text:
# Rambling Thoughts

## Some thoughts on Pi Day

As everyone should know by now, yesterday was Pi Day (March 14), the most important holiday of the year. Pi Day is a day to celebrate the amazing properties of the number $\pi$, and every year on 3/14, at 1:59:26, every competent person must spend 53 to 58 seconds reciting 97 digits of pi.

What do you get when you write 3.14 on a sheet of paper and hold it up to a mirror? Try it and see! It’s a sign from the gods of mathematics.

This year, there was a government conspiracy to cheat Americans out of an hour of this most glorious of holidays. Daylight saving time means that we skipped the hour from 2am to 3am. This is simply unacceptable, and provides further evidence of the incompetence and complete failure of democratically elected government. We must try to recover from this lost hour of Pi Day, and here is what I suggest we do: We shall celebrate from 1am to 2am on November 7, when we get this hour back. We will not allow our government to take away our right to Pi Day!

I do have some intelligent posts planned, but Pi Day is simply too much fun.


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QUESTION

# PSY 496 Week 2 DQ 1

This paperwork of PSY 496 Week 2 Discussion Question 1 Protecting Participants from Harm shows the solutions to the following problems:

In considering past research, it is sometimes easier to see when physical harms are occurring as opposed to psychological harms. If you were conducting research on a psychologically sensitive topic, what steps might you need to follow to ensure that no psychological harm was occurring? In other words, how do you know if psychological harm is occurring during a research study? If you were to discover the occurrence of psychological harm, what would be your next steps as a researcher?Guided Response: Review several of your classmates

• @
Tutor has posted answer for $5.19. See answer's preview$5.19

format: plain


text:
# Uncyclopedia:Protection Request/archive1

## Curious George

The temporary semi-protection didn't work, the IPs are back doing the same vandalism. -- Frosty dah snowguy contribs KUN PLEB 10:18, June 1, 2011 (UTC)

Sure. MrN  Fork you! 10:49, Jun 1

## George Washington

Full of IP reverts in the edit history, semi-protection? -- Frosty dah snowguy contribs KUN PLEB 11:03, May 29, 2011 (UTC)

Ok. -- 14:00, May 29, 2011 (UTC)

## Ass

I'm tired of unblanking this page, semi-protection would be of help against users that create accounts to blank it seconds later and idiot IPs -- Frosty dah snowguy contribs KUN PLEB 08:05, May 23, 2011 (UTC)

## Call of Duty: Black Ops

It's complete crap, but it keeps getting worse, mostly from IPs. Perhaps semi-protection would give the {{fix}} a chance to kill it... *incredibly shifty eyes* 21:04, 2 April 2011

## Rebecca Black

Repeated shit edits mainly by IPs, new users, and a temp op. It should be semi-protected for a month so some of the hype around the girl can die down. MegaPleb Dexter111344 Complain here 18:47, March 26, 2011 (UTC)

## Rape

I'm seeing a bunch of talk on Twitter about people on Tumblr planning to vandalize this in a couple of days because it's "offensive." Can it just be semi-protected for a month? MegaPleb Dexter111344 Complain here 02:03, February 24, 2011 (UTC)

If that doesn't scream "vandal tsunami" then I don't know what does. -- TKFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCK 02:14, February 24, 2011 (UTC)
Come on. Do it, brah. MegaPleb Dexter111344 Complain here 02:16, February 24, 2011 (UTC)
I would if I could, but it's already been semi'd for over 3 years. -- TKFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCK 02:17, February 24, 2011 (UTC)
Well, now I look like an ass... I honestly didn't see that till just now... I blame Codeine. MegaPleb Dexter111344 Complain here 02:20, February 24, 2011 (UTC)

## Nazi Zombies

Semi-protect. I'm trying to prevent a revert war with an IP adress. --Gamma287 03:14, January 22, 2011 (UTC)

As I said, Semi-Protect against IP's. Now I am getting insults on the main page from 9 year olds and n00bs who cant edit ("This page iz soooo unfinni!!!!1111eleven!!!11!!one! goes and plai with yoer dickipedea!!!!eleven!!!111"). This must stop. -- Gamma287 23:59, February 23, 2011 (UTC)
Banned that particular vandal. So far the vandalism train isn't riding so quickly or consistently on this page as you say. Using protection request as a preventative measure could be useful on extremely high traffic pages, but I still don't think it necessary here, seeing as the page didn't get edited for a month before the last vandal struck. -- TKFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCK 01:52, February 24, 2011 (UTC)
Actually, I'm going to do a complete about-face and go down the "since you were nice enough to ask" route that I took with The Twilight Virus. Really, no one ever uses this page anymore and it's nice to see someone be diligent enough to try to protect their work (though that kind of defeats the "wiki that anyone can edit" thing). Just don't get too paranoid. Every page gets vandalized once in a while. Every page. -- TKFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCK 01:57, February 24, 2011 (UTC)
That's because requests get ignored half the time... easier to just poke-prod someone on IRC into submission if it really needs it. 02:02, 24 February 2011
I didn't mean to get paranoid. I am beginning to sound like a megalomaniac (anyway, I dislike IP's, they lack discipline). Thank you anyway. -- Gamma287 02:17, February 24, 2011 (UTC)
I saw the ban too. -- Gamma287 02:18, February 24, 2011 (UTC)

## Template:Walrus

Full-Protect. I don't want my work stolen. Maybe now I can delete that off of my Userspace page. -- Gamma287 04:36, January 14, 2011 (UTC)

This, I don't see necessary. You can easily revert it if vandalism does occur once or twice, but if it happens persistently then come back here. -- TKFUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUCK 04:39, January 14, 2011 (UTC)
Doesn't matter. It's deleted now. --Gamma287 03:15, January 22, 2011 (UTC)

## Template talk:Tasty

Spambots seem to really like this one for some strange reason... semi-protection, please? *kitty eyes* 04:14, 13 January 2011

## The Twilight Virus

Semi-protect. I got a weird post on the talk page, so I'm expecting a bomb to fall. -- Gamma287 06:55, January 13, 2011 (UTC)

## Template:Box

I'd protection from idiots on this. As in, indefinite protection from everyone, especially users who think they know what they're doing, because they don't. Well, besides Socky, apparently, but that's not really possible, now is it, so I'll just stick to my original 'everyone' line. People kept adding crap to this to the point where it completely broke (or wikia changed stuff and it broke, but either way, it was the tacked-on stuff that broke...), and now that I've reverted all of that back to a working version from 2006 that was just find the way it was, thankyouvery much, it would be nice if it stayed that way. Cross-browser-compatible working, I mean. Please? 22:00, 7 December, 2010

## Template:HowTo

Not a big deal, but it is kind of surprising how often this gets hit by IP vandals, and as I'm not sure why they should be editing it, anyway, I suppose this is a request for semi-protection. With a pretty please and cookies and chocolate and whipped cream toppings... ~ (talk) • (stalk) -- 20101127 - 05:12 (UTC)

Done. -- 06:06, November 27, 2010 (UTC)
Hmm... well, since... eh, here's some whipped cream, and thanks. ~ (talk) • (stalk) -- 20101127 - 06:11 (UTC)

## RIT

I have no idea what's going on with this, but this page has been getting such an excess of pathetic IP and new person edits that slowing them down might be wise. Thus, I am hereby requesting semi-protection for a page I don't actually give a rat's arse about. But still, it seems to need it, judging by the fact that it doesn't even seem to be improving at all. ~ *shifty eyes* (talk) (stalk) -- 20101013 - 01:45 (UTC)

On the other hand, as long as they're occupied with a page you don't care about, they are not occupied with a page you do care about. Also, if you don't care about it, how do you know that they are not, in fact, RIT superfans, incapable of unawesome RIT-related edits, hmmm? 04:20, October 13, 2010 (UTC)
...because. And I might have lied. But the fact that I still don't care would indicate the contrary... eh, whatever. ~ *shifty eyes* (talk) (stalk) -- 20101013 - 04:28 (UTC)

## UnBooks:My Daddy Has Two Yachts

Some IP keeps changing the second picture to random numbers.jpg for some reason, so semi-protection could save Aleister some effort reverting it in the long run. Or would this be the sort of thing ban patrol is for? Ah, whatever. ~ *shifty eyes* (talk) (stalk) -- 20101013 - 01:45 (UTC)

Semi-protected for a month. And, yes, this is a thing that's Ban Patrolable. 04:17, October 13, 2010 (UTC)

## Template:AoED

There is some long standing issue of less than helpful people editing this, and some other people complaining about trying to revert it. I suggest that nobody edits for a while until the condoms, cocaine and tequila have been distributed appropriately.--(Talk 14:55, October 8, 2010 (UTC)

Has anyone tried, y'know, talking to each other? It's already blocked for IPs and new accounts. The only level higher than that is admin-only, which is crazy for a template. Crazy! 04:15, October 13, 2010 (UTC)

This thing keeps getting vandalized, mostly satire being replaced by immature IP editors who only post swear words. I'd like this to be semi-protected for that reason. InMooseWeTrust 10:56, October 3, 2010 (UTC)

I semi-protected it for a month. After that, be prepared for more crappy edits (only foreigners will edit it, foreigners don't have accounts, and foreigners suck. There. I said it. No, I'm not apologizing). 04:11, October 13, 2010 (UTC)

## Boris Yeltsin

This one hasn't been vandalized nearly as much, but I would like this to also be protected because it is a really good quality, well-written article and should be protected for protection's sake. InMooseWeTrust 10:56, October 3, 2010 (UTC)

## Major League Baseball

This article is a damn mess, but salvageable with a lot of work. Once the time comes I'll deal with it, but for now I think semi-protection from IP edits would go a long way. -- CUN RotM FBotM VFH SK Maj. ΥΣΣ 02:52 EST 6 Aug, 2010

How about we wait and do that thing when you do that thing? 09:03, August 6, 2010 (UTC)

## Virginia

IP's and random users keep doing drive-by edits that are reducing my long rewrite to the kind of garbage it was before I got my dirty fingers all over it. If we could revert the article back to this version and then give it semi-protection, that would be swell. -- GUN WotM RotM FBotM VFH SK Maj. ΥΣΣ 05:38 EST 2 July, 2010

It's semi-protected now, if you want to revert to that version then you would be best discussing it with the other user who has contributed to the article since then. -- 09:41, July 2, 2010 (UTC)

## Washington Capitals

Upgrade to semi-protection. This page has encountered various IP vandalizations since the Caps were eliminated from the playoffs a few weeks ago. I say reopen the page once the offseason starts around July and we'll see if the vandalism continues. -- GUN WotM RotM FBotM VFH SK Maj. ΥΣΣ 01:30 EST 11 May, 2010

Done (for one month). Also, since when has Washington had a hockey team? 06:14, May 11, 2010 (UTC)
The vandalism has persisted. I request semi-protection indefinitely. -- Sf13 00:33 EST 29 July, 2010
Done. I should point out that sucky IP edits on a page that sucks about a team that sucks are, in fact, illustrative of perfect synchronicity. That is the face of God, there. 09:02, August 6, 2010 (UTC)

## NFL

Upgrade to semi-protection: No IP edits. The majority of the last 50 edits have come from IP users, the article is incredibly long, incoherent and in general need of rewriting and the article is a magnet for IP vandalism from individual teams fans. In short, the article is constantly vandalized from biased angles and generally is full of suck, oh and its a really big and important topic. -- GUN WotM RotM FBotM VFH SK Maj. ΥΣΣ 12:27 EST 9 April, 2010

Yeah, OK. I added a rewrite tag too, I'd say it needs it. --UU - natter 12:41, Apr 12

Reduce to semi-protection so I can clean it up again. If the vandalism and deconstructive edits start again then I'll just request for full protection (again). --Hotadmin4u69 [TALK] 01:58 Feb 16 2010

Sure. MrN  Fork you! 02:09, Feb 16

## Template:Main

I'm worried that more vandalism like this (diff of reversion) might happen in the future. This template is used often enough to be considered high-risk. --Pentium5dot1 t~^_^~c 06:48, 27 June 2009 (UTC)

Yep. MrN  Fork you! 02:09, Feb 16

## Africa

Semi-protection, please. As you can imagine, this topic garners a lot of anonymous vandalism -- it's the only article on my watchlist I have to revert on a regular basis. Also, user Sockpuppet of an unregistered user has added some fancy formatting to the most-often edited part of the article (the Pro/Cons table) that I fear will require almost constant maintenance to fix alignment breaks introduced by inexperienced editors. Semi-protection should cut out 90% of the cruft while allowing more constructive edits. Thanks! --Jordanus 02:11, 11 June 2009 (UTC)

Done. MrN  Fork you! 02:09, Feb 16

## Sycamore

Could I have semi protection - I've been getting a fair bit of crap, might be an idea to limit it?--(Talk 11:52, 4 December 2008 (UTC)

## Barney

Semi-protect. IPs and 1st-day users continually add unfunny, poorly formatted, and poorly spelled stuff to it --Kurgan's Back. Prepare to get pwned. (Unless you are Chuck Norris) 21:34, 22 April 2008 (UTC)

## Cheltenham Bournside School and Sixth Form Centre

This vanity-cruft was recreated four times. Either tag with {{VPV}}, redirect to CVP or list on UN:PT-- 20:29, 16 February 2008 (UTC)

• This should probably be deleted in a week or so. But, nevertheless, -- 20:45, 16 February 2008 (UTC)

## Vagina

I dont think the anonymous vandalism is going to change. The picture gets taken out almost every day. Thats all thats been happening on this page since the picture was brought in. Semi protection keeping anons out would help. --Allahgator 03:32, 14 February 2008 (UTC)

• Sure. -- 20:45, 16 February 2008 (UTC)

## Encyclopedia Dramatica (Disambig)

Fully lock as there's no need for editing. Recent vandalism and I'm sure there's more to come...-- 00:11, 14 February 2008 (UTC)

• Maxed. -- 20:45, 16 February 2008 (UTC)

## user:AE

There's to many anon assholes editing my userpage, please semi-protect-- 23:23, 11 February 2008 (UTC)

Done. -- 01:27, 12 February 2008 (UTC)

## Hillary Clinton

I think this needs infinite semi-protection until further notice. Vandalism by IPs and you realize this woman could become the next President?-- 00:15, 11 February 2008 (UTC)

Done by Spang. -- 01:27, 12 February 2008 (UTC)

## 01000010 01101001 01101110 01100001 01110010 01111001

No need for any editing what so ever. All of the recent edits have been vandalism -- 00:48, 10 February 2008 (UTC)

Done. -- 02:12, 10 February 2008 (UTC)

## All work and no play makes Jack a dull boy

I don't know how it happened, but an IP managed to break the semilock. Please relock it so they can't spam. -- Kip > Talk Works 00:26, Feb. 10, 2008

Done by Hinoa. -- 02:13, 10 February 2008 (UTC)

## Uncyclopedia:CVP/archive3

This somehow isn't protected right now, but it obviously should be. --Pentium5dot1 03:41, 10 January 2008 (UTC)

I dunno why, but I did it. -- 14:52, 10 January 2008 (UTC)
Clarification: I was asking for full protection for consistency with the other CVP archives; the page did not appear to have been more than semi-protected at the time I made the request (although even that is doubtful, as the log was empty at the time of my request). Why do I see an unprotection now? Is more stuff going to be added to the archive in the near future? --Pentium5dot1 02:43, 11 January 2008 (UTC)
Yeah, I'm pretty confused right about now. I think I fixed it. -- 03:03, 11 January 2008 (UTC)

## Stoner High School

Please revert to clean version & semi protect. Is being repeatedly vandalized by an IP/leveebreaker05 and I don't want to enter a revert war with a vandal. Thanks -- 05:53, 8 January 2008 (UTC)

• I've protected the page for two hours and placed a warning on Leveebreaker05's talk page. MadMax 06:11, 8 January 2008 (UTC)

## All work and no play makes Jack a dull boy

Please semi-protect. Just like AAAAAAAAA!, this is a target for anonymous IP's to spam more "All work and no play makes Jack a dull boy" or to vandalize it. -- Kip > Talk Works 19:30, Jan. 7, 2008

Done.

## Template:Tl

Some well-meaning but misguided newbie mistakenly removed the opening and closing braces that the template is supposed to display [1]. This needs full protection to stop similar mistakes from happening in the future. (Wikipedia considers it a high-risk template.) Thank you. Pentium5dot1 02:49, 25 November 2007 (UTC)

## American (species)

Request at least semi-protection. Most of it isn't vandalism, but the nature of the article (being the functioning replacement for the deleted American article) attracts a lot of lame and unfunny edits. --CUN RA Talk to me _ 03:46, 13 October 2007 (UTC)

## An article that contains nothing but a cut-down version of itself that does not contain itself

An intricate philosophical in-joke. Needs protection for the same reason as An article that contains nothing but a full stop. Pentium5dot1 23:02, 12 September 2007 (UTC)

## List of Mortal Kombat Characters

Most of the IP edits are really bad and stupid sex-related jokes. I'd like to have it protected from any further edits from such users as there's already too much sexual humor as it is on the article. -- Hanyouman 01:51, 30 August 2007 (UTC)

Ok, done. Spang 02:13, 30 Aug 2007

## Beginner's Guide

I'd like every page in the Beginner's Guide that is currently not unprotected to be unprotected so that I may finish my work on updating guidelines and rules and all that lovely crap. I'll let you know when I'm done. --Hotadmin4u69 [TALK] 06:59, 11 August 2007 (UTC)

## Bible

Preferable semi-protection to prevent future cruddy IP edits. --Hotadmin4u69 [TALK] 09:19, 29 July 2007 (UTC)

## International Page Blanking Day

Because the original edit history which made the page funny is fast disappearing off the bottom because everybody wants a piece of blanking action. -- (but) Untrue  Whhhy?Whut?How? *Back from the dead* 08:33, 26 July 2007 (UTC)

## Russian Reversal

Before AAA & SBU get into an edit war. 11:41, 25 July 2007

I wasn't about to get into a war with him Tom, as it says in the edit summary. -- (but) Untrue  Whhhy?Whut?How? *Back from the dead* 08:31, 26 July 2007 (UTC)

## An article that contains nothing but a full stop

Likely to be meet futured vandalisms. It only contains (.) and it needs to stay that way. --Kip the Dip 20:57, 23 July 2007 (UTC)

## Forum:Index

I think that this page should be fully protected after You-know-who attempted to create a You-know-what forum by editing this page. -- 21:39, 19 March 2007 (UTC)

## Armenia

Blanked 3 times so far this week. I've reported the two IP addresses involved to the Ban Patrol, and the first has already been banned, but...why is this person using more than one IP address? Whoever this is, we need to inform them that blanking is not the proper way to dispute content. --Pentium5dot1 01:14, 9 March 2007 (UTC)

No way. Completely unreasonable request. 03/9 01:53
Sorry for not clearly specifying that semi-protection was all I was asking for not noticing that the article had already been protected at the time I made this request. Pentium5dot1 02:35, 9 March 2007 (UTC)

## Eragon

• I don't know what it is about this page, but itt's not so much vandalism as it is really stupid edits. You know the type, unfunny, detrimental changes that could have been produced by a six year old. They're mostly by IP's, so someone please semi-protect this page. --Señor DiZtheGreat  CUN AOTM ( Worship me!) (Praise me!) (Join me!) AMEN! 20:43, 1 March 2007 (UTC)

## Uncyclopedia:Protection Request

• Requesting that this page be protected so that n00bs don't mess it up, and create additional work for the adminatti. 22:54, 7 September 2006 (UTC)
For times infinity. $4\infty$ --User:Nintendorulez 00:17, 9 September 2006 (UTC)
Request Granted 22:54, 7 September 2006 (UTC)

Even though the Supersecret admin page does not exist, it still needs to be protected against the vabnalism it receives. ~ 15:09, 8 September 2006 (UTC)

Would be protected if it existed. But it doesn't, so it hasn't. ;)  >Major Sir Hinoa|Talk|KUN   15:17, 8 September 2006 (UTC)
Should be semi-protected if it existed. --User:Nintendorulez 00:17, 9 September 2006 (UTC)

Score: +1

## Vandalism

See Talk:Vandalism#Whoever took off the giant "Penis" sucks and Forum:Vandalism article needs protection?. Needs full protection, not just semi. Pentium5dot1 19:09, 3 December 2006 (UTC)

I still don't see exactly why, but I'll make it happen. 12/3 23:41


text:
combining z-scores into a single z-score value
0
2
Entering edit mode
3.7 years ago
Star ▴ 50

Hi all,

I have a list of z-scores (obtained via effect size/std.err of effect size). I want to combine all the z-scores via Stouffer's method but without weights. Till now I have seen "Stouffer.test" implemented in metaseq package but it requires weights along with the z-score. I have tried "sumz" method implemented in metap package which according to my understanding can work without weights as follows:

sumz(p, weights = NULL)  -> where p is the vector of values; in my case z-scores

My understanding of Stouffer's method is

sum of all the z-scores/sqrt of total number of samples

when I compared the results of the "sumz" method as described above, it is not the same as the above formula when I calculated it in excel using the following

=SUM(C2:C8219)/SQRT(8218)

My question is : Is there any R function which works like above (sum of all the z-scores/sqrt of total number of samples) so that I can cross check the results? Or I have to do it manually?

Thanks!!!

R excel bioinformatics statistics stats • 8.9k views
1
Entering edit mode

Maybe sum(p)/sqrt(numberOfSamples) ?

0
Entering edit mode

what does p stands for here? z-scores?

0
Entering edit mode

You mentioned p is a z-scores vector:

where p is the vector of values; in my case z-scores

sum(p)/sqrt(8218) is exactly the same thing you are trying to do with Excel =SUM(C2:C8219)/SQRT(8218)

0
Entering edit mode

Thankyou for the clarification zx8754. I confused "sum(p)" with pvalues instead of zscores. Now that I have combined z-scores, I am confused about how to interpret it? Shall I convert the z-scores into p-values(one or two-tailed?) to see the significance? Apologies if the question seems to be naive. I am pretty new to genetics and statistics.

0
Entering edit mode

Hey, you stated that:

sumz(p, weights = NULL) -> where p is the vector of values; in my case z-scores

So, you have vector, p, that contains Z scores.

The actual sumz() function from metap package expects p-values, not Z-scores.

Description
Combine p-values using the sum z method

Usage
sumz(p, weights = NULL, data = NULL, subset = NULL, na.action = na.fail)
## S3 method for class 'sumz'
print(x, ...)

Arguments
- p, A vector of significance values
- weights, A vector of weights
- data, Optional data frame containing variables
- subset, Optional vector of logicals to specify a subset of the p-values
- na.action, A function indicating what should happen when data contains NAs
- x, An object of class ‘sumz’
- ..., Other arguments to be passed through

[source: https://cran.r-project.org/web/packages/metap/metap.pdf]

If you have just Z-scores and do not want to consider weights, you can indeed calculate the overall Z-score by STouffer`s method using:

sum of all the z-scores / sqrt of total number of samples
0
Entering edit mode

Thanks for the clarification kevin Blighe. I have combined the z-scores using Stouffer's method. But am not sure how to interpret it.

0
Entering edit mode

In that case, perhaps you should consider why you chose to use the test in the first instance (?). Do you even need to use it?

0
Entering edit mode

I am trying to find the differentially expressed genes present within the tissues. So I have the z-scores for all the genes in the tissues. I have combined the z-scores for the genes in each tissue and now I want to see if I could identify or rank the tissues based upon their pathogenicity using the z-scores?

0
Entering edit mode

Oh, I see, you now have a combined Z-score for each tissue. Are the results what you expected, if you order them high-to-low?

0
Entering edit mode

I don't know how to interpret the z-scores? I am assuming that I need to convert z-scores into p-values first and CI first?

0
Entering edit mode

Hey, oh, then why did you choose that test if you do not know how to interpret the result? You must have seen it in a publication, right? Are you sure that you need to do the analysis that you are doing?

If you feel that you need greater statistical advice, then you could try CrossValidated (StackExchange), which is more aligned toward statistics. Biostars is a broad/general forum for bioinformatics.

0
Entering edit mode

Thankyou Kevin for the reply. Actually my main goal is to combine either a z-score or p-value so that a single value could be the representative of a single tissue. I was using Stouffer's method initially which did not give the results as expected because Stouffer's method takes into account the direction of the effect of the gene (positive or negative) which we are not considering at this stage. So now I am exploring some other methods.

0
Entering edit mode

What if you only consider the genes that have positive Z scores? I think that most define a tissue by what is highly expressed, not by what is not expressed. I find better results this way, too.

0
Entering edit mode

Another method you may consider is to simply define a list of genes for each tissue based on Z>2 or Z>3, and then use GSVA to enrich your data against these lists. This will then return 'scores' for the samples in your data for each tissue. As in, it will say by how much each tissue is enriched in your data.

0
Entering edit mode

Hi. Kevin. Thanks for the reply. At this stage I am trying to find the differential expression of tissues regardless of high expression or decreased expression of genes (if this makes sense).

In the sentence you used above, what do you mean by "This will then return 'scores' for the samples in your data for each tissue". What does the word "sample" refers to? Can it refer to the "genes" in a particular tissue?

0
Entering edit mode

Hey, GSVA will take this data:

Sample1  Sample2  Sample3
BRCA1      6        4        3
TP53       3        3        2
BRCC3      7        12       8
...        ...      ...      ...

It then compute's an algorithm against:

Signature1
TP53; BRCC3; ...

Signature2
BRCA1; TP53

GSVA will then return:

Sample1  Sample2  Sample3
Signature1   3.4      12.6     8.3
Signature2   2.7      10.4     5.5


text:
## Hamburg

Since I moved to Hamburg,   Alessandro Valentino and I have been organizing one series of seminar talks whose goal is to bring people (mostly graduate students, and some postdocs and others) up to speed on the tools used in Jacob Lurie’s big paper on the classification of TQFT and proof of the Cobordism Hypothesis.  This is part of the Forschungsseminar (“research seminar”) for the working groups of Christoph Schweigert, Ingo Runkel, and Christoph Wockel.  First, I gave one introducing myself and what I’ve done on Extended TQFT. In our main series We’ve had a series of four so far – two in which Alessandro outlined a sketch of what Lurie’s result is, and another two by Sebastian Novak and Marc Palm that started catching our audience up on the simplicial methods used in the theory of $(\infty,n)$-categories which it uses.  Coming up in the New Year, Nathan Bowler and I will be talking about first $(\infty,1)$-categories, and then $(\infty,n)$-categories.   I’ll do a few posts summarizing the talks around then.

Some people in the group have done some work on quantum field theories with defects, in relation to which, there’s this workshop coming up here in February!  The idea here is that one could have two regions of space where different field theories apply, which are connected along a boundary. We might imagine these are theories which are different approximations to what’s going on physically, with a different approximation useful in each region.  Whatever the intuition, the regions will be labelled by some category, and boundaries between regions are labelled by functors between categories.  Where different boundary walls meet, one can have natural transformations.  There’s a whole theory of how a 3D TQFT can be associated to modular tensor categories, in sort of the same sense that a 2D TQFT is associated to a Frobenius algebra. This whole program is intimately connected with the idea of “extending” a given TQFT, in the sense that it deals with theories that have inputs which are spaces (or, in the case of defects, sub-spaces of given ones) of many different dimensions.  Lurie’s paper describing the n-dimensional cobordism category, is very much related to the input to a theory like this.

## Brno Visit

This time, I’d like to mention something which I began working on with Roger Picken in Lisbon, and talked about for the first time in Brno, Czech Republic, where I was invited to visit at Masaryk University.  I was in Brno for a week or so, and on Thursday, December 13, I gave this talk, called “Higher Gauge Theory and 2-Group Actions”.  But first, some pictures!

This fellow was near the hotel I stayed in:

Since this sculpture is both faceless and hard at work on nonspecific manual labour, I assume he’s a Communist-era artwork, but I don’t really know for sure.

The Christmas market was on in Náměstí Svobody (Freedom Square) in the centre of town.  This four-headed dragon caught my eye:

On the way back from Brno to Hamburg, I met up with my wife to spend a couple of days in Prague.  Here’s the Christmas market in the Old Town Square of Prague:

Anyway, it was a good visit to the Czech Republic.  Now, about the talk!

### Moduli Spaces in Higher Gauge Theory

The motivation which I tried to emphasize is to define a specific, concrete situation in which to explore the concept of “2-Symmetry”.  The situation is supposed to be, if not a realistic physical theory, then at least one which has enough physics-like features to give a good proof of concept argument that such higher symmetries should be meaningful in nature.  The idea is that Higher Gauge theory is a field theory which can be understood as one in which the possible (classical) fields on a space/spacetime manifold consist of maps from that space into some target space $X$.  For the topological theory, they are actually just homotopy classes of maps.  This is somewhat related to Sigma models used in theoretical physics, and mathematically to Homotopy Quantum Field Theory, which considers these maps as geometric structure on a manifold.  An HQFT is a functor taking such structured manifolds and cobordisms into Hilbert spaces and linear maps.  In the paper Roger and I are working on, we don’t talk about this stage of the process: we’re just considering how higher-symmetry appears in the moduli spaces for fields of this kind, which we think of in terms of Higher Gauge Theory.

Ordinary topological gauge theory – the study of flat connections on $G$-bundles for some Lie group $G$, can be looked at this way.  The target space $X = BG$ is the “classifying space” of the Lie group – homotopy classes of maps in $Hom(M,BG)$ are the same as groupoid homomorphisms in $Hom(\Pi_1(M),G)$.  Specifically, the pair of functors $\Pi_1$ and $B$ relating groupoids and topological spaces are adjoints.  Now, this deals with the situation where $X = BG$ is a homotopy 1-type, which is to say that it has a fundamental groupoid $\Pi_1(X) = G$, and no other interesting homotopy groups.  To deal with more general target spaces $X$, one should really deal with infinity-groupoids, which can capture the whole homotopy type of $X$ – in particular, all its higher homotopy groups at once (and various relations between them).  What we’re talking about in this paper is exactly one step in that direction: we deal with 2-groupoids.

We can think of this in terms of maps into a target space $X$ which is a 2-type, with nontrivial fundamental groupoid $\Pi_1(X)$, but also interesting second homotopy group $\pi_2(X)$ (and nothing higher).  These fit together to make a 2-groupoid $\Pi_2(X)$, which is a 2-group if $X$ is connected.  The idea is that $X$ is the classifying space of some 2-group $\mathcal{G}$, which plays the role of the Lie group $G$ in gauge theory.  It is the “gauge 2-group”.  Homotopy classes of maps into $X = B \mathcal{G}$ correspond to flat connections in this 2-group.

For practical purposes, we use the fact that there are several equivalent ways of describing 2-groups.  Two very directly equivalent ways to define them are as group objects internal to $\mathbf{Cat}$, or as categories internal to $\mathbf{Grp}$ – which have a group of objects and a group of morphisms, and group homomorphisms that define source, target, composition, and so on.  This second way is fairly close to the equivalent formulation as crossed modules $(G,H,\rhd,\partial)$.  The definition is in the slides, but essentially the point is that $G$ is the group of objects, and with the action $G \rhd H$, one gets the semidirect product $G \ltimes H$ which is the group of morphisms.  The map $\partial : H \rightarrow G$ makes it possible to speak of $G$ and $H$ acting on each other, and that these actions “look like conjugation” (the precise meaning of which is in the defining properties of the crossed module).

The reason for looking at the crossed-module formulation is that it then becomes fairly easy to understand the geometric nature of the fields we’re talking about.  In ordinary gauge theory, a connection can be described locally as a 1-form with values in $Lie(G)$, the Lie algebra of $G$.  Integrating such forms along curves gives another way to describe the connection, in terms of a rule assigning to every curve a holonomy valued in $G$ which describes how to transport something (generally, a fibre of a bundle) along the curve.  It’s somewhat nontrivial to say how this relates to the classic definition of a connection on a bundle, which can be described locally on “patches” of the manifold via 1-forms together with gluing functions where patches overlap.  The resulting categories are equivalent, though.

In higher gauge theory, we take a similar view. There is a local view of “connections on gerbes“, described by forms and gluing functions (the main difference in higher gauge theory is that the gluing functions related to higher cohomology).  But we will take the equivalent point of view where the connection is described by $G$-valued holonomies along paths, and $H$-valued holonomies over surfaces, for a crossed module $(G,H,\rhd,\partial)$, which satisfy some flatness conditions.  These amount to 2-functors of 2-categories $\Pi_2(M) \rightarrow \mathcal{G}$.

The moduli space of all such 2-connections is only part of the story.  2-functors are related by natural transformations, which are in turn related by “modifications”.  In gauge theory, the natural transformations are called “gauge transformations”, and though the term doesn’t seem to be in common use, the obvious term for the next layer would be “gauge modifications”. It is possible to assemble a 2-groupoid $Hom(\Pi_2(M),\mathcal{G}$, whose space of objects is exactly the moduli space of 2-connections, and whose 1- and 2-morphisms are exactly these gauge transformations and modifications.  So the question is, what is the meaning of the extra information contained in the 2-groupoid which doesn’t appear in the moduli space itself?

Our claim is that this information expresses how the moduli space carries “higher symmetry”.

### 2-Group Actions and the Transformation Double Category

What would it mean to say that something exhibits “higher” symmetry? A rudimentary way to formalize the intuition of “symmetry” is to say that there is a group (of “symmetries”) which acts on some object. One could get more subtle, but this should be enough to begin with. We already noted that “higher” gauge theory uses 2-groups (and beyond into $n$-groups) in the place of ordinary groups.  So in this context, the natural way to interpret it is by saying that there is an action of a 2-group on something.

Just as there are several equivalent ways to define a 2-group, there are different ways to say what it means for it to have an action on something.  One definition of a 2-group is to say that it’s a 2-category with one object and all morphisms and 2-morphisms invertible.  This definition makes it clear that a 2-group has to act on an object of some 2-category $\mathcal{C}$. For our purposes, just as we normally think of group actions on sets, we will focus on 2-group actions on categories, so that $\mathcal{C} = \mathbf{Cat}$ is the 2-category of interest. Then an action is just a map:

$\Phi : \mathcal{G} \rightarrow \mathbf{Cat}$

The unique object of $\mathcal{G}$ – let’s call it $\star$, gets taken to some object $\mathbf{C} = \Phi(\star) \in \mathbf{Cat}$.  This object $\mathbf{C}$ is the thing being “acted on” by $\mathcal{G}$.  The existence of the action implies that there are automorphisms $\Phi(g) : \mathbf{C} \rightarrow \mathbf{C}$ for every morphism in $\mathbf{G}$ (which correspond to the elements of the group $G$ of the crossed module).  This would be enough to describe ordinary symmetry, but the higher symmetry is also expressed in the images of 2-morphisms $\Phi( \eta : g \rightarrow g') = \Phi(\eta) : \Phi(g) \rightarrow \Phi(g')$, which we might call 2-symmetries relating 1-symmetries.

What we want to do in our paper, which the talk summarizes, is to show how this sort of 2-group action gives rise to a 2-groupoid (actually, just a 2-category when the $\mathbf{C}$ being acted on is a general category).  Then we claim that the 2-groupoid of connections can be seen as one that shows up in exactly this way.  (In the following, I have to give some credit to Dany Majard for talking this out and helping to find a better formalism.)

To make sense of this, we use the fact that there is a diagrammatic way to describe the transformation groupoid associated to the action of a group $G$ on a set $S$.  The set of morphisms is built as a pullback of the action map, $\rhd : (g,s) \mapsto g(s)$.

This means that morphisms are pairs $(g,s)$, thought of as going from $s$ to $g(s)$.  The rule for composing these is another pullback.  The diagram which shows how it’s done appears in the slides.  The whole construction ends up giving a cubical diagram in $\mathbf{Sets}$, whose top and bottom faces are mere commuting diagrams, and whose four other faces are all pullback squares.

To construct a 2-category from a 2-group action is similar. For now we assume that the 2-group action is strict (rather than being given by $\Phi$ a weak 2-functor).  In this case, it’s enough to think of our 2-group $\mathcal{G}$ not as a 2-category, but as a group-object in $\mathbf{Cat}$ – the same way that a 1-group, as well as being a category, can be seen as a group object in $\mathbf{Set}$.  The set of objects of this category is the group $G$ of morphisms of the 2-category, and the morphisms make up the group $G \ltimes H$ of 2-morphisms.  Being a group object is the same as having all the extra structure making up a 2-group.

To describe a strict action of such a $\mathcal{G}$ on $\mathbf{C}$, we just reproduce in $\mathbf{Cat}$ the diagram that defines an action in $\mathbf{Sets}$:

The fact that $\rhd$ is an action just means this commutes. In principle, we could define a weak action, which would mean that this commutes up to isomorphism, but we won’t be looking at that here.

Constructing the same diagram which describes the structure of a transformation groupoid (p29 in the slides for the talk), we get a structure with a “category of objects” and a “category of morphisms”.  The construction in $\mathbf{Set}$ gives us directly a set of morphisms, while $S$ itself is the set of objects. Similarly, in $\mathbf{Cat}$, the category of objects is just $\mathbf{C}$, while the construction gives a category of morphisms.

The two together make a category internal to $\mathbf{Cat}$, which is to say a double category.  By analogy with $S / \!\! / G$, we call this double category $\mathbf{C} / \!\! / \mathcal{G}$.

We take $\mathbf{C}$ as the category of objects, as the “horizontal category”, whose morphisms are the horizontal arrows of the double category. The category of morphisms of $\mathbf{C} /\!\!/ \mathcal{G}$ shows up by letting its objects be the vertical arrows of the double category, and its morphisms be the squares.  These look like this:

The vertical arrows are given by pairs of objects $(\gamma, x)$, and just like the transformation 1-groupoid, each corresponds to the fact that the action of $\gamma$ takes $x$ to $\gamma \rhd x$. Each square (morphism in the category of morphisms) is given by a pair $( (\gamma, \eta), f)$ of morphisms, one from $\mathcal{G}$ (given by an element in $G \rtimes H$), and one from $\mathbf{C}$.

The horizontal arrow on the bottom of this square is:

$(\partial \eta) \gamma \rhd f \circ \Phi(\gamma,\eta)_x = \Phi(\gamma,\eta)_y \circ \gamma \rhd f$

The fact that these are equal is exactly the fact that $\Phi(\gamma,\eta)$ is a natural transformation.

The double category $\mathbf{C} /\!\!/ \mathcal{G}$ turns out to have a very natural example which occurs in higher gauge theory.

### Higher Symmetry of the Moduli Space

The point of the talk is to show how the 2-groupoid of connections, previously described as $Hom(\Pi_2(M),\mathcal{G})$, can be seen as coming from a 2-group action on a category – the objects of this category being exactly the connections. In the slides above, for various reasons, we did this in a discretized setting – a manifold with a decomposition into cells. This is useful for writing things down explicitly, but not essential to the idea behind the 2-symmetry of the moduli space.

The point is that there is a category we call $\mathbf{Conn}$, whose objects are the connections: these assign $G$-holonomies to edges of our discretization (in general, to paths), and $H$-holonomies to 2D faces. (Without discretization, one would describe these in terms of $Lie(G)$-valued 1-forms and $Lie(H)$-valued 2-forms.)

The morphisms of $\mathbf{Conn}$ are one type of “gauge transformation”: namely, those which assign $H$-holonomies to edges. (Or: $Lie(H)$-valued 1-forms). They affect the edge holonomies of a connection just like a 2-morphism in $\mathcal{G}$.  Face holonomies are affected by the $H$-value that comes from the boundary of the face.

What’s physically significant here is that both objects and morphisms of $\mathbf{Conn}$ describe nonlocal geometric information.  They describe holonomies over edges and surfaces: not what happens at a point.  The “2-group of gauge transformations”, which we call $\mathbf{Gauge}$, on the other hand, is purely about local transformations.  If $V$ is the vertex set of the discretized manifold, then $\mathbf{Gauge} = \mathcal{G}^V$: one copy of the gauge 2-group at each vertex.  (Keeping this finite dimensional and avoiding technical details was one main reason we chose to use a discretization.  In principle, one could also talk about the 2-group of $\mathcal{G}$-valued functions, whose objects and morphisms, thinking of it as a group object in $\mathbf{Cat}$, are functions valued in morphisms of $\mathcal{G}$.)

Now, the way $\mathbf{Gauge}$ acts on $\mathbf{Conn}$ is essentially by conjugation: edge holonomies are affected by pre- and post-multiplication by the values at the two vertices on the edge – whether objects or morphisms of $\mathbf{Gauge}$.  (Face holonomies are unaffected).  There are details about this in the slides, but the important thing is that this is a 2-group of purely local changes.  The objects of $\mathbf{Gauge}$ are gauge transformations of this other type.  In a continuous setting, they would be described by $G$-valued functions.  The morphisms are gauge modifications, and could be described by $H$-valued functions.

The main conceptual point here is that we have really distinguished between two kinds of gauge transformation, which are the horizontal and vertical arrows of the double category $\mathbf{Conn} /\!\!/ \mathbf{Gauge}$.  This expresses the 2-symmetry by moving some gauge transformations into the category of connections, and others into the 2-group which acts on it.  But physically, we would like to say that both are “gauge transformations”.  So one way to do this is to “collapse” the double category to a bicategory: just formally allow horizontal and vertical arrows to compose, so that there is only one kind of arrow.  Squares become 2-cells.

So then if we collapse the double category expressing our 2-symmetry relation this way, the result is exactly equivalent to the functor category way of describing connections.  (The morphisms will all be invertible because $\mathbf{Conn}$ is a groupoid and $\mathbf{Gauge}$ is a 2-group).

I’m interested in this kind of geometrical example partly because it gives a good way to visualize something new happening here.  There appears to be some natural 2-symmetry on this space of fields, which is fairly easy to see geometrically, and distinguishes in a fundamental way between two types of gauge transformation.  This sort of phenomenon doesn’t occur in the world of $\mathbf{Sets}$ – a set $S$ has no morphisms, after all, so the transformation groupoid for a group action on it is much simpler.

In broad terms, this means that 2-symmetry has qualitatively new features that familiar old 1-symmetry doesn’t have.  Higher categorical versions – $n$-groups acting on $n$-groupoids, as might show up in more complicated HQFT – will certainly be even more complicated.  The 2-categorical version is just the first non-trivial situation where this happens, so it gives a nice starting point to understand what’s new in higher symmetry that we didn’t already know.


text:
# Overview

The main goal of the CARLA Autonomous Driving Leaderboard is to evaluate the driving proficiency of autonomous agents in realistic traffic situations. The leaderboard serves as an open platform for the community to perform fair and reproducible evaluations, simplifying the comparison between different approaches.

###### Index

Autonomous agents have to drive through a set of predefined routes. For each route, agents will be initialized at a starting point and will be directed to drive to a destination point, provided with a description of the route. Routes will happen in a variety of areas, including freeways, urban scenes, and residential districts. Agents will be evaluated in a variety of weather conditions, including daylight scenes, sunset, rain, fog, and night, among others.

Agents will face multiple traffic situations based on the NHTSA typology. The full list of traffic situations can be reviewed in this page, but here are some examples.

• Lane merging.
• Lane changing.
• Negotiations at traffic intersections.
• Handling traffic lights and traffic signs.
• Coping with pedestrians, cyclists, and other elements.

# Participation modalities

The leaderboard offers two participation modalities, SENSORS and MAP. These modalities differ in the type of input data that your agent can request from the platform.

Additionally, agents in both modalities will receive a high-level route description indicating the key points that the path has to follow in order to reach the destination. The route is represented as a list of tuples and has two variations.

For the first case, the first element of the tuple contains a waypoint, expressed as a latitude, a longitude, and a z component.

[({'z': 0.0, 'lat': 48.99822669411668, 'lon': 8.002271601998707}, RoadOption.LEFT),
({'z': 0.0, 'lat': 48.99822669411668, 'lon': 8.002709765148996}, RoadOption.RIGHT),
...
({'z': 0.0, 'lat': 48.99822679980298, 'lon': 8.002735250105061}, RoadOption.STRAIGHT)]

The second case is very similar to the previous one, but instead of using GPS coordinates, the route is expressed in world coordinates instead.

[({'x': 153.7, 'y': 15.6, 'z': 0.0}, RoadOption.LEFT),
({'x': 148.9, 'y': 67.8, 'z': 0.0}, RoadOption.RIGHT),
...
({'x': 180.7, 'y': 45.1, 'z': 1.2}, RoadOption.STRAIGHT)]

The distance between two consecutive waypoints could be of up to hundreds of meters. Do not rely on these as your main mechanism to navigate the environment.

The second element contains a high-level command. The set of available high-level commands is:

• RoadOption.CHANGELANELEFT: Move one lane to the left.
• RoadOption.CHANGELANERIGHT: Move one lane to the right.
• RoadOption.LANEFOLLOW: Continue in the current lane.
• RoadOption.LEFT: Turn left at the intersection.
• RoadOption.RIGHT: Turn right at the intersection.
• RoadOption.STRAIGHT: Keep straight at the intersection.

There might be cases where the semantics of left and right is ambiguous. In order to disambiguate these situations, you could consider the GPS position of the next waypoints.

Important: You are not allowed to make use of any privilege information offered by the CARLA simulator, including planners or any type of ground truth. Submissions using these features will be rejected and teams will be banned from the platform.

### SENSORS track

 GNSS IMU LIDAR RADAR RGB camera Speedometer sensor.other.gnss sensor.other.imu sensor.lidar.ray_cast sensor.other.radar sensor.camera.rgb sensor.other.speedometer 0-1 units 0-1 units 0-1 units 0-2 units 0-4 units 0-1 units GPS sensor returning geo location data. 6-axis Inertial Measurement Unit. Velodyne 64 LIDAR. Long-range RADAR (up to 100 meters). Regular camera that captures images. Pseudosensor that provides an approximation of your linear velocity.

Units of each sensor are limited to keep the computational budget under control.

### MAP track

Provides the same set of sensor as the SENSORS track does. Additionally, agents can request to access an HD map, which is provided as an OpenDRIVE file parsed as a string.

You are fully responsible to parse or convert this file into a representation that can be useful to your agent.

 GNSS IMU LIDAR RADAR RGB camera Speedometer sensor.other.gnss sensor.other.imu sensor.lidar.ray_cast sensor.other.radar sensor.camera.rgb sensor.other.speedometer 0-1 units 0-1 units 0-1 units 0-2 units 0-4 units 0-1 units GPS sensor returning geo location data. 6-axis Inertial Measurement Unit. Velodyne 64 LIDAR. Long-range RADAR (up to 100 meters). Regular camera that captures images. Pseudosensor that provides an approximation of your linear velocity.
 OpenDRIVE map sensor.opendrive_map 0-1 unit Pseudosensor that exposes the HD map in OpenDRIVE format parsed as a string.

# Evaluation and metrics

The driving proficiency of an agent can be characterized by multiple metrics. For this leaderboard we have selected a set of metrics that help understand different aspects of driving. While all routes have the same type of metrics, their respective values are calculated separately. The specific metrics are as follows:

• Driving score: $${R_i P_i},$$ — Main metric of the leaderboard, serving as the product between the route completion and the infractions penalty. Here $$Ri$$ is the percentage of completion of the $$i−th$$ route, and $$Pi$$, the infraction penalty of the $$i−th$$ route.

• Route completion: Percentage of the route distance completed by an agent.

• Infraction penalty: $$\prod_j^{\text{ped., ..., stop}} ({p_i^j})^{\text{#infractions}_j}.$$ — The leaderboard tracks several types of infractions and this metric aggregates all of these infractions triggered by an agent as a geometric series. Agents start with an ideal 1.0 base score, which is reduced each type an infraction is commited.

When all routes have been completed, a global metric for each of the previous three types is also generated, being the arithmetic mean of all the individual routes combined. The global driving score is the main metric on which you will be classified with respect to other participants.

### Infractions and shutdown events

The CARLA leaderboard offers individual metrics for a series of infractions. Each of these has a penalty coefficient that will be applied everytime it happens. Ordered by severity, the infractions are the following.

• Collisions with pedestrians0.50.
• Collisions with other vehicles0.60.
• Collisions with static elements0.65.
• Running a red light0.70.
• Running a stop sign0.80.

Besides these, there is one additional infraction which has no coefficient, and instead affects the computation of the route completion ($$R_i$$).

• Off-road driving — If an agent drives off-road, that percentage of the route will not be considered towards the computation of the route completion score.

Additionally, some events will interrupt the simulation, preventing the agent to continue. In these cases, the route which is being simulated will be shut down, and the leaderboard will move onto the next one, triggering it normally.

• Route deviation — If an agent deviates more than 30 meters from the assigned route.
• Agent blocked — If an agent doesn’t take any actions for 180 simulation seconds.
• Simulation timeout — If no client-server communication can be established in 60 seconds.
• Route timeout — If the simulation of a route takes too long to finish.

Each time any of the above happens, several details are recorded, which will be displayed as a list for you to see at the route’s individual metrics. Below is an example of a route where the agent both run a red light and deviated from the route.

"infractions": {
"collisions_layout": [],
"collisions_pedestrian": [],
"collisions_vehicle": [],
"outside_route_lanes": [],
"red_light": [
"Agent ran a red light 203 at (x=341.25, y=209.1, z=0.104)"
],
"route_dev": [
"Agent deviated from the route at (x=95.92, y=165.673, z=0.138)"
],
"route_timeout": [],
"stop_infraction": [],
"vehicle_blocked": []
}

The global infractions compress the individual route’s data into a single value and is given as the number of events per Km.

# Get started

In order to get familiar with the leaderboard we recommend you to read carefully through the Get started section. Please, spend enough time making sure everything works as expected locally.

Once you are ready, check the Submit section to learn how to prepare your submission.

# Terms and Conditions

The CARLA Autonomous Driving Leaderboard is offered for free as a service to the research community thanks to the generosity of our sponsors and collaborators.

Teams are provided with a time budget (currently 200 hours) to evaluate their submissions. Each submission will be evaluated in AWS using a g3.8xlarge instance. This gives users access to a dedicated node with a modern GPU and CPU.

Teams are provided a number of submissions (currently 20 submissions) for a given a month.

Both budgets are automatically refilled every month. The organization of the CARLA leaderboard reserves the right to assign additional budget to a team. The organization also reserves the right to modify the default values of the monthly time budget and/or the number of submissions.

It is strictly prohibited to misuse or attack the infrastructure of the CARLA leaderboard, including all software and hardware that is used to run the service. Actions that deviate from the spirit of the CARLA leaderboard could result in the termination of a team.


text:
# Math Help - polar enclossed area integral mmn 15 2b

1. ## polar enclossed area integral mmn 15 2b

i forgot to mention that y>=0 and theta is from 0 to pi

2. Drawing them would be easiest if you converted both equations to cartesians, using $\displaystyle x = r\cos{\theta}, y = r\sin{\theta}, x^2 + y^2 = r^2$.

3. was told to use polar by my prof

4. But you give one equation, $x^2+ y^2= 1$, in Cartesian coordinates! In polar coordinates, that is r= 1. That should be easy to draw. As for $r= 1+ cos(\theta)$, that is what is called a "cardioid". Look it up. As far as graphing is concerned, you could just use the "old fashioned" way- calculate r for a number of $\theta$ values. The are beween them will be the integral of $f_1(\theta)- f_2(\theta)= (1+ cos(\theta))- 1= cos(\theta)$. And the integration will be between values of $\theta$ where the graphs cross: solve $1+ cos(\theta)= 1$.

5. Originally Posted by transgalactic
was told to use polar by my prof
Yes, use polars to evaluate the integral, but you can use Cartesians to aid in graphing...

6. i managed to draw it
but when i made 1=1+sin theta
theta=pi*k
but the drawing gives me pi/2 point
i dont know how to complerte the integral


text:
NumberDBbeta
(searching...)
search tips
The advanced searchbar can be used to search for:
• Lists of real numbers
Use Sage syntax to enter a number, a list of numbers, or a dictionary of the form {param: number}. The lists and dictionaries may be nested. The numbers might be given via formulas involving standard functions such as sin and sqrt, as well as standard constants such as e and pi.
Examples:
• Lists of complex numbers
Similarly one can search for complex numbers. Recommended parents are CIF (complex interval field), CBF (complex ball field), and SR (symbolic ring), although CC (complex field via floats) should work as well unless too much precision is lost during the computation.
Similarly one can search for p-adic numbers in $\mathbb{Z}_p$ and $\mathbb{Q}_p$.
• Lists of polynomials over $\mathbb{Q}$
Similarly one can search for multivariate polynomials over $\mathbb{Q}$. As only expressions are accepted (mainly for safety reasons), we can define the variables as in the following example:


text:
# How to prove $n < \left(1+\frac{1}{\sqrt{n}}\right)^n$

I want to know how to prove the following inequality.

For $n = 1, 2, 3, \ldots$

$$n < \left(1+\frac{1}{\sqrt{n}} \right)^n$$

I tried with math induction but I failed.

• Have you tried putting continuous variable instead of $n$ and then doing some analysis? Nov 25, 2014 at 22:54
• Display the work that you did with induction and we will point you in the right direction for that proof. Nov 25, 2014 at 23:07
• yes, I did with derivative but it's too complex Nov 26, 2014 at 0:13

We have $$\left(1+\dfrac1{\sqrt{n}}\right)^n = \sum_{k=0}^n \dbinom{n}k \dfrac1{n^{k/2}} \geq \underbrace{1 + \sqrt{n} + \dfrac{(n-1)}2 + \dfrac{n(n-1)(n-2)}{6} \dfrac1{n^{3/2}} > n}_{\text{For n \geq 3}}$$ Check for $n=1,2$ manually.

EDIT If you do not want to do the dirty calculus of showing $$1 + \sqrt{n} + \dfrac{(n-1)}2 + \dfrac{n(n-1)(n-2)}{6} \dfrac1{n^{3/2}} > n$$ by showing that the appropriate function is increasing, here is a more logical way. We have $$\underbrace{1 + \sqrt{n} + \dfrac{(n-1)}2 + \dfrac{n(n-1)(n-2)}{6n^{3/2}} > \dfrac{n+1}2 + \dfrac{n^{3/2}}{24}}_{\text{For }n \geq 3}$$ The above inequality comes from the fact that $\sqrt{n} > 0$, $n-1 \geq \dfrac{n}2$ and $n-2\geq \dfrac{n}2$ for $n\geq 3$. We have $\dfrac{n^{3/2}}{24} \geq \dfrac{n}2$ for $n \geq 144$. Put all this together to obtain the result for $n \geq 144$. Write a code to check if it is true for $n=1$ to $n=143$.

• You can lower that limit of 144 even further. Note that $$1 + \sqrt{n} + \dfrac{(n-1)}2 + \dfrac{n(n-1)(n-2)}{6} \dfrac1{n^{3/2}} = \frac{n^{3/2}}{6} + \frac{n}{2} + \frac{n^{1/2}}{2} + \frac{1}{3n^{1/2}} + \frac{1}{2}$$. The RHS is greater than (using the first three terms) $$\frac{n}{2} + \frac{n^{1/2}(n + 3)}{6}$$. It is quite easy to show that $$\frac{n^{1/2}(n + 3)}{6} > \frac{n}{2}$$. This gives you the result, without needing calculus or computing for particular values. Nov 26, 2014 at 8:21

A general approach to study a sequence is first to force some continuous parameter into the problem, and then to use differentiability.

Taking logarithms, one sees that the required inequality holds for some given $n$ if and only if $u(\sqrt{n})\gt0$, where, for every $x\gt0$, $$u(x)=x^2\log(x+1)-(x^2+2)\log(x).$$ Equivalently, $$u(x)=x^2\log\left(1+\frac1x\right)+2\log\left(\frac1x\right)=x^4v(1/x),$$ where the function $v$ is defined by $$v(z)=z^2\log(1+z)+2z^4\log(z).$$ Thus, $$v'(z)=2z\log(1+z)+8z^3\log(z)+\frac{z^2}{1+z}+2z^3.$$ For every $z$ in $(0,1)$, $$z\log z\geqslant-\mathrm e^{-1},\qquad 2\log(1+z)\geqslant2z-z^2,$$ hence $$v'(z)\geqslant2z^2-z^3-8\mathrm e^{-1}z^2+\frac{z^2}{1+z}+2z^3=(3-8\mathrm e^{-1})z^2+\frac{z^4}{1+z}\gt0,$$ since $3\mathrm e\gt8$. Thus, $v$ is increasing and, since $v(0)=0$, $v(z)\gt0$ for every $z\gt0$, hence $u(x)\gt0$ for every $x\gt0$, which implies the result.

• How did you get the last equality ($3^{rd}$ last line, the middle part), I get; $2z^2-z^3-8e^{-1}z^2+\frac{z^2}{1+z}+2z^3\overset{3e\ge 8}\ge 2z^2-z^3-3z^2+\frac{z^2}{1+z}+2z^3=\frac{z^2(z^2-1)+z^2}{1+z}>0$ BUT in the beginning after equivalently, I have: $u(x)=x^2\log(1+\frac1x)-2\log(\color{red}{x})$ Just say, if I'm wrong
– OBDA
Nov 26, 2014 at 11:15
• @OBDA Well, $-2\log(x)=+2\log\left(\frac1x\right)$.
– Did
Nov 26, 2014 at 12:41

We have that

$$n < \left(1+\frac{1}{\sqrt{n}} \right)^n\iff \ln n< n\ln \left(1+\frac{1}{\sqrt{n}} \right)\iff \frac{\ln n}{n}<\ln \left(1+\frac{1}{\sqrt{n}} \right).$$

Now, we use the inequalities (see $(3)$ in http://ajmaa.org/RGMIA/papers/v7n2/pade.pdf)

$$$$\frac{2x}{2+x}\le \ln (1+x)\le \frac{x}{2}\frac{2+x}{1+x}, \quad x>0.\tag{1}$$$$

In our case, we get from $(1),$ $$\ln \left(1+\frac{1}{\sqrt{n}} \right)\ge \frac{2}{\sqrt{n}+2}.$$

Thus we only have to show

$$\frac{2}{\sqrt{n}+2}>\frac{\ln n}{n}.$$ That is,

$$\ln n<\frac{2n}{\sqrt{n}+2}.$$ Since $\ln n=2\ln \sqrt{n}$ previous inequality is equivalent to

$$\ln \sqrt{n}<\frac{n}{\sqrt{n}+2}.$$ Now, using again $(1)$

$$\ln \sqrt{n}=\ln (1+\sqrt{n}-1)\le \frac{\sqrt{n}-1}{2}\frac{\sqrt{n}+1}{\sqrt{n}}=\frac{n-1}{2\sqrt{n}}.$$ Thus we have to show

$$\frac{n-1}{2\sqrt{n}}<\frac{n}{\sqrt{n}+2}.$$ But

$$\frac{n-1}{2\sqrt{n}}<\frac{n}{\sqrt{n}+2}\iff 2(n-1)<(n+1)\sqrt{n},$$ which holds for any $n\in\mathbb{N}.$

• @mfI How do you prove the last inequality? Aug 22, 2015 at 9:50
• Also.. formula copied is incorrect. It's 2x/(2+x); and not 2x/(2x+1) right? @mfl Aug 22, 2015 at 10:12
• @Kugelblitz You are right. Typo fixed. In order to prove the las inequality just note that $$\frac{n-1}{2\sqrt{n}}<\frac{n}{\sqrt{n}+2}\iff (\sqrt{n}+2)(n-1)<2n\sqrt{n}\iff 2(n-1)<(n+1)\sqrt{n}$$
– mfl
Sep 7, 2015 at 0:39

Hint:

$U=\left\{\left(1+\dfrac{1}{x}\right)^x: x\geq1\right\} \implies \inf U=2<\left(1+\dfrac{1}{\sqrt{n}}\right)^\sqrt{n}$

$$\color{blue}{\boxed { n \leq 2^{\sqrt{n}} \implies {n<\left(1+\dfrac{1}{\sqrt{n}}\right)^n}\ \ \ \forall n\geq16}}$$

• "Hint"??
– Did
Nov 26, 2014 at 7:20
• if n = 8, then the left side is no longer valid? Nov 26, 2014 at 11:32
• @AllenJung: Now the range of the values is included.
– user170039
Nov 26, 2014 at 13:12
• @Did: See the edit.
– user170039
Nov 26, 2014 at 13:38

$n<(1+\frac{1}{\sqrt{n}})^{n}$

$n^{1/n} < 1+1/\sqrt{n}$

$n^{1/n + 1/2} < \sqrt{n}+1$

$(n^{(2+n)/2n} -1) < \sqrt{n}$

$n^{(2+n)/n} - 2n^{(2+n)/2n} +1 < n$

$n*n^{2/n} - 2\sqrt{n}*n^{1/n} +1 < n$

For large possible values of "n", then we can use $$lim_{n->∞}n^{1/n} = 1$$ to approximate the original $$n*n^{2/n} - 2\sqrt{n}*n^{1/n} +1 < n$$ quite closely as $$n*1^2 - 2\sqrt{n}*1 +1 < n$$ or, more simply, $$n - 2\sqrt{n} +1 < n$$ $$1-2\sqrt{n}<0$$

This works for all possible values of "n" large enough for the previous approximation to work for, and if you are looking at "n" values that you feel are too small for the approximation to work, then you are looking at "n" values small enough to use trial and error.

• Can you please add the number of cases you want to solve be trial and error to prove that the statement holds for n > 1. Nov 26, 2014 at 0:02


text:
# 1989 AHSME Problems/Problem 19

## Problem

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What is the area of the triangle?

$\mathrm{(A) \ 6 } \qquad \mathrm{(B) \frac{18}{\pi^2} } \qquad \mathrm{(C) \frac{9}{\pi^2}(\sqrt{3}-1) } \qquad \mathrm{(D) \frac{9}{\pi^2}(\sqrt{3}-1) } \qquad \mathrm{(E) \frac{9}{\pi^2}(\sqrt{3}+3) }$

### Solution

The three arcs make up the entire circle, so the circumference of the circle is $3+4+5=12$ and the radius is $\frac{12}{2\pi}=\frac{6}{\pi}$. Also, the lengths of the arcs are proportional to their corresponding central angles. Thus, we can write the values of the arcs as $3\theta$, $4\theta$, and $5\theta$ for some $\theta$. By Circle Angle Sum, we obtain $3\theta+4\theta+5\theta=360$. Solving yields $\theta=30$. Thus, the angles of the triangle are $90$, $120$, and $150$. Using $[ABC]=\frac{1}{2}ab\sin{C}$, we obtain $\frac{r^2}{2}(\sin{90}+\sin{120}+\sin{150})$. Substituting $\frac{6}{\pi}$ for $r$ and evaluating yields $\frac{9}{\pi^2}(\sqrt{3}+3)\implies{\boxed{E}}$.

-Solution by thecmd999

## Solution 2 (no trig)

Since we know that the triangle is inscribed, we can use the properties of inscribed angles to solve the problem. At first, we can ignore actual lengths in this problem, and use the $3$, $4$, and $5$ as ratios instead of the actual numbers. There are $360$ degrees in a circle, so $3x + 4x + 5x = 360$, where we find $x$ to be $30$ degrees. Thus, the arc measures in degrees becomes $90$, $120$, and $150$. With this knowledge, the angle that cuts off the arc of length $3$ is $45$ degrees (an inscribed angle is $\frac{1}{2}$ the measure of the arc that it intercepts). Similarly, the angle cutting off length $4$ is $60$ degrees, and the last angle of the triangle is $75$ degrees.

Upon observing this figure, we can draw an altitude in the triangle, breaking it into two triangles, one being a 30-60-90 and the other being a 45-45-90. For now, we can set the leg of the 30-60-90 angle that is adjacent to the 60 degree angle as "x." This makes the other leg of the 30-60-90 degree angle to be x√3, and since that happens to be the altitude and also part of the 45-45-90 triangle, it makes both legs of the 45-45-90 triangle to be x√3. We sum together the areas of both triangles and get (x^2√3 + 3x^2)/2, or x^2(√3+3)/2.

Now it's time to actually find the value of x and plug it in. In order to find the value of x, we can use the length of the radius, which we identify as "r." Now, looking back at what we had earlier about the arcs, the arc of length 3 is 90 degrees, which is one-fourth of the circumference. The circumference itself is equal to 2rπ. So we can write this equation: 3 = 2rπ/4, making r = 6/π. Now we must find the relationship of r to x, but we don't have to look far to find it. In fact, if we draw the center of the circle and connect two radii from it to points of arc length 3, we see that it creates another 45-45-90 triangle, where r is the length of the leg, and as we see from earlier, the length of that hypotenuse is 2x. Since the hypotenuse is equal to the leg multiplied by √2 in such a triangle, we write this equation: 2x = 6√2/π, and x = 3√2/π. Now, we plug our new value of x into the equation x^2(√3+3)/2. Doing so, we get $\frac{9}{\pi^2}(\sqrt{3}+3)\implies{\boxed{E}}$.


text:
## Lexical and sublexical effects on diachronic stability and instability of phonological systems : A case study on Proto-Indo-European dorsal stops

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##### Files
There are no files associated with this item.
2022
Journal article
Published
##### Published in
Lingua ; 273 (2022). - 103308. - Elsevier. - ISSN 0024-3841. - eISSN 1872-6135
##### Abstract
Lexical and sublexical conditions such as a word’s phonological contrast to other words in a lexicon or the informativity of a segment in its context can influence the likelihood that certain linguistic changes occur. This paper sets out to investigate whether the effects of segment informativity and segment contrast apply to larger sets of phonological units, thus contributing to the diachronic stability or instability of natural classes or phonological series in a language. The test case for this analysis are the Proto-Indo-European dorsal stops and laryngeal series which underwent iconic changes in many daughter languages. The investigation replicates previous findings and shows that phonological contrast and segment informativity have contributed to the changes and pathways of these Proto-Indo-European consonant series. As a result, the findings suggest that lexical and sublexical effects can contribute in part to the diachronic stability of larger phonological units in a language.
##### Subject (DDC)
400 Philology, Linguistics
##### Cite This
ISO 690HARTMANN, Frederik, 2022. Lexical and sublexical effects on diachronic stability and instability of phonological systems : A case study on Proto-Indo-European dorsal stops. In: Lingua. Elsevier. 273, 103308. ISSN 0024-3841. eISSN 1872-6135. Available under: doi: 10.1016/j.lingua.2022.103308
BibTex
@article{Hartmann2022Lexic-58051,
year={2022},
doi={10.1016/j.lingua.2022.103308},
title={Lexical and sublexical effects on diachronic stability and instability of phonological systems : A case study on Proto-Indo-European dorsal stops},
volume={273},
issn={0024-3841},
journal={Lingua},
author={Hartmann, Frederik},
note={Article Number: 103308}
}

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Yes
Yes


text:
# Gender Equality in STEM Programs

Recently I’ve been interested in investigating how gender equality – or equivalently, inequality – has evolved over time in Canada. Using the University of Waterloo’s public Cognos cubes, specifically those for undergraduate enrollment, I have found some pretty interesting results. Below, I will detail a brief summary of these findings.

To begin, let’s talk a bit more about our population of study and the data that is used in our analysis. The target population that I’m examining here is set of all undergraduate university students and the sample population is the set of all undergraduate students who have enrolled at the University of Waterloo. The sample chosen in the analysis is the sample population restricted to students who have enrolled between 1996 to 2013 where terms are only selected in the sample if there are at least 20 distinct programs with at least 1 student in them. We make no distinction between students enrolled in or not enrolled in a co-operative program.

All analysis and visualization is done in the free academic version of Revolution R, Version 7.

For each date, at the Program (e.g. Life Sciences) and Faculty (e.g. Science) level, a total is computed for each of the female and male genders and the percentage of females is then calculated as |Females|/(|Males| + |Females|). A rendered ordered bar chart at each date, with the Program on the x-axis and percentage female on the y-axis, is then generated using the ggplot2 R package and a GIF animation of these charts is produced to study the time evolution as seen below.

Bar colors are dependent on the Faculty of the Program. Click the image above to properly view the animation.

The abbreviations for each Program can be clarified here. A quick scan over the image shows that there does not appear to be any noticeable change in the overall shape other than a -very- slight flattening of the center bars and slight increase in the slopes near the extreme ends during later years.

Using this data, I use the following method as a crude estimate for Faculty-wide, time dependent gender bias, where I define this as how gender bias a Faculty is relative to past or future states or enrollments of the university. Suppose that for a fixed date we have $n$ programs and $P=\{P_{1,F1}, P_{2,F2}, ..., P_{n,Fn}\}$ is a set of ordered values of percentages of females in $n$ different programs, ordered by least to greatest percentage of females in the first index, and where the second index is representative of the Faculty in which the program falls under. Let $P_{F}=\{P_{k,Fk} \in P: Fk = F\}$ and $n_{F} = | P_{F} |$. Then for each Faculty $F$, we denote the (female-dominated) gender bias as

$G(F)= (P_{n_{F},Fn_{F}}+P_{n_{F-1},Fn_{F-1}}+P_{n_{F-2},Fn_{F-2}}) / 3n$

Which we can think of as a three term average [1] of the quantile of the three most female dominated programs. A value close to 100% (less biased) is generally preferred.

Taking only the STEM Faculties into consideration (SCI, ENG, MATH), we plot out this measure over time using the lattice R package below:

The blue circles indicate points in time, the red lines are LOESS curves and the green lines are smoothing splines. The science faculty seems to follow a rather sinusoidal trend, the engineering faculty a mostly linear trend, except for the sudden rise in the 2003-2005 date range, and the maths faculty being the most sporadic of the three. There is an apparent outlier near the 2008 year in the maths faculty, although this may be explained by the increased interest in the new FARM program and other finance related programs in light of the latest U.S. recession.

A least squares regression with slope and intercept interaction factors is also done in R for computing long term trends and is shown below:

Here, Idx is just a normalized Date variable. From the results, we can see that the long-run growth in the MATH and SCI Faculties are not significantly different from one another and we can expect a long-term growth of female gender bias of approximately 0.23% every term in these faculties in the near future, while for engineering, this is closer to 0.03%.

With this in mind, it looks like we won’t be seeing fair gender equality for at least 2 decades for the sciences and several times that amount for the mathematics and engineering faculties.

To replicate these results, as well as see the charts above in higher resolution and examine the source data, you can check out the relevant Skydrive directory here.

If you have any comments or suggestions for future statistical projects, let me know in the comments section below.

[1] An average is done here in order to smooth out any outliers, which from the data we can see a few, particularly in the architecture program.


text:
# When are Monte Carlo methods preferred over temporal difference ones?

I've been doing a lot of research about Reinforcement Learning lately. I followed Sutton & Barto's Reinforcement Learning: An Introduction for most of this.

I know what Markov Decision Processes are and how Dynamic Programming (DP), Monte Carlo and Temporal Difference (DP) learning can be used to solve them. The problem I'm having is that I don't see when Monte Carlo would be the better option over TD-learning.

The main difference between them is that TD-learning uses bootstrapping to approximate the action-value function and Monte Carlo uses an average to accomplish this. I just can't really think of a scenario when this is the better way to go.

My guess is that it might have something to do with performance but I can't find any sources that can proof this.

Am I missing something or is TD-learning generally the better option?

The main problem with TD learning and DP is that their step updates are biased on the initial conditions of the learning parameters. The bootstrapping process typically updates a function or lookup Q(s,a) on a successor value Q(s',a') using whatever the current estimates are in the latter. Clearly at the very start of learning these estimates contain no information from any real rewards or state transitions.

If learning works as intended, then the bias will reduce asymptotically over multiple iterations. However, the bias can cause significant problems, especially for off-policy methods (e.g. Q Learning) and when using function approximators. That combination is so likely to fail to converge that it is called the deadly triad in Sutton & Bart.

Monte Carlo control methods do not suffer from this bias, as each update is made using a true sample of what Q(s,a) should be. However, Monte Carlo methods can suffer from high variance, which means more samples are required to achieve the same degree of learning compared to TD.

In practice, TD learning appears to learn more efficiently if the problems with the deadly triad can be overcome. Recent results using experience replay and staged "frozen" copies of estimators provide work-arounds that address problems - e.g. that is how DQN learner for Atari games was built.

There is also a middle ground between TD and Monte Carlo. It is possible to construct a generalised method that combines trajectories of different lengths - from single-step TD to complete episode runs in Monte Carlo - and combine them. The most common variant of this is TD($\lambda$) learning, where $\lambda$ is a parameter from $0$ (effectively single-step TD learning) to $1$ (effectively Monte Carlo learning, but with a nice feature that it can be used in continuous problems). Typically, a value between $0$ and $1$ makes the most efficient learning agent - although like many hyperparameters, the best value to use depends on the problem.

If you are using a value-based method (as opposed to a policy-based one), then TD learning is generally used more in practice, or a TD/MC combination method such as TD(λ) can be even better.

In terms of "practical advantage" for MC? Monte Carlo learning is conceptually simple, robust and easy to implement, albeit often slower than TD. I would generally not use it for a learning controller engine (unless in a hurry to implement something for a simple environment), but I would seriously consider it for policy evaluation in order to compare multiple agents for instance - that is due to it being an unbiased measure, which is important for testing.

• First off, thanks for the answer. I see how in theorie an unbiased algorithm could be preferred over a biased one. But considering the high variance Monte Carlo can give at the start of training, I don't see how this really matters. Both Monte Carlo and TD will start with inaccurate approximations and from what I've read, TD will converge much faster. I just can't really come up with a practical advantage of using Monte Carlo. (Amusing the deadly triad can be avoided) – Anne-dirk Mar 27 '18 at 8:10
• @Anne-dirk If you are using a value-based method (as opposed to a policy-based one), then TD learning is generally used more in practice, or a TD/MC combination method such as TD(λ) can be even better. I am not sure what you mean by "practical advantage"? Monte Carlo learning is conceptually simple, robust and easy to implement. I would generally not use it for a learning controller engine (unless in a hurry to implement something for a simple environment), but I would seriously consider it for policy evaluation in order to compare multiple agents for instance. – Neil Slater Mar 27 '18 at 8:53
• @Neul Slater Aaaah I see... That's the kind of answer I was looking for :) Thanks for your help! – Anne-dirk Mar 27 '18 at 9:16

Essentially it depends on your environment.

TD exploits the Markov property, i.e. the future states of a process rely only upon the current state, and therefore it's usually more efficient to use TD in Markov environments.

MC does not exploit the Markov property as it bases rewards on the entire learning process, which lends itself to non-Markov environments.

• I don't think this is correct or, at least, obvious to see. The Markov property, in the context of RL, is associated with the states. Can you please clarify why MC algorithms would work better when the Markov property would not be satisfied? – nbro Feb 22 '19 at 16:30
• To be clear, I was referring to efficiency. If you can exploit the Markov property then TD is advantageous because you can start in any given state, take and action and the result will always be the same, so you can compute the TD error with high levels of certainty. With non-MDP if you get a state that is partially observed then TD may not be very efficient. That's not to say you can't use TD in non-MDPs, you can, but it might be inefficient and may get better success with TD lambda rather than TD(1). – BigBadMe Feb 23 '19 at 0:04
• "If you can exploit the Markov property then TD is advantageous because you can start in any given state, take and action and the result will always be the same", it will be the same if the environment is deterministic. What does this have to do with the Markov property? I don't get your claims. Where did you read that TD will be more inefficient than MC in e.g. POMDPs? – nbro Feb 23 '19 at 10:46
• It literally has everything to do with it being Markov; if you're in a Markov environment then once you establish taking action a in state a it will lead will state a' with reward x - that will always be the case in a markov environment, so you don't need to evaluate it over and over - you can take bigger steps and TD enables you to exploit that. But it won't be the case in a POMDP because you can have exactly the same state, take same action, but end up in completely different states and rewards. – BigBadMe Feb 23 '19 at 14:55
• "if you're in a Markov environment then once you establish taking action a in state a it will lead will state a' with reward x". No. This is only true if the environment is deterministic. The environment can also be stochastic. "that will always be the case in a markov environment", No, this is an orthogonal issue to the Markov property. – nbro Feb 23 '19 at 14:59


text:
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IM

# The following bar graph shows each month's average daily lowtemperature in degrees Fahrenheit for Barrow, Alaska. Use this graph to answer Exercises 87 through 92(Graph cannot copy)Find the average of the temperatures shown for the months of April, May, and October. (To find the average of three temperatures, find their sum and divide by 3 .)

## $4.7^{\circ} \mathrm{F}$

### Discussion

You must be signed in to discuss.

### Video Transcript

Okay, This question is asking us to find the average for April, May and October. So April May in October. And so if you look back at your picture, April is negative. 9.1 May is 14.4 and October is 8.8. So to find the average, we're gonna add these three numbers up and then we'll divide by three. So if you had your 1st 2 numbers up, let's see 14.4 minus 9.1 four minus one is 3 14 minus nine five. So we have 5.3 plus 8.8. If you add up 5.3 and 8.8, let's see 5.3 8.8 Adam up gives you a one carry. The one gives you a four Gary, the ones of 14 0.1 and then define the average. We divide by three because they were three months so 14.1, divided by three with equal two point. Sorry not to for 0.7. Here, let me redo that. Tim So 14.1, divided by three is four point

IM
University of Oregon


text:
# Nodal analysis - w/ dependent current source

Discussion in 'Homework Help' started by castrogfx, Apr 13, 2012.

1. ### castrogfx Thread Starter New Member

Apr 13, 2012
4
0
Hi,
I think this problem is easy, but I can't do it.

---
Node A is on the left, node B is on the right.

So,
A) $i_2 + i_4 = i_1 + i_3$
B) $i_3 + i_7 = i_6 + i_5$

$i_1=\frac{v_1}{5}$, $i_2=-3A$, $i_3=\frac{v_1 - v_2}{20}$, $i_4 = i_5 = 3 i_1 = \frac{3 v_1}{5}$, $i_6=\frac{v_2}{10}$, $i_7= 10 A$

A) $-3 + \frac{3 v_1}{5} = \frac{v_1}{5} + \frac{v_1 - v_2}{20}$

B) $\frac{v_1 - v_2}{20} + 10 = \frac{v_2}{10} + \frac{3 v_1}{5}$

I have this system of linear equations:

$-60 = -7v_1 - v_2$
$200 = 13v_1 + 3v_2$

$v_1 = -2.5 V
v_2 = 77.5 V$

$i_1 =\frac{-2.5}{5} = -.5 A$

Thanks for the help!

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
The dependent source seems to be a CCVS despite having a symbol typical of a CCCS. However the answer of 2A is correct if it is a CCCS. I note you have I7 as 10A. Do you now see the error?

Last edited: Apr 13, 2012
castrogfx likes this.
3. ### castrogfx Thread Starter New Member

Apr 13, 2012
4
0
I've tried this so many times that I copied wrong in a moment.
Unbelievable.
Thanks t_n_k for the help, I really appreciated it.

4. ### Jony130 AAC Fanatic!

Feb 17, 2009
4,774
1,340
castrogfx likes this.


text:
# Thread: Simplify and write each as a single power.

1. ## Simplify and write each as a single power.

Hey guys,

the task: Simplify. Write each as a single power. Do not evaluate.

(-Q)^2 (-Q)^5 (-Q)

my final answer would be = -Q^8

It should be = -Q^8 = (-1*Q)^8 = (-1)^8 Q^8 = Q^8

Could somebody explain why?

2. ## Re: Simplify and write each as a single power.

$\displaystyle (-q)^2=+q^2$

$\displaystyle (-q)^5=-q^5$

(-2)^7
-------
(-2)^3

4. ## Re: Simplify and write each as a single power.

=(-2)^(7-3=4) = +(2)^4


text:
1. Home
2. Algebra
3. Radical Functions and Equations

# Transformations of radical functions - Radical Functions and Equations

### Transformations of radical functions

It is always so much easier to tell the domain and range of a function from its graph. In this lesson, we will learn how to graph out a radical function by using a table of value and transformations.


text:
# Syllabus

## Description

This course picks up where Harvard College’s CS50 leaves off, diving more deeply into the design and implementation of web apps with Python, JavaScript, and SQL using frameworks like Django, React, and Bootstrap. Topics include database design, scalability, security, and user experience. Through hands-on projects, students learn to write and use APIs, create interactive UIs, and leverage cloud services like GitHub and Heroku. By semester’s end, students emerge with knowledge and experience in principles, languages, and tools that empower them to design and deploy applications on the Internet.

## Prerequsisites

CSCI E-50, CS50x, or prior experience in any programming language.

## Expectations

You are expected to

• watch all lectures,
• implement five assigned projects, and
• design and implement a final project.

Your final grade will be based on your performance on the course’s projects, each of which will bear equal weight. Projects (except for Project 0) will be evaluated along the axes of correctness, design, and style, with each project’s overall score computed as 3 × correctness + 2 × design + 1 × style. Scores are normalized across TFs at term’s end, so mid-semester comparisons among students of scores are not reliable indicators of standing.

• Correctness refers to the extent to which your code is consistent with the project’s specifications and free of bugs.
• Design refers to the extent to which your code is written well (i.e., efficiently, elegantly, and logically).
• Style refers to the extent to which your code is readable (i.e., clear, consistent, commented, indented, with variables aptly named). This includes, but is not limited to, adherence to Python’s style guide, which you can verify using pycodestyle.

For Project 0, only the axis of correctness will be evaluated.

## Lectures

date topic
Lecture 0 8/31 HTML and CSS
Lecture 1 9/7 Git
Lecture 2 9/7 Python
Lecture 3 9/14 Django
Lecture 4 9/28 SQL, Models, and Migrations
Lecture 5 10/12 JavaScript
Lecture 6 10/26 User Interfaces
Lecture 7 11/9 Testing, CI/CD
Lecture 8 11/23 Scalability and Security

## Sections

Lectures are supplemented by weekly sections led by the teaching fellows. A schedule will be posted on the course’s website.

## Office Hours

Office hours are opportunities for guidance and feedback from the staff on projects as well as for discussion of the course’s material more generally. A schedule will be posted on the course’s website.

## Projects

released due
Project 0 Mon 8/31
Project 1 Mon 9/14
Project 2 Mon 9/28
Project 3 Mon 10/12
Project 4 Mon 11/2
Final Project Mon 11/16

## Late Policy

For each minute that a project is turned in late, the course will impose a 0.01% deduction on your grade for the project. (Therefore, a project that is a week late will earn no credit at all.) Only in extenuating circumstances will exceptions be considered.

Late work will not be accepted for the final project.

This course’s philosophy on academic honesty is best stated as “be reasonable.” The course recognizes that interactions with classmates and others can facilitate mastery of the course’s material. However, there remains a line between enlisting the help of another and submitting the work of another. This policy characterizes both sides of that line.

The essence of all work that you submit to this course must be your own. Collaboration on assigned projects is not permitted except to the extent that you may ask classmates and others for help so long as that help does not reduce to another doing your work for you. Generally speaking, when asking for help, you may show your code to others, but you may not view theirs, so long as you and they respect this policy’s other constraints. Collaboration on the course’s final project is permitted to the extent prescribed by its specification.

Below are rules of thumb that (inexhaustively) characterize acts that the course considers reasonable and not reasonable. If in doubt as to whether some act is reasonable, do not commit it until you solicit and receive approval in writing from the course’s heads. Acts considered not reasonable by the course are handled harshly. If the course refers some matter for disciplinary action and the outcome is punitive, the course reserves the right to impose local sanctions on top of that outcome that may include an unsatisfactory or failing grade for work submitted or for the course itself. The course ordinarily recommends exclusion (i.e., required withdrawal) from the course itself.

Regret clause. If you commit some act that is not reasonable but bring it to the attention of the course’s heads within 72 hours, the course may impose local sanctions that may include an unsatisfactory or failing grade for work submitted, but the course will not refer the matter for further disciplinary action except in cases of repeated acts.

### Reasonable

• Communicating with classmates about projects in English (or some other spoken language).
• Discussing the course’s material with others in order to understand it better.
• Helping a classmate identify a bug in his or her code at office hours, elsewhere, or even online, as by viewing, compiling, or running his or her code, even on your own computer.
• Incorporating a few lines of code that you find online or elsewhere into your own code, provided that those lines are not themselves solutions to projects and that you cite the lines’ origins.
• Sending or showing code that you’ve written to someone, possibly a classmate, so that he or she might help you identify and fix a bug.
• Sharing a few lines of your own code online so that others might help you identify and fix a bug.
• Turning to the web or elsewhere for instruction beyond the course’s own, for references, and for solutions to technical difficulties, but not for outright solutions to projects.
• Whiteboarding solutions to projects with others using diagrams or pseudocode but not actual code.
• Working with (and even paying) a tutor to help you with the course, provided the tutor does not do your work for you.

### Not Reasonable

• Accessing a solution to some project to (re-)submitting your own.
• Asking a classmate to see his or her solution to a project before (re-)submitting your own.
• Decompiling, deobfuscating, or disassembling the staff’s solutions to projects.
• Failing to cite (as with comments) the origins of code or techniques that you discover outside of the course’s own lessons and integrate into your own work, even while respecting this policy’s other constraints.
• Giving or showing to a classmate a solution to a project when it is he or she, and not you, who is struggling to solve it.
• Paying or offering to pay an individual for work that you may submit as (part of) your own.
• Searching for or soliciting outright solutions to projects online or elsewhere.
• Splitting an assigned project’s workload with another individual and combining your work.
• Submitting (after possibly modifying) the work of another individual beyond the few lines allowed herein.
• Submitting the same or similar work to this course that you have submitted or will submit to another.
• Submitting work to this course that you intend to use outside of the course (e.g., for a job) without prior approval from the course’s heads.
• Viewing another’s solution to a project and basing your own solution on it.

## Acknowledgement and Authorization

Harvard plans to record audio, photos, and video of this course’s lectures, labs, sections, office hours, and other events and activities related to the course (the “Recordings”), with the aims of making the content of the course more widely available and contributing to public understanding of innovative learning (the “Projects”). The Recordings, or edited versions of them, may be made available to other Harvard students, to students at other educational institutions, and to the broader public via edX, the Internet, television, theatrical distribution, digital media, or other means. It is also possible that the Recordings may be used to make other derivative works in the future. Students may elect not to appear in photos and video used in the Projects and may still participate fully in the course.

When you submit the course’s first project, you will need to sign online an Acknowledgement and Authorization in the following form:

I understand that, if I do not wish any photos or video of me to be used as part of the Projects, I should so inform the course’s instructor by emailing recordings@cs50.harvard.edu within one week of enrolling in the course. In that event, I understand that I should sit in the designated “no-film” zone of the course’s classrooms and should not walk in the field of view of the cameras. I understand that Harvard will take reasonable steps, with my cooperation, to avoid including identifiable images of me in the Projects’ photos and video shot in classrooms and other course locations after I opt out as just described. I understand that I am free to opt out of the Projects’ photos and video in this way, and that doing so will not affect my grade or my ability to participate in course activities.

Unless I opt out of the Projects’ photos and video as described above and take the steps that will be outlined by the instructor to avoid being filmed, I authorize Harvard and its designees to record and use photos and video of my participation in the course and activities related to the course (the “Recordings”). I understand and agree that the Recordings may include my image, name, and voice. I also understand and agree that, even if I opt out of the Projects’ photos and video, my spoken name and voice may be picked up by microphones outside the “no-film” zone and may be included in the Recordings.

I understand and agree that Harvard and its designees will have the irrevocable, worldwide right to make, edit, modify, copy, publish, transmit, distribute, sell, publicly display, publicly perform, and otherwise use and make available its respective Recordings and any other works that may be derived from those Recordings, in any manner or medium now known or later invented, and to authorize others to do so as well. I hereby transfer to Harvard any rights, including copyrights, I may have in the Recordings that Harvard makes. I will remain free to use and disseminate any ideas, remarks, or other material that I may contribute to course discussions.

I acknowledge and agree that I will not be entitled to any payment, now or in the future, in connection with the Recordings or any works derived from them. This Acknowledgment and Authorization is a binding agreement, and is signed as a document under seal governed by the laws of the Commonwealth of Massachusetts.

Unless you opt out as described in the Acknowledgment and Authorization, you are agreeing, by attending the course, that your participation in the course and related activities may be recorded and used by Harvard in connection with the Projects without further obligation or liability to you, even if you do not sign any authorization.

If you have any questions about the above, contact recordings@cs50.harvard.edu.