The Mechanics of Marine Heavy Helicopter Squadrons 361, 462, 465, and 466 are who keep the CH-53E Super-Stallions of the 3rd Marine Aircraft Wing in flight. Each Marine must ensure every possible issue is addressed after a Super-Stallion completes 200 hours of flight time. Each maintenance crew is made of electronics technicians, airframe mechanics, flight line mechanics, and ground support mechanics. Every time a CH-53E is taken apart, a team of two to five maintenance crew members must go over each portion of the aircraft to ensure every safety measure is met. These Marines' attention and detail during inspection and repair continues to keep the MCAS Miramar Super-Stallions airborne. From Marine Corps Air Station Miramar, this is Lance Corporal Erica DeSalle.


The Data Analysis Workflow. I'm Professor Vernon Gale. I'm Professor of Sociology and Social Statistics at the University of Edinburgh and part of the National Centre for Research Methods. At the current time, the National Centre for Research Methods are unable to provide any face-to-face teaching. I hope that you and your families are all healthy during this difficult period. This presentation and its associated resources are all about the Data Analysis Workflow. A thought experiment. Be honest. Have you ever lost a file? Have you ever wondered if you've deleted a file? Have you and a colleague ever been working on different versions of a file? Have you ever struggled to identify data files? For example, a file called chapter1-2019.dat and a second file called chapter1-2019.dat Well, if you experienced any of the above, you could improve your social research workflow. The examples in this presentation tend to lean towards statistical analyses of social science data, but many of the issues around the workflow and being well-organised permeate across a number of research processes, so it's worth continuing to listen in. Here's me one Saturday morning. I look fairly frazzled. I'm working fairly hard at this stage, but if I'd improved my workflow, it could be a different picture. Here's me on an alternative Saturday morning. This is the West Coast of Scotland, believe it or not, at a time before corona when we could still go outside. Who worked for you? What is it? Well, for me, it's the whole process from conceiving of an idea right through to its publication. Commonly, you'll download some data. Here is the National Archive at Essex University. You'll download the data. You'll be using a computer or either your laptop or a machine on your university network. You'll probably be using a statistical software or programming language, so something like SPSS, Stata, R or Python. And the first stage will be data wrangling. Next stage will probably be something like exploratory data analysis followed by something more formal and statistical, such as statistical modeling. Then these results will be written up and submitted, for example, to an academic journal. Then after a peer review, hopefully they'll be published in the journal. For many of you, the process will look the same, but the output might be something like an MSC dissertation or your PhD thesis. Analyzing data without a planned and organized workflow can be compared to drinking and driving. In both situations, it doesn't matter how careful you are, it's still highly likely to end in a wreck. These are the wise words of Professor Philips Stark, UC Berkeley. Therefore, just like drinking and driving, we strongly warn against not having a systematic workflow. The workflow. The workflow should be planned and carefully orchestrated. The workflow must not be ad hoc, so it mustn't be worked on piecemeal and it mustn't be developed in reaction to mistakes. The workflow cycle is relatively straightforward to conceptualize. Plan, organize, compute and then document. After gaining access to your data, having downloaded it, this is a picture of the UK Data Archive at Essex University. You'll probably have your data on a laptop or on a machine on your university network and you'll tend to be using a statistical software such as SPSS or STATA or programming language such as R or Python and you'll begin your data wrangling. The first piece of advice is don't use drop-down menus. I'll say it twice. Don't use drop-down menus. If you use drop-down menus, you'll have no audit trail. The audit trail is nothing more than a line of breadcrumbs that leads you back to where you started and you won't have one if you use drop-down menus. Write out your data wrangling commands in syntax. Using GUIs, graphical user interfaces, will leave you in a sticky mess. Data wrangling. What does the data wrangling phase involve? It involves a number of steps. Commonly, selecting variables. Surveys tend to have a large number of variables, but we will only want a small number of them for our specific analyses. We'll need to operationalise measures. The data may have information on income. It may be net income or gross income or household income and we need to operationalise the measure given our research question. We'll need to recode variables to get them into the specific format we need for the data analysis that we're going to undertake. We'll need to often select cases. Surveys tend to be large in general. We may be only interested in a subset of cases. For example, just married couples or just households with people from certain ethnic minority backgrounds and so on. Inevitably, any dataset will have missing data or missing information. We'll need to think hard and work out how we're going to deal with that information. The question is, can these actions be traced in my audit trail? Every action that transforms the raw data into the analytical dataset should be able to be traced within the audit trail. Minor actions in the data wrangling phase can have major consequences later on. After we've transformed our raw data into an analytical dataset in the data wrangling phase, we tend to go forward and do some exploratory data analysis after which we go forward and do some more formal analysis, usually something like statistical modeling. But it's not a straight linear phase. We quite often have to loop back around and do some more exploratory data analysis. We sometimes have to go further back and do some more data wrangling as well. And then we end up with a set of results that we'll write up and ultimately submit for peer review. In the data analysis phase, there are many, many operations that we routinely undertake that are very easy to overlook. For example, which cases do we choose in an analysis or the format of the variables? How do we treat missing data? Which estimation method do we use? We may be estimating the model and we may have to decide between using maximum light, head estimation, or generalized least squares, for example. We may have to think about what weights suit our analysis or how we're going to represent the structure of the survey. We may be doing something exotic like bootstrapping and we need to think about setting a seed for generating random numbers. We may be doing something like fitting a random effects model and we're trying to decide the number of quadrature points. Do we use the standard or the default number or do we need a different number of mass quadrature points? We may, when working with software such as R or Python, have to think about which library to choose to undertake a certain procedure or, indeed, which version of a software package we're using. And often, many of these operations are overlooked, but they're vital parts of the data analysis phase. The question again is, can these actions be traced in my audit trail? And once again, every single one of these actions should be traceable in the audit trail, improving the workflow. The workflow should better support you and what you do, not changing you into something you're not. So really, what you want to do is improve your workflow to support you and how you work rather than implementing a kind of very regimental, very kind of Stalinist, almost, view of how you should work. Because if you do that, then you won't be able to stick to it. So you need a workflow that better supports you and what you do. Remember, all serious work must be reproducible. There must be an audit trail. And I'll return to this point again, but I'll say it again now. All serious work must be reproducible. There must be an audit trail. A planned workflow has a number of benefits. I sometimes call these the four pillars of wisdom, their accuracy, programming efficiency, transparency, and reproducibility. What do these mean? The four pillars of wisdom. The first is accuracy, minimizing information loss and errors in analyses and outputs. Programming efficiency. Automation, for example, maximizing the use of features in software. So for example, rather than doing something 10 times for 10 waves of data, you need to do something like write a loop that will loop over the 10 waves of data. So you're using the software or the programming language to work more efficiently. Transparency. You need to be able to show what you did, why you did it, when you did it, and how you did it. So transparency, showing what you did, why you did it, when you did it, how you did it. So this leads on to reproducibility. Can you get the same result every time? Whoever it is doing it or wherever it is you're doing it, do you get the same result if you run the analysis on your laptop or on a university network machine? The work should be reproducible. And this will help, especially when editing. This is a point I'll come back to. So when you're rewriting things like rewriting parts of your thesis, having to undertake new analyses, for example, or when you've submitted a paper and you've got evil referees' comments back and you have to go back to the work and do more or change things. So this will be natural benefit. I'll tell you Long's law now, this is J. Scott Long from Indiana. He says it's always easier to document today than it is tomorrow. Corollary number one of Long's law, nobody likes to write documentation. Corollary number two, nobody ever regrets having written documentation. And the final thing Long says is, has anyone in the history of data analysis ever said, these files are too well documented? Keep calm and write comments. So I'm going to get you to visualize for a moment. It's about 4.15 on a Friday. You're working on something. You need to go relatively soon. In fact, members of your department are meeting up for a drink after work. What do you do? Well, it's very, very tempting to just save your file and think I'll put some comments in first thing on Monday morning. Well, that's a good intention, but we can all guess what's going to happen when you come in on Monday and there's another 40 email to answer and students waiting to see you, for example, if this is all going to fall apart. Write comments, however cursory, comment, comment, comment. This is the key to a good workflow, is having lots and lots of commentary, lots of narrative in your documentation. But the good news, this is a good news story. Improving a workflow can be done with a modest amount of effort. And the other bit of good news is the less experience you have, the better, because you can just start from scratch. If you're a very experienced researcher, one of the things you can do is wake up and say that from tomorrow, every new project you're going to engage in, you're going to improve your workflow. But if you're starting out, if you're a master's student or a PhD student or an early career researcher, you can just say like from now on, from tomorrow, I'll wake up and I'm going to try and follow good workflow practices. At this point, you may be sitting there thinking, please give me some practical strategies and tactics and tips for improving my workflow. And there are a number of things you can do quite easily that will help your workflow. Having a standard directory structure will help you enormously in your workflow. Here's one that's suggested by J. Scott Long. It's quite elaborate. He's got a code books in one folder, clean data in a folder, raw data in another folder, his Stata Do files in another folder, and other folders for documents, figures, logs, tables, a temporary folder that could be used, for example, when merging files or matching data, a trash folder, clearly, for the things he doesn't want, a working folder that he may be using for kind of day-to-day working before something is lodged more permanently in one of the other folders. File naming conventions are very important. That takes us back to the start of this presentation when I said, have you ever wondered about a file? Here's another J. Scott Long suggestion, one that I've worked with for many years now. So a file name for me has a name. It's normally something that is very i-readable. So something that will give me a clue as to what it's all about. A date, the depositors' initials, the version and the type. And the versioning is particularly important in terms of keeping track. So for example, British Household Panel study, BHPS, the Wave A individual response file. You can see that from the i-readable name, and that's their protocol down at ISO. It's a very good one. So the BHPS, Wave A individual response. So that's BHPS, a Indresp. Then I've got the date of the file. So I've got the year, the month and then the day. You'll produce many files in a year. So having it round this way is very important because you don't want to have loads of files ending in 2014. I have produced some other files since 2014. So I've got the i-readable name, the date, the depositors' initials, that's me, VG, and the version. So it's V1 and this is a .dta file. So it's a Stata data file. So this would be a BHPS file, a Indresp. It's deposited on the 6th of May, 2014. It's deposited by Vernengale VG and it's version 1. And the file type is a Stata .dta file. So a good file naming convention. Again, you can start from tomorrow. If you do so, it will help you enormously. Certainly there'll be a time in the third year, the final part of your PhD, it might be later in the third year even, where you're looking for files produced in year one. And this sort of protocol will save you lots of time, lots of anxiety, lots of stress. It will help you keep track. The analysis file, depending on what software you use, if you use SPSS, it will be a syntax file. If you use Stata, it will be a .do file. If you use R, it will be an R script. It might be, you might be working in R Markdown, you might be using R Studio. If you're in Python, for example, when I work in Python, I tend to use Jupyter Notebook. But whatever system you use, whatever software or data analysis language you're using, whatever you're using, have a system so that when you write out your syntactical commands, both in the data wrangling phrase and the data analysis phase, you have some general information. So for me, this is the sort of information that might come at the start of a file. The information on the author, the project, the subproject it's part of, the date of the next meeting or my next supervision, what the date of the latest update is and a track of the previous updates. And you notice I have my next actions at the top of the file. What lots of people do is they write some kind of note to themselves about what they've got to do next, but that comes after a thousand lines of code. So I have to scroll all the way down. When I open up one of my files, I can see what I'm supposed to do next right at the top. So that kind of headlining helps me understand where I've got to and what I've got to do next. Variable naming protocols. Good data providers will tend to stick to clearly defined variable naming conventions. So if you download a data set like the PSID from the US or the SERP from Germany or the British Household Panel Study or the UK Household Longitudinal Study or any of the British birth cohorts, the data providers will have done lots of work to curate the data and they'll tend to have fairly good naming conventions. This, for example, is way one of understanding society, the UK Household Longitudinal Study.  So in wave A of the survey, wave one of the survey is underscore sex. In wave two, it's b underscore sex and so on. And if you go to the UK data archive, you'll see this in study number 6614. Similarly, if you go to the Youth Cohort Study series, time series for England, Wales and Scotland, this spans 1984 to 2002, the variable T0 SEH type, school type. Once again, I-readable, very, very useful. So it's T0, time zero, time point zero, school type. It's the type of school that the people attended in year 11. So it's at time zero of the survey. And if you go to the UK data archive, this is in study number 5965. However, look at this survey question. Here's a survey question. It says, here are some things, both good or bad, which people have said about their fourth year and fourth and fifth years at school. We would like to know what you think. Please tick a box for each one to say whether you agree or disagree. School does help to give me confidence to make decisions. And the person, either the pupil, either agrees or disagrees. In the data set, this is what it looks like. It's by contrast, the Youth Cohort Study of England and Wales and Cohort Four, this is, which is study number 3107. This variable here is given the opaque name, DX11 underscore A. Not particularly I-readable, so you can't guess what it could be and how you'd ever get some information about that. So again, a protocol, think about your protocols. This isn't a particularly useful one for naming variables in the data set. I'm going to move aside for a moment and just talk about estimating work time, just so that I say this because it's often overlooked. I worked at Stirling University for a long time. I worked with my colleague and personal friend, Professor Paul Lambert, and the students there quite often joke that it was something called the Gail Lambert constant. The idea that work takes five times longer than you think it does, and I actually got some people to test this. A load of data analysts in the last couple of years to estimate the time that certain tasks would take and really the five times constant is very, very, very, very close to being correct a lot of the time. So essentially, if you think a piece of work is going to take an hour, it will probably take you five hours. If you think it's going to take a day, it will probably take you about five days. If you think it's going to take you a week and it's probably going to take you five weeks and so on. Why is this important? Well, this is very important when we plan work, but it's also important when we decide to turn work into supervisors, when we estimate how long things are going to take. It becomes absolutely critically important, for example, when writing grant proposals and costing data analysis when doing consultancy work and so on. So I would say data wrangling, data analysis always takes five times longer than you estimate. So think really hard about that. And it's five times when you've got a good workflow. So you can make it much longer than five times by having a kind of shoddy workflow. But I think you can probably really get in the habit of thinking about how long the task is going to take and then thinking, well, I need a slot that's about five times that to do a good job even with a good workflow. The benefits of a good workflow. There are a number of benefits to having a good workflow. First of all, it limits the duplication of effort. A good example is if you've got a good workflow and you've analyzed a single wave of a household panel study, for example, this will allow you to analyze subsequent waves without duplicating as much effort. The next is systematic work minimizes errors. And I would say that systematic work in most walks of life will minimize errors. It also helps us to detect errors. It becomes critical when editing work, whether this be revised in thesis chapters or revisions that are made after evil referees have sent back comments and sometimes these require quite a lot of work. One of the things we know about the publication process is sometimes there's a large lag between undertaking the work and submitting it and then getting comments back. And if you can rapidly return, pick up where you left off and also go back in the workflow process and sort things out, this will be a major benefit. It will aid collaboration. So if you're working across teams or if you're doing interdisciplinary research or working with people in another university or even another country, having a clear workflow so that they can look in, see what you've done, add to it, change parts of what you've done and you can understand what they've done and change parts of work or add to things, that will aid your collaboration and speed up outputs from it. It will support additional work in the future. So whether that be work that immediately follows on or new work that you take up that draws on the work that's previously done, having a good workflow that is well documented will always help to support additional work. This researcher here was aided by an early career researcher. It was this researcher here. Help your future self by having a good workflow. What to do? First, always have an audit trail. Second, don't use drop-down menus. A GUI will land you in a sticky mess. Write out the commands you need for data wrangling operations and the commands you need for data analysis operations. Have a systematic directory structure. Have a convention for file names and for variable names and pay attention to version control that helps you keep track of things. Finally, most importantly, plan. Don't do ad hoc work or work on the fly. And write comments. You can never have too many comments. Write comments. Comments are your friends. Jay Scott Long produced a book called The Workflow of Data Analysis Using Stata. It's a real bible on the subject of the workflow and whatever age or career stage you're at, it's worth a read. He's also posted a really good PDF version of a talk on the workflow. The link is below. And a few years ago, myself and my colleague Paul Lambert wrote The Workflow A Practical Guide to Producing Accurate, Efficient, Transparent and Reproducible Social Survey Data Analysis. And that's an NCRM working paper that's available from the address here. Remember, all serious work must be reproducible. There must be an audit trail.


Now, what is very important is that what if two events are correlated? Now, if two events, for example, I am tossing die, I die twice. Once I get five, another time I get three, are they correlated? They are independent, if the, my experiment is then two independent event will be, they are just probability of happening two is pa times pb. So, if it is in case of my, I am throwing a die, then one over six into one over six, that becomes one over 36, like if I have one and five, then I get one over 36 for that giant power distribution. This is very important because in real world, in many, many cases, these independence, these independence theorem you can say, independence is not valid. So, not at all affected by one, getting one three of dies is not important by the two, hence the probability as I said is multiplicative. Again consider two events a and b. Now, we want to know what happened in this case, they are not correlated at all. One outcome of second experiment does not depend my outcome of the first experiment. However, as I keep saying in the most of the case in the world, these two are indeed correlated. That is what is interesting. What is important when there is a correlation? You have a phase transition when there is a correlation. You know, we live in the world because things are correlated. If they are independent ideal gas, then we won't survive. So, now if we can ask the question given an event a, what is the probability of the occurrence b? This is the called the conditional probability that I give you an information. Now, if a has already occurred, then probability b depends that a has occurred. I give an example, I take a liquid molecule and around the liquid molecule there are 10 neighbors. I tell you that there is a 10 neighbors now. Now, next time about say 1 picosecond later or 100 femtosecond later, I ask you what are the probability the number of molecules will be 10 or 11 or 12. And you will know now it is within that number that will be either 10, 11 or 12. So, conditional probability says knowing an information of an experiment. When you know that, then before even you do the next experiment, you have an idea of what would be the outcome. So, this is the what is the presence of correlation or correlated events. This is a very common term we used in probability theory or physics or chemistry that the two events can be correlated by many different ways, but in the examples I am giving you, they are correlated by intermolecular interaction. So, the study of statistical mechanics. So, we have now talked about random variable. We have talked of sample space. We have talked when the two events are not correlated like throwing a dice or tossing coin. However, in real world, as I said, things are interesting only when they are correlated. And so, study of statistical mechanics is that is what Bojman tried to do all his life. This correlation between two particles in a binary system. Ideal gas does not have a correlation, but you can see when ideal gas has such rich predictive power. When you take binary thing into account, you again go very far, but you have to work much harder now. So, study of statistical mechanics is a study of different types of correlations between atoms and molecules, whether liquid or gas or solid, superconductivity or whatever you do. This is essentially studies of these correlations in different form of other. So, this we call ideal behavior when total absence of correlation of molecules that we call very important term non-interacting limit. So, this non-interacting limit is the limit that I said we will do later. As I already said that the correlation is essentially conditional probability. So, when you talk of conditional probability, the two events, one happening and what is the probability, the next experiment will have this outcome. That is essentially is the our beginning of the correlation. So, this is a quantitative measure. So, conditional probability provides a quantitative measure of such correlation. That is how we construct, for example, radial distribution function or other things. As I said this is one of the central quantity in many body systems whether colloids or liquids or your austral ripening all these things essentially depends on this kind of things.  Calculate the probability that you already did. What is the probability of the number? This is the simple thing. Now, I will give you an interesting result that the, what is the probability that numbers of the two dies are different. And you can see that if I sum of the two outcomes and plot the probability, of course, nothing can be below 2, nothing can be above 12. But this is interesting structure because the one that is here is the maximum way it can happen. 2 is 1 plus 1, 12 is 6 plus 6, this. So, as you have, for example, 8, 8 can be 5 plus 3, 3 plus 5 plus 4 plus 4. So, this is 6 possible outcomes and you can get the answer. Another thing is that from a well suffered pack of 15 playing cards find the probability of drawing an ace king and equine. The order of draw is maintained. You know, you are doing that combinatorics and permutation. The order is not important. Now, this is again, when order is important, then of course, you have many more outcomes. When order is not important, when order is not maintained, when order is important, yes, you have less number, but order is not maintained. Every time you have lot more outcome. And next is, this is my favorite. I have talked about it there. And let us see a monkey typing a line from Shakespeare's Hamlet. He thinks it is like a whistle. Then you have 27 characters probability of writing. So, very interesting is that suddenly from this kind of rather in a class textbook war in all your high school math suddenly it graduated to a frontline research problem. This happens statistical mechanics. This is protein folding and most important paper of protein folding the Leventel paradox. So, this is the beauty of the probability theory that everywhere you have to construct the elementary model. And the basic idea again, that if you do, if the monkey has no, like it typed randomly, then it takes, how long it will take, it will have 10 to the power of some 33 attempts. On the other hand, if you, this 2 to the power of 78 is something like 27 to the power of 8. And then this 2 to the power of n. This is 10, somewhere that is 10 to the power of 33. Because I have done that, but anyway, you can do it yourself. And yeah, it is a little bit more complicated that would be block of the correct 8 letters. This is a little bit simpler. You know, this block of 8 letters is made simple. But if you do, there should be a blank here. We think it's like a weasel, then you will have 27, 28 including blank, 28 pieces. So, you have to have 27 to the power of 28. That many, that's your sample space. 27 to 28 and that is what I said 10 to the power of 33. Here it makes it a little bit simpler. There is a block of 8 letters. But whatever, so this is a leventhal paradox that leventhal post in terms of protein folding. Now, so this is the elementary probability theory. Now, I am going to do something extremely important and that is the central limit theorem. Now, as I told you that, you know, assumptions are not given to use this kind of terminologies that they have one thing they call fundamental theorem of fundamental theorem of algebra. Now, what is the fundamental theorem of algebra? Anybody remembers? You read it many, many times in your high school and your B.Sc. Fundamental, I told the mathematicians don't at all. Nothing is interesting for them. When they use a language like that, it's very important. What is the fundamental theorem of algebra? Guys, you should read up your algebra a little bit. No doubt people don't respect chemists. So, that is the theorem is that you have a polynomial of degree N. How many roots it has? N roots. And now, if this depending on the values of ABC you can have all real or you have complex conjugate in PS. Why it is so important? All your numerical work, whenever you are finding a solution we solve by method of roots. Even you are underlying the programs you are using. Fundamental theorem of algebra is being used. Now, this central limit theorem is an amazing theorem just an amazing theorem. It is the most fundamental theorem of not one of the most fundamental theorem of probability theory. Saying that it is very important chemistry. It is a sum of N number of, we have talked about random variables. Variables which can take random numbers within a sample space. N number of random variables, let me do, I am tossing the coin N number of times, the dice N number of times. Now, I define S as a sum of the random variables. I give you the average number. Then this central limit theorem comes from nowhere. It tells you the probability that the sum has value S is this thing. But it is magical theorem. I think in my book I have probably three times I have discussed central limit theorem. That is really magical. I have gone to many, many comprehensive, in physics I do not have to ask. They will always ask a static comprehensive or cumulative exam what is central limit theorem and explain central limit theorem. So, this is now why your energy of the system is Gaussian and this full width at half of energy distribution, what is the full width at half in energy distribution? Specific heat. This is delta E square is Cv, Kv d square Cv. Volume, which is sum of the volume of course, that is not fluctuating, but you have to consider the empty space. That is also then Gaussian and that also isothermal compressibility. And the way we used to do, we did not always trust the computer program to give us random variables. So, we used to, but we have to sample from Gaussian distribution. If you are simulating an arrangement dynamics, then your force has to be Gaussian distributed. And then we used to form this, from an ICD we form the Gaussian distribution, then we sample from that distribution. So, this is what we use everywhere. It is something we are routinely using in term dependence statistical mechanics. Equilibrium statistical mechanics or anywhere. So, many of the results, if you know the center limit theorem of statistical mechanics, they become trivially A. So, total energy of the system, then weakly correlated, they have to be weakly correlated among themselves. This is a very strong theorem actually. And so, this is the specific heat as I just described. In variably Gaussian with the standard deviation, then the other thing that you know, end-to-end distribution in a polymer chain and where the total end-to-end distribution is sum over sum over these things. And then this end-to-end is Gaussian distribution. And that again follows trivially. You do not have to do anything. No random calculation. It follows from center limit theorem.  Now, in statistical mechanics, we have the phase space density and all the probabilistic description goes there. Pair correlation function as I described. Brownian motion I described. Protein folding, leventhal paradox. The monkey typing Shakespeare's sonnet. So, these are the things. They are all essentially the A of probability theory. So, to summarize this part of the probability theory is that it is something essential and you have to, you never know when you will, but you better develop a good understanding of the correlations and sample space and the probability that would really stand you in good way when you are doing these things. Any questions? No. Basic idea is to following. You have a random variable X. Let us say position. And you now do an experiment, find out what is the position. Now you do one more. So, whenever you think of random variables, you have to think what is the outcome. What are the values it can have? That define the sample space. Now, first I do the experiments, find all the sample space. Now, if I do an experiment, I get a value, say 10. Now I am repeating the going to the experiment. If it is not correlated, next value can be anywhere in the sample space. However, if they are correlated, then it will be a constraint on that. It will be near about that 10, something like that. Now, this is, anything else? Any other question? Yes. Sure. Very good question. This is just a very well-defined discrete experiment. Outcome is discrete. We are tossing, we are doing a dice. And that is the reason it is cosplay thing. But if your outcome is a continuous, within again a sample space, then you have no problem. Then you have your smooth thing that you are looking for. That is what is important. Even when you do computer simulations, we always tell students to look at individual values. What are your outcomes? And have many times, one or two results go out of bounds, then something is wrong. And ultimately many times the program becomes unstable. So, an idea of, for example, in a many-body simulation, energy has to be conserved. What do you mean energy has to be conserved? It is fluctuating, of course. But it has to be fluctuated within a given bound. If you do NPT simulation, then volume is fluctuating. But you need to know if it fluctuates too much, we discard it. Because then we say, my sample space is not what it should be. So, instead of blindly going and using a computer program, it is very important to realize what is going on inside, not inside the program, but in the problem. What are the kinds of things? Because one of my students now simulating the old problem I did long, long time ago, the diffusion, 30 years ago, diffusion in a triangular potential, which is a very interesting trapping incident. Once one professor from Cambridge, came to me and was very excited about that work. He heard of that work and he heard Bangalore. He came to study of chaos. And I was least interested. In my young age, I would do what I want to do. Anybody coming and telling me that let's do this problem, I would not take that. I should have done that. But that problem now, my student, I told him just simulate it. Find out, what happened, there is a trapping. It is not trapping in local, it is trapping in a trajectory space. So then it goes like this along a line. Then after some time it goes off. It becomes diffusive in a very long time. So how it goes from one trap trajectory to another trap trajectory. And how the diffusion sets scene. When you publish that we did some work but we didn't have this kind of computer power. So we could do only up to for example, elementary steps of 1 million or so. To do this you need to run many billions. So I am asking, I am telling this student, look into it carefully as a problem of mechanics. Now we will, anything else? 1 over root over n in all the power distribution that comes in that comes in of course from center limit theorem. If you do just the binary coin then 1 over root n comes in and so basic idea of course one gets from other than center limit theorem you want a physical insight 1 over root n. Is that what your question? So one of the thing is that you know the statistical mechanics that when we get delta E square and we divide delta E square by n and a system is stable if it goes is n going to infinity the relative fluctuation has to go to 0. So we get root over n by n 1 over root n that goes to 0 and that saves our day and we become okay with that. Now precisely 1 over root over n comes from in the tossing of coin that I believe comes from our application of starlings theorem okay but physical insight of that I have to think about it is a very good question probably I knew but now I do not remember it why it is 1 over root n why not 1 over why not n to the power of 1 third yeah that is different that is very different thing that is when you have instability or you have things going out of bound yeah you get always 1 over root n central limit theorem gives you 1 over root over n and many of the times we are happy with the central limit theorem giving 1 over root n is there anything deeper into that that is why 1 over root n why not a little different probably there is a very simple explanation of that but I have to think about it and I will get back to you about that right now I am more into probably getting into the next phase


Hi, I'm Denji. So in today's video I'm wearing these headphones which I normally use for music production on my band, Sabadia. And if you've been to the band's website as of recently, sabadia.xyz, then you may have noticed this new article at the top talking about a physical release of one of my albums, World of Denji. Now this is graciously made possible by Art from Arson, a New York-based label which is able to get both a CD and a cassette made of my album. So if you've ever wanted a physical release of my music, there's your chance. The link is in the description. But today's video isn't just about this new release. All the proceeds from this release will be going straight to the Cystic Pharbosis Foundation which works to help people with Cystic Pharbosis and a fight for a cure to this genetic illness. Just in case you don't know, I talk about it a little bit more in my article on the website, but basically there's something in your body called the CFTR protein. Now this protein is normally responsible for the fluids secreted in your body like sweat and most notably mucus. So normally, under normal human functioning, these different fluids are pretty easy to break down. They're pretty thin. However, with Cystic Pharbosis, if your CFTR protein has this mutation, what happens is these fluids are actually quite thick and difficult to break down, which causes problems with respiration and actually causes infertility. Now approximately 100,000 people in the world are affected by Cystic Pharbosis. So it's not a massive genetic illness, but it's still pretty important and I thought that I had a lot of reasons to support this foundation. If you go to their research and clinical trials page, you'll notice that scrolling all the way down to what they actually fund, the biggest slice of this investment pie over here, if you click on the cure one, this is the biggest slice of all their money. So they're not just working towards short term treatment for people with CFF and making them live longer, which by the way is another thing which they've been able to accomplish. You know, if you look at the 1950s, as I talked about in the little article, it was rare for the average person suffering from Cystic Pharbosis to reach the age of 18, whereas nowadays people are living well into the 30s with Cystic Pharbosis. So they are working on treatment, but they're also working towards a cure and the three different methods for a cure that could possibly stop this from even being a genetic illness in the future. So if you ever wanted to support my music and also support a really good foundation, then this is your chance.  Anyways, I've been Denchi, I hope you enjoyed this video, goodbye.


YouTube team keep it clean. What's going on? It's engraving here with another video and I can't even lie. I'm shocked I'm shocked not shocked that it didn't work out Not shocked that Tim T bulls transition to tight end. It went south but I'm shocked that the Jaguars they cut him this early because I Just I mean we knew from jump. It was a business move We knew that like you got the number one overall pick Jags fans are super excited about Trevor Lawrence as they should be and So you want to capitalize on that excitement? Why not add even more excitement to it? Oh, man Jaguars are thinking about adding Tim T bull as a tight end. It's like whoa, what and then they actually go through with the Sign and it's like whoa whoo all up now And that that was just when we knew again. It was a business move. It was a business move that made business sense and Tim T boy at one point. They said he even had the top-selling Jersey. So now I guess all those people have throwbacks Within what a couple of months your Jersey turns into a throwback But shout out to the NFL shout out to the Jaguars. Shout out to Tim T bull for making that bread So I'm not mad at them at all for that, but I'm just shocked that it happened this early Honestly, I really thought that Tim T bull was going to make the roster I didn't think he would be there starting tight end But I thought that he would be a guy that they would keep on the roster especially again them take your sales Take yourselves everything like especially in the year with the NFL Has to sort of make up for last year Because there were no fans at the majority of stadiums for the majority of the season So I really thought T bull was not a lock, but a lock So this him being released it. Yeah, it kind of came out of left field for me Now and then after after those blocks where those blocks went viral I guess Jack was like look T bull man.  We know you you play with the gators up the road from here But I mean a look man this thing After those blocks went viral. It just this ain't gonna cut it. It's it's not gonna work out. It's it's not you It's me. That's probably what con told him So now Tim T bull to the Jaguars is over and His NFL career probably is too I mean it already was but then with the transition to tight end and him being Well, 30 something years old not to say you couldn't come back and do it, but Yeah, this is uh, this is probably gonna be it. This is a wrap So just like Tim T bull is officially now with the Jacksonville Jaguars I'm out


Okay, so how do I synthesize nitrials? There's a couple of ways to synthesize them, one you already know from organic one, it's the synthesis of a nitrile through SN2 reaction using an alkyl halide and sodium cyanide. So this again is going to be an SN2 reaction. So sodium cyanide, sodium CN minus, so cyanide actually looks like this, and where does the negative charge line on this carbon, of course, right? Okay, so this thing, primary alkyl halide, right, goes primary or secondary, probably do the SN2 mechanism. In fact, this is the way to make primary or secondary nitrile. You can't make a tertiary nitrile doing it this way. Why? Because SN2 reactions don't happen where there's a lot of steric bulk, right? And you can't hit that backside if you've got a big backside. Okay? So knock it out, and there's your one step reaction, and in fact, I'm going to draw it, not that it matters at all, but just to emphasize that we did that backside attack. Is everybody cool with that? The mechanisms were easy. Any questions? Okay. Thank you. Bye. Bye. Bye. Bye.


Welcome to Access to Trader, the number one community for those who are committed to taking control of their trading in order to achieve success, profitability, and longevity. Thank you for joining us. Here's Dan Shapiro to help you find your edge, master your process, and own your future. Hey guys, good evening everybody. Welcome to another edition of the Access to Trader.com Nightly Update. Hope everybody is doing well. Hope everybody had a good day of trading. A lot going on today as you can imagine between the Fed minutes, between earnings, between the video after the close. We'll get to those in a minute. But first, if you are brand new to the channel guys, thank you very much for tuning in. Welcome aboard. The only thing we ask is if you like the content and you enjoy the daily videos, all we ask is for a like, a like, share, and subscribe to the channel. All you have to do is just sit back, relax, and kind of dissect the information. So let's talk about the tape. Number one, market continues to act very, very well. Despite the red date, again, they use the word red. Maybe it's kind of tongue-in-cheek. Dow down 62 points. The Dow, S&P down 9. The NASDAQ down half of a percent or 84 points. You had a lot of retail numbers coming out this morning from names like AEO, right? AEO and Abercrombie and Fitch, which had a nice, really nice rebound turnaround. Best Buy, I could have told you Best Buy was going to miss their numbers. Stock didn't react that bad, but I could have told you Best Buy. I went to buy my kid's printer at Best Buy Saturday. It was around a quarter to 12. I was literally the only one in the store. And I was expecting, I don't remember the last time I bought a printer, but I was expected to pay, what, three, four hundred bucks. There was a printer there, I think it was a Hewlett Packard. It was marked down from like three twenty-five to a hundred bucks. So only one in the store, right? Only one in the store, a hundred bucks for a printer. I could have told you. So basically you're seeing the same thing. Look at Cole's numbers as well. Again, you can see Wall Street and Main Street are completely disconnected. Don't let the performance of the market, how strong the market is, kind of take away or kind of resemble what's going on in Main Street America. I believe they said that the average household income is like fifty-eight, sixty-thousand dollars. So tack on some inflation, high interest rates and all that stuff. You can see the retailer is not doing great, not doing great at all. That's why it's so amazing that Target actually had a very, very good quarter. It actually still looks really, really good consolidating its earnings. But again, weak retail sales continue to come out. We had the Fed minutes come out at two o'clock, and basically the Fed really gave no indication. With the market kind of tried to decipher from the last FOMC meeting that they were going to not only pause interest rate hikes, but they're going to start to take them down. Well, the Fed minutes read a little bit differently. Really no indication of a rate cut that is imminent. Market actually did not do anything. It actually did not give back anything on those Fed minutes and actually held up very, very well in the common denominator of what we've been seeing on any red days. And again, it hasn't been many red days in the last three weeks. But the common denominator that's still going on is we're still putting in higher lows. We never took out previous days' channel. This channel never took out this channel. This channel never took out this channel. So the market continues to do very, very well. Even news of Amazon, for example, and you see this at the open word came, I think of CNBC who reported that Jeff Bezos was selling, I think it was 1.7 million shares of the stock, whatever X amount of billions of dollars that is. Initially, the stock got hit. And then in true fashion, the stock rallied literally rallied about $3 off its lows. Again, very, very strong market. It doesn't make a difference what the news is, very, very strong. And the one name, the one name that we, if you watched the video last night, again, thank you very much for tuning in. If you watched the video last night, the first thing I said today at Morning Strategy, there's only one stock I want to trade to me. There's literally only one stock I want to trade because I'm getting a little bit tired. It's a day before a busy travel holiday. I'm kind of starting to get into holiday mode. Holiday mode. Like many of you guys, I am hosting Thanksgiving on Thursday. So I'm thinking, oh my God, my wife's going to give me a laundry list of things to do on Wednesday. You've got to clean. You've got to buy food. You've got to pick up food and this and that and the other thing. So it's a whole big thing. So it's kind of in just like one mode. And we talked about this last night in the video, the options market was dictating yesterday a big, big call buying coming in. And despite the weakness from the market, Tesla and we'll get to the pivots in a second. We'll literally pivot because this is literally the only trade I took today. It reclaimed the 50-day moving average. It had a really nice run. Give us a really, really awesome run right from the word go. Reclaimed the previous day's channel and just gave us like a five and a half dollar move. Literally in about, you know, seven to 10 minutes. Great movement. We still have a runner from the 238, 238 range. It's holding up here a little bit, holding up here a little bit. So we'll see what happens there. But it really does show you the importance of being prepared, the importance of, you know, in at least in my opinion, being familiarize yourself with a group or a group of stocks that he's could continuously trade over and over and over again. You know their personalities. You don't care what happens with the rest of the market as long as you are dialed in on the technical levels of certain stocks. And yesterday, we, you know, I think I made a pretty good case of what happens if they reclaimed the 50-day moving average. It did so today. Put up again nearly a $6 candle. And now let's see what happens. And what happens next on Tesla is if it can hold, right? If it can hold today's range for tomorrow. You see the top of the range here, guys? See the November 15 highs? This is literally the last supply zone, right? Literally the last supply zone. They are still coming very aggressively today for the 245, the 250s. We saw it 260s for next week. Guys, there's literally one hurdle left in this trade. Okay. Whether it comes tomorrow, it doesn't come at all. That's what she said. That's what I said. But the point is eventually, right? Eventually, if Tesla can get rid of this last supply zone right over here. Boy, oh boy, look how much room we have here. So next couple of days is going to be super and duper important for Tesla. I will definitely be adding more on the top of the range here because we have all aerospace. What all this was here was a channel break to the next channel. Channel break to the next channel. Now we have one channel left and hopefully Tesla could get really, really going. It's actually holding up here after hours. We'll get to the video in a second. But again, it was basically one and done. It was a Ben Simmons scenario. Maybe that's not the best example in the world, but you guys kind of get my point. So let's talk about the big story after hours. That is NVIDIA. Right? That is NVIDIA. NVIDIA, again, just to kind of rewind. And by the way, it came in long. It came in. I had a runner on NVIDIA yesterday. I had a $5 runner on NVIDIA yesterday, which I got stopped outbreak even today, but great trade yesterday on NVIDIA. But anyway, so NVIDIA has this big, big run, 150, 120 points off its lows. They came out with earnings. The numbers actually looked really good, right? They beat on top bottom line. I think the revenue trip, like everything was good. I mean, every single, I'm just reading it here. Like every single metric was beat. I think they guided higher like everything stock right now, right now, right now, literally right now. After going up first, then going down first stock right now. And right now it's five o'clock Eastern time. Okay. Stock is currently down about three points. Okay. It's about three points. You'll see the whole big mishmash here. It's only down three points, which is, again, it's going to change by the time you guys are going to be watching this video. By the time you guys watching this video, NVIDIA is either going to be like at 520 or it's going to be like at 460, right? Because the conference call is going to be in a little bit. And we're going to see the true reaction of NVIDIA after the conference call. So by the time you watch it, like I said, I'm guessing it's probably going to be like either 510 or 470. So again, I'm just recording the video now. I have to go drive my kids to basketball. But the point is we'll see what happens tomorrow. The good part about it is we know going into tomorrow's session, you know, I'm going to watch both sides, right? No matter what the conference call says, we're going to be ready for both sides tomorrow. You know, we have the bottom of the channel here, right? The bottom of the channel here, which represents the five-day moving average, which was a low from five, six days ago. And we're going to use the top of the range here that we saw after hours today. So something will give us a trade for tomorrow. At some point, it'll give us a trade to tomorrow. The question is, where is it going to be after the conference call to be determined? There's no reason to guess. We're prepared tomorrow. For the upside of the video, we're prepared tomorrow. For the downside of the video, all it just needs to confirm. Other than that, you know, other than that, market continues to be pretty healthy.  Even in the initial reaction today, when the video went down initially 15 points, you know, stocks were down basically 50 cents of dollars. It really does show you how individualized is kind of the latest v-shape recovery bull market is. It's just super-duper explosive. And sellers are comfortable with levels. Again, can that change going into tomorrow's session? Absolutely, right? Absolutely. Again, we're trading day to day. We're trading trade for trade. Now nobody's trying to predict what's going to happen three weeks from now, let alone two days from now. We're just trying to win our interval for tomorrow. And again, if you look at a lot of names, you're not going to see explosive setups just because everything had such a big run. But you are seeing a lot of value going into tomorrow's sector in different sectors, right? Let me give you guys some ideas. Target, again, is holding up incredibly well, right? Really, really well. Doing incredibly well here. It just needs to take out earnings highs for this thing to start waking up. Look at AIG obviously in the financial space. Looking pretty good, right? Looking pretty good as well. A nice-looking chart on AIG. Again, AIG is not something that I'm going to trade, but again, to each his own. Who might have told you what looks bad or good? If the market kind of continues shakes off the video's earnings, look at Google, right? Look at Google. The only reason why Google stopped a couple of days ago was this linear regression line. This looks ready to go. But obviously, the one that, again, I want, again, I have a runner overnight from the 238 breakout. 238, excuse me, 238 reclaiming the 50-day moving average. Where I want to add is Tesla. I mean, that's the one I want to add, man. Again, I'm hoping it shakes off weakness. If there is any weakness in the morning and starts attacking this top of the range here, because boy, oh, boy, if we could, again, guys, if we can close above the 100-day SMA, look, guys, there's literally no supply until 285. Again, it's not going to get there one day, but boy, oh, boy, that's what you want to see. You want to see airspace. If you ever watched the PS60 workshop or been kind of in our webinar or anything, there's something called the Barry Sanders effect, which basically means if all you guys who are old football fans or not football fans at all, but there was one of the greatest running backs of all time was Barry Sanders. And he played on absolutely one of the worst offensive lines during that time with the Detroit Lions. And he would have a game, you know, one carry, two yards, two carries, five yards, three carries, nine yards. And then next thing you know, the hole would open just a little bit, and he would take it 80 yards to the house, right, to the touchdown. And that's exactly what Tesla's doing, right? Here it is. Here's your one carry, three, four yards, another carry, two yards, another carry, three yards. And here's your last line of defense. You just need that hole to open up here. And Mr. Barry Sanders is going to take it right to the house. We'll see. You know, we'll see. I hope it happens, but we will obviously be prepared. If nothing, obviously somebody's break, even as my stop for tomorrow. And if you look at, if you look at our watch list, and literally our watch list for this morning, I literally had one, two, three, four pivots, four pivots, three of them didn't confirm. This was the one right here. 237.40 needs to build. This was literally my only trade of the day. And honestly, what else do you need? You have nearly a $6 move in five, seven minutes. Again, this was the whole pivot, right? Here was the whole pivot. This one absolutely nuts. And this is the highest close in the whole formation. Hopefully Tesla does what I hope it's going to do in the next couple of days so we can get some pretty big airspace above us. Other than that, again, we're waiting for an NVIDIA's conference call. A lot of people are going to be off tomorrow. A lot of people are going to be traveling tomorrow. A day ahead of Thanksgiving. Again, we are closed on Thursday and is a half a day on Friday. So let's see how much value we have tomorrow. Obviously my focus continues to be Tesla and I'd like to see where we can get the value tomorrow on the video, whether it's long or short. Guys, have a great, great day. Have an awesome Wednesday. Have an awesome Thanksgiving in case you guys are off tomorrow. That's help. I'll see you all again tomorrow. Take care.


U.S. strikes enemy weapons storage facility in Syria. U.S. military forces conducted a self-defense strike, November. Eight on a facility in eastern Syria, used by Iran's Islamic Revolutionary Guard Corps and affiliated groups. This strike was conducted by two F-15 aircraft against a weapons storage depot, said Secretary of Defense Lloyd Austin in a statement yesterday.