| 00:11 | okay saying good works. It So they also have a little bit |
|
| 00:27 | grab the number of generators. mostly make you wear out problems and |
|
| 00:37 | you about a few simple ones. huh. To get really good quality |
|
| 00:44 | numbers. It's complicated business and so . Was trying to make you aware |
|
| 00:50 | . I nearly you should get familiar such things software and let's protest whatever |
|
| 00:58 | numbers generated you're using unless you want be very so that's kind of the |
|
| 01:09 | of today. Mm hmm. I of the rest of the course just |
|
| 01:14 | you aware of when things can go and be critical and then find ways |
|
| 01:19 | challenging very fine whatever you get. this is a little bit of background |
|
| 01:28 | everyone has transpired in the best. that was the system. Random number |
|
| 01:37 | kind of used everywhere. And we're much used in every day. Even |
|
| 01:40 | you don't think of it. I I was then there is then used |
|
| 01:46 | blood protocols. So they are dependent random numbers being good. The difficult |
|
| 01:55 | is when we test something and then don't data or but even she ha |
|
| 02:05 | it's common to generate contestant using random generator. And so in our case |
|
| 02:17 | , make sure that things kind of the way you intended. You may |
|
| 02:21 | need to know something about the quality the distribution of these random numbers. |
|
| 02:28 | other ones that's pretty much thank you understood doesn't need any explanations but in |
|
| 02:35 | things is, but people design all of, um, service things or |
|
| 02:42 | tropic close being forgotten. Sit down , statistical models of customers arriving and |
|
| 02:51 | times and all kinds of stuff from underlying statistics. Um when you're designing |
|
| 02:59 | for a variety. Um, other is people. The last company, |
|
| 03:10 | , chemistry, biology, chemistry also several Carlo methods that are based on |
|
| 03:21 | methods as well as in optimizations. things tends to be hard, sometimes |
|
| 03:28 | resort to statistical methods are very Two hold it may be harder to |
|
| 03:36 | how good they are and solutions have be understood in the percent. So |
|
| 03:44 | the third that TCP and DNS use and modern design. So you're being |
|
| 03:52 | from everything. Just as a way where things play out. The only |
|
| 04:01 | to be aware of. Everybody talks random number generators but they are not |
|
| 04:06 | random numbers and that's part of their . So most of their best they |
|
| 04:13 | the Foreign Minister. We just try make sure that for practical purposes in |
|
| 04:20 | of behavior as if they were random it's limited. The property is by |
|
| 04:28 | word length on the computer or the that you're using. So it's certainly |
|
| 04:36 | a short time range of numbers that be represented and eventually things start to |
|
| 04:42 | . They have a period determinist is both by the detector algorithm you use |
|
| 04:48 | well as the how many dates you in your bank account What this one |
|
| 04:58 | . So someone has to watch out these things and there will be an |
|
| 05:03 | . So things that people thought were and they turned out not to be |
|
| 05:07 | in the past and that's problems. the chance. So that's a problem |
|
| 05:16 | finding random good random number generators is trivial. People, I'm in a |
|
| 05:28 | come up with something new that now trying to figure it out and it |
|
| 05:33 | out that is not the case. , um, so one thing to |
|
| 05:41 | the US and something called this, National Institute of Standards and Technology. |
|
| 05:49 | continuous ongoing effort trying to come up random number generators as well as |
|
| 06:00 | for figuring out what properties it seems a little more than they have. |
|
| 06:06 | then the recommendation, they give recommendations companies and the public at large for |
|
| 06:12 | type of generators to use and Um, so again, pretty much |
|
| 06:23 | home message today to make you aware kind of to find tests of which |
|
| 06:31 | are many to try to assess your number generator. So there is one |
|
| 06:42 | we talked about in the garden and in the beginning and for a long |
|
| 06:48 | close in elimination or opposition was used breaking computers in terms of speed the |
|
| 06:58 | performance impact, which is basically a composition. And so companies in particular |
|
| 07:06 | bragging rights on two around this link access to try to then claim that |
|
| 07:13 | have the fastest material. Yeah. in that case, what people who |
|
| 07:22 | the initialized the major since using a number generator numbers. So random numbers |
|
| 07:29 | kind of a good thing. It's some sense, it's kind of an |
|
| 07:32 | right behavior that as you may hopefully come solving linear systems of equations |
|
| 07:44 | the matrix is singular, it kind doesn't work whether it's a riveting or |
|
| 07:50 | , it doesn't work. We got elimination whether you that composition, so |
|
| 07:56 | is the basis for the site performance . So at one It's about 20 |
|
| 08:04 | years ago now, I think there so companies necessarily want to run this |
|
| 08:09 | for bragging rights. So they used generator, random number generator of this |
|
| 08:16 | . I'll talk more about that Um and it turns out that this |
|
| 08:24 | , the number generator, the way used it with particular initialization will come |
|
| 08:33 | , it turns out that they generate matrices. So people and just the |
|
| 08:37 | benchmark didn't work out. So I the tremendous error that they thought there |
|
| 08:44 | be somebody in the toe or maybe hard work. None of that's |
|
| 08:49 | Software was fine, it was it was fine, but the data |
|
| 08:54 | was not cool. So, And is matrices up to 500,000. This |
|
| 09:00 | table here shows a particular size nature for which there is at least two |
|
| 09:09 | or rows in this matrix that are . So there are repeated for the |
|
| 09:15 | is singular and depending a little bit initialized in the midday Sun policies, |
|
| 09:22 | it may be more than two rows columns that are the same. So |
|
| 09:26 | numbers one inference, is that the place telling you know how many copies |
|
| 09:32 | the same? No more column, is a matrix of the so it |
|
| 09:39 | . So and then it took about people think it up that the matrix |
|
| 09:44 | singular and there's nothing wrong with anything . There was a random number generator |
|
| 09:47 | was bad for clinicians station. So other things in terms of ssL for |
|
| 09:57 | inscription protocol, the early version of , one of the houses dominating browser |
|
| 10:06 | whatever. Also technology also had So we have to try to figure |
|
| 10:13 | how to fix it. Um, another one from the Windows 2000 Windows |
|
| 10:22 | have problems and usually, thanks, don't usually publishes after what they're |
|
| 10:29 | Um, some of these guys something have to do, reverse engineering to |
|
| 10:35 | out what was wrong and then companies to and it's asked for the one |
|
| 10:42 | somebody figures out it just didn't And here's one that's actually even from |
|
| 10:49 | standards institute that recommended a particular type and the number generator and some |
|
| 11:01 | Now this is not the great for things because that is why you saw |
|
| 11:04 | cracking the algorithm and get the back down here is anyone knows what then |
|
| 11:13 | it is. No, yes. agency and get some sports in the |
|
| 11:23 | . So they wanted a backdoor. they bribed this company With 10 million |
|
| 11:27 | use this perfectly random number generator. then my dad was discovered, missed |
|
| 11:34 | standards, people decided not recommended Um and here is another one that's |
|
| 11:45 | too long ago. Again, there's problem. Again, we're going to |
|
| 11:49 | to generate random numbers and as I , there are stds and other things |
|
| 11:59 | somebody developer about something went wrong and the code etcetera and try to fix |
|
| 12:05 | things. So they combined it into in the process based quality. |
|
| 12:15 | it was one of the dominated the public key factors schemes are safe |
|
| 12:22 | they also figured out depending upon other numbers for the factory in Pakistan, |
|
| 12:27 | is a waste of figuring in knots to raise the security. So a |
|
| 12:37 | bit of what you want. So of the thing is you want the |
|
| 12:42 | number generator obviously to generate good quality numbers, they want them to have |
|
| 12:49 | distribution, you want to The long 6000 repeat as I said, there's |
|
| 12:55 | maximum here, depending on the Portland the data type you're using but of |
|
| 13:02 | the period may be much shorter than . So I tried to design it |
|
| 13:07 | . So you get the long that's the uniform it is all depending |
|
| 13:13 | and a subsequent picked out of the sequence around the numbers. They should |
|
| 13:18 | be correlated and repeated. So it be very hard to find repeating patterns |
|
| 13:24 | the screen And of course the one to be fast. So um this |
|
| 13:34 | the reason that they wanted to generate of the headache in terms of for |
|
| 13:39 | failures in the past that you know that is computational simple but it turns |
|
| 13:45 | not to work too. So there a good moment. That's hopefully everyone |
|
| 13:54 | that more or less the partner of But and it was a mathematician that |
|
| 14:03 | to point out that as soon as used. Uh huh. That's the |
|
| 14:10 | procedures. You can't So then I to just show you these are not |
|
| 14:22 | per se, but it's a way conduct yet a sentence for how this |
|
| 14:30 | of random numbers finished. Um So are fairly simple um ways of mhm |
|
| 14:43 | potential qualities or lack thereof of random on this line. Three different versions |
|
| 14:52 | is known as the face based representations enlisted Take a sequence of four numbers |
|
| 14:58 | them for 10 -3 to end. you look at the three different Paraguay's |
|
| 15:05 | kind of in the succession of the numbers and you look at these three |
|
| 15:11 | as coordinates in free space and then project can figure out what you |
|
| 15:17 | Sometimes it is from the you probably expect. And I'll show examples from |
|
| 15:24 | . And another one is just to a sequence of three numbers and treat |
|
| 15:27 | as X one c coordinates of this . And that's kind of the common |
|
| 15:32 | is space representation. And then we we can work polar representation as well |
|
| 15:38 | three successive friendly numbers from these I'm sure many examples of that. |
|
| 15:47 | he was just a long less than couple of slides. Again, this |
|
| 15:53 | this National Institute of Standards and Technologies come up with a bunch of tests |
|
| 15:58 | can download, I think for all these tests stealing from their website. |
|
| 16:04 | they do have just suddenly come down constructive themselves. But one thing is |
|
| 16:13 | look at the distribution of zeros and , uh, and the random numbers |
|
| 16:21 | have suggested that I should have taking opportunity to speak the crap on |
|
| 16:26 | So, so a little bit decide and thanks stuff. So yeah, |
|
| 16:34 | has been a lot not as a A. But as a grad student |
|
| 16:41 | . And one of the projects that's doing and discovered that that test using |
|
| 16:48 | numbers consumed a lot more our energy other forms of initialization. So we'll |
|
| 16:57 | interested to understand that a little bit part of that. Also look at |
|
| 17:02 | distribution of zeros and ones and check out. Flowers. Do you remember |
|
| 17:09 | number generators? Almost the same birds and it's kind of Yeah, pretty |
|
| 17:16 | normal. But it's not centered at so the main point and their differences |
|
| 17:24 | little bit still respect the anyway, that there is this distribution that people |
|
| 17:32 | at in terms of how many zeros months there are. I can kind |
|
| 17:36 | the strain of whatever lemons. another is to do things that said one |
|
| 17:44 | interested in potentially blocks or sub sequences trying to figure out how correlated correlated |
|
| 17:55 | plots. So that's kind of behind block frequency test and spectral test and |
|
| 18:03 | young best we're looking at the frequency for them branches on the occurrence of |
|
| 18:08 | and ones or if you have blocks or numbers or that's what there's been |
|
| 18:19 | . I don't think that we looked the test that is anatomically non decreasing |
|
| 18:27 | increasing. So it just goes up goes down. And what is the |
|
| 18:32 | of such sequences related is kind of at the length of the strengths with |
|
| 18:40 | ends up covering consecutive bits being the . How many zeros that were there |
|
| 18:46 | one shows up for commerce. Once zero shows up. And depending upon |
|
| 18:52 | properties that um, and show it . Mm hmm. The run length |
|
| 19:00 | no too large. There is something is very common and used that is |
|
| 19:06 | as practice. I'll show you an of that and that's one thing that |
|
| 19:12 | useful for and then there's a whole of other tests exists. So they |
|
| 19:23 | 15. All them adjust at some of miniature if they changed the number |
|
| 19:28 | or in recent months. So this some time ago and then there's some |
|
| 19:34 | not for further tests that um people at to find different properties of this |
|
| 19:42 | number sequences. So it's just this service. But to actually go to |
|
| 19:50 | website and do anything that potentially depends whether you actually have put random numbers |
|
| 19:57 | not familiarize yourself with the tests and out which ones make sense for an |
|
| 20:05 | . Mhm Or just for fun and some of these tests on whatever comes |
|
| 20:11 | or limericks or windows or anyone. let me see what the property looks |
|
| 20:20 | . Still more here and start. , please frank test that I talked |
|
| 20:24 | . Some of those could take the and then turn it into a kind |
|
| 20:30 | M x two blocks based on So basically did sequence. Hmm, |
|
| 20:37 | and two columns and from the little matrix. And then you've got a |
|
| 20:42 | of these blocks for the entire stream benefits, security, subsequent choices And |
|
| 20:51 | are these don't not overlapping and again this box and then you best to |
|
| 20:58 | out when you're right and this rank comes in tend to figure out whether |
|
| 21:06 | collection years or m rows and two and all of the bits And whether |
|
| 21:11 | has full rank in this case 4 or in this case the from |
|
| 21:18 | rolls of the same in this So as I said, typical 33 |
|
| 21:26 | two and I don't remember from which night random number generator discourse example was |
|
| 21:35 | up but you can see enough in case Of this 32 x two sub |
|
| 21:43 | of the cars and bits. not even the third. That's cool |
|
| 21:51 | I'm supposed to 60%. So we deficient but only honestly. So and |
|
| 22:00 | there is not too bad, but minutes plus percent that has the rank |
|
| 22:07 | at most. I don't know how have Iran it's match. So the |
|
| 22:13 | is to get to try to there is no this petition basically they |
|
| 22:23 | so all the subsidies to all the . Um, just the bits around |
|
| 22:33 | . So now I want to show what has been after and these examples |
|
| 22:40 | from using here that they, what the latest version of illustrating things or |
|
| 22:49 | space or the polar. So you see different illustrations or probably is random |
|
| 22:55 | generators. Good news from numbers. hmm. So, so here's an |
|
| 23:06 | from IBM quite a few years ago . So. So what do you |
|
| 23:14 | about this thing? Doesn't look friendly . It seems like there's, |
|
| 23:21 | it's more likely to choose a number closer to the middle. Okay. |
|
| 23:28 | that would represent? That is And uh now, so this is |
|
| 23:37 | just sort of a few spots of then I wanted to do this. |
|
| 23:41 | me face. That's what you So then I'm very special for some |
|
| 23:47 | marked by elements and it means random . So this is by the |
|
| 23:58 | the three numbers and treat them as free space you can see. But |
|
| 24:05 | this institution is totally uniform negative numbers falling on streets. So this |
|
| 24:14 | they're not not pretty good. And we'll have to excellent. It took |
|
| 24:20 | while and to understand what was but they don't use this and they |
|
| 24:25 | using academy quickly after the discovery began some ways of testing in this government |
|
| 24:33 | I remember this and that's, here's another one From Windows 95 and |
|
| 24:41 | is the TCP protocol and as one see in this case is by no |
|
| 24:48 | are reminded. Okay, correlated over plants give some notion that space is |
|
| 24:56 | uniform the field. So it's really that good in this case is even |
|
| 25:00 | of the status property that already in of the lack of quality ah Trying |
|
| 25:09 | brought us another 1-98 to fix it they've got something else that wasn't so |
|
| 25:17 | cannot melt down. It's hard. So and then when has also had |
|
| 25:24 | involving um, Another four. Then safety protocol and it's finally, so |
|
| 25:37 | in the student 1000 we've got something . And then its service package |
|
| 25:42 | there was an update. No, doesn't pull the space, but it's |
|
| 25:48 | least much better distribution of previous And there's another one that's on stood |
|
| 26:00 | . Um, but anyway, you see it's, it's not final means |
|
| 26:05 | this now it's fair blocks. It's , but against um, not |
|
| 26:14 | it's better than they had before. predicting that facebook can tell by those |
|
| 26:24 | . Um, 2003 adult, there's , there's another one or it's not |
|
| 26:35 | nicely. And you can see here that that's starts in the corner. |
|
| 26:42 | more Windows XP. So, Well, so I'm just making your |
|
| 26:52 | the, this is a difficult Companies don't take it like that and |
|
| 26:58 | hard and here's another one. Service to try to fix things. How |
|
| 27:06 | is that better? It's different. , there's more, you can see |
|
| 27:11 | , try this one. Yeah. side down. Um, And the |
|
| 27:17 | one year is 2000 month yesterday you can see kind of parliament similar |
|
| 27:24 | them or something. Another random number . This kind of shape and a |
|
| 27:31 | kind of cute. There's other ones exports From the were not just speaking |
|
| 27:39 | 5%. Again, they're all from and this is fun. Some of |
|
| 27:45 | Solaris operating system ah, generating and another one. No, and this |
|
| 27:56 | considerably better. Um hmm, I'm showing you here, you know, |
|
| 28:04 | they're trying to fix things and you tell the people, all the companies |
|
| 28:08 | learning, nobody wants to tell the one is what they're doing. But |
|
| 28:12 | this case the platform to taken from and so on the generations of the |
|
| 28:17 | generators and this was from silicon fixed that doesn't exist anymore. Not because |
|
| 28:26 | the random number generators, but there not a business kind of for the |
|
| 28:33 | . Uh huh. Also picking on , they also have problems. So |
|
| 28:40 | , I miss the sale. Everybody about fiscal, but also again, |
|
| 28:49 | be an internet protocol. They are important factor and they also have |
|
| 28:55 | you know, they ran the Here's more examples, tons of |
|
| 29:01 | I think ah, the previous C operating system, open source, I |
|
| 29:08 | have issues, things are changing and just try and so I think right |
|
| 29:15 | , okay, sure. Being and of the strong sequence of our |
|
| 29:23 | of other random numbers tend to fail generate good numbers here is another one |
|
| 29:30 | shows parents. Um, so, , so this is pretty much showing |
|
| 29:39 | little bit lower. Again, a of it, despite of the |
|
| 29:45 | The defense couldn't agree on five friend my efforts, but, but was |
|
| 29:52 | in terms of examples, so open convincing. You have to be conscientious |
|
| 30:00 | the quality depending on what to It may not be very nice important |
|
| 30:04 | all. But that's a charming in previous. Sometimes things are awfully wrong |
|
| 30:16 | many of the so the more complex for either your optimization of things depends |
|
| 30:26 | to have a good sampling of the you're in. And if you don't |
|
| 30:33 | kind of a nice uniform sampling your answers may talk to the kind of |
|
| 30:39 | you want. It's not representative of problems with no. The linear conventional |
|
| 30:49 | are the most popular and on the new RGM that didn't work too well |
|
| 30:53 | with the impact that didn't work too . And an example of this then |
|
| 31:01 | conventional generators and they they work with . Okay. But it's very tricky |
|
| 31:07 | figure out how to initialize them and on what numbers you use in the |
|
| 31:16 | function. So here is the there's a list of things that has |
|
| 31:22 | used. Um so the form is multiply with and you provide a. |
|
| 31:30 | and starting seed, which should say is 10. So the first argument |
|
| 31:38 | yeah. Bring your numbers on the you're using And a is the multiplier |
|
| 31:45 | one, Number two The next and be it's kind of they have in |
|
| 31:50 | . So this is what you see this expressions here for the Congress of |
|
| 31:58 | statisticians Says he used to do this , which is kind of a 10 |
|
| 32:03 | one because the supplier of to make very simple um, to do the |
|
| 32:09 | function. That is not a good . And then here is your |
|
| 32:15 | here's a C. I mean, part of the starting scene for the |
|
| 32:21 | , random number generators, but and is this other one that uses the |
|
| 32:29 | That is one of these former seven numbers. So that is a lot |
|
| 32:35 | in terms of limiting the period of extending the period of the statements and |
|
| 32:46 | uh, here's around, Uganda said didn't work well and part with those |
|
| 32:51 | didn't For the car of two. it the computer that was again they |
|
| 32:56 | to pass one is in the computer didn't work well. And then it |
|
| 33:01 | also using that's such a great multiplier using this particular number. So, |
|
| 33:12 | the next one year's December seven, prime means another one that is to |
|
| 33:18 | this kind of programming language. right. And here is the accidents |
|
| 33:28 | America algorithms group that's kind of a to math lab. They have a |
|
| 33:34 | focus but they do math software, then focus more on software for solving |
|
| 33:41 | differential equations and optimization. Yeah, kind of a little bit more complex |
|
| 33:50 | outside. They won't respond to these manipulation languages. Start America. So |
|
| 34:05 | is, has shown that the they have been popular and they are |
|
| 34:10 | They lost the simplicity, um, in the sense that fairly easily to |
|
| 34:16 | depending upon the month function. They more or less insane from the |
|
| 34:23 | Sorry, it's just from the books the book discusses around the number generator |
|
| 34:29 | chapter can so much. So what told is not covered. So here |
|
| 34:38 | that this happens to be in the and this was one of those minimum |
|
| 34:44 | generator and stuff things. So in book, it's very simple procedure |
|
| 34:50 | contravention of efficient except as of this function. It's a bar of two |
|
| 34:57 | trivial, but if it's not, for the prime number is not |
|
| 35:06 | And this is very much just summarizing to show on the pictures of their |
|
| 35:13 | random. And so one way that used to stage a sequence and new |
|
| 35:21 | into the higher dimensional space. And kind of a common trick, |
|
| 35:27 | to kind of expose profit. Is enough? So it's easy to |
|
| 35:33 | And so we're just sitting here or this place. Oh, what is |
|
| 35:44 | funny song? So this first, we remember the random thing, there |
|
| 35:53 | a bunch of planes and free space two D planes and this just shows |
|
| 35:59 | , depending upon what in this case that's used for the mod function. |
|
| 36:07 | . It shows to the number of is that contains. Um, so |
|
| 36:13 | ended up also the sequence of these . So that's going to fall |
|
| 36:19 | So all that's the specials are by means kind of random. They wanted |
|
| 36:24 | be extreme as possible here. Once around here we got the registration and |
|
| 36:34 | the body. It doesn't look too in terms of the random numbers but |
|
| 36:39 | the status box instead, uh, the three departments. Then we need |
|
| 36:45 | see that the following. And here kind of another one that was using |
|
| 36:55 | same script. One is to, . This was a minimal and I |
|
| 36:59 | that things costs and fines and it's gonna be going on screens and to |
|
| 37:06 | . Ah, this is a lot and that it's the same script and |
|
| 37:11 | another cent right. But the not supplier that this guy and that |
|
| 37:16 | be the difference. Otherwise They won't no B0. The same starting point |
|
| 37:25 | shows the difference. Um, given same month function, the multiplier, |
|
| 37:30 | makes a big difference. And how come up with this multiplier. So |
|
| 37:34 | has been, how do you figure out? And here is kind of |
|
| 37:41 | slice again, show on that for of them you get very clear |
|
| 37:47 | It's not such a long. So is a lot better. Again, |
|
| 37:56 | know, finding different initialization or So this. Hmm. And so |
|
| 38:07 | were often in their confidential showing Yeah. First that we can get |
|
| 38:14 | of the numbers if they are very and take the seed and the ma |
|
| 38:18 | be used for B and B family in your interest. And I can't |
|
| 38:23 | what it was. Okay. Yeah. So in terms of what |
|
| 38:33 | kind of an assembly brian based, have gotten left today. Six. |
|
| 38:47 | . Kind of for that. So thing to try to improve this fairly |
|
| 38:55 | generator is to use some of the alter. So in this case instead |
|
| 39:01 | just having one and then just the value, we depend on the sequence |
|
| 39:06 | previous values and then you do them after having a bunch of multipliers. |
|
| 39:12 | so in that case it does improve period of someone that case depending on |
|
| 39:19 | many um previous random numbers you use your winning a congress that generated and |
|
| 39:30 | security. So on the other ones can do not linear ones. But |
|
| 39:35 | could work for squares. Mm Or have been there inspires. So |
|
| 39:42 | are many tricks people play to try improve the rental numbers and characters and |
|
| 39:47 | see what it is. Just scaling from some other interval. That standard |
|
| 39:54 | That's becoming between zero and 1. it's not shift and scale and stretch |
|
| 40:03 | shift. So now it's okay. don't want to talk about the |
|
| 40:16 | I just want to show a few . So for that and the computer |
|
| 40:28 | part of a computer. So even phone that must of course. And |
|
| 40:34 | um, if you trying to, run cold and you want to do |
|
| 40:39 | coal bores or things like busters, best ever production of parable operations. |
|
| 40:52 | . Now it is important to try make sure either who are having, |
|
| 40:59 | can not to generate and examining long of random numbers and then you have |
|
| 41:09 | different threads in your execution. This create samples from this very long |
|
| 41:17 | So they do subsets on the single or in the other way you try |
|
| 41:23 | generate physically the sequence for each Now, if you do the |
|
| 41:32 | then if you see they random number in the same way you've got identical |
|
| 41:45 | for each one of their friends And are 100% correlation and that's probably not |
|
| 41:53 | you want. And then the others sub samples for each one of the |
|
| 42:02 | . The even though the cold it has a very long period |
|
| 42:11 | The subsequent servant of certain point obviously significantly shorter. So I interviewed for |
|
| 42:23 | state that they are computers the young have a few 100,000 friends. So |
|
| 42:35 | one sequence and generally hundreds or thousands subsequent is out of it. It |
|
| 42:41 | that the period gets short and there's whole also risk of the different subsequent |
|
| 42:46 | according. So it's very tricky. is even more tricky than it used |
|
| 42:53 | be run your town to do things currently people struggled today trying to figure |
|
| 43:04 | what's a good way of doing But I'm just pointing out that the |
|
| 43:09 | has gotten much worse with increased resources and we're gonna show a couple of |
|
| 43:19 | and that's um, I think you me already. So let's see what |
|
| 43:28 | . So one thing, yes, can ask is a non centralized one |
|
| 43:32 | number generator that can things out to or replicated and distributed from that place |
|
| 43:40 | on how the generation is done. then there's the question, if they |
|
| 43:43 | on one sequence on multiple sequences. you. Multiple sequences, significant |
|
| 43:50 | You have to be very careful to sure that the seeds doesn't call because |
|
| 43:55 | that we did. So ah What's up and this advantage. Mm |
|
| 44:14 | . So these are the kind of um, depending upon on ah this |
|
| 44:22 | santa was thinking in the first quarter a chronicle survey client model. Then |
|
| 44:29 | central guy have potential no control or one of the cost disease gets what |
|
| 44:37 | on that place. The best reproducibility can suffer. So that's another part |
|
| 44:46 | been touched upon. So to have reproducibility, you may also all those |
|
| 44:55 | , experiments what you do ah make either if you want to get statistics |
|
| 45:04 | make sure that saving the statistical if you want to to kind of |
|
| 45:15 | and make sure things are correct, we want to ensure that the ceiling |
|
| 45:19 | the random number generator, it's always same. So you always worked with |
|
| 45:23 | same random sequence than it is for What You Want. So listen, |
|
| 45:38 | this is the second part of the that it's tough and don't make |
|
| 45:45 | Yeah. Mhm. So it I understand. So, there are |
|
| 45:55 | considerations. Again, in terms of that the collection of random number generators |
|
| 46:04 | the parallel environment has the properties actually that to happen. Mm hmm. |
|
| 46:13 | the different animals of our state systems I think the number of friends can |
|
| 46:21 | carried out. So, so um here is kind of Yes, currently |
|
| 46:35 | briefly just be aware of people have trying. Ah so this is kind |
|
| 46:45 | what they call the random tree method basically have two sequences. I kind |
|
| 46:50 | wonder. General seats for the um secret that right from the seeds and |
|
| 47:00 | the report, it's one of them around the sequence based on what the |
|
| 47:09 | generates and just 1%. Mm That's so, so it's fairly simple |
|
| 47:20 | implement. Well, yes. So response because it can happen. |
|
| 47:32 | So you can get this warning sequences sequences. Mm hmm. The following |
|
| 47:43 | based on skipping things. So this what you can see here that ah |
|
| 47:50 | sequence gets handed over and then on point it's a baby around Robin is |
|
| 47:56 | , so the right sequence and uh can see some of the properties for |
|
| 48:04 | , they start from that. I no statement or no real hard evidence |
|
| 48:11 | which one works better. What so that needs to do do it, |
|
| 48:17 | need to go extinct from the Yes, it is. So |
|
| 48:26 | Early process. Yes. And that's you can do can change their all |
|
| 48:32 | the left and right guys, which generate seats for the other one for |
|
| 48:39 | ? This is different. So playing with this thing seeding and different having |
|
| 48:46 | different generators. What do you want ? Yeah. Um check this |
|
| 48:54 | Show you this one and what I . So you can see there's a |
|
| 49:00 | list here of standard number generators out . So somewhere in here, I |
|
| 49:07 | they should be here. This crystal has become quite popular. Um So |
|
| 49:16 | this case, as I said, is, it's reproducible and start, |
|
| 49:22 | kind of a single perfect person. a good because it has a very |
|
| 49:27 | period um Yeah, and it's, it's not entirely simple and its |
|
| 49:38 | Your comments relatively large space um the um that are, so this one |
|
| 49:50 | also after um but I guess at point at this point properties or not |
|
| 50:03 | entirely well understood. Mhm. The is not very large. So that's |
|
| 50:10 | of potentially a problem with this one and another one again, in terms |
|
| 50:18 | things being uh, easy not taking lot of space. And they passed |
|
| 50:28 | , these two things are obvious. then that's a problem. Only one |
|
| 50:37 | number generators much completely structures alerted to fact that it's hard to get good |
|
| 50:46 | and software protest under a nominally generates of us I guess just use it |
|
| 50:54 | we need and use whatever to the system or some software and pay attention |
|
| 51:00 | it. And the film itself safe good. They don't know. So |
|
| 51:09 | here length, structural properties that, correlation and subsequent cases. Mm |
|
| 51:19 | Check the literature into Japan quality. that was it short. Thanks to |
|
| 51:29 | answer. But so on monday. . Yes. For the finals. |
|
| 51:43 | . It's very, so after I no friday, friday. No, |
|
| 51:56 | this. Yeah. You know what saying? There's not much time between |
|
| 52:01 | last lecture, the finalists. It's time than mine. Thank you so |
|
| 52:15 | for today. Thank you. Thank . Yeah, we'll try to do |
|
| 52:23 | review. I will not cover any material. I would just trying to |
|
| 52:27 | through things and remind you what we done after the midterm. So, |
|
| 52:34 | will not remind you about that. course. Just. Mm |
|
