simulations are presented in (Fig. 4) and in the Supplementary Materials document. Both scenarios demonstrated their consistency across all three models tested (standard MLR, Backward-AIC and Forward-AIC) in favour of the stronger forecast potential of the scenario derived from the inclusion of the self-diagnosis variable. Although statistically not significant as a direct regressor, it nevertheless can lead to a model structure where predictors reflect public interest (and potentially other tacit concerns) in the topic temporally much better than the scenario with traditional risk variables alone.

Here we also observe that the thematic composition of both scenarios is rather symmetrical (with the exception of the Smoking category, which is absent from the self-diagnosis (or information-seeking behaviour (ISB))) model scenario. Topic allocation of our results to such categories as Ethnicity, Poverty, Existing medical condition and Lifestyle, the primary role of which is currently being discussed in the research literature, illustrates that ISB model scenario indeed contains a bigger fraction of candidate risk factors, describing Lifestyle (27 per cent as compared to 8 per cent in the case of another model). This model has also somehow reduced the fraction of variables, associated with pre-existing Medical conditions (29 per cent as compared to 8 per cent in the case of another model), whilst categories of Ethnicity and Poverty remain fairly similar.

We used Google Trends data and compared weekly fluctuation rates of the search keywords and word-combinations (a complete list is available in the Supplementary Materials) corresponding to the risk variable (e.g., how to lose weight) and the disease itself (diabetes). Figures 5 and 6 illustrate Fisher-transformed correlation coefficients (rs), aggregated to reflect the broad risk categories, currently utilized by medical practitioners and the mainstream media, respectively. Both figures demonstrate slightly stronger correlation advantage for the ISB model scenario, specifically for the risk factors, associated with lifestyle preferences and dietary habits, for example the Treated hypertension category in the ISB model is represented by the variable ‘High cholesterol’. Both models have the same factors, associated with the deprived living conditions: ‘Barriers to housing’ and ‘Poor indoors living conditions’.

Our simulation results demonstrate that application of Google Trends to chronic disease tracking can also be considered advantageous from the perspective of disease dynamics; It is becoming possible to monitor temporal growth or decrease of different risk factors in different geographic areas, which can provide valuable insights into the actual disease determinants (Type 2 diabetes in our case) and instigate further research into how they can be addressed.

## Discussion

Accurate behavioral surveillance of chronic diseases is a well-known challenge in healthcare35. Emerging data streams, also known as novel data streams (NDS) and alternative data (AD), comprising such signals as web search histories, social media updates or another user-generated content (UGC) are considered to hold promise for enhancing the capabilities of public health surveillance28, 29, 35, 36.

There are several ways these datasets could add value to existing disease surveillance: by increasing the timeliness of surveillance data, by improving resolution and data dissemination, by measuring unanticipated outcomes or by measuring aspects of transmission currently not captured by traditional surveillance data and methods (i.e., behaviour, perception). Normally, such datasets would not include official data sources, such as electronic health records, disease registries, emergency department visits or prescription history – although ready access to aggregated data from such sources is itself still novel in many health settings28.

From the perspective of epidemic studies, risk factors currently employed in the modeling of various lifestyle-related conditions fall into categories of traditional demographic variables. Such variables are routinely collected via surveys and other similar methods, which include user participation and observation. Survey methods have distinct advantages37 and, indeed, in this study, the self-diagnosis variable we introduced into the model is also collected in this way. However, it is being increasingly acknowledged that the proliferation and widespread adoption of online services such as search, purchasing of goods and social media opens up opportunities to improve on survey-based methods for capturing people’s behaviour and attitudes38. Often referred to as post-demographics in the field of digital anthropology39, the widespread adoption of these new population metrics still remain largely unaccounted for by epidemiological researchers. Nevertheless, the potential of using such naturally occurring data streams has been successfully demonstrated in a number of other fields, including natural hazards analytics40 and psychology41.

The advantages of the hybrid modeling approach we used here have already been argued by several authors33, 34. The contribution of self-diagnosis variables to the quality of disease surveillance demonstrated in this study could be explained by the fact that it can reflect such complex phenomena as disease perception42 and bodily experience of the emerging disease43. The trend for simplification (i.e., a commonly acknowledged reductionist pathology in general medicine during the last 200 years44) has led to the criticism that some emerging disease trends may be overlooked because they cannot be explained by the risk factors currently employed, or alternatively, lead to erroneous diagnoses if individuals have all the risk factors present, but no sign of an emerging illness. The importance of fine-tuning variables in such models therefore cannot be underestimated. Another question is how to appropriately select mediator variables for different illnesses. Several authors45, 46 hypothesize about the universal role of psychological conditions across the wide range of emerging bodily dysfunctions. In this study, we used the most obvious behavioural variable, which may reflect those psychological states, to lay out a method using additional variables that are widely mentioned in the medical research literature, but have not yet been empirically tested alongside other risk factors47,48,49,50.

## Methodology

### Data

Various commercial organizations (e.g., Experian, Acxiom, Qualtrics and Teradata) combine marketing records with other databases, thus providing value-added data services for research programmes conducting specific population studies. In this study, we make use of one such data service, provided by Experian, the Mosaic Public Sector v.1.04. Figure 1 in the Supplementary Material document illustrates the main topic variables constituting this data service. The Grand Index consists of 12 broadly defined categories (e.g., ‘Community safety’, ‘Health’, etc.), consisting of 1200 variables, which originate from a large number of databases. This dataset consists of 66 distinct social groups A1-O66, which are broadly classified according to age, socio-economic status, living arrangements and lifestyle. Figure 1 illustrates the detailed structure of the populations within the Experian Mosaic Public Sector dataset, each associated with distinct social, economic and behavioural profiles. The complete list of selected Mosaic variables per each Type 2 diabetes risk category, and how they correlate with both medically diagnosed and self-diagnosed diabetes variables, is presented in (Fig. 3).

We also collected weekly aggregated search terms from the Google Trends for the time period 2013–2016. The complete inventory of the risk- and disease-related keywords is provided in the Supplementary Materials section.

### Methods

Taking into consideration the linear relation between risk factors and diabetes in the currently used models, we tested several regression models (R stats v3.4.0) on both sets of independent variables (without and with the diabetes self-assessment variable) in order to extract the best statistically valid combinations. Prior to regression modeling, we used variance inflation factors (VIF) to identify collinearity among explanatory variables (Figs 2 and 3 in Supplementary Material section illustrate the Pearson correlation matrix and significance of correlation at p < 0.05, respectively). VIF calculations are fairly straightforward for interpretation: the higher the value, the higher the collinearity. For the case of a single explanatory variable, VIF is calculated using the R-squared value of the regression of that variable against the rest of the selected explanatory variables:

$$VI{F}_{n}=\frac{1}{1-{R}_{n}^{2}},$$
(1)

where VIF for a variable n is the reciprocal of the inverse R 2 from the regression.

SMR is a semi-automated routine for building a model by successively adding or removing variables based solely on the t-statistics of their estimated coefficients and is known to be useful in cases of testing large numbers of potential independent variables. The fact that variables we used are variants of the risk factors commonly accepted by healthcare professionals also substantially reduces the risk of their convergence on a poor model.

$$y={\beta }_{0}+{\beta }_{1}{x}_{i1}+{\beta }_{2}{x}_{i2}+{\beta }_{n}{x}_{in}+{u}_{i},$$
(2)

where u i are values of an unobserved error term u. We follow the general assumptions that terms u i are mutually independent and identically distributed, with $$\bar{x}=0$$ and constant variances.

The parameters $${\beta }_{0},{\beta }_{1}\ldots {\beta }_{n}$$ are estimated using the least squares procedure, which minimizes the sum of squares of errors:

$$RSS=\sum _{i=1}^{n}{({y}_{i}-(\alpha +\beta {x}_{i}))}^{2}$$
(3)

The stepwise options allow starting the model-building process with no variables and proceeding forward (adding one variable at a time), or starting with all potential variables in the model and proceeding backward (removing one variable at a time). To run the models we used packages in the open source R software library that use a sequence of Akaike Information Criterion (AIC) values to add or eliminate a variable. During each iteration, the program performs the following calculations: for each variable currently in the model, it computes the t-statistic for its estimated coefficient, squares it and reports this as its AIC-to-remove statistic; for each variable not in the model, it computes the t-statistic that its coefficient would have if it were the next variable added, squares it and reports this as its AIC-to-enter statistic. At the next step, the program automatically enters the variable with the highest AIC-to-enter statistic, or removes the variable with the lowest AIC-to-remove statistic (for the detailed program outputs see Supplementary Material). The optimal model scenario uses the lowest AIC possible.

$$AIC=2k-2ln(L),$$
(4)

where k denotes estimated parameters in the model and L is the maximum value of the likelihood function for the model.

F-value was used to illustrate whether the model as a whole has a statistically significant predictive capability. Under the null hypothesis that the model has no predictive capability (all population regression coefficients simultaneously approach zero values), the F statistic follows an F distribution with k numerator degrees of freedom and n − k − 1 denominator degrees of freedom. The null hypothesis is rejected if the F ratio is large:

$$F=\frac{EV(MSR)}{UV(MSE)}$$
(5)
$$EV\,(ExplainedVariance)=\frac{{\sum }_{i}{n}_{i}{({\bar{x}}_{i}-\bar{x})}^{2}}{k-1},$$
(6)

where $${\bar{x}}_{i}$$ denotes the sample mean in the $${i}^{th}$$ group, $${n}_{i}$$ is the number of observations in the i th group, $$\bar{x}$$ is the overall mean of the data and k is the total number of groups.

$$UV(UnexplainedVariance)=\frac{{\sum }_{ij}{({x}_{ij}-{\bar{x}}_{i})}^{2}}{n-k},$$
(7)

where $${\bar{x}}_{ij}$$ is the j th observation in the i th out of k groups, and n is the overall sample size.

In order to compare temporal behaviour of the risk-related and disease-related search terms, extracted from Google Trends, we used standard Keyword Slope Formula:

$$KSF=\frac{rise}{run}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}},$$
(8)

where y variables denote average search interest, measured during two distinct time points and x variables indicate number of time steps.

And, finally, in order to generate risk category specific notions of the correlations between risk- and disease related search terms, we apply Fisher z transformations to convert rs to zs, and then subsequently convert averaged z values back into rs51:

$$z=arctanh(r\mathrm{).}$$
(9)

## References

1. Kirk, A. One in four self-diagnose on the Internet instead of visiting the doctor. http://www.telegraph.co.uk/news/health/news/11760658/One-in-four-self-diagnose-on-the-internet-instead-of-visiting-the-doctor.html [The Telegraph: posted 24-July-2015].

2. Donnelly, L. One in four patients cannot get through to GP surgery. http://www.telegraph.co.uk/news/nhs/12019423/One-in-four-patients-cannot-get-through-to-GP-surgery.html [The Telegraph: posted 27-November-2015].

3. PushDoctor. One in four people in the UK admit to self-diagnosis of an illnesses rather than making time for a doctor’s appointment. http://www.pushdoctor.co.uk/digital-health-report.

4. Roberts, D. Online self-diagnosis can cause surfers to fear the worst. http://www.telegraph.co.uk/news/health/4986309/Online-self-diagnosis-leads-surfers-to-fear-the-worst.html [The Telegraph: posted 15-March-2009].

5. BMA. Self care: question and answer. https://www.bma.org.uk/.

6. APA. The dangers of self-diagnosis via the Internet. http://www.patients.org.au/news/externalnews/the-dangers-of-self-diagnosis-via-the-internet.aspx. [ABC News: posted 21-May-2012].

7. Usborne, S. Cyberchondria: the perils of Internet self-diagnosis. http://www.independent.co.uk/life-style/health-and-families/features/cyberchondria-the-perils-of-internet-self-diagnosis-1623649.html. [Independent: posted 15-March-2009].

8. Cioffi, D. Beyond attentional strategies: a cognitive-perceptual model of somatic interpretation. Psychological Bulletin 109, 25–41 (1991).

9. Gijsbers van Wijk, C. & Kolk, A. Psychometric evaluation of symptom perception related measures. Pers Individ Differ 20, 55–70 (1996).

10. Semigran, H., Linder, J., Gidengil, C. & Mehrotra, A. Evaluation of symptom checkers for self diagnosis and triage: audit study. British Medical Journal 351 (2015).

11. Nolan, T. et al. Patient reaction to a web-based cardiovascular risk calculator in type 2 diabetes: a qualitative study in primary care. Br J Gen Pract, doi:10.3399/bjgp15X683953.

12. Rahman, M., Simmons, R., Harding, A., Wareham, N. & Griffin, S. A simple risk score identifies individuals at high risk of developing Type 2 diabetes: a prospective cohort study. Family Practice 253, 191–196 (2008).

13. Noble, D., Smith, D., Mathur, R., Robson, J. & Greenhalgh, T. Feasibility study of geospatial mapping of chronic disease risk to inform public health commissioning. BMJ Open, doi:10.1136/bmjopen-2011-000711 (2012).

14. Lawrence, J. & Robinson, A. Screening for diabetes in general practice. Prev Cardiol 6, 78–84 (2003).

15. Lawrence, J., Bennett, P. & Young, A. Screening for diabetes in general practice: cross-sectional population study. BMJ 323, doi:10.1136/bmj.323.7312.548.

16. Colagiuri, S. & Davies, D. The value of early detection of of Type 2 diabetes. Curr Opin Endocrinol Diabetes Obes 16, 95–99 (2009).

17. Holland, C., Cooper, Y., Shaw, R., Pattison, H. & Cooke, R. Effectiveness and uptake of screening programmes for coronary heart disease and diabetes: a realist review of design components used in interventions. BMJ Open, doi:10.1136/bmjopen-2013-003428.

18. Szklo, M. Population-based Cohort Studies. Epidemiologic Reviews 20(1), 81–90 (1998).

19. RightDiagnosis. Diagnostic Tests for Diabetes. http://www.rightdiagnosis.com/d/diabetes/tests.htm.

20. DiabetesUK. What are the signs and symptoms of diabetes? https://www.diabetes.org.uk/Guide-to-diabetes/What-is-diabetes/Diabetes-Symptoms/.

21. Noble, D., Mathur, R., Dent, T., Meads, C. & Greenhalgh, T. Risk models and scores for Type 2 diabetes: systematic review. BMJ, doi:10.1136/bmj.d7163 (2011).

22. Hippisley-Cox, J., Coupland, C., Robson, J., Sheikh, A. & Brindle, P. Predicting risk of Type 2 diabetes in England and Wales: prospective derivation and validation of QDScore. BMJ 338, doi:10.1136/bmj.b880 (2009).

23. DiabetesAustralia. Diabetes Risk Calculator. https://www.diabetesaustralia.com.au/risk-calculator.

24. AmericanDiabetesAssociation. Aric diabetes risk calculator. http://aricnews.net/DiabRisk/DiabRC1.html.

25. ClinRisk. QDiabetes. http://www.qdiabetes.org/.

26. UKPDSRiskEngine. https://www.dtu.ox.ac.uk/riskengine/.

27. NHS screening plan for type 2 diabetes ‘inaccurate’. http://www.bbc.co.uk/news/health-38506713 [BBC Health: posted 5-January-2017].

28. Althouse, B. et al. Enhancing disease surveillance with novel data streams: challenges and opportunities. EPJ Data Science 4 (2015).

29. Ayers, J., B, A., S, N. & J, C. Do celebrity cancer diagnoses promote primary cancer prevention? Preventative Medicine 58, 81–84 (2014).

30. Althouse, B., Allem, J., M, C., M, D. & J, A. Population health concerns during the United States’ Great Recession. American Journal of Preventative Medicine 46, 166–170 (2014).

31. Lazer, D., Kennedy, R., King, G. & Vespignani, A. The Parable of Google Flu: Traps in Big Data Analysis. Science 343, 1203–1205 (2014).

32. Santillana, M., Zhang, D., Althouse, B. & Ayers, J. What can digital disease detection learn from (an external revision to) Google Flu Trends? American Journal of Preventative Medicine 47, 341–347 (2014).

33. Ortiz, J. et al. Monitoring Influenza Activity in the United States: A Comparison of Traditional Surveillance Systems with Google Flu Trends. PLoS ONE. doi:10.1371/journal.pone.0018687 (2011).

34. Olson, D., Konty, K., Paladini, M., Viboud, C. & Simonsen, L. Reassessing Google Flu Trends Data for Detection of Seasonal and Pandemic Influenza: A Comparative Epidemiological Study at Three Geographic Scales. PLoS Computational Biology. doi:10.1371/journal.pcbi.1003256 (2013).

35. Ayers, J., B, A. & M, D. Could behavioural medicine lead the web data revolution? JAMA 311, 1399–1400 (2014).

36. Noar, S., Ribisl, K., B, A., Willoughby, J. & J, A. Using digital surveillance to examine the impact of public figure pancreatic cancer announcements on media and search query outcomes. J Natl Cancer Inst Monographs 47, 188–194 (2013).

37. Murphy, J. Innovations in Digital Research Methods, chap. Survey methods: challenges and opportunities (SAGE, 2015).

38. Housley, W. et al. Big and broad social data and the sociological imagination: A collaborative response. Big Data & Society 1, 2053951714545135 (2014).

39. Rogers, R. Post-demographic machines. In: Dekker, A. and Wolfsberger, A. (eds.) Walled Garden, Virtual Platforms: Amsterdam (2009).

40. Tkachenko, N., Procter, R. & Jarvis, S. Predicting the impact of urban flooding using open data. Royal Society Open Science, doi:10.1098/rsos.160013 (2016).

41. Almaatouq, A., Radaelli, L., Pentland, A. & Shmueli, E. Are you your friends’ friend? Poor perception of friendship ties limits the ability to promote behavioural change. PLoS ONE. doi:10.1371/journal.pone.0151588 (2016).

42. Lange, L. & Piette, J. Perceived health status and perceived diabetes control: psychological indicators and accuracy. Journal of Psychosomatic Research 58, 129–137 (2005).

43. Ingham, J. & Miller, P. The determinants of illness declaration. Journal of Psychosomatic Research 20, 309–316 (1976).

44. Anderson, W. Perception of disease and its meanings. The Lancet 2000, 354 (1999).

45. Kapci, E. & Cramer, D. The accuracy of dysphoric and nondepressed group’ predictions of life events. J Psychol 26, 430–436 (1998).

46. Farmer, M. & Ferrano, K. Distress and perceived health: mechanisms of health decline. J Health Soc Behav 39, 298–311 (1997).

47. Lustman, P., Clouse, R. & Carney, R. Depression and the reporting of diabetes symptoms. Int J Psychiatry Med 18, 295–303 (1988).

48. Tessler, R. & Mechanic, D. Psychological distress and perceived health status. J Health Soc Behav 19, 254–262 (1978).

49. Alloy, L. & Abramson, L. Judgement of contingency in depressed and nondepressed students: sadder but wiser? J Exp Psychol Gen 108, 441–458 (1979).

50. Robinson, N., Yateman, N., Protopapa, L. & Bush, L. Unemployment and diabetes. Diabet Med 6(9), 797–803 (1989).

51. Corey, D. M., Dunlap, W. P. & Burke, M. J. Averaging correlations: Expected values and bias in combined pearson rs and fisher’s z transformations. The Journal of General Psychology 125, 245–261, doi:10.1080/00221309809595548 (1998).

## Acknowledgements

The lead author gratefully acknowledges funding by the UK Engineering and Physical Sciences Research Council (grant no. EP/L016400/1) for the EPSRC Centre for Doctoral Training in Urban Science. The authors are grateful to Professor Graham Cormode (Warwick DCS), Dr Maria Liakata (Warwick DCS), Dr Narushige Shiode (King’s College London) and Dr James Millington (King’s College London) for the introductory training during the Warwick-CUSP London Data Dive week in 2015. The authors also thank the team members and students from the Center for Urban Science and Progress from New York University who participated in the event.

## Author information

Authors

### Contributions

N.T. conceived the experiments, conducted analyses, analyzed the results and drafted the manuscript, S.C. and N.G. contributed to the analyses, E.B. and C.G. provided data access and software demonstration, W.G., H.C., E.S. and M.T. provided initial data interpretation scenarios, R.P. and S.J. are co-supervisors of the lead author and contributed to drafting the manuscript and approved it for publication.

### Corresponding author

Correspondence to Nataliya Tkachenko.

## Ethics declarations

### Competing Interests

The authors declare that they have no competing interests.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Tkachenko, N., Chotvijit, S., Gupta, N. et al. Google Trends can improve surveillance of Type 2 diabetes. Sci Rep 7, 4993 (2017). https://doi.org/10.1038/s41598-017-05091-9

• Accepted:

• Published:

• DOI: https://doi.org/10.1038/s41598-017-05091-9

• ### Environmental risk factor assessment for major respiratory disorders in metropolitan cities of India using VIIRS Suomi Aerosol data and Google Trends

• Diptarshi Mitra
• Shiva Reddy Koti
• Sameer Saran

Environmental Sustainability (2021)

• ### Poor Medication Adherence in African Americans Is a Matter of Trust

• Gregory L. Hall
• Michele Heath

Journal of Racial and Ethnic Health Disparities (2021)

• ### Google trend analysis of climatic zone based Indian severe seasonal sensitive population

• Jai Chand Patel
• Pankaj Khurana

BMC Public Health (2020)

• ### Google trends as a surrogate marker of public awareness of diabetic retinopathy

• Rajna Rasheed

Eye (2020)

• ### Emerging Approaches in Surveillance of Type 1 Diabetes

• Sharon Saydah
• Giuseppina Imperatore

Current Diabetes Reports (2018)


text:
auctex
[Top][All Lists]

## Re: [AUCTeX] Extra braces in math mode

 From: Maarten Bergvelt Subject: Re: [AUCTeX] Extra braces in math mode Date: Sun, 5 Mar 2006 08:37:36 -0600 User-agent: Mutt/1.4.2i

* [Sun 2006-Mar-05 05:53] Alastair Irving <address@hidden> :
> I have just installed the recent version of auctex, 11.82.  When I
> switch to math mode, with c-c ~, the math shortcuts work, but they
> insert a pair of braces after every symbol.  For example, if I type f,
> I get \phi{}, and the cursor is put between the braces.  These braces
> are totally meaningless, and have to be deleted.  Is this a known
> problem, or am I doing something wrong?

This happens to me when I am actually not between $and$ or $and$, so when I am in text. So probably there is a typo in your
file. Try to produce a minimal example where this happens and you will
find where auctex became confused.

> Also, how do I create extra shortcuts?  The manual talks about editing a
> variable, but I don't understand how to do this.

Don't know what you want.

--
Maarten Bergvelt

`


text:
## Left ideals generated by idempotents

Posted: June 10, 2010 in Elementary Algebra; Problems & Solutions, Rings and Modules
Tags: , , ,

Problem 1. (Richard Brauer) Let $I$ be a minimal left ideal of a ring $R$. Then either $I^2= \{0\}$ or $I=Re,$ for some non-zero idempotent $e \in I.$

Solution. Suppose that $I^2 \neq \{0\}.$ Then there exists some $x \in I$ such that $Ix \neq \{0\}.$ Thus $Ix=I,$ because $Ix \subseteq I$ is a non-zero left ideal of $R$ and $I$ is a minimal left ideal of $R.$ Hence there exists $0 \neq e \in I$ such that $ex=x$ and so

$(e^2-e)x=0. \ \ \ \ (1)$

On the other hand, $J= \{r \in I: \ rx = 0 \}$ is obviously a left ideal of $R$ which is contained in $I.$ Since $Ix \neq \{0\},$ we have $J \neq I$ and thus, by the minimality of $I,$ we must have $J=\{0\}$. Therefore $e^2-e=0$, by $(1).$ So $e \in I$ is a non-zero idempotent. Now $Re$ is a left ideal of $R$ which is contained in $I.$ Also $0 \neq e=e^2 \in Re$ and so $Re \neq \{0\}.$ Therefore $Re=I,$ by the minimality of $I. \ \Box$

Note that we did not need $R$ to have $1.$ Also, a similar result holds for minimal right ideals of $R$, i.e. if $I$ is a minimal right ideal of $R,$ then either $I^2 = \{0\}$ or $I=eR,$ for some non-zero idempotent $e \in I.$  If $R$ is a semisimple ring (with $1$), for example full matrix rings over division algebras, then every left (resp. right) ideal of $R$ is generated by some idempotent, as the next problem shows.

Problem 2. Let $R$ be a semisimple ring and $I$ any left (resp. right) ideal of $R$. Then there exists some idempotent $e \in I$ such that $I=Re$ (resp. $I=eR$).

Solution. We’ll only prove the claim for left ideals of $R.$ The proof for right ideals is similar. Since $R$ is semisimple, there exists a left ideal $J$ of $R$ such that $R=I \oplus J.$ So $1=e+f,$ for some $e \in I$ and $f \in J.$ Hence $e=e^2+ef$ and so $e^2=e$ and $ef=0$, because $e, e^2 \in I$ and $ef \in J$ and the sum is direct. So $e$ is an idempotent. It is clear that $Re \subseteq I$. Now if $x \in I$, then $x=xe+xf$ and therefore $x=xe.$ Thus $I \subseteq Re$ and we’re done.


text:
# Mean of a function

In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over the interval (a,b) is defined by

${\displaystyle {\bar {f}}={\frac {1}{b-a}}\int _{a}^{b}f(x)\,dx.}$

Recall that a defining property of the average value ${\displaystyle {\bar {y}}}$ of finitely many numbers ${\displaystyle y_{1},y_{2},\dots ,y_{n}}$ is that ${\displaystyle n{\bar {y}}=y_{1}+y_{2}+\cdots +y_{n}}$. In other words, ${\displaystyle {\bar {y}}}$ is the constant value which when added to itself ${\displaystyle n}$ times equals the result of adding the ${\displaystyle n}$ terms of ${\displaystyle y_{i}}$. By analogy, a defining property of the average value ${\displaystyle {\bar {f}}}$ of a function over the interval ${\displaystyle [a,b]}$ is that

${\displaystyle \int _{a}^{b}{\bar {f}}\,dx=\int _{a}^{b}f(x)\,dx}$

In other words, ${\displaystyle {\bar {f}}}$ is the constant value which when integrated over ${\displaystyle [a,b]}$ equals the result of integrating ${\displaystyle f(x)}$ over ${\displaystyle [a,b]}$. But by the second fundamental theorem of calculus, the integral of a constant ${\displaystyle {\bar {f}}}$ is just

${\displaystyle \int _{a}^{b}{\bar {f}}\,dx={\bar {f}}x{\bigr |}_{a}^{b}={\bar {f}}b-{\bar {f}}a=(b-a){\bar {f}}}$

See also the first mean value theorem for integration, which guarantees that if ${\displaystyle f}$ is continuous then there exists a point ${\displaystyle c\in (a,b)}$ such that

${\displaystyle \int _{a}^{b}f(x)\,dx=f(c)(b-a)}$

The point ${\displaystyle f(c)}$ is called the mean value of ${\displaystyle f(x)}$ on ${\displaystyle [a,b]}$. So we write ${\displaystyle {\bar {f}}=f(c)}$ and rearrange the preceding equation to get the above definition.

In several variables, the mean over a relatively compact domain U in a Euclidean space is defined by

${\displaystyle {\bar {f}}={\frac {1}{{\hbox{Vol}}(U)}}\int _{U}f.}$

This generalizes the arithmetic mean. On the other hand, it is also possible to generalize the geometric mean to functions by defining the geometric mean of f to be

${\displaystyle \exp \left({\frac {1}{{\hbox{Vol}}(U)}}\int _{U}\log f\right).}$

More generally, in measure theory and probability theory, either sort of mean plays an important role. In this context, Jensen's inequality places sharp estimates on the relationship between these two different notions of the mean of a function.

There is also a harmonic average of functions and a quadratic average (or root mean square) of functions.


text:
# Placing equation numbers on the right

I am new to TeX and am using scribtex to write a maths paper. When I put the followng code, the equation number is automatically displayed on the left, instead of in the right as is usually done. What is the problem and how do I fix it?

\documentclass[12pt,oneside]{amsart}
\usepackage{amssymb}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\begin{document}
Let us consider a spherical symmetric metric in curvature coordinates:
$$\label{metric} ds^2=-e^\lambda dr^2-r^2(d\theta^2+\sin^2\theta d\phi^2)+e^\nu dt^2$$
\end{document}

The output I get is

-
"What is the problem ..." Hmmm! Aren't you the one to tell us? –  Svend Tveskæg Feb 15 at 9:38

Add the reqno document class option to your current file:

\documentclass[12pt,oneside,reqno]{amsart}

This will override the default left equation numbering scheme of the amsart document class. The following, taken from the AMS document class documentation provides some background (p 7):

Equation numbering on the left or right

The option leqno - equation numbers on the left - is the default in AMS styles. Therefore we provide also a reqno option.

-
leqno and reqno are options of all document classes. I think your answer is too localized to amsart. –  Marco Daniel Oct 26 '11 at 11:31
@MarcoDaniel: I don't read the answer as implying that the leqno applies only to the amsart package; the answer was merely taking the OP's specific example and showed how to add the required option. –  Mico Oct 26 '11 at 12:04
@Mico: The answer is correct. My sentence based on the part default left equation numbering scheme of the amsart –  Marco Daniel Oct 26 '11 at 12:34
Assume one has put leqno in the preample. Can one change the position to the right locally in one equation? –  Mappi Dec 10 '14 at 15:09
–  Werner Dec 10 '14 at 15:24


text:
# Reading and discussion of Lectures on the Philosophy of Mathematics, Amsterdam, March 2021

This will be an event for the $\Phi$-Math Reading Group at the Institute for Logic, Language, and Computation (ILLC) at the University of Amsterdam, 19 March 2021 6pm CET (5pm GMT). Zoom access here.

I shall make a brief presentation of the overall contents of the book, including a discussion of my perspective on the subject, and then get into some of the detailed issues with which the book engages. After this, we shall open up for discussion and comments.

## 2 thoughts on “Reading and discussion of Lectures on the Philosophy of Mathematics, Amsterdam, March 2021”

1. the email wordpress sent to me said 5pm CET (4pm GMT)
This web page says 6pm CET (5pm GMT)

Which is correct?

• I believe it is 6pm CET (5pm GMT). I had it wrong in a first version of this page, which I guess you got sent by email, but then I updated. (The problem was that the Phi-Math web page showed me my local time version of their schedule, and so I had made a mistake about it at first by *another* time adjustment. My opinion is that we as a world of people would benefit from a single global time system.)


text:
# A Double Smoothing Technique for Constrained Convex Optimization Problems and Applications to Optimal Control

In this paper, we propose an efficient approach for solving a class of convex optimization problems in Hilbert spaces. Our feasible region is a (possibly infinite-dimensional) simple convex set, i.e. we assume that projections on this set are computationally easy to compute. The problem we consider is the minimization of a convex function over this region under the additional constraint $Au \in T$, where $A$ is a linear operator and $T$ is a (finite-dimensional) convex set whose dimension is small as compared to the dimension of the feasible region. In our approach, we dualize the linear constraints, solve the resulting dual problem with a purely dual gradient method and show how to reconstruct an approximate primal solution. In order to accelerate our scheme, we introduce a novel double smoothing technique that involves regularization of the dual problem to allow the use of a fast gradient method. As a result, we obtain a method with complexity $O({1 \over \epsilon} \ln {1 \over \epsilon})$ gradient iterations, where $\epsilon$ is the desired accuracy for the primal-dual solution. Our approach covers, in particular, optimal control problems with trajectory governed by a system of linear differential equations, where the additional constraints can for example force the trajectory to visit some convex sets at certain moments of time.

## Citation

CORE Discussion paper 2010/34 (updated version), Center for Operations Research and Econometrics (CORE), Universite catholique de Louvain (UCL), Belgium. Modified version accepted for publication in SIAM Journal of Optimization under the title: 'DOUBLE SMOOTHING TECHNIQUE FOR LARGE-SCALE LINEARLY CONSTRAINED CONVEX OPTIMIZATION'


text:
# Choice of time increment in Monte Carlo/ Geometric Brownian Motion (GBM) stock price prediction

I am playing around with writing a daily stock price prediction algo in Python using a Monte Carlo/GBM methodology. I know there are many other questions on here about this topic (here, and here), but I'm super confused on the inputs and choice of time delta to give sensible results. It seems that unless you have a time delta (dt) increment that is suitably tiny, the results are garbage, and vary wildly with the choice of dt. Obviously I can see that dt is involved in the exponential component, so any change to it will have a big effect. My question is how does one choose a dt?

I'm basically using the great example here, which uses numpy (apologies to the non-python people).

I want to model daily price movements, and look at the results after a certain number of steps (n). I see a lot of examples use a dt of 1/252 (number of trading days in a year, then look at the n-th index of the each sims array to see the values.

Why do we need to have dt as 1/252 to model daily movements? Can we use 1/50 say? Does dt have to be 'suitably tiny'?

As an example, let's use FB. It is trading at 118.72. I want to know the probability of it being above 125 after 60 trading days. I will run 10,000 paths. FB standard deviation is 0.12.

Using a dt of 1/252, and looking at the 60th value of each result, gives me 1912 paths with a value above 125, so a 19% chance.

Using a dt of 1/50 gives me 3294 paths, a 33% chance.

Very confused.

Apologies if this is a stupid question to all the quants on here - I'm primarily a coder.

• What is the standard deviation of the price 60 days hence in the two simulations (At 60*dt in the first case and 12*dt in the second)? Are they comparable? They should both be approx $0.12*\sqrt{60/252}$ since you have an 0.12 annual standard deviation. – noob2 Jun 9 '16 at 16:53
• Your problem is that you're mixing units... when you say FB standard variation is 0.12 you must be careful. Is it the standard variation of facebook share prices or facebook (log-)returns? Similarly, on what time horizon is it measured, daily, monthly, annually returns... ? When people use $\delta t=1/252$ it's because they also use annualised rates/volatilities and volatility in BS is the STDEV of log-returns. – Quantuple Jun 9 '16 at 17:01
• Also note that under such a model, you don't really need MC simulations to forecast the future prices since you assume they follow a lognormal distribution, you can get the probabilities in "analytically". – Quantuple Jun 9 '16 at 17:01
• If you assume that daily (log-)returns are iid with a constant variance $\sigma^2_d$, the variance of a $N$-days (log-)return, which is the sum of $N$ independent daily gaussian (log-)returns, is $\sigma^2 = N \sigma^2_d$ (additivity of variance). Thus, when you are using annualised quantities, and assuming there are $N=252$ trading days in a year which is a mere convention (approximately 5 trading days a weak during 52 weeks) then you must pick $\Delta t = 1/N$ to simulate daily returns for the variance to remain consistent – Quantuple Jun 9 '16 at 17:44
• This is because reciprocally $\sigma^2_d = 1/N \sigma^2$, if $\sigma^2$ denotes the variance of $N$-days log-returns. Remember that all this works because returns are assumed to be independently and identically distributed. – Quantuple Jun 9 '16 at 17:47

Typically when running a Monte Carlo simulation we might simulate an SDE similar to $$\dfrac{dS}{S} = \mu\:dt + \sigma \: dW(t)$$ by some appropriate method (e.g. Euler-Maruyama, Milstein, etc). We notice by dimensional analysis that if $t$ is in units of $\textrm{years}$ then $\mu \sim \textrm{years}^{-1}$ and $\sigma \sim \textrm{years}^{-1/2}$.

Typically we chose $dt = 1/252$ because there are around 252 trading days in a year, and when analysts crunch the daily values, they "pretend" that there are 252 days in a year for convenience. Hence if you want to simulate on a "daily" (252 days in a year) time scale then we would have the scaling $\mu \to \dfrac{\mu}{252}$ and $\sigma \to \dfrac{\sigma}{\sqrt{252\:}}$.

Provided we are using a Monte Carlo method then we can use whatever timescale we like if we're only interested in the final value. (Compare this to finite difference schemes where our choice of increments always has effects on convergence).

Caveat:

We are using the Monte Carlo approach to simulate what the final value would be, and sometimes this is path dependent (suppose $\sigma \to \sigma(S)$, which is called a local volatility model). Then the distribution of final values we compute is only an approximation to the actual distribution of solutions to the SDE. Hence if we use a smaller $\Delta t$ then our approximate distribution converges to the true distribution (cf strong and weak convergence), and generally for the Euler-Maruyama scheme the convergence is $O(\Delta t)$, which means smaller time scales give better results.

If this is the case then there are methods for choosing an appropriate $\Delta t$, but this depends on what Monte Carlo scheme we use, Classical MC, Quasi MC, Multilevel MC, etc.

I hope this helps.

• Yes, very helpful. Lots to think about. So if my FB example standard deviation (0.12) was calculated over 50 days, I'd have to scale it to 0.12 * sqrt(50/252)? – professorDante Jun 9 '16 at 17:56
• You just divide by sqrt (50) to obtain the daily volatility and indeed multiply back by sqrt (252) if you want the annual volatility. – Quantuple Jun 9 '16 at 18:00
• So it really depends on if you want to use $\Delta t =1$ (day) + daily volatility or $\Delta t =1/252$ (year) + annual volatility to simulate your daily returns. But it's exactly the same – Quantuple Jun 9 '16 at 18:01


text:
دانلود مقاله ISI انگلیسی شماره 25893
عنوان فارسی مقاله

# تجزیه و تحلیل حساسیت محدود رگرسیون L1L1 خطی: آشفتگی ها به محدودیت های و حذف مشاهدات

کد مقاله سال انتشار مقاله انگلیسی ترجمه فارسی تعداد کلمات
25893 2006 19 صفحه PDF سفارش دهید محاسبه نشده
خرید مقاله
پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید.
عنوان انگلیسی
Sensitivity analysis of constrained linear L1L1 regression: Perturbations to constraints, addition and deletion of observations
منبع

Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : Computational Statistics & Data Analysis, Volume 51, Issue 2, 15 November 2006, Pages 1213–1231

کلمات کلیدی
11 تجزیه و تحلیل حساسیت - ثبات - رگرسیون 11 - حداقل انحراف مطلق - استحکام - تشخیص - مجموعه ای فعال - کاهش الگوریتم گرادیان -
پیش نمایش مقاله

#### چکیده انگلیسی

This paper extends the direct sensitivity analysis of Shi and Lukas [2005, Sensitivity analysis of constrained linear L1L1 regression: perturbations to response and predictor variables. Comput. Statist. Data Anal. 48, 779–802] of linear L1L1 (least absolute deviations) regression with linear equality and inequality constraints on the parameters. Using the same active set framework of the reduced gradient algorithm (RGA), we investigate the effect on the L1L1 regression estimate of small perturbations to the constraints (constants and coefficients). It is shown that the constrained estimate is stable, but not uniformly stable, and in certain cases it is unchanged. We also consider the effect of addition and deletion of observations and determine conditions under which the estimate is unchanged. The results demonstrate the robustness of L1L1 regression and provide useful diagnostic information about the influence of observations. Results characterizing the (possibly non-unique) solution set are also given. The sensitivity results are illustrated with numerical simulations on the problem of derivative estimation under a concavity constraint.

#### مقدمه انگلیسی

Consider a linear model View the MathML sourceyi=xiTβ+ɛi, i=1,…,ni=1,…,n, where the p×1p×1 parameter vector ββ is known to satisfy additional linear equality constraints View the MathML sourcexiTβ-yi=0 and/or inequality constraints View the MathML sourcexiTβ-yi⩽0. Important applications occur in parametric (and non-parametric) curve and surface fitting, and in the estimation of solutions of ill-posed and inverse problems from noisy data (see Wahba, 1990). In many such problems there is some extra information about the unknown curve or solution that can be used to constrain the parameters. In particular, if the solution (or some linear functional, e.g., an integral) is known to have a certain fixed value at some point, we obtain an equality constraint on the parameters. If the solution is known to be positive, monotone, concave or convex, this leads to certain linear inequality constraints on the parameters (see Wahba, 1982; and O’Leary and Rust, 1986). Constrained regression problems also arise in certain biometric and econometric models (see Judge et al., 1985). Using the method of least absolute deviations, we define the constrained L1L1 regression estimate of ββ to be the solution of the problem (denoted LL1LL1): equation(1.1A) View the MathML sourceminimizeS(β)=∑i=1nxiTβ-yi,β∈Rp Turn MathJax on equation(1.1B) View the MathML sourcesubject toxiTβ-yi=0,i∈E=n+1,…,n+nE, Turn MathJax on equation(1.1C) View the MathML sourcexiTβ-yi⩽0,i∈I=n+nE+1,…,n+nE+nI, Turn MathJax on where EE and II refer to equalities and inequalities, respectively, and we assume that nE<p<n+nE+nInE<p<n+nE+nI. Shi and Lukas (2005) investigated the sensitivity of the solution to (1.1) with respect to perturbations in the responses yiyi and row vectors View the MathML sourcexiT, 1⩽i⩽n1⩽i⩽n, of the design matrix XX. The analysis was done using the active set framework of the reduced gradient algorithm (RGA) developed in Shi and Lukas (2002). In this paper we use the same framework and extend the sensitivity analysis to cover perturbations to the constraints (both the constants and coefficients) and the addition and deletion of observations. It is well known that unconstrained L1L1 regression is robust; the L1L1 estimate is resistant to outliers in the response yy and may not be changed at all by some large perturbations in yy. The same is true for constrained L1L1 regression, and the estimate is stable, but not uniformly stable, with respect to small perturbations in yy and xixi, i=1,…,ni=1,…,n (Shi and Lukas, 2005 and Ellis, 1998). Here we show that similar results apply for perturbations to the constraints in (1.1); the constrained estimate is stable for small perturbations and it may not even change with some large perturbations in the constraints. The stability is not uniform but depends on the degree of ill-conditioning and, for the constraint coefficient vectors, also on how close the estimate is to being non-unique. For unconstrained L1L1 regression, the effect of deletion of observations has been investigated by Narula and Wellington (1985), Dupačová (1992) and Castillo et al. (2001). These works are based on the LP formulation of the L1L1 regression problem. Here we use the direct active set approach on the general LL1LL1 problem (1.1) to find conditions under which an existing solution remains optimal after the deletion of an observation. We also show how the RGA can be used to find a new solution to the problem with a deleted observation, starting from the original solution. The L1L1 version of the Cook distance can then be computed efficiently to determine the influence of each observation on the L1L1 regression estimate. This provides important diagnostic information about the model. A result about the addition of an observation shows that constrained L1L1 regression is robust with respect to the new response. A brief description of the RGA framework and optimality conditions for (1.1) is given in Section 2. It is known that the solution of an L1L1 regression problem can be non-unique (Bloomfield and Steiger, 1983). In Section 3 we derive results characterizing the solution set of (1.1) and show that it can be computed efficiently using the RGA. In Sections 4 and 5, we investigate the effect on the solution to (1.1) of a perturbation to the constants and coefficients of the constraints, respectively. Results relating to the deletion and addition of an observation are derived in Sections 6 and 7, respectively. In Section 8 we consider the problem of estimating the derivative f(t)=g′(t)f(t)=g′(t) from data yi=g(ti)+ɛiyi=gti+ɛi, i=1,…,ni=1,…,n, under the concavity constraint f″(t)⩽0f″(t)⩽0. The estimation of derivatives arises in many applications, in particular in the analysis of growth curves (Gasser et al., 1984 and Eubank, 1988) and pharmacokinetic response curves (Song et al., 1995). Numerical differentiation is an ill-posed problem, meaning that the solution is sensitive to errors in the data (see Anderssen and Bloomfield, 1974), and such problems were a major motivation for this work. We use a truncated trigonometric series for the estimate fp(t)fp(t) of the derivative and find the estimate by solving a constrained linear L1L1 regression problem. Results of numerical simulations illustrate the sensitivity results from 4, 5 and 6, and also a result from Shi and Lukas (2005) on perturbations to the responses. We also consider the effect of increasing the number of points at which the constraint View the MathML sourcefp″(t)⩽0 is evaluated.

خرید مقاله
پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید.


text:
# What is the significance of reverse polish notation?

I teach computing to 18 year olds. After having reverse polish notation explained to them one asked why is it significant enough to be in the public exam. I explained the historical significance of 70s calculators but this failed to really address the issue. So are there and concurrent practical or theorhetical applications of RPN.

-
I have been programming for almost ten years and have completed a masters in CS but I don't think I have ever seen or used reverse polish in any serious context. Are you certain it is relevant, in particular for teaching students? –  Raphael Sep 23 '12 at 14:08
Here is an implementation of a regular expressions engine that uses postfix notation: swtch.com/~rsc/regexp/regexp1.html#thompson. Ken Thompson used it in his first implementation also. Also, it's a popular technique for evaluating expressions at run-time (if you are building a compiler). –  saadtaame Sep 23 '12 at 15:01
In RPN you can write down any expression without using brackets. –  Seg Fault Sep 23 '12 at 15:09
The wikipedia article on RPN covers much ground. Logic texts sometimes refer to polish notation (because it is bracket free), when they explain what can be omitted from proofs as pure "syntactic sugar". However, RPN is important because of its close relationship to stacks. Understanding stacks is important for interactive debugging, because the famous "backtrace" is normally just a stack dump. Pure functional languages are still struggling to offer something comparable to a stack dump for debugging, even so they would have much more detailed information to offer (if they could represent it). –  Thomas Klimpel Sep 23 '12 at 15:54
I have to retract my former comment partially. I have seen somebody use post-fix notation to string-dump trees. It was horrible to read, but easy to code. So in very specific use cases, RP may be useful, but I am not sure whether this extends to education (in general). You can use it to show that syntax is not fixed, I guess. –  Raphael Sep 23 '12 at 16:15
show 1 more comment

In computer reverse polish notation is often used in stack-based and concatenative programming languages. It is also common in dataflow and pipeline-based systems, including Unix pipelines.
computer uses stack for evaluate the arithmetic expressions
suppose following expression
3+4
in computer stack, it pushesh the element in following order

 3
4
+

i.e. top pointer points to + symbol

  +   //top pointer points here
4
3

when computer starts to evaluate, it first pop the operator +, here computer checks, whether it is operator or any other characters, if it is operator then understand that it has to do addition operation, then it pop the two operands for arithmetic addition, i.e. these are the next elements of the stack. that is 4 & 3
here pop order is + 4 3
in short for solving complex expressions reverse polish notation is used

If there are multiple operations, the operator is given immediately after its second operand; so the expression written "3 − 4 + 5" in conventional infix notation would be written "3 4 − 5 +"in RPN: first subtract 4 from 3, then add 5 to that.

An advantage of RPN is that it obviates the need for parentheses that are required by infix. While "3 − 4 * 5" can also be written "3 − (4 * 5)", that means something quite different from "(3 − 4) * 5". In postfix, the former could be written "3 4 5 * −", which unambiguously means "3 (4 5 *) −" which reduces to "3 20 −"; the latter could be written "3 4 - 5 *" (or 5 3 4 - *, if you wish to keep similar formatting), which unambiguously means "(3 4 -) 5 *".

-

I've used RPN several times for rapid prototyping, e.g. of programs that have to read and interpret a user-supplied mathematical expression.

Whereas regular mathematical notation would require at least a recursive parser (think brackets, operator order, etc...), an RPN parser is basically a stack with a switch`-like statement. I guess it's this combination of simplicity and expressive power that led HP to use it initially.

This is, however, usually for rapid prototyping and for convenience. I would never assume that a user can, or wants to, understand RPN.

-

Just to expand the previous answers/comments: don't forget that RPN is alive and on great form ... indeed it is currently used in stack machines like the Java virtual machine.

From Wikipedia: "... a stack machine implements a stack with registers. The operands of the arithmetic logic unit (ALU) are always the top two registers of the stack and the result from the ALU is stored in the top register of the stack. 'Stack machine' commonly refers to computers which use a Last-in, First-out stack to hold short-lived temporary values while executing individual program statements. The instruction set carries out most ALU actions with postfix (Reverse Polish notation) operations that work only on the expression stack, not on data registers or main memory cells ..."

-
Hm, looking at bytecode you don't see RPN per se; of course the instructions show up in "post-fix" order but that doesn't look like RPN in arithmetics, and its reason is rather clear. Register machines have to proceed in the same way: load values, then combine. –  Raphael Sep 24 '12 at 11:21

With regards to calculators: See What is RPN?

• Benefits: RPN saves time and keystrokes. You avoid using and keeping track of parentheses while doing calculations. The process is similar to the way you learned math on paper.

• You can see the intermediary results as you perform your computations rather than just the answer at the end. This is extremely helpful for learning the logic. Math teachers are using this feature to improve student understanding of mathematics.

• An intermediate result allows the user to check the answer and correct errors more easily. It's easier to follow the stream of calculation. The user defines the priority of operators.

• RPN is logical because the user first gives the number and then tells what to do with it.

-


text:
# Climate and Temperature: Sinusoidal Models

High schoolers explore the concept of sine and cosine.  In this sine and cosine lesson, students model temperature and climate using sine and cosine.  High schoolers determine the sine or cosine function to represent temperature data over the course of a year.  Students determine amplitude, wavelength, etc. of their model.

Concepts

Resource Details

9th - 12th
Subjects
Math
3 more...
Resource Type
Lesson Plans
Instructional Strategy
Inquiry-Based Learning
Technology
Calculator
Year
2000
Usage Permissions
Fine Print: Educational Use


text:
# Contents

## Idea

A symplectic manifold serves as the target space for the 2-dimensional sigma-model TQFT called the A-model. If the symplectic manifold arises as the complexification of a phase space of some physical system, then one finds that the boundary path integral of the A-model on cosiotropic branes computes the path integral and the geometric quantization of this physical system.

The setup is reminiscent of how the deformation quantization of the phase space is computed by the 2-dimensional Poisson sigma-model. See holographic principle for more on the general pattern.

## References

The main original article is

A relation to the path integral is discussed in

Relation to the B-model via mirror symmetry is discussed in

Revised on July 11, 2012 02:02:38 by Urs Schreiber (89.204.139.170)


text:
<meta http-equiv="refresh" content="1; url=/nojavascript/"> Radioactive Decay as a Measure of Age ( Activities ) | Earth Science | CK-12 Foundation

# Radioactive Decay as a Measure of Age

%
Progress
Practice Radioactive Decay as a Measure of Age
Progress
%