So I guess we're a little, we're definitely early. We're definitely on the clock Welcome to speaker workshops and now it is the 210 talk and Once they just have a little bit to say about our presenters Sam Herb. So Sam Herb, but just real quick, Counselor 9 and I Also, I I think you're the very first black badge holder. I know personally Is way is that a radio? That's radioactive, right? Is that the radioactive one or thou shall not speak of it? Are we gonna like to sing on fire? Without much ado, Sam Herb. Thank you So A long time listener first time speaker, so let's get going So you're gonna connect to the wrong domain name. So for whatever reason for the past few years, I've been very interested in domain names and this is kind of a look at some of the Different ways that you can be tricked or your computer can be tricked Or you could be fished to connect to the wrong domain name So a bit about myself Software engineer, I work at a cool company called Akamai.  I have to say that and I have a Defcon 23 and Defcon 24 Uber black badge with Counselor 9 Yeah, that's me at clothing ceremonies last year a disclaimer The opinions expressed here are my own and known with fish in the creation of this presentation, which will become a bit more obvious later on Yeah, so I'm gonna start out from kind of least severe and kind of build up from there And so just to get going we have to start out with typosquadding Humans aren't perfect. They're gonna connect. They're gonna mistype the domain name they type in and unless this person could register these and Trick somebody into entering their bank credentials for instance So so this example here is looking at all the one keyboard letter off variants of American Express comm If you actually look up the registration status of each of these Like the example is Q American Express comm all but two of them are actually currently registered or actively registered as of April I believe I Did all this in they most of the research here in April 2017, so that's roughly when all the status from So the reason why I chose American Express here is that it's long enough that no one's company name It's gonna be Q American Express comm whereas with a shorter website You might get some legitimate websites, whereas I could argue that none of these are actually legitimate So building up from there we have to look at bitsquadding This is one where your computer is actually gonna get the domain name wrong by flipping a bit If the example I gave here is a I swapped a bit on Google analytics and I end up with Eagle analytics This is a very low probability event, but as most Phones and compute personal electronic devices don't have error correcting memory. This happens at a non-zero rate across the internet So in order to give a demo for this talk I actually want to register one of these domains and so I actually searched for the one-bit variance of Google analytics comm So part of the reason for looking at Google analytics comm is you want a website that people are gonna visit a lot, but not mistype Google analytics falls in that as though most CDNs So when I searched for domains, this was the only one available So I went ahead and registered it And I put up a server on it and got TLS certificate for it and within 24 hours. I saw two what I would call hits one HTTP one HTTPS This is two One an Android browser and one Android application actually connecting to my server If you actually go and look at the source Website of where this came from the source website says Google analytics comm but something within their phone Caused a bit to flip in such a way that they went to the wrong website now One other thing when I actually so with it with a very popular website This is from what I've seen. This is about what to expect. You'll get a few random hits per day Once I got these heads I actually took this down But I when I turned on this website. I immediately was getting spammed by this one very particular no main name And so I went to it and then it was actually a It was a Swedish diving companies website had somehow managed to Mess up their Google analytics tag to point to my website. So every person that was visiting their website was also been connecting to this That's a picture of the code at the bottom there. It's a little bit hard to read from a distance But it's pointing to eagle analytics comm Yeah So That's just the example of how to do this. There's a If you're looking for more information on this, there's actually a really great white paper that Cisco put out And I believe it's actually on defconn.org if you search for it Or sorry, no, that's something later. I'm getting these confused There was a talk at DC-19 on this. I believe that's what it was Yeah and so Being familiar with bitsquadding I wanted to look at Or no, so yeah, there was a Cisco white paper. Yeah, that was this so I Wanted to look at some other variants of bitsquadding And one thing that I noticed is that there are have been some recent registered Top-level domain names or TLDs that actually bitsquad on other TLDs so in this case the registrar Requested.got.got which bitsquads.gov I reported that one in April of 2016 to the registrar and they claim to have implemented a fix It's not actually testable right now because you can't actually register those domains, but That's a very tractable problem because there's a limited number of.gov websites However a recent one which is.bom actually bitsquads.all of.com which is a much more Intractable problem as there are a large number of.com domain names A funny thing about.bom is that it was actually objected to by Verisign because it looks too similar to.com And that objection was overruled, but it also bitsquads.com which is very unfortunate I know it didn't report that one as I Not sure what value there would be from reporting that But yeah, so it's this is actually something that was mentioned in the Cisco white paper, but these are More recent TLDs from that point So gain of so Bitsquad and can only like I said before it only really targets random end users you can't really target a Pacific user with it but you could target a user base such as a Bank if you could only steal a few credentials per day that could still be a lot of money or if you're bitsquad.gov website that could You know get you a few inbound emails to Intelligence agency per day which could be significant So going to the next slide So I'm getting a bit more serious So a lot of the reason why I gave this talk actually is I want to look at IDN homoglyphs A homoglyph are homoglyphs are two characters that look the same But have different meanings And IDN is an internationalized domain name, which is something that if you're an English language speaker you might not come across very often It's and depending on your browser you'll either see the Their source Pini code, which is Xn dash dash Or the ASCII equivalent of that Pini code is a way to encode a encode a larger character set into a smaller space and the format that's used you have the Xn dash dash identifier This is all standardized followed by the Essentially English alphabet letters or standard letters followed by a dash followed by a There's a standardized algorithm for actually computing what comes after that There's a RFC on and everything I'm Yeah, I'm not gonna give a great estimation of that so I won't And so with that you can end up with a so the same machine will determine which letter and what location it will get placed into the URL that gets rendered And I so I gave two examples here These are actually both registered domain names Google.com where both the O's are Cyrillic O's and Time I believe there's Cyrillic O's. It might be Latin. Sorry, and Time.com where every letter is actually from the Cyrillic alphabet And I'll show you how I found those later. Those are both actually registered domain names So I wanted to conduct a survey of existing homo glyphs And IDN domain names against popular.com domain names I wanted to look for people who are impersonated.com domain names I chose to focus on comm as that's where most of the popular English language websites are and I only speak English So I'm very limited there. So there's really three options if you want to gather a large number of domain names One is you could get the zone files for .com that requires filling out form, which Really isn't that fun and some of the some of the zone files are actually impossible to acquire Such as North Korea's who actually leaked I believe last year You go to certificate transparency, which is a log of certificates Or you could go to a third party and their third parties You could pay a few hundred dollars and get a list of domain names, but that isn't that fun either So I chose to go with certificate transparency And for this I pulled down the Google pilot log This contains about a hundred million certificates That's ninety six point five million Domain names roughly. This is also completely searchable if you go to start dot sh Certificate transparency is a if you haven't heard of it before is an initiative to Log every publicly trusted certificate on the internet It's largely like Google initiative But it is There are logs hosted by other companies. I chose the Google pilot log simply as it's the largest right now So There's another reason that I wanted to use for transparency if certificate was if a certificate was registered That means it's far more likely to have been used There are especially with the BitSquadding and typosquadding domain names a large number of these are registered But never actually utilized which I found interesting so In order to use the CT log, I built a pipeline. I pulled down the log I pulled out the common domain and subjects alternative domain fields from that I then filtered out all of the Pini code domain names Then I found so there's a great Python library called you need to code package Where somebody actually went through and said what each Unicode character it looks like it's asking or what? Yeah, what it's asking equivalent looks like and actually went through character by character and did that which is a great amount of work it's very impressive and so that maps Ascii letters to their English or what looks like their English equivalent I then cross-referenced that list with the Alexa top 1 million domain names and at the end of the day I got 1900 CT certificates that impersonated The top one elixir top 1 million domain names. I then also went ahead and modified the Chromium unit test To check whether or not they would actually be rendered as Pini code or whether you end user would see xn-dash In a chrome in Firefox right now that test is actually standardized across all languages So this would be applicable to all end users in other browsers. I believe Internet Explorer Or Microsoft will take into account your local language of whether or not to determine whether or not you actually render the Pini code variant So I've actually posted that list online There are a few false positives in there like there are valid websites. They just simply happen to Look like their English equivalent website But I chose to include those as I didn't want to actually filter all these so What is much more interesting is actually showing the results So these are all real domain names. I would encourage you not to visit any of these There are some really bad ones in here in that list unfortunately, and I spent a decent amount of time actually reporting fishing websites to the Google fishing page Yeah, so some of the work these are just some of the worst ones that I saw grouped by What character they used? So there's a Latin small letter K and the L with a stroke looks pretty bad and then The adult was I was one of my personal favorites. I didn't know that was actually a thing before this and so that's actually part of the reason why I took this approach was I'm not a Ascii expert if there isn't even is such a thing. I really tried to go about Finding the worst abusers without having to necessarily have a knowledge of Ascii in the first place or knowing which letters to look for and Yeah, kind of as expected the most popular websites for the top towards the top of the list were much more likely to actually be Improvinated So one of the more interesting things that I saw Which actually bypassed the chromium check so the formatting here is the last The last entry in that field is whether or not a pie past the chromium check in this case They'd actually be rendered as you know time comm So they only used Cyrillic characters to represent The English equivalent So a breakdown of the unicode blocks that I observed while going through this So land and Cyrillic I kind of as expected but there was a long tail And I really want to call out one at the very end, which is the Canadian so it Canadian aboriginal celibate Unicode block that one really struck me as odd as it wasn't really familiar with what that was So I went ahead and I looked at that unicode block and the characters that are contained in it So I went ahead and made a bunch of sample domain names and I plugged them into the firefox and chrome Browser and they weren't converted to their puny code equivalent None of these were actually registered I Simply tested whether or not they bypassed the firefox and chromium check and then went ahead and report security bugs and The end result of this was that chromium actually Will now not allow the mixture of Canadian aboriginal celibate characters and English characters What they did before and they're actually working on a much more comprehensive anti-fishing fix which I believe is still a work of progress and Within firefox this check is a bit more interesting because Canadian aboriginal celibate actually fell under this thing called Aspirational unicode blocks which allowed them to be mixed as part of the standard firefox profile with their English language characters We think of language characters, sorry and In order to resolve this issue. They simply increased the level of that check to disallow mixture of English characters and this aspirational character block and I believe they actually File the request with some I'm not exactly sure what agency tracks this but some external requests to actually update the Rules regarding this aspirational block as some of the characters do look like English characters so As was news to me and the firefox and chromium engineers who actually were working on the fixes for these You can't actually register any of these domain names And this is where believe it or not policy comes to the rescue when you try to register any of these domains you're stopped and the The reason for this is that varus sign actually has a policy that You can't mix Canadian aboriginal Silver characters with certain other characters which includes English language characters and they have this for every unicode block which I was completely unfamiliar with One of the more interesting things about this is when I actually tried to register these domain names Because this is a failure at such a late stage in the register process Most registrars actually took my money and in one case I actually had to fight to get it back wasn't the biggest fan of that So kind of walk through three different examples of different ways that You're gonna you you were your computer could connect to the wrong domain name So now we're just gonna look at personal mitigations I'm kind of preaching to the choir here So the reason to use a password manager is simply because your computer won't be confused by any of this However, if you actually own or responsible for any popular domain name It's probably worth looking into whether or not somebody's impersonating you You could actually file an ICANN complaint and issue a takedown request, especially if your train marks being violated and if your work in IT or are at our all from Curious I would be something that's worth checking is what happens when you plug these into your Email clients what renders? Yeah, that's probably going to depend on the email client so as I had a super transparency log. I went ahead and Just had some fun with it. I graphed the key types over time RSA 2k keys dominate and followed by ecdsa p2 to 6 keys and then RSA 4k keys There was also this fun long tail which proves that when you give users options you Think you can always trust them to keep be consistent Some of my favorite ones in there is somebody actually issued an RSA 500 key And there's also an RSA 2600 key as well And at the very end there there's a dsa 512 key which is really unfortunate So we actually have a Intern this year within my company who's actually looking more into this and I'll if you're at all interested in this. I'll publish a link to it on my Twitter feed With much more details on what's actually contained the certificate transparency log when you look at the log as a whole so Yeah questions Questions every new anyone yeah, if you have any question feel free to have the stage and feel free to come to Mike feel free We had a question. I might have missed something in the beginning, but I think you showed examples of Domains that were registered with those Mix mixture of English and non English characters. Yes, and then later you said that they're that's not allowed Is that just something that changed or so it depends on which? Block you're looking for so the reason why Canadian Aboriginal Sylvics actually appeared in this list I actually went back later and looked at that domain name and it was two Canadian Aboriginal characters Not mixed with any English characters But it's simply when register when God when it was passed through the Python package looked like a I believe it was like a like a BB character the characters looked like bees and so it Looked like BB.com like as the English language a couple in So that's why it actually appeared on this list, but you can actually register the mixture Yeah, okay, thanks So regarding the don't-click links suggestion. Yes, do you have any recommendations for like any any other mitigation? like for example say there's like a 40 character hex thingy at the end of a URL I don't think most users are gonna like type in everything. Oh oops. I mistyped the 23rd letter or something They're just gonna copy and paste it. So it's there like another way It's a good question You know, it's really a question of trust. I feel like You know, do you trust the recipient? Can you Somehow verify that the link is valid in other ways You know or just couldn't face the end of it I'm gonna type in the start of it It's an intractable problem at the end of the day, right? Okay. Thanks. I once again shammer up everyone shammer


You have four AFSCs or Air Force Specialty Codes within the Air Force that fall under Air Force Special Warfare. CCT or Combat Control, which has a Scarlet Beret. You have Parasque or PJ, which have a Maroon Beret. You have Special Reconnaissance or SR, they have a Gray Beret. And then you have TACP or Tactical Air Control Party, which are wear Black Beret.


This lecture is part of an online course on the theory of numbers and will be about multiplicative functions. So a multiplicative function is a special case of an arithmetic function. An arithmetic function is just a function from positive integers to something. Something is usually might be integers or it might be reals or something else. So some examples of arithmetic functions we might just take the polynomials for example fn equals 1 or fn equals n or fn equals n squared. These aren't really all that interesting and don't have much to do with number theory. So a typical example of a number theoretic arithmetic function is the function sigma 0 of n which is just the number of divisors of the number n. Explain what the subscript 0 is doing a little bit later. So let's just start by computing some values of it. So let's take n to be 0. Let's start with 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and then sigma 0 of n is just 1, 2, 2, 3, 2, 4, 2, 4, 3, 4 and so on. So you see it's 2 whenever n is a prime and otherwise it sort of seems to go up and down a bit randomly. It doesn't look like a very smooth function if you draw a graph of it. So let's try and work out what it is. And to do this we write n as a product of primes using the fundamental theorem of arithmetic. So it might be p1 to the n1, p2 to the n2, p3 to the n3 and so on. And then we want to know what are the what are the factors of this? Well, they're going to be p1 to the a1 times p2 to the a2 and so on with nought less than or equal to a1 is less than n1, nought less than or equal to a2 is less than or equal to n2 and so on. So we can now easily count how many possible divisors there are. There are n1 plus 1 choices for a1 and n2 plus 1 choices for a2 and so on. So the number of divisors, sigma 0 of n, is going to be n1 plus 1 times n2 plus 1 times and so on. Now I was going to talk about multiplicative functions. So what is a multiplicative function? Well, you might guess that it's a function such that mn is equal to f of m times f of n for all mn greater than 0. And it turns out this condition is really a bit too strong. I mean, there's nothing really wrong with it. It's just that most functions we're interested in don't satisfy well, they don't satisfy this condition. Functions that satisfy this condition are called strictly multiplicative. So a multiplicative function is one that satisfies f mn equals f mfn, which sounds like exactly like the condition I wrote down before, except you say whenever m and n are co-prime. And the first example of a multiplicative function is sigma 0 of n, because you can see that sigma 0 of mn is equal to sigma 0 of m times sigma 0 of n, provided m and n are co-prime. You can see this because sigma 0 is the product of 1 plus the exponents appearing the prime decomposition of n. You notice this definitely doesn't hold when m and n are not co-prime. For instance, sigma 0 of 4 is just equal to 3, whereas sigma of 0 of 2 times sigma 0 of 2 is 2 times 2, which is 4. So if m and n aren't co-prime, this definitely breaks down. So what sort of questions can you ask about arithmetic functions? Well, you can ask things like what are their minimum values or their maximum values or their average values? Well, the minimum value of sigma 0 is not terribly interesting because sigma 0 of n is 2 whenever n is prime, and it's never less than that if n is greater than 1, so the minimum value for large n is just 2. The average value is slightly more interesting. So let's ask what's the average value of sigma 0 of n? Well, you can't really take an average over all integers, but you take an average value for integers up to some constant. So we might try and work out sigma 0 of 1 plus sigma 0 of 2 plus sigma 0 of n and divide it by n. So we're looking at the average value for all numbers from 1 to n. And we can estimate this sum because 1 is a divisor of n numbers from 1 to n, and 2 is a divisor of about n over 2 numbers from 1 to n. I mean, if n is even, it's exactly n over 2. If n is odd, it's slightly less than n over 2. And 3 is a divisor of about n over 3 numbers from 1 to n because it's every third number. And so you go all the way up to n is a divisor of about n over n numbers from 1 to n, in fact, exactly 1 number from 1 to n. There's no point going above that. So now if you add up all the divisors, so sum of all divisors of all numbers from 1 to n, it's just the sum of these things here. So it's about n plus n over 2 plus n over 3 up to plus n over n, which is n times 1 plus 2 plus, sorry, 1 plus a half plus all the way up to plus 1 over n. So the average value of sigma nought from 1 to n is about 1 plus a half plus a third sum plus 1 over n. And you remember how to estimate this sum from calculus. So sums are roughly equal to integrals. So this is approximately the integral from 1 to n of 1 over x dx, which is just log of n. So this suggests that if n is large, then sigma nought of n is on average about log of n. In other words, we expect a large number to have about log of n factors, although these will obviously vary quite a bit, like you might sometimes get numbers that are products of lots of small primes, lots and lots of divisors and primes only of 2, but on average it's about this. So next we can try the number sigma 1 of n. So this is going to be the sum of the divisors. So instead of counting the divisors, we're now adding them up. And we can write sigma 2 of n. This is now going to be the sum of the squares of the divisors. And similarly, we get sigma k of n. And you can probably figure out what that is. It's just the sum of the kth powers. In particular, sigma 0 of n is just the sum of the zeroth powers of the divisors, which is just the number of the divisors. So that's why sigma 0 of n is used for the number of divisors. So let's just start by working out some values for n from 1 up to 10. So sigma 1 of n goes something like 1, 3, 4, 7, 6, 12, 8, 15, 13, 18. I hope I've worked those out right. And sigma 2 of n looks like 1, 5, 10, 21, 26, 50, 50, 85, 91, 130. Now we can ask, are these multiplicative? Well, we can have a quick check. If it's multiplicative, then f of 6 would have to be f of 2 times f of 3. So we have a quick look. Well, here f of 6, in both cases, is indeed f of 2 times f of 3. So this is quite promising. It suggests these might actually be multiplicative functions. So let's actually check this. Let's first do sigma 1 of n. So let's try and calculate sigma 1 of n. Well, let's suppose that n is equal to p1 to the n1 times p2 to the n2 and so on. And a divisor looks something like p1 to the a1 times p2 to the a2 and so on. So we want to sum these over all a1, a2 and so on with nought less than or equal to ai is less than or equal to ni. So how do we do that? Well, let's look at the following sum. Following product, we take 1 plus p1 plus p1 squared up to plus p1 to the a1. And let's multiply that by 1 plus p2 and so on plus p2 to the a1. Let's multiply that by 1 plus p3 and so on. And if you multiply out this product, you can see that this product is equal to the sum over all choices of exponents. So this sum is just the same as this product here. And we can work out what this product is. This is a geometric series.  So there's a formula for the sum of the divisors of every number. And now you notice that this is multiplicative that sigma 1 of mn is equal to sigma 1m times sigma 1 of n. Because if m and n are co-prime, then the terms for m and the terms for n kind of don't interfere with each other. So the sum of the divisors of a number is a multiplicative function. For the sum of the squares of the divisors, it's kind of similar. So sigma 2 of n, where n is equal to p1 to the n1 times p2 to the n2 and so on. This time we need to take 1 plus p1 squared plus p1 to the 4 plus p1 to the 2n1 and multiply it by 1 plus p2 squared and so on times 1 plus p3 squared and so on. And this product will be the sum of squares of divisors. So we get a formula for the sum of the squares of the divisors in much the same way. We find sigma 2 of n is the product over all primes dividing n. This is a common way of writing a product over primes dividing a number. This would be just the product of all the primes of p to the 2 times np, whatever the exponent of that is, plus 2 minus 1 divided by p squared minus 1. And again this shows that sigma 2 is multiplicative because again if m and n are co-prime then these expressions don't interfere with each other. So we can write sigma 1 of n as being the sum over all divisors of n of d and sigma 2 of n is the sum over all divisors of n of d squared. So as before this notation means you're summing over all numbers d that divide n. And now these things here are certainly multiplicative functions of d. And we'll see next lecture that more generally if f of n is multiplicative then so is the function given by sum over d divides n of f of d. So this sort of explains why sigma 1 of n and sigma 2 of n are multiplicative. They're sums over the divisors of n of certain multiplicative functions. Now let's look at some arithmetic functions that aren't multiplicative but have a slightly different but related property. Here we're going to put little omega of n is the number of distinct prime divisors of n and big omega of n is the total number of primes dividing n. So for instance if you take 12 this is 2 squared times 3 so omega of n is just 2 because there are just two primes 2 and 3 but big omega of n is going to be 2 plus 1 because we're taking the sum of the two exponents to get the total number of primes countered with multiplicities. And these are generally quite similar functions. I mean if we sort of look at n being 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 then little omega of n goes 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, whereas big omega goes 0, 1, 1, this time we have 2, 1, 2, 1, 3, 2, 1. So so they're quite often the same unless n happens to be divisible by a square or a cube or something in which case this one is a little bit bigger. Now these functions are obviously not multiplicative but they have a slightly different closure related property that they are additive. You can see that omega of m, n is equal to omega of m plus omega of n whenever m and n are co-prime. This is sort of obvious.  And additive arithmetic functions aren't really that much different from multiplicative ones because if you just sort of exponentiate an additive function you get a multiplicative one. And then we can ask questions like, you know, what are the average values of these functions? So let's ask what is the average number of primes dividing an integer?  And you notice that what happens is there are usually only a very small number of prime factors, one, two, or three or something. So the number of primes dividing an integer seems to be pretty small. So let's work out what it is. So we can ask what is, well we can't take an average over all integers because that's going to be infinite, but we can take omega 1 plus omega 2 plus omega n over n. So we can look at the average of the number of primes dividing numbers for all numbers up to some fixed number n. Well, we can't really find an exact formula for this very easily, but we can estimate it roughly. So 2 is going to divide about half of the numbers from 1 to n. So let's write n over 2. And then we get n over 3 plus n over 5 plus n over 7 and so on up to plus n over p over n. So let's just remember what these bits are. So this is, this means about half of the numbers from 1 to n are divisible by 2 and similarly about a third are divisible by 3. So the total number of primes dividing all the numbers from 1 to n will be about this sum here. And here p is the largest prime less than or equal to n. So this sum is just a half plus a third plus a fifth and so on. So you're summing over the reciprocals of primes up to about 1 over p. And this is a little bit trickier to evaluate. You're not summing over reciprocals of integers. You're summing over reciprocals of primes up to some limit. And I'm just going to quote what it is. This is approximately log of n. This is shown by Euler using, it's a slight extension of his proof that there are an infinite number of primes. He not only showed that the sum of reciprocals of primes is infinite, but he also, by being a little bit clever, managed to estimate the partial sums. So how big is log log of n? Well, in theory, if you go to, you know, a calculus course, they'll tell you that the limit as n tends to infinity of log log of n is infinity. Well, this is theory. I'm here to tell you that that's not really true. In practice, log log of n is about three. Okay, so you're probably being a bit skeptical. So let's try it out. Let's work out some values of n and see what log log of n is. So for n is a thousand, log log of n is about 1.9. For n being a million, log log of n is about 2.6. A billion, it's about 3.0. 10 to 12, it's about 3.3. 10 to the 15, it's about 3.5. And you notice that all these values are about three. So yeah, I mean, in theory, log log of n sort of diverges, but in practice, it's done nearly constant. And what this means is that pretty much any number you try and factorize, unless it's ridiculously small or ridiculously large, will typically have maybe three prime factors. So let's have the last, today's last example of a multiplicative function is going to be Euler's totient function. Totient means just a number co-prime to n and less than it. So Euler's totient function phi or possibly phi of n, I'm never quite sure how you pronounce this, is the number of integers m such that one is less than or equal to m less than or equal to n and such that m and n are co-prime. So it's just counting things co-primes at m that are less than or equal to it. And again, we should start by making a little table of it just to see what it does. So if n is equal to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, then phi or phi of n is 1, 1, 2, 2, 4, 2, 6, 4, 6, 4. So again, like most interesting arithmetic functions, it kind of jumps up and down quite a bit and there's a little bit difficult to study. So let's try and find a formula for it. Okay, well let's do a couple of examples first just so we can see what's going on. So let's work out phi or possibly phi of 12. So let's write down all the numbers from 1 to 12 and figure out which of them are co-prime to it. So I'm going to write down the numbers in a slightly funny way. So let's say 2, 4, 6, 8, 10, 12, 3, 9, 1, 5, 7, 11.  And we want the numbers that are co-prime to 12. So we should start by throwing out the ones divisible by 2. And there are 12 over 2 of these. So we want to throw them out. So we start with 12 numbers and then we should subtract 12 over 2. We don't want those. Those are divisible by 2. And then we should throw out the ones divisible by 3. 3 being the other prime dividing 12. So and there are 12 over 3 of these. So we subtract 12 over 3. But we've over counted because we threw out 6 and 12 twice. And there are 12 over 6 of these. So we should add in 12 over 6. So 5, 12 is equal to this number here, which is 4. And you see there's 1, 5, 7 and 11 left over. And now we can simplify this expression slightly because it's 12 times 1 minus a half times 1 minus a third. So we're sort of throwing out the numbers divisible by 2 and then throwing out the numbers divisible by 3 and being careful not to throw things out too many times. So here we have a sort of, we have to remember to keep track of how many times we're throwing out numbers. So let's see what's going on. Let's do this in a slightly more complicated example. Let's work out 5 of 30, which is 2 times 3 times 5. So this time we've got 3 primes to keep track of. So let's see what we've got. So here we've got, we should put in multiples of 2. And here we should put in multiples of 3. And here we should put in multiples of 5. And the things that are multiples of all of them are just 30. And here we get 15. And here we get 10, 20. And here we get 6, 12, 18, 24. And here we get the multiples of 2 that have nothing to do with 3 or 5. And we get 2, 4, 8, 14, 16, 22, 26, 28. And here we get 3, 9, 21, 27. Here we get 5 and 25. And now we need to figure out how many numbers are left over. Well, well, I mean the ones left over 1, 7, 11, 13, 17, 19, 23, 29. So all together we've got 30 numbers here. And then the ones we need to throw out, we need to throw out 30 over 2. And we need to throw out 30 over 3. And we need to throw out 30 over 5. And then we need to add back in 30 over 3 times 5. And this is getting a bit complicated. Let's write it down. So it's 30 times 1 minus a half minus a third minus a fifth. So we need to throw out multiples of 2, 3, and 5.  So we have to add in these and add in these and add in these. And now if you check, we've thrown out 33 times. But then we added it back in three times. So we've got to throw it out again. And now you see this is just 30 times 1 minus a half times 1 minus a third times 1 minus a fifth. And now you can see what's happening in general. If we've got a number p, which is number n, which is p1 to the n1 times p2 to the n2 and so on, then phi of n is going to be n times 1 minus 1 over p1 times 1 minus 1 over p2 and so on. And you can think of this as being probabilistic. So this is the chance of a number being co-prime to p1. And this is the chance that it's co-prime to p2. And what you're saying is that if you sort of pick a random number from 1 to n and you ask for it to be co-prime, well, the chance of that happening is the chance of it being not visible by p1 times the chance of it not being divisible by p2 and so on. So this is the total chance of a number from 1 to n being co-prime to n. So the total number should be that. So in particular, you see from this formula that phi is multiplicative. This game was one of Euler's first theorems about phi. So we've got a formula for it and we've shown that it's multiplicative.  Let's find all numbers n with phi of n equals 24. Okay, so one good way of handling multiplicative functions. Well, if you've got a function of the integers f of n, you can try forming a power series f0 x to the 0 plus f of 1 x to the 1 plus f of 2 x to the 2 and so on. You've probably seen how this can often be used to prove things about the function f. This doesn't actually work terribly well for the sorts of functions we have in number theory. It turns out it's often much better to form a Dirichlet series. So Dirichlet series is, so we don't start with nought, we start with 1, f1 over 1 to the s plus f2 over 2 to the s plus f3 over 3 to the s and so on. So let's call this big f of s. So what we're going to do in next lecture is to study these Dirichlet series as a way of studying multiplicative functions.


Hey friends today, we are hanging out at the magic kingdom all of the Halloween decorations are out So I got so excited I wanted to come out and check them out Mickey's not so scary Halloween party is only three days away And I am so excited for that and then also I hear skipper canteen has a couple new menu items So I was able to grab a reservation and I figured we'd ride some rides eat some food and just have a beautiful Magic kingdom kind of day. Anyhoo, let's go do this And take a look at this. This is Halloween I'm so excited for Mickey's not so scary Halloween party and just coming out today and checking out all the Halloween decorations They're all out. All the pumpkins are here As I was sitting there looking at all the pumpkins and decorations I heard the omnibus beeping its horn and I think it's coming out and we might be able to ride it Have an evening ride on the omnibus down Main Street. I'm up for this This will be so awesome if we get to ride this down Main Street and check out all the pumpkins Oh, what a look normally you don't see these out like later in the afternoon It usually is first thing in the morning, but I think we're gonna. I think we're gonna be a look. I Am so excited they said that we can sit in front with them So we're gonna be sitting in the front of the omnibus driving down Main Street. I feel so honored I feel super honored. I Am so excited. We're gonna be riding in the front. Look at this All right, thank you Very very cool.  Look at all the buttons here Let's see if it says dome step wiper start We've got the emission switch down here This is gonna be so much fun This is seriously so cool and just in time for the Halloween decorations. Oh, yeah, thank you Look at the pumpkins up here Well, I don't think there could have been a better way to start off a day than that Right there. It's like all downhill from here and it was so rare to actually take the omnibus up during a stage show They didn't take us all the way up because they couldn't get in there But what a great day huh, I Had to make my way back down Main Street because the omnibus just dropped us off up there They couldn't even turn the vehicle around because they you know I mean they were doing the stage show and there was too many people But wow that was so cool. That was seriously just so amazing Honestly looking around the only thing I don't see yet are the Mickey pumpkins that hang on the lights But I am so excited and I still can't eat I like I said, I still can't get over that Mickey's not so scary Halloween party He's just three days away. Well two days away depending on when you guys are seeing this video Looks like the omnibus is gonna try to make its way through all these people now It's so cool seeing this from the outside now. Look here they come Clear the way. Let's hear that horn There we go. Bye-bye Hey, how are you? Have a good time Okay, enough of the omnibus business, but I gotta say that made me so happy like the littlest things like Taking an omnibus down mainstream. I mean it's not even a little thing. It's a big deal. It's a big deal to me But anyway, that was really awesome. Now I want to head on over to Frontierland and Adventureland I'd love to ride Big Thunder Mountain and if we're gonna be dining at Skipper Cantina I'd love to ride the Jungle Cruise because that's a ride that inspired the restaurant a Couple of the things I'm probably most excited for this year for Mickey's not so scary Halloween party is the return of the headless horseman and then also of course the boot to you parade and Also being able to hug all my favorite characters and their Halloween costumes dressed up in their spooky bests I'm really crossing my fingers and really hoping that this is gonna be a full Mickey's not so scary Halloween party Just like the way it was. I'll be so excited Those are some of my favorite things and probably some of my favorite memories ever come to Disney World Holy moly it says a 65 minute wait for Big Thunder Mountain Railroad 65 minutes. That's a long long time. I think I might want to download the genie and see if I can get a lightning lane Well, I cave in and I bought the genie plus. I mean once I seen 65 minutes I knew I was like, oh boy, that's gonna be a long wait and they have Passes from 825 to 925 so I can book that if I want to but I better if I keep refreshing I'll find one like within the next 20 minutes and then also Jingle Cruise or your Jungle Cruise is also on here And that's at a 75 minute wait. So it might come in handy today And just like that, I just kept refreshing and bada bing bada boom I am in the Big Thunder Mountain Lightning Lane within 15 minutes And here comes our train for the day Which one is it?  Here we go. Oh, I like this part too. Oh How's it roughen? Oh I love it though as many of times I have road Big Thunder Mountain It is still the wildest ride in the wilderness for me. I love it. I get so excited It really tosses you around and it's just it'll never get old It'll I will never get sick and tired I'll never get like like not wanting to ride Big Thunder Mountain any time I come to Magic Kingdom I feel like I got to do it All right now that we got to ride Big Thunder It's time to make our way in to the skipper canteen. Oh, hi. How are you? I'm so excited. World famous jungle cuisine This isn't my first time eating here. In fact, I'm pretty sure I have tried everything on the menu here Everything from it tastes like chicken because it is chicken to the pork to everything and like I said I heard that they have some new menu items. I think they have some dandan noodles Well, I think they're like skipper dandan dandan noodles and then also I think they have lamb chops like bah bah bah lamb chops I think they're called and I'm excited. I got to make sure I get to try everything Here is a little bit of the menu that they have outside And like I said, this restaurant is based off of the jungle cruise and set course for adventure Explore the bold flavorful cuisine of Asia South America in Africa or more sure a Mercerer immerse yourself in a legacy of the world famous jungle cruise and they have an enchanted orange dream They'll whip orange blended with vanilla sauce serve and served with an orange candy rim. That sounds amazing They have a lot of good stuff. Oh, here's the bah bah lamb chops. That's I might actually get those And hopefully afterwards like I said, it would be awesome to go over and be able to ride the jungle cruise I keep saying jingle cruise as if it's Christmas, but it's Halloween season. I don't know why I'm getting that mix up But I'm excited It's really a fun restaurant and the ride is fun and to do them both in the same day It's really something like you kind of got to do it All right, they just called us it's time to head in and I have to vote this is probably My favorite waiting area at any Disney restaurant. This is like the waiting lobby itself It's so pretty in here and the AC works really good They used to let you sit out here, but I think they blocked it off and that was such a great view Kind of sad that was really awesome to be able to sit out there We have made it to our table I went over the menu with you guys a little bit out front But I do want to point out the two menu items that are new and I think we're both gonna get that I'm actually meeting up with some friends and of course can't forget the kangaloo Here is a look at the menu and how fancy is it that they actually have a menu with pictures I feel like that's a next step up, but the newest thing the newest entrees are the Baja Baja Baja man No, the Baja lamb chops and they look actually phenomenal I think I'm gonna get the lamb chops and then my friend is gonna get the skipper Dan's Dan Dan noodles Which kind of could be a tongue twister skipper skipper Dan Dan Dan noodles If you guys aren't familiar there is a special Walt Disney World exclusive beer And it's called the Kungaloo and it has a lot of meaning here at the skipper canteen And you can only get it here at the skipper canteen over at the nomad lounge and animal kingdom and then down at the hangar bar Disney Springs, so you got to go for it Kungaloo Kungaloo So good On top of the Kungaloo I had to get the enchanted Ordin's dream and it's dole whip orange blend it with vanilla sauce or served with an orange candy rim So it's basically a milkshake with a dole whip. It's a dole whip milkshake It's basically like a citrus swirl milkshake and they give you a really big straw for it and that I appreciate All right, that's pretty good I like it It also reminds me of like a Halloween beverage, you know what I mean because of the Halloween decorations I Decided to get the seasonal soup as my appetizer and it's a carrot ginger soup with crushed peanuts on it Look at it. It looks fantastic, and I'm excited to try it. Oh, yes, very creamy. Look at that You got to get a little bit of the peanuts in there. This is the way I'm actually really excited for this so with the little crushed peanuts on there That's good It looks like our food has come out and my buddy Sean ended up getting the Skipper Dan's Dan Dan noodles. It's so hard. It's Skipper Dan's Dan Dan noodles. Yeah Yeah, it's very it looks good nice portion and some crispy pork on there And I ended up getting the lamb chops. Look at this. These actually looks phenomenal though Look at that nice little char on there.   There we go. Oh, that actually fell apart very easily Here we go. I'm excited for these. I'm excited for the lamb chops That's good The congelouche tastes like a nice Christmas beer.  So here we go Dan's got a kick. Hey, they're delicious though One's a kick in Okay, so I might be good, but they are very good, but I don't feel kicked yet. Maybe you have to eat them a couple of times The lamb chop is actually really good and the outside has this really really nice crust to it that I like I haven't really dived into the sauce yet But I think I will give it a go and then also they have I think it looks like potatoes and onions over here Like look at these I came with the Bible. I'm gonna actually I'm gonna grab one of these potatoes a whole potato The potatoes look interesting. Oh, that's good. I Feel like I probably like the Dan Dan noodles a little bit more Johnny are you what which one do you like more? I'm not a big lamb guy, but I like the noodles you like the noodles. Yeah, I agree with Sean I did like the Dan Dan noodles a little bit more, but I'm still gonna finish up the lamb. I Think some lambing tin would go very well with this lamb though, and I've given up on the fork I think I'm just gonna eat it like ribs. I'm gonna eat the lamb like ribs After taking a couple more bites of it, I just don't think I'm a lamb fan Like I think the dish itself tastes good. The char is very good, but I don't like the taste of the meat I don't like the like it's kind of strange and like I said, I really haven't had lamb that much I think I've only ever had it at Epcot before so Yeah, I don't know. I should have probably just went with Dan Dan should have stuck to Dan Dan Newlin He knows the way Well skipper canteen was really really awesome Like I said, I wasn't the biggest fan of lamb chops just because I didn't like the lamb But I feel like that would be a really good dish if you do like lamb I Preferably probably would have went with the Dan Dan noodles or the chicken the chicken's good The cungolouche beer is always amazing. The orange drink was great and the soup was phenomenal But we're all ahead of great experience. It's nice to try the new stuff And now we're gonna go explore a little bit around Magic Kingdom try to ride the jingle cruise I mean jungle jungle. I don't know why I keep saying jingle like it's Halloween not Christmas Now we've made our way down to the jungle cruise It's just about time for our lightning lane, and I'm excited either way It says the standby is 55 minutes, so I'm happy that I ended up getting the genie plus for the day Definitely came in handy Wow, this is so crazy. It's at 55 minutes, but I'm pretty sure the lightning lane is a longer line than the standby line What are the chances of that like this is all the lightning lane on this side and the other side there was nobody in line that was for the standby That is crazy Well, I guess I take back what I said about genie plus being very worth it today, but I guess it wasn't Seriously, if you look over there, it looks like there are 10 people waiting in line 10 people here comes four more so it was pointless to get the lightning lane Absolutely pointless even though it does say 55 minutes. They're definitely they're telling they're telling fibs here Looks like we've got Volta Val as our trusty vote to the day Volta Val So Doing the jungle cruise right after eating at skipper KT was such a great idea and our skipper was fantastic I love it when the skippers kind of like laugh at themselves And she was just like that and she also said jokes. I haven't heard before that's always a plus for me And I loved it. It's always fun. Now. I think we're gonna explore a little bit around Magic Kingdom a little bit more All right, I think we're gonna make our way over to fantasy land since I bought the genie plus service I really wanted to get one lightning lane in that would be worth it to me for I mean We did get to do big thunder mountain so that does count but jungle cruise was a walk-on So that was basically a pointless like lightning lane. So see if we get one more. Maybe winning the poo. I Was able to grab a lightning lane from we need the poo right now. Oh, I think the fireworks are gonna start Enchantments gonna start in just ten minutes It just looked like another pointless lightning lane. There is nobody in the standby line. Well, I'm really I really wasted $15 today I can tell you that like watch when we get up here to separation point There is nobody gonna be in the standby line itself. Look at Look at this guys just go. Yeah There's nobody there. I'm not upset though I'm just happy to be here and I love winning the poo so whether I had to wait like two minutes or probably 20 minutes I would still be happy either way Here comes my honey pot. Oh, I get so excited like winning the poo Also got a milky way in here that Mickey's not so scary Halloween party start already One day in the hundred acre wood the east wind traded places with the west wind and that stir things up a bit I like how they smell lettuce Let us Oh How fall omson Oh Boy, it's actually kind of scary knowing the fact that I'm the only one in this room right now Oh, they brought that back Sensor's nobody behind me and there's no other cart in here right now I'm the only one in the half-alumzo woozo room and like I said that could be a little scary Oh I'm so happy that we decided to get one more ride in and also enchantment is going on for now I can hear the fireworks now. I'm just hanging out on a honey pot Hanging out in a honey pot during enchantment not too many people can say they've done that But I can say it because I'm doing it right now I'm sure as soon as we walk out of the gift shop. We're gonna see tons of fireworks Let's see Look at that But I don't care We're not gonna stick around and watch the fireworks We're gonna try to make our way out of Main Street and avoid a little bit of the crowds But it still might be busy though because the fireworks are going on Look at how empty it is over here in Tomorrowland We're about to head into the unknown. Oh Boy, I see a lot of people over there Well, honestly, I don't know if this is a good idea or a bad idea Oh boy, we're gonna try to cut through here Love that this music is playing as we're about to walk into this big crowd of people Don't don't Well, oh If only Kristen from right down Main Street was around Oh look, there she is Look at this. I didn't even know you were allowed to watch fireworks back here This is pretty this is pretty intense, but it makes sense. I bet you this like alleviates so much room Wow Holy moly I'm kind of interested to see right now. We're on the opposite side. So we're technically backstage I can't wait to actually show you guys what the fireworks viewing from here is look at this This isn't that bad of a viewing area Oh Well that tree kind of ruins it a little bit you can actually see the finale happening right behind me That is pretty nifty That's the best any are literally on stage right now watching enchantment Of course look at that See you real soon. See you actually in two days for Mickey's not so scary Halloween party And with that I think we are done here. What an exciting evening at Magic Kingdom I'm so happy I came out and I got to make a video got to see all the Halloween decorations I got to eat at Skipper canteen ride some rides and really just enjoyed the day I really honest just love today so much I think anytime I close out the park and you get to see the fireworks at the end of the night Kind of you just feel complete, you know, but I hope you guys enjoyed the video. We still got a couple more I'm gonna have one more video probably before Mickey's not so scary Halloween party But if not, that'll be the next video and it's gonna I'm gonna be there opening night. I can't wait So make sure you guys stick tune in make sure you guys keep an eye out for that video because that's gonna be amazing We're gonna do this special Mickey's not so scary Halloween dessert party, which I am so excited to show you there's gonna be a lot of good things But I hope you guys enjoyed the video. I enjoyed making it. We'll see you next time. Bye


How much product manager can make during recession? If you join tier one company such as TikTok as a product manager with only two years experience, you can still get it paid over $300,000 per year. If you join a startup as well-funded, you can get over $200,000 paid. And the base salary for the startup is $170,000, easily plus other kind of bonuses, over $200,000 no problem. And for all the tier one companies, they still pay you over $300,000. The problem is that most people do not know how to lend a job offer because the market is too competitive. So therefore, I want you guys to focus on how you're able to improve your interview skills. Check out more videos regarding interview skills. This is Dr. Nancy Lee. Watch the next video to learn more product management, interview tips and tricks.


And welcome to the 4 p.m. to 4 30 p.m. session of the 2017 Open Simulator Community Conference. As a reminder to our in-world and web audience, you can view the full conference schedule at conference.opensimulator.org. And please tweet your questions or comments to OpenSimCC with hashtag PoundOSCC17. In this session, we are happy to introduce a terrific session called an Educator's Approach to Developing Usable Prototypes for Serious Games in Open Simulator. Our speakers today are Evelyn Gossett and Rachel Oomerin. Evelyn Gossett is an assistant clinical professor of nursing at Indiana University Northwest School of Nursing in Gary, Indiana. Her interests are in using online and virtual environments for interprofessional education. Rachel Oomerin is an assistant professor of pediatrics at the University of Washington School of Medicine. And she's the director of immersive learning for the UW neonatal education and simulation based training program. Her research interests are improving neonatal outcomes through team science and measuring the educational outcomes of partnerships with global public health. She has published and presented internationally on using virtual environments for health professional education. Welcome, Evelyn and Rachel. Let's begin the session. Thank you so much, Barbara. It's so great to be here with you all and with my co-presenter, Evelyn. We've been collaborators in using virtual worlds for healthcare education since 2012. And I want to especially thank any attendees who are in the east on the east coast or in Europe because I know it's quite late for you. So for our in-world listeners, please feel free to ask questions in the chat as we go along and we'll answer them all at the end. And we'll also leave our contact information at booth 20 and expo zone 3 where you may meet us after this talk as well. So our objectives today are to assess our approach to the development of serious games in open simulator really from an educator's perspective. So you'll find that we have an institutional lens and a focus on healthcare. So we'll be discussing early prototypes and how they've evolved along with our usability testing approaches over the years. And we'll end us on tips for success. And we'd really welcome those of you who have been in this field for a while along with us to share tips that have worked for you. Initially, our focus in developing the various learning activities in the virtual worlds is to develop clear goals and objectives. And in considering those goals and objectives, we always ask ourselves the questions, why would a virtual learning environment work better than a lecture or some other way of teaching on the particular topic that we have chosen? And so our first example is Global Health Traveler. We developed this in 2013. And the objective here was to represent the challenges of working in a global health setting to orient medical students traveling abroad. It was initially built on a homestead region next to Indiana University Island, the second life, also shown on that slide, and was actually an upgrade from a small skybox above the main island, which really we should have called Phase Zero. We were very glad to upgrade this particular simulation to our Phase Two project, which Lear was referring to earlier. And I think many of you have had the opportunity of visiting. We were able to collaborate with survivors of educators and use their open simulator installation to expand Global Health Traveler from a small homestead region to a full island with eight learning activities that were based in East Africa region. We were able to, in addition, collaborate with the Moses Group on their grid and create an activity that was quite similar, but represented the West African perspective the next year in 2014. So this activity continues to be used by nursing students at Indiana University. And we're happy to have that activity. The students love it. Our next project took us to create the SPH Places, which is a challenge for the students in relation to public health and providing care. So the focus at SPH Places is about the students learning about social determinants of health. And we continue to build on that scenario by adding training for my senior nursing students on nursing leadership and management in 2016. We began with SPH Places in 2014, but in 2016 we added the training for nursing leadership with a focus on conflict management strategies. The nursing students in this that are participating in this challenge are taking nursing management and leadership. And so we learned a lot of valuable lessons in building the various scenarios that we've shown you. This slide explains a focus and case study on our trans and illustrates our transition to games in the e-learning platform. Here we use the agency for healthcare research and quality, team steps, strategies and tools to enhance performance and patient safety, to teach the nursing students and medical students about teamwork, cooperation and collaboration. And that was the first part. The second part of adding the team steps to our virtual worlds. This slide we began to focus more on the team steps communication strategies. And here in the second part of this phase we added open SIM bots to increase the engagement and interaction for the students. And as Lear mentioned earlier, we gained a lot of experience of using bots across the two different platforms. So second life and open SIM, but we found that the open SIM bots are a lot more flexible and adaptable to various uses. And so we started using open SIM exclusively for that. However, what we did still lack in using the, in the phases that we've described so far are is a real inefficiency in data collection. So we were not able to collect data efficiently from the users and we were not able to monitor and track users as much as we would have liked once we moved to open SIM. So we were fortunate to receive some funding to program a multiplayer Unity 3D environment which allowed us to use the browser interface and track responses more efficiently. And we were to present this version as an international meeting on simulation and healthcare and win an award. But just in 2016, the graph up there shows the number of users and scenarios that were accessed as we were able to also track the choices that users made throughout the scenario. And then moving on, we're currently in another phase of development with a focus on healthcare providers who are working in the University of Washington, neonatal care unit. And we're using again a multiplayer environment which is out of unity with scenarios that can be accessed in world or by learning management systems. So I think what we're trying to illustrate here is that prototyping can take different phases and translations to different platforms. But we always return to open SIM. I feel like we keep coming back each time, you know, we want to test out a new idea or develop a new program. So we couldn't have done this without a large team, had expertise in medicine, pediatrics, nursing, social work, and many other areas. Barbara here is our expert in instructional design. And so I was just saying it's so lovely to have her on the platform here with us today, as well as in multimedia and graphics and then research administration. And over time, we were able to standardize our virtual scenario development process. So we have six stages, which range from identifying and discussing learning objectives and narrowing them down for each scenario, all the way through writing questions and including a debrief, which encourages reflection and promotes our focus on adult learning. And additional lessons that we've learned over the years include that you should not limit your options for communication or collaboration. We began using the second life voice capabilities. And as you know, that's not so stable. So we quickly transitioned to using Skype. And later, we've begun to use Zoom. So we've used various virtual world environments, the learning management browser based the second life in the open sem. And as Dr. Marin mentioned, we used Google analytics for analysis. And we've used Google platform, Sakai on course, Canvas learning management system to present basic information to the students in there for their participation in the virtual environments. And this year, we started formal usability testing for all our scenarios. So our approach comes to using open ended questions that are directed at selected users and usability tests, such as the one click test, where we give the user a task and then ask them questions about their actions as they try to accomplish that task. And the other one that we are using more of now is the second test for the user gives their initial impression of a representative image. So this is one way that we're trying to improve the design of our platform in order to ensure that by the time we roll it out, the more larger groups of students, it's easy for them to use and acceptable for them. So talking about collecting data, and this is one of the key things that has been the focus, at least for our team, is to really make sure that what we do is meeting educational objectives and is acceptable for our learners. IRA protocols for educational studies are generally exempt. They're very easy to get. And within virtual worlds, as you all know, and much more easily now than in the past, it's easy to collect data on what the user is doing within the simulation, as well as through surveys outside the system. So thinking about that as you design is really important. And then we really want to put out a call to share your work. We talked about quite a bit in the last day and a half on how to go over the world. It's impossible to do that without putting out, you know, in public forums, wonderful work that we're all doing. So present an abstract, look for forums where you can actually publish some of the work that you're doing. And we know that funders look for evidence of prior success in the process of deciding where they're going to put their money. So research and development funding, as we know, is so crucial. And it supports faculty time, it supports servers, it supports design and development, research assistance, lots of things. So always be on the lookout for internal grants. Private foundations are relatively easy to get funding from if you tie your activity to something that is really, truly interesting to them. And then add on to research and quality improvement projects, which require an educational component. This is such a really good way if you can't get a standalone grant to add on a piece to a grant that is already existing or is being submitted.  Of course, time management, managing faculty and student schedules and matching schedules across time zones and busy lives and such has been a challenge. We've used various means of social communication to work around those barriers such as texting, cell phones and world meetings and such. A second barrier or pitfall is team cohesion, but we learned very early, especially working with the TeamSTEPPS strategies, we learned to work as a team. And the important component there is to listen to every team member's perspective and come to a consensus and arrive at your best solution. The third challenge that we have faced has been technical difficulties. As you know, the virtual world will lag. We've had voice challenges, which we were able to overcome through using Skype and Zoom. And many of the students have older systems and then we also have challenges with some of the students use Mac, some of the students use PC, and so that's been an issue. As Dr. Umarin mentioned, lack of funding has been an issue for us over the years to deal with this challenge. In the beginning, we did our own work, our own building, and as we received some funding, we were able to get assistance. And our final challenge or pitfall or barrier has been lack of institutional support. In the beginning, many around us thought we were playing games, and that may be true, we are playing games, but we're playing serious games. Yes, and indeed we have fun while we do it. So with this, I think another main tip for success is have fun. You know, the only way that you can persist along a certain track is if it's something that you enjoy doing. And I think we're all here because we enjoy being in the virtual environments and creating and building and using them for various purposes. So that is the first tip for success. Other tips are pay attention to your learners and their needs. We have over the years really, really simplified what we expect learners to do in our environment because many of them really don't have much exposure to games of any kind. And virtual worlds have their own challenges for them.  You don't need to know anything else. From the standpoint of instructors, we have occasionally some instructors that are very familiar with virtual environments, but the vast majority are not. And so again, we've adapted our approach to having those instructors just review reports that are submitted by learners from their activities within the virtual environment. So we don't necessarily expect the instructors to go in to virtual worlds, collaborate, collaborate, collaborate. Can't say that enough. You know, the world is hard enough as it is to face it with a team. And it'll be a lot easier be scholarly. And that can be even as, you know, just in how you test out your initial skills. You know, as we talked about with the usability testing, it doesn't have to be publishing a paper, but it certainly could be. And it's a way that you document your work and your progress. Taking an incremental approach is something that we've also learned over time. It's easy to want to do everything all at once, but that takes time and takes funding, you know, do a small activity, do an initial test, see how it goes, see whether your learners like it, add on as you go along. And that's what people are able to do successfully. The last tip is to talk with your IT department early and often. This is your instructional design group. Whoever manages the servers for your institution, you just never know where you might be able to get some help or someone to after your team from that group. So that's the, I think all that we have time for today, but we're really, really interested in chatting with you, answering any questions that you have. I know there are already some questions in the chat. Thank you very much for your time. Thank you very much, Rachel and Evelyn. We do have time for just a couple of quick questions. There was a question about following up with you on the OARs that you use with these different regions. If any of these, if anyone can participate in those or if they're open access. They are available. If you want to follow up with me, I have them all. And we currently have Dream World. Thank you for installation at our university. And so if you would like to access them there, it's available. And there is also an Indiana University installation that is still up and running at Evelyn University. Fantastic. Yes. And I know that another question surrounded the usability and you mentioned, I know in your data collection process, because you had a research design that you used as you would make these innovations for the students and you would reach out and you would have other faculty and other students get involved.  Can you just elaborate on that a little bit, or what you would prefer or recommend others to do? So what we had done consistently over the years is establish some form of data collection. Currently what we do with our existing simulations is that we have surveys before and after. And we also have data collection within the simulation. But one thing that we wanted to pre-empt as we got a little more experience with this is those negative comments that always come up. You can't please everyone, right? But nonetheless, we wanted to be sure that our simulations were usable before we wrote them out. And so we started doing some formal usability testing just very recently on our new simulation with a handful of students from the same class and group that would, or level of learning that would be using the actual bills. And a lot of good information and perspectives, you know, things that you wouldn't expect to be a challenge for a challenge. And so we were able to make modifications before rolling them out. But I would highly recommend that. Okay, great. Well, thank you again, Rachel and Evelyn for a terrific presentation. And for our audience, I want to let you know that the next presentation will be right here. It's called Virtual Worlds Database Connect with the Metaverse. It will begin at 4.30 p.m. So we're going to get off the stage right away. And we also encourage you to visit the poster expo. Their booth is booth 20 in Expo Region 3. And don't forget to visit the other hypergrid tour areas and the crowdfunder booths as well. But thank you again, everyone, for attending our session. And we will see you at the next one.


Russian Army prepares to enter Kiev and Odessa. Medvedev announced new phase of invasion in Ukraine. Russia needs to create a protective cordon that will shield from any intrusions into its lands. Russian Security Council Deputy Chairman Dmitry Medvedev said, we must safeguard our interests in full, the politician said in his interview with the Russian media. Medvedev explained that this means two things. Firstly, to accomplish the objectives of the special military operation which the president named. Secondly, to create the necessary protective cordon which will secure against any encroachments on our lands, not only shelling attacks, but also active offensive operations, Medvedev said. Medvedev has claimed that in order to achieve the goals of the special military operation, Russian forces will have to march on Kiev again, if not now, then at some point, and that Russia has long desired the city of Odessa. Where should we stop? I don't know. I guess, given what I said, we still have to work hard and focus. Will it be Kiev? Yes, it should probably be Kiev. If not now, then at some point, perhaps in some other phase of this conflict. Medvedev claimed that there are two reasons for this. The first is that Kiev is supposedly a Russian city, and the second is that it allegedly poses an international threat to the existence of the Russian Federation, as Kiev is supposedly run by an international brigade of Russia's opponents, led by the United States of America. So yes, it may be Kiev. Medvedev speculated. He also added that Odessa has long been desired in the Russian Federation. Odessa, come back home. We have long desired Odessa in the Russian Federation, even by virtue of the history of the city, the kind of people who live there, the language they speak. It is our Russian city. He called the behavior of the Kiev clique in demolishing monuments and destroying other Russian cultural heritage in Odessa short-sighted. In this way, they simply alienate some of the people, even those who were loyal to their government until recently. Well, in general, this looks monstrous, because we are talking about opposition to the entire Russian culture and our common path. Noted, Medvedev.