Hello and welcome to this session. This is Professor Farhad in which we would look at covariance and correlation coefficient as they apply in a portfolio of two risky assets. These topics are covered on the CPA as well as the CFA exam, essentials or principles of investment course. As always, I would like to remind you to connect with me on LinkedIn if you haven't done so. YouTube is where you would need to subscribe. I have 1800 plus accounting, auditing, tax, finance, as well as Excel tutorial. If you like my lectures, please like them, share them, put them in playlists. If they benefit you, it means they might benefit other people, share the wealth, connect with me on Instagram. On my website, farhadlectures.com, you will find additional resources to supplement this course as well as your other courses. I strongly suggest you check out my website, especially if you are studying for your CPA, CFA or CMA exam. So let's take a look at a portfolio of two risky assets. Now, the question is why did I choose or why do we choose two risky asset to illustrate this portfolio? Well, because it's relatively easy to analyze. You only have two assets or two securities and they illustrate the principles. It doesn't matter in consideration that apply the portfolio of many. So whether you have two, five or 50, the concept is the same. So we're going to be assuming two assets will be a bond fund and a stock fund. So think about it, a bond and a stock, but we're going to be using a fund. Once we understand the portfolio of two risky assets, we will reintroduce the choice in the next session of the risk-free assets. So we'll add one more component to this portfolio. Structing an efficient portfolio of many risky securities is a straightforward extension of this stripped-down asset allocation exercise. So simply put, we're going to take this two risky asset portfolio and project to other efficient portfolio. So to optimally construct the portfolio of risky assets, we need to understand how the uncertainties of the asset returns interact. How do they interact with each other? Okay, so a key to this interaction of the portfolio risk is the extent to which the return of the two assets vary either in tandem or in opposition. What does that mean? It means when you are since we're on selecting two risky portfolio and you said we're going to have stocks and bonds. Now, why did we say stock and bonds? Because from history, when stocks go up, bonds go down.  So there's kind of an inverse relationship or they work. It doesn't have to be inverse, but they don't work the same way. They work in opposition. Now, how much that opposition is or that inverse relationship we're going to look at it shortly. But the point is you don't want two securities that work together. For example, if you buy PepsiCo and you buy Coke, guess what? To a great degree, PepsiCo and Coke work together. When people are consuming soda product, they either buy PepsiCo or Coke. So if you have a portfolio with both PepsiCo and Coke, well, those two stocks, they should work the same way. So maybe you want to have PepsiCo and have something else than maybe a software company, maybe Apple computers. Now, the consumption of PepsiCo and Apple product may not have a relationship. So people could consume more PepsiCo product, could consume less of Apple, or they could consume more of Apple product and less of PepsiCo. So they don't work the same way. And that's what you want. You want to have portfolios. They don't work in the same direction. And we're going to explain this little bit further using numbers. But that's the basic idea. So portfolio risk depend on the covariance and we're going to learn about this term between the returns of the asset and the portfolio. So we're going to look at their covariance. How do they vary among each other? And we will illustrate this concept using a simple scenario analysis. And this simple scenario analysis, as long as you understand it, we're going to generate some rules from it and apply it to any other portfolio. So the portfolio we're going to be using will be using this data. So it's very important to understand what you are giving and how we are computing these numbers. So I'm going to show you only a computation of one sample that you should be able to do the rest. Here what we have, if we have a stock fund and we have a bond fund, those are the two assets. And we have scenarios. We have severe recession, mild recession, normal growth and boom. And we have the probability of those recession occurring. And remember, your probability should add up to 100%. This should be all a review for you because we already did this. So the stock fund in a severe recession, we expect negative 37% return. Well, if we take 0.5 times negative 37, it will give us an expected return under this scenario of negative 1.9. And we'll do the same thing for the mild recession, normal growth and boom. And when we add them all up, the expected return of the stock portfolio alone is 10%. We'll do the same thing for the bond portfolio. In a severe recession, in a severe recession, which is a 5% chance, we could earn negative 9%. We'll take 0.05% times negative 9%. We'll give us negative 0.45%. Then we'll do the same thing for the other scenarios and the expected return of the portfolio alone of bonds is 5%. And hopefully this makes sense. The stock portfolio will have, usually the stock portfolio will have a higher risk. Therefore, we have a higher return than the bond portfolio. So this is something you should be familiar with. Let's compute the variants and the standard deviation of these two investments. Again, this should be a review. So how do we compute the standard deviation and the variance for the portfolio? Basically, what we do is we first compute the range. So how do we compute the range? Remember, the stock portfolio has an expected return of 10%. Under an expected return of 10%, if it's a severe scenario, the expected return is negative 37. So what's the range? What's the range? The range is we go from, let me go back, we go from 10 to negative 37. The range is negative 47. Notice it's negative 47. And under a mild scenario, we have 10% and the expected return is negative 11. Well, the difference between the range from the expected is negative 21. So this is negative 21. And this is how we compute it for the normal and the boom. And this is how we compute the deviation or the range for the bond. Same thing. Remember, the bond has an expected return of 5%. So you want to go from 5 to negative 9. From 5 to negative 9 is negative 14. Now, what we do then, and this is again a review, if you're not sure how I'm doing this, go to my previous recording or go look into the playlist for the variance and the standard deviation. To find the variance, you will square negative 47. So to find this number, you'll take 47 times 47, which is 47 square. Then you multiply this by the probability 0.05 for the severe recession and you will come up with 110.45. And you will do the same thing for the other scenarios. Then you compute everything and the variance for the stock portfolio is 347. Remember, we don't care about the variance. We want to compute the standard deviation. You'll take the variance and you compute the standard deviation and it is 18.63. You will do the same thing for the bond. You compute the variance. Then you compute the standard deviation. The standard deviation for the bond is 8.27. And I hope this makes sense. The stocks are riskier because they have a higher standard deviation. And bond is less risky, bond less risk relative to stocks. And this should make sense. And this is represented showing in the standard deviation. So this makes sense. So remember, the expected return here is 10%. The expected return here is 5%. You expect less return. You should expect less risk. If you expect more return, you should expect more risk. Hopefully, we know the basic concept. So let's form a portfolio. And here what we're going to do, we're going to look at a portfolio. We're going to mix, rather than have a stock alone, rather than have a bonds alone, we're going to have a portfolio 40%, 40% in stocks and 60% in bond. So simply put, we're going to take 0.04. This is our weight in stocks multiplied by the return plus this is for stocks. We're going to take the weight and bonds and the weight and bonds is 60% multiplied by the return of the bond for each scenario. And remember, we're going to multiply 0.4%. This is the weight multiplied by the return and a severe recession and a severe recession for the stock. We're going to get negative 37. This is multiplied by negative 0.37. And for a severe recession for a bond, we're going to get negative 9. We're going to get negative 9. So what we want to find out first is this rate of return. When we mix things up 40% stocks, 60% bonds. Let me get my calculator and just show you how we compute this because it's very important that you know where the numbers are coming from. So we're going to take 0.4, the weight, the weight of the portfolio, 0.4 times 0.37. It's negative 37. So that's negative 0.148 plus. We're going to take the weight of the stocks 0.6 times 0.09. It's 9%. That's 0.09. And that's going to give us 0.054. That's also negative because that's a negative return. When we add the two negatives together, we're going to get negative 20.2. So the expected return under a severe recession is negative 20.2. We'll do the same thing for the mild recession. We'll do the same thing for the normal growth. We'll do the same thing for the boom. Now, when we take these returns, multiply them by the probability, we're going to get the expected return for each scenario than the expected return of the whole portfolio. So the expected return of the whole portfolio, 40% stocks, 60% bond is 7%. So remember, the stocks had an expected rate of 10. The bonds had an expected rate of 5. When we combine them 40% to 60% together, we're going to give us an expected return of 7. It's less than 10, but more than 5, 7%. Now, what we're going to find out is the variance and the standard deviation for the portfolio. Remember, the expected return now is 7. Now, we compute the variance. We're going to go from 7 to negative 20.2. So remember, the expected return is 7. And negative 0.2 is one of the scenarios under the severe recession. Therefore, the variance, the range is negative 27.2. And we'll do the same thing for the mild recession, normal growth and boom. Then we're going to take those deviation from the mean, and we're going to square them. So we're going to take negative 0.27 times 2 squared, and that's going to give us 739. We're going to take 2.4 squared, 3.4 squared. And we're going to multiply them by the probability 5%, 25% by these probabilities. Then we add them all up, and we're going to come up with the variance. Again, the variance, we don't use the variance. We use the standard deviation. We're going to take the variance and square it, and we're going to come up to the standard deviation. Now, what does that tell us? Well, it tells us the standard deviation of 6.65 is lower than the previous standard deviation. Remember, the standard deviation was 8.27 for the bond and 18.63. When we build a portfolio 60 to 40, the standard deviation is lower. That's good. Here we see the benefit of diversification. It means we lowered our risk. Yes, we did lower our return a little bit if we invested 100% of stocks, but we also lowered our risk. So let's just kind of learn what we have on the screen so we could move on. Again, this should be computing the variance and the standard deviation should be a review. So the lower risk portfolio is due to the inverse relationship between the performance of the bonds and the stocks. So here what we're starting to find out, it seems they don't work in tandem. They don't work together. They work inversely. And we actually, we can clearly see that. Now, in a mild recession, stocks fair poorly, but this offset by a large positive in the fund. In a mild recession, the stocks don't do well, but the bond will do well. So that's good. Conversely, in a boom scenario, when you have a good time, bond prices fall, stock prices do very well. So notice here, this is the benefit of diversification in a stock that has different type of securities that are inversely related. So portfolio risk is reduced because variation in return of the two assets are generally upsetting. And this is the benefit of diversification when the two securities didn't work in the same way. Now, we want to know how to measure that relationship. Okay, now we know that somehow they benefit when we combine them, the risk goes down. But how can we measure this, this relationship? Well, we're going to look at something called covariance and correlation, a correlation coefficient. So how can, how can, how one can measure the tendency of the return on two assets to vary in tandem or in opposition? We use two statistical measures. One is covariance and one is the correlation coefficient. So the covariance, look, look, it's coming from the word variance, okay? But this is covariance. The covariance is computed similar to the variance. How do we compute the variance? The variance, we take the range, which is the difference, the mean to the expected return and we square it. Here, what we're going to do instead of multiplying the difference of asset return from its expected value, we multiply it by the deviation of other assets returned from its expectation. And we'll see how, in a moment, the sine and magnitude of this product are determined whether the deviation from the mean moved together and whether they are small or large. And by doing so, we're going to find out how far, how much is the covariance? What's the magnitude of this multiplication? So let's take a look at the example here. So here's how we compute the covariance and the correlation coefficient. Here's what we do. First, we're going to find the deviation, which is what we already did, for the stock fund as well as for the bond fund. Remember how we did for the stock fund? We said the expected return is plus 10% for the stocks. And under a severe recession, we are at the expected return is negative 37. To go from 10% to the negative 37, we have the range of 47 or negative 47. Same thing with the bond. We said the expected return is five under a severe scenario. They're going to get negative nine. Five to negative nine is negative 14. So these are the ranges and we'll do the same thing for the other scenarios. Now, we're going to take the ranges and multiply them. We're going to multiply negative 47 times negative 14. It's going to give us positive 685. We're going to do the same thing here. But notice here, we have negative and positive. It's going to give us a negative number. It's good when we have a negative product because it means they are working in the opposite direction. A normal growth, they're positive, boom, one positive, one negative. Then what we do is we take those, multiply them by the probability, 0.05, 0.25, 0.4, and 0.3. Then we're going to get to these figures. We add up all these figures and we'll come up with the covariance of negative 47. Now, the covariance, that's fine, but we really want something other than the covariance. It's like the variance. So what we do, we want to find the correlation coefficient and we're going to explain what the correlation coefficient is. It's like the standard deviation. It makes more sense when you interpret the covariance in the correlation coefficient context. What we do is we'll take the covariance and we'll divide it by the standard deviation of the stocks times the standard deviation of the bonds or whatever standard deviation funds we have. And the correlation coefficient is negative 0.49. And this will make more sense. We'll discuss this in a moment because we need to learn this. But first, you need to learn how to compute it. So in column E, we multiply the stock fund deviation from its mean by the bond fund deviation. We talked about this. The product will be positive if both are positive. If both are positive and it will be negative, if it will be positive also of both are negative too. It will be negative of one positive and one negative. This is basically, we talked about this. And if we look at row four, again, the stock fund returns false short of its expected value by 21% while the bond exceeds its expected value by 10%. Again, what's happening here, these two products are working in the opposite direction. When one goes up, the other one goes down. So let's take a look at the covariance computation first from a statistical perspective. The covariance is the probability of weighted average of the product. It's called covariance measured by the average tendency of the asset return to vary in tandem. And this is the kind of the statistical formula. And basically, each particular scenario in this equation is labeled as I. So this is the severe recession for the stocks, the return of the stocks minus expected return. And we sum them all up and we'll do the same thing for demand. In our scenario, we had 10, when our example, we had 10 scenarios. Okay. And the negative value for the covariance indicate that two assets on average vary inversely. And this is really what you want. Now let's talk about the correlation coefficient, because this is important. Like variance, the unit of covariance is a percent square, which is why it's difficult to interpret, because it's a percent square, that's not what we want. We want a correlation coefficient. For instance, how do we interpret negative 74.8? Okay, we really can do that. The best way to find out whether it's a strong or not strong relationship is to interpret this as a correlation coefficient. So how do we compute the correlation coefficient? It's the covariance. We're going to take the covariance, which is negative 74.8. And we're going to divide this by the product of the standard deviation of the return of each fund. So we're going to divide this by the standard deviation of stocks times the standard deviation of bonds. Okay. And it's represented by the Greek letter rho. So our correlation coefficient for our example is negative 0.49. Now what does negative 0.49 mean? Well, the correlation is a pure number. It can range from negative one to one. So notice the maximum is one, you know, the maximum is one, and the lowest one is negative one. How do we interpret this? If we have a correlation of negative one, it indicates that one asset return varies perfectly inversely with the other. That's perfect. If you have a correlation of negative one, that's perfect. It means if you know what's going to happen to one stock, you know what's going to happen to the other stock. It's the exact opposite. So here, if you could have a portfolio with a correlation of negative one, it means get those stocks and put them together because now diversification is the best one. One goes down, the other one goes up. You can predict 100% the variability of one asset return if you know the return of the other asset. So this is like perfect, perfect inverse correlation. If you have a positive one, it would indicate perfect positive correlation. Here, diversification is not useful. It's like have a PepsiCo and Coke. And here, I'm simplifying so you understand. So PepsiCo and Coke, you would assume that those two stocks work together. So if you have a portfolio of PepsiCo and Coke, you're not really diversified because they work together. You want a portfolio that when one stock does bad, the other one, the other investment does well. So they work the opposite or not in tandem of each other. So the diversification here is not affected. You don't gain anything from diversification. Here, if you compute the portfolio standard deviation and the mean, they are a weighted average of the component of the security because they work the same way. There's no benefit from having one stock over the other. So the choice amount, the choice amount portfolio depends on how risk aversion you are because the diversification is out of the question. Are you comfortable with this portfolio? A correlation of zero means the two assets are unrelated. So one goes south, one goes north. There's no relationship between them. There's no correlation between them. Historically, the correlation coefficient between stocks and bonds is 0.2, historically based on historical data. 0.2, which is good. It means they vary positively, but not in the same direction. That's fine. So the correlation coefficient of point row of 0.49 confirms the tendency of the return of the stock and the bond varies inversely. So here in our example, the stock fund and the bond fund that we have varies inversely. And this is the best. When one goes up, the other one goes down. So what did we learn so far about tourist asset portfolio? Here's the three rules that we learned. Rule number one, the rate of return on a portfolio is the weighted average return on the component securities with the portfolio proportion as weight. Simply put, the return of the portfolio, you will take the weight times the return, the weight of the stock times the return.  The expected return of the portfolio is the weighted average of the expected return of the component, which is, again, the expected return of the portfolio is the weight of the bonds times the expected return of the bond plus the weight of the stock. You remember, we said 60%, 40%, and we had different scenarios for the return, then we add them up, then we find the expected return. And our example was 7%, if you remember this. So far, so good. So far, what we learned is the rule one and rule two says that the portfolio actual return and its mean are linear function of the component security. Simply put, if you have more bonds, well, you're going to have the return closer to the bond value. If you have more stocks, it's based on the weight. You're going to have more return closer to the stock. It's based on the weight. This is not true when we compute the portfolio variance. The portfolio variance does not care about the weight. The portfolio variance on a risky portfolio is a little bit different. So this is the formula for it. This is the formula for it. And what's going to affect the variance of the portfolio is not the weight. So the weight does not really matter. It's the nature of the stock, not the weight of the stock. I'm sorry, not the nature of the stock, the nature of the relationship between the two stocks. So the weight is irrelevant. What we, the variance tells us how do they interact? And based on the interaction, if the interaction is negative, that's a good covariate, good in a sense that we want it. If we want to build a portfolio, we don't want them to work together. We want the stocks to work differently. So when some do well, the others don't, and the opposite is true. So we can assess the benefit from the diversification from rules two and three to compare the risk and the expected return of a better diversified scenario benchmark. So let's take a look at, illustrate this concept again. Let's assume we have the expected return of the bond is 5%. The standard deviation of the bond is 8%. We have stocks, the expected return of the stock is 10%. The standard deviation is 19. And the correlation coefficient is 0.2. This is what we have. This is the, this is what we have. So if we have a stock that's 100% and bond, if we have stock that 100% and bond easy, we expect 5% return with a standard deviation of 8, 100% of bonds. Let's assume we want to invest 40% in stocks, 60% in bond. Here's what's going to happen. The expected return is 7%. No, the 7% is greater than investing only in bonds. Now, that's good, which represent a 2% increase in bond. Now, using rule number three, let's compute the standard deviation. When we compute the standard deviation of this 40 and 60%, we find that the standard deviation is 9.76, which is good. It means it's way lower than 19 and just a little bit higher than 8. But let's, let's do a quick computation to show you why rule number three doesn't go with the weight. If we compute the weighted average component of the standard deviation, it will give us 12.4. This is not how we compute it. But what I'm saying is the standard deviation doesn't care about the weight. That's what we're trying to say. Unless we're going to see later, yes, I mean, unless the correlation is perfect, is plus one, then you know, then it's going to be, this is how you do it. But this is not how it works. So because we combine those two stocks together, we combine them. We were able to lower the risk to 9.76, not 12.4. Because if the risk is based on the weight, the standard deviation should be 12.4. So the difference is 2.64. And this reflects the benefit of diversification because we diversify. Okay, so this benefit is cost free in a sense that diversification would allow us to experience full contribution of the stock, stocks higher expected return while keeping the portfolio below the average of the component of the standard deviation. And this is the beauty of diversification. You can lower your risk. You could lower your risk and still have a decent return. So your return is not based on your weight. The benefit of the diversification will give you a decent return with lower risk. And that's what you want. You always want. Remember, when I started this, and we're going to see this again, you have risk and you have return. And here's what's going to happen. The more risk you take, the more expected return you take. But if somehow, if somehow you can, rather than this is being a linear somehow, if you can take less risk, so basically what you really want, and we're going to see this in a moment, you want to take less risk and higher return. You want something like this taken less risk, but the return goes up very quickly. Like it's going to be like little bit banded. That's what you want. You want less risk and higher return. So here's what we can say. What analysts can and must do is show the investor and an entire investment opportunity. So what we did is we said 40, 60. This is the scenario that we kind of looked at. 40, 60. Let me highlight it for you. This is the scenario. So here we have stocks. Here we have bonds. The expected return is seven. The standard deviation is 9.77. This is the portfolio that we have. And initially we said, let's assume everything is in bonds. When assume everything is in bonds, we had an expected return of five and standard deviation of eight. But here what we did, we're going to build an investment portfolio set, which is set of all attainable combination of risk and return offering by the portfolio formed using the available asset in different proportions. Here we're looking at different proportion. Now we can play with this little bit more. So can you find out what is the lowest risk? Well, I'm going to look here and find out what's the lowest standard deviation. Which portfolio gives you, if you're looking for the portfolio with the lowest standard deviation, you would need to look here. So let's look. The lowest standard deviation is right here, 7.80. 7.80, right here, let me highlight this line, gives you the lowest standard deviation, which would give you a return of 5.46. It means if you invest your money, 90.8, almost let's say 90 and 10% in bonds, 10% in stocks, which is 90.8 and 0.092. Let's say 90 and 10, no, let's say not 90, because we have 90 here. If you invest 90.8, let's see, if you invest 90.8 and 9.2, 9.2, you will get the lowest risk, the lowest risk of the portfolio. So if you are risk averse, 100% risk averse, you would tell your advisor, I want to invest in this portfolio, put 90.8 and bonds, and 9.2 in stocks, which would give you the lowest. With this proportion, the portfolio standard deviation will be 7.8, and portfolio expected return 5.46. Is this your preferred portfolio? Well, it all depends on your risk. That depends on your risk aversion. So I'm going to take this data, and we're going to show you a graph. And notice the graph, because of the diversification, it bends. And we're going to look at this later on. So here's what we mean. This is the bond portfolio. If you are asked, a bond portfolio versus a portfolio here, which one will you choose? Notice here, they both have the same or close standard deviation, same risk. But this one here, let's call this 1A, this one here has a higher return. So you would always take, if you are choosing between portfolio A and portfolio B, you always take portfolio A. Why? Because look, this is the risk, and this is the return. You are taking the same risk, but getting more return. Wouldn't you take this? I'm taking the same risk, but I can earn 1% more. Of course, I will take this. In this relationship, there's a name for it. It's called the mean variance, mean variance. And look, I mean, it sounds very complicated, but all what it means, mean means return, and variance means risk. So you're comparing the risk to the return. I like to call it risk return relationship, but it's a mean variance. And here's what's going to happen. When we have all this, when we graph this investment opportunity set, again, it would look, it would look a little bit bended. Now, would you choose this stock or would you choose this stock here? Now, obviously, those are basically the same. What do I mean by this? Here, you might earn 8.5, but you're taking 15% risk. Here, you are earning a little bit more, but you are taking more risk. Now, it all depends on your risk tolerance. Would you prefer to take more risk or less risk? For example, you would never choose portfolio Z over this portfolio. Why? Because look at portfolio Z. Portfolio Z, compared to the stock portfolio, the risk is you are taking a standard deviation of 21%, and your earning is a little bit above 8. Here, the stock portfolio, your risk is 19, and your return is closer to 10. Obviously, I would never choose portfolio Z because this will not make any sense. Why will I take more risk with less return? So basically any portfolio in this area, you really don't want it. You really want this portfolio here, here, and here. Why? These portfolio, they're going to give you a higher return with less risk. For example, if you're going to compare this ABC portfolio to this portfolio, you will take ABC. Why? Because they're giving you the same return, but this portfolio ABC has a 14-point standard deviation. So hopefully, this will start to make sense. And we're going to carry on with this in the next session. But notice here, it bends a little. And the reason it bends because of the benefit of diversification. And here, at this point here, we have minimum variance portfolio. And this is this portfolio right here. Minimum variance portfolio is this portfolio right here where the return is 5.46. And the standard deviation is 7.8. The minimum variance portfolio, then it will start to go up. Notice it will start to go up. Now in the next session, we're going to do, we're going to look at the optimal risky portfolio with risk-free assets. So we're going to take everything that we learned. The first thing I'm going to start this session next session, I'll say, okay, make sure you view the prior session, because in addition to the two risky portfolio or many risky portfolios, I'm going to be adding the risk-free asset. As always, I'm going to ask you to please like this recording if you like it, share it, put it in playlist. If it benefited you, it means it might benefit other people. Connect with me on Instagram. Don't forget to visit my website for additional resources for this course as well as your other courses. Stay safe, study hard, and good luck.


Russians constructed 30 km defence line with 2,000 railway cars. The Russians built a 30 km line of defence from more than 2,000 railway cars. This was reported by Deep State Analytical Community. The continuous construction stretches along the branch line from the railway station in Olenivka to Volnovakha and has about 2,100 wagons of various types. It is reported that the construction of this massive defensive line began in July 2023. For its construction, apparently, rolling stock was used, stolen, from the temporarily occupied territories. Such a defensive structure, which in fact represents a solid wall, is a very serious obstacle in the way of advancing troops. Given that some sections of the railway track are built with a high roadbed, such a defensive line is a full-fledged defensive shaft. It is possible to overcome it only after large-scale engineering works, disengagement of wagons, removal from tracks or movement to another place. However, these engineering works will be accompanied by the counteraction of the Russians. In addition to problems for Ukrainian troops, such a line of defence also creates problems for the Russians themselves. Logistics for advanced positions can be difficult due to an obstacle. In addition, such a barrier creates an obstacle to maneuver. This is a very specific engineering structure, the effectiveness of which is difficult to assess. The idea is clear, an obstacle to the advancement of the defence forces. It can be considered as a separate line of defence because it is extremely difficult to damage, move or blow up a 30 kilometer mass of metal and the movement of equipment through such a blockage without breaking through the corridor is impossible, writes the deep state team. This is not the first time the Russians have built huge engineering barriers as part of a full-scale Russian-Ukrainian war. In April 2023, it became known that the Russians built a solid 70 kilometer anti-tank ditch in Zaporizia, which stretched from the village of Semenivka to the village of Marinovka.


Hey everyone welcome back to my kitchen I've gotten so many requests to show you some of my long-term food and meal prep Okay, you guys so today the first thing that we are going to be working on for a long-term food prep is we're gonna be canning some peas Our household loves peas. It's probably the thing we eat the most and I want to free up some freezer space Plus they're ready just to heat up and eat. It just makes it a little bit easier for us So we've got some clean sterilized jars over here and you guys may be more used to boiling your lids However ball says that you really don't need to lately. I haven't been and I have gotten seals on everything So that's completely fine. Now some people may boil their water to do this I'm actually going to be putting in just regular room temperature water into these jars and letting it heat up with the canner Something I did forget to mention is that I did let the peas sit out on the canner and completely thaw out overnight Before putting them into these jars and if you were using fresh peas out of the garden I would recommend steaming them or blanching them first, but since these have been already frozen I just went ahead and put them right into the jars Another thing you could add to these jars is a half teaspoon of salt I actually forgot to do that in this batch So I'll just have to remember to make note of it on my labels and then add extra salt whenever we open the jars up All right So these are ready to go into the canners now because I do this in a traditional method With traditional timing and all of that I'm going to leave the true instructions in the description box below along with the disclaimer About this method because I know a lot of you are very concerned Because I do a lot of things in a traditional way that being said I'm gonna put this into my canners I have two of them because they only fit seven and I got nine core out of this So I'll split it between the two canners and I'm going to put them onto my second stove in my basement and get them rolling Okay, next I have a little tip for you on how I save some money on bacon This is already open because we got into it for some bacon for breakfast But if you have a box food store near you or you can even get bacon in large quantities from butchers You can package your own bacon into smaller packages for the freezer and be able to kind of save Money per pound so these are actually five pound packages and buying these makes the bacon a lot less per pound Versus buying one pound at a time So what I basically do is I'm gonna get out my scale I forgot to grab that and I like to weigh out about roughly a pound per pack and then this is a food saver or a vacuum sealer and This is actually my second one I tried to get away with one that was a knockoff brand that was a little bit cheaper But I had to go ahead and get a food saver because the knockoff brand did not work as well So I will link this one below but these are not cut bags so basically they're one huge long bag and I like this style for bacon because you don't always know how long of a piece you're going to need So you can just kind of cut these as you go and you seal one end You shove the bacon in and then you seal the other end in vacuum packets so that it does not get freezer burnt So this has been a really great way for us to save a little bit of money. We go through a lot of bacon in our house We love love love bacon and we can just pull the packs right out of the freezer I throw them in a little bit of warm water right before we throw it into the frying pan And there you've got to bacon made for breakfast or any other recipe I want to thank yeety for sponsoring this week's video I have been using their yeety vac max robot vacuum and mop and I've been loving it Yeety vac max is a multitasker it vacuums and mops at the same time with a 3000 PA strong suction and power and a smart mopping system leaving your floor twice clean with a single use It avoids carpet whenever it's mopping and features an advanced carpet detection sensor yeety vac max Intelligently recognizes your carpet and avoids mopping it. It is compatible with the yeety self-emptying Station and lets you upgrade your yeety vac max to a robot vacuum and mop that self empties It's dustbin for up to 30 days yeety's visual mapping technology works in unison with a floor tracking Sensor to map out your space like a GPS so your yeety will always clean edges corners and the entire floor in neat rows Another great feature is that is also compatible with Amazon Alexa and Google home I have a great discount code that is in the description box below for you guys to check out You will love this vacuum and mop as much as I have been it saves me so much time and it does a great job cleaning All right back to prepping so I've been using this scale It's not digital, but you do need to adjust it back to zero every time you weigh things on it Just to make sure that it's accurate It has a little piece on the bottom of it that you can turn and it will adjust it to zero when there's nothing on The scale and the first thing that I did was just cut my bags to the length that I needed them to be and I sealed One end before I started to put the bacon inside I cannot stress this enough and you're gonna see it here and there as I'm packaging this bacon But cleanliness disinfecting and keeping things wiped up and very clean when you're working with packaging meat is of the utmost Importance you're gonna see me Pausing and washing my hands another great method is to make sure you're grabbing the bag with one hand and grabbing the meat With the other hand so you kind of are keeping your two hands Separate or just washing your hands in between is really important another note I want to make with saving money on bacon is that I feel like you can get a higher quality Bacon or even a thick cut bacon for a much cheaper price by buying it in large quantities All right So the only thing left to do with these is to label them and date them And I cannot stress that enough whether it's canning or freezing So you know when you find it a year from now in the bottom of your freezer You know what year it was from and the chances of it being frostbitten or not So the nice thing about these packages is they have actually a little spot for that And you can go ahead and just write it with a sharpie Right on the packaging and then I throw it in my freezer I'm hoping soon to show you all how my deep freezers are organized So stay tuned for that that will be on my home channel, which is linked below Thing that we are going to prep for long-term storage is some dried kiwi I have a discount store that I like to shop at and they had a really great deal on kiwi And I'm going to use my dehydrator. I love this thing I will say that this is a pretty good size investment as far as food preparation goes They do make one that is I think about half this size in this brand. I just feel like it does great It keeps its temperature the fan is in the back so it blows outward so everything gets dried evenly It just does a really great job this one has nine trays in it And I'm hoping that I can fit all of this in here if not the girls will just eat them fresh tomorrow morning So I'm doing this at night because I want to run this during the night that way in the morning I can get up and they'll be hopefully done or almost done and I can clear this thing off of my counter because it does take up a good amount of space on My countertop some people dry these with the skin on if you're going to dry them with the skin on You want to soak them and wash them like you would with other produce, but since I'm going to be peeling them I prefer to dry them peeled I'm just going to go ahead and peel them and then I will get my mandolin out slice them And we will put them on the tray. The other thing I want to mention is this peeler I like to get peelers that have a serrated edge so that has tiny little teeth on there It just does a better job peeling most things I will leave the link below for peelers that are like this. I have more than one Especially whenever we are working on a large food preservation project like canning or something like that Another tool that's really helpful when it comes to dehydrating is a mandolin slicer And I was actually thinking I was going to use my mandolin to slice these but they were extremely ripe Which really makes a great Sweeter dried fruit when you're done, but they were too soft to use the mandolin So I ended up just slicing them with a knife and putting them on that way You just want to make sure that they're all sliced right around the same size We also did a bunch of apples in the Dehydrator whenever I had done some applesauce and the girls really love those as well So once I had the trays loaded up, which it didn't even fill my full dehydrator I went ahead and sat it at the fruit setting, which is around 135 and I also set the timer for about 15 hours Okay, so it is the next day and I have had these in here for about 12 hours And then I let them cool and they may stick a little bit to the tray But they're pretty much just like this they're flat the girls were already Snacking on a few of them and they love these so another term for these is pucker candy they're just a tart little treat and I'm going to be setting them up so that I can put them on the shelf down in my long-term storage area And we can go grab them for a fun little treat. I don't know how many of these they will fill It's usually a lot less than you think because of how much smaller everything gets when you dehydrate it But I'll be putting them in here and conditioning them which I'll explain what that means But once they are conditioned I will be putting some of these moisture absorbers in now These are different than oxygen absorbers Oxygen absorbers absorb oxygen these actually just absorb moisture and they're a pretty big packet So I'm not going to put them in yet because of conditioning So basically what you need to do is anything that you dry in a dehydrator once you put it in a jar You want to for about three days Every once in a while maybe about twice a day come and roll the jar around and make sure that there is no moisture Left inside of the jar and make sure you hear a Plinking sound if you hear a lower plunk sound I know it's gonna sound funny for me to say this but once you try it You will know exactly what I'm talking about if there is a Deeper sound that means that something inside has more moisture And it's not plunking and making a higher sound because if it has almost no moisture You're going to get a higher sound. So basically I will fill these up I will set them somewhere in my kitchen in the next three days I will be conditioning them making sure there's no moisture if I do see any moisture inside the jar I will put them back into the dehydrator make sure that they're truly dry Which I really think they are I really they are very very dry and then once the three days is up And I'm convinced that they're very dry on the inside I will throw my moisture absorber in and I will use my brake pump to seal the lids and they will go on my shelf Downstairs with all of my canned goods So I pulled out one of the moisture absorbers just to show you all what they look like and you kind of have to Fold them for this size of jar I did decide to package these in smaller jars just because they are a very sour treat and they aren't something that We eat a lot of at one time And then I had a little helper come along that wanted to help Package these up and this is such a great job for them when they want to dive in and help you The next couple of clips is actually some long-term food prep I have shared before but you all have requested that I put a lot of the canning freezing food storage Recipes together into their own videos So here is a few more recipes to inspire you or to re-inspire you doing baby carrots It saves me time on cutting up carrots. You can do regular carrots as long as they're all around the same size It doesn't really matter, but this is just fast and simple. So you're cold pack the jars With the cold carrots or you know just raw carrot Then you're gonna add around a teaspoon of salt to each jar now I think it's a little bit tastier to have a little less than a teaspoon per jar But that's up to you you can do one batch taste them and see what you think these are my magnets for my lids back here I just stuck them to the side of the stove. So after I have all of my carrots in here I'm going to wipe the rims. These are clean sterile jars I just washed them in very very hot water and put them over here I have my lids back here in this pot Boiling so they're getting sterilized and then I have Purified water in here that's getting hot the next step will be to ladle in the really hot water that is in here and Once they are up here and have about an inch of headspace I will add my lids and screw on my rings back there And then I will put them over here in my canner if you hear something hissing. That's what's going on this is getting to a boiling point and So it's all very very hot. I do have some carrots over here that I just pulled out. Oh, that's hot And so I will let them sit for a couple hours to make sure that they seal really really well And obviously test the seals and then I'll take the rings off label them And they will be ready for storage and then right here is my labels I will link them below they are from Amazon and I actually get them in huge packs But they're great because they dissolve right off the jar when you go to wash the jar So you don't have any sticky stuff on your jar plus they're very simple to write on with just a regular pen We had some popcorn last night so it's over here But this is how the carrots look whenever they're done. They are super super simple and they can keep for you know a year Depending you may want to do a little research on how long you want to store yours. This is the finished product I'm gonna go ahead and load up my next batch So one more thing I do process these for three hours in my water bath canner. This is just from Walmart super cheap canner And I will leave the link for it below again You can do your own research and decide how long you want to can them for but three hours is What I do for these I'm actually going to jar up some maple syrup. I got a gallon of maple syrup this week This is two half gallons and really they would be fine to store right in these jugs However, number one, I just don't think I'll work through it fast enough and number two I would rather have them stored in glass. I got this at a really great price So I'm going to actually put all of it into these glass jars. I'm not sure how many jars I'm gonna get out of it I'm hoping at least six and we'll see if I need the other two then I'm gonna do something called dry canning And I want to be very clear on this There is only certain things that you can do this with please do your research This does not replace any other type of canning. This is mainly for dry goods Hence why it is kind of called dry canning and you're not putting in water and all of that But I'm also using this as a method to store maple syrup because maple syrup has a super high sugar content It can store on its own just like honey and one thing that helps it last longer is to take the air out of the jar So I'm gonna pour them in here and then I'm going to show you this is a little kit that comes on Amazon There is a regular mouth, which is what the size is and a large mouth I don't have it out piece for this it also comes with this tiny little hand pump But I use something called a break bleeder This is actually something that mechanics use but it works perfectly It has even a little attachment that works perfect to suck the air out of this and because it has a gauge And I can see how much air is being sucked out of it It kind of helps the whole process Although this works fine, too You can do like 15 to 20 pumps out of this and your lid will seal on top of these I hope that I'm explaining this okay, and I'm no expert. I always put that disclaimer out there I'm just doing things the way I know how to do them or how my grandmothers did them So definitely proceed at your own risk do whatever is best for your family But this is just a way that you can preserve things and take the air out of them So you're gonna be seeing me doing some things with my dehydrator And this is another way to store things that have been dehydrated things like banana chips or Different dried fruits and things like that you can put them in a jar and suck the air out of them So basically what it does is it fits over top of the lid not the ring just the lid and It's pulls on it strong enough that it's pulling air out of the seal until there's no air left And all that's left to do is for the lid to actually seal down onto the jar When you're going to preserve something I really encourage you to do your own research on the different ways that you can preserve Something for a longer period of time and then make the decision on how you want to choose to preserve it It also helps a lot if you can talk to older people a lot of them have been doing food preservation For years and they can give you a lot of tips and tricks on ways to preserve things But this is one really handy inexpensive way the little brake bleeder is very inexpensive So are the attachments for the jar lids? So this is something to keep on hand to even be able to store your pantry items and be able to get a good Seal on things like sugar and flour All right, I got nine jars out of this They're obviously not completely filled now one other note. I want to make about storing maple syrup I'm going to get some labels out here in a second and label these and put the date and all that But you want to store these in the dark my basement I have the windows blacked out where these are stored so it's no problem light will definitely affect The quality and all of that of these but they can store a good long time and you will have Maple syrup so you can buy maple syrup in bulk and save a little bit and then kind of repackage it this way Especially if it's not already stored in a glass bottle and the labels are washable, which I love they I use them for all of my Canned goods Basically when you go to wash the jar the label bit pretty much melts off So it saves you a lot of time and you don't have to write on the lids and you can see from the side when it's on the shelf What is it not some apples from a local farmer who said they were apples from last year? They were kind of on their last leg and he gave them to me at a great discounted price so of course I said I can make those into applesauce and actually this variety of Apples is a sauce apple. These are called summer Rambo apples And so all I did was wash them off really good and I do have a Victorian strainer Which I'll show you here in a minute So all I had to do was put them into some big pots skins and all you don't even have to core them I do try to cut some of the seeds out because I feel like that can clog up my strainer and then you just want to put a little water in the bottom of the pot and Have them completely cook steam You don't have to fill the whole the pot the whole way with water Just seen up in the bottom that they don't scorch to the bottom of the pan and Within a short amount of time on your stove on medium heat. They will cook up. This is my Victorian strainer setup I will leave a link for it below. This also makes tomato sauce. So it's a great investment It has there is other things you can make with it as well But I mainly will be using it for applesauce and tomato sauce and I did this as a kid I cranked that thing when my mom had one and made a lot of applesauce And it's really great because it takes out all of the seeds That's what you'll see coming out of the funnel on the other end is the skins and the seeds and all of the Stuff you don't want in your applesauce It does all the hard part for you and it just makes making applesauce So incredibly simple depending on what variety of apples you're using and you may want to add sugar to it This variety is pretty sweet. Just kind of taste it and decide if you want to add sugar This is also a point you can add other fruit so you can make different flavored applesauces Or you could even add cinnamon to it anything like that Just make it your own and I got rolling with this and completely forgot to film the canning portion of this But if you go back and you watch how I canned carrots a few weeks ago. It's pretty much a very similar Process and I can leave the instructions below But you will want to water bath can these core in quartz This is for quartz for 20 minutes and you will have canned applesauce on your shelf That will last you at least 18 months and I'm making a ton of applesauce this year because my daughter's Last week I showed you all how I make really easy bread and right at the end of it One of my daughters was holding the piece of bread with some of my jelly on it And I got requests. Can we please have your jelly recipe or jam? I always say jelly because I just grew up saying that but this is technically jam because if it was jelly You would strain out all of the pulp from the strawberries, which I leave it in so this is not anything sugar-free It's not anything healthy. This is like your grandmother's recipe for Homemade strawberry jam and I will leave it in the description box below It's got lots of sugar in it But remember you're only using a small amount of it on your bread or your waffles or whatever you're going to spread it on So just keep that in mind plus it doesn't have Corn syrup in it, which a lot of store-bought jams and jellies have that kind of stuff in it so this is just a good alternative to those things and Canning it means that you have it on the shelf for a year or more, which is really awesome So you just want to cook them up with all of the ingredients and I just you can tell just put my hands over the pot To see if it was hot you can get this to a rolling boil But honestly, I was so tired after this day I just wanted to get the project done and I knew I could get away with getting it really hot and Dissolving the sugar and blending it up and probably being good So you could definitely throw this in a blender if you don't have a hand blender It's just a lot less messy to just be able to put your immersion blender in and blend it all up So you'll see me chasing strawberries around because I wanted to get them all blended up And then I did let it simmer a little bit longer until I felt like the sugar was dissolved I took a spoon and just tasted some just to make sure the sugar wasn't like gritty in there But I knew that the pectin everything was dissolved. So after you let it simmer just a little bit It's ready to go into the jars you want to have nice clean jars And you want to leave yourself about like an inch headspace on the top of your jars I did get 24 out of this and I did about double the recipe So you can get 12 to 14 jelly jars out of this recipe and actually the whole reason I'm making this batch is I had a bunch of strawberries in the freezer And I actually already made a ton of strawberry jam this year have it down on the shelf already But I'm trying to clean my freezers out right now because I know that we've got a lot coming with summertime to go into the freezer and So this is actually strawberries that were frozen totally fine to do if you want to get strawberries out of the freezer and do something with them and So we have a lot of strawberry jam which is totally fine because it is a favorite and With me making homemade bread a lot right now We have been going through it after you have it all in the jars you just put your lids on I boil my lids first Put my rings on and put it right into the water bath canner and you can can it for like 10 to 15 minutes I double layer mine so meaning I put one Layer of jars and then put a second layer of jars because my canner is tall enough to do that So since I do that I do like to process them for more like 15 minutes just to make sure that they're all good in there pull them out and Let them set up whenever you see me holding this jar. It's actually like still Not cooled at all. So it does get more jelly than that. It's not quite that runny, but that is how I make mine It's so simple. You've seen how quickly I put this together. Thanks a lot for watching today If you're new here, don't forget to subscribe. I'd love it if you joined my channel I hope this inspired you leave me a comment that always helps me out and I will see you guys in my next video


you're learning marketing, you're going to come across this idea of conversion rates, which is the rate at which people do the thing that you want them to do. So buy your thing or to sign up for your email list. And so a lot of people think that, wow, now that you've discovered conversion rates, you know, isn't all marketing, shouldn't it be about increasing conversion rates? Well, if you go down that rabbit hole, you're going to discover that a lot of what that's about is making people do stuff without knowing that you're making them do stuff, without them knowing that you're making them do stuff. So essentially, conversion rate optimization is a lot of ulterior motive, tactics and techniques that you are not revealing to the audience. Otherwise, it would be uncomfortable for them to know that you are using certain things to try to get them to do things that you want them to do. Is there an alternative? Of course. That's what I'm here to provide you. So instead of focusing on getting a higher conversion rate, I invite you to do the following. Authentic marketing. Now, let me summarize this for you. Basically, on the one hand, work on getting better product market fit. And I'll explain this. And on the other hand, work on growing your warm audience. And by doing these things, you do worthwhile marketing. And it feels good to the heart. I often say that authentic marketing is like making friends at scale, making friends at scale. So think about making an authentic friendship. What does that mean? Do you try to go to somebody you don't know and charm them into being your friend? I mean, do things that are not your natural state to make them your friend. And then to make them do things you want them to do. If someone were doing that to you, how does that feel? It feels like a calculating psychopath. I don't know. So what we want is for somebody, if someone were trying to become a friend with you, what would you want them to do? You want them to be their natural self so that you know what they're usually like. And you want them also to find out about you and try to find some common ground so that you can talk about something interesting together and to do things that you both enjoy. That's called finding product market fit. So you as the business owner, it's your job to find out of all the interests that you have. You have more than one interest, right? You probably have five, 10. Some of you have 85 interests. Some of you have like 12 different things you could possibly offer to your market, to your audience. Okay, of all the 12 things you could offer, which of the 12 things is most interesting to your audience? By the way, all of you have an audience. Yeah, you do. Even if you just got started in your business today, you have an audience. It's called the people you can already reach. It's your friends. It's your colleagues. It's the people that your friends and colleagues can introduce you to. That's your audience. So you start there. So the product market fit is to work with your audience on finding out what is the common interest that you have that you and they have. The thing that one of the things that you could offer for sale that also interests them. So if you have that common interest, then you don't have to try very hard to sell. You don't have to use persuasion. You don't have to have gorgeous branding. Maybe you could do you could do branding if you enjoy it. If you enjoy the art of it. Great. Go for it. But you don't have to try so hard to get people to do things you see with product market fit. And on the other hand, growing your warm audience means that you are continually putting out authentic content. Just like you would with a with a new friend. You are continually see, talking with them when you have a chance to talk with them, right? You are exploring what's real for you. And you're also trying to help your friends serve your friend, find out what they like and serve your friend. And that's what content is. It's exploring yourself publicly because you're making for new friends at scale. So you're exploring yourself publicly, finding out also what's useful to your audience and giving them more of that. So authentic content is this is this dual action of self exploration in service to your audience. So if you do the these two things, right, product market fit, you always do market research and then you grow your warm audience through authentic content. And guess what? Really, you are like I said, making new friends at scale. It's an enjoyable activity because it's a very human. It's you are you are you are activating the best of humanity. And you are activating your purpose. So marketing is no longer a chore. It's no longer a means to an end. All I have to do marketing so that I can do my deep purposeful work. Baloney, marketing is part of your deep purposeful work. Did you know that marketing when done authentically is part of your deep purposeful daily work? It's about collaborating with your audience to to find common ground and to do something together. And it's also about serving your audience and exploring yourself. All of that is purposeful. All of that's meaningful. Why does it have to be outside of your meaningful work? You should approach marketing with joy as you can. If it's like this, it's worthwhile. And lastly, as you grow your warm audience more and more, by doing more and more authentic content and learning how to distribute content, etc. Guess what? Your warm audience grows more and more and more of them trust you such that you eventually can sell just about anything and they will buy it. Just like when a friend and you have a good relationship and they trust you, you may have a new topic that you want to talk about or you want to you want to go to a new event that they had no interest in before. But because they trust you, they said, Sure, let's go. Let's give it a try. You seem so passionate about it. Let's give it a try. So with a large enough warm audience, the same thing happens. You can say, I've got this new idea. I've got this new product. I've got that new service. I've got this new idea I want to I want to serve you with and then enough of your warm people will sign up. And so your marketing gets easier and easier over time. And you don't ever have to worry about conversion rates again. I hope this is helpful. Always open to your comments and your questions. I wish you well. Thanks for joining me.


work I'm going to present to you today is the first step of a big project which consists of building a model and numerical simulations to study vesicular release at neural synapses. So the first step is about asymptotic analysis of the mean first passage time of a renown particle to a small hole. Okay so this the I will first present a short overview of synaptic transmission at chemical synapses very short no problem and then I will show you the asymptotic analysis of narrow escape time. So the synapse maybe you everybody knows what it is is a structure not very well known today in the is the functioning that permit to transmit an electrical signal from one neuron the presynaptic neuron to another the post-synaptic so when an electrical signal arrives an action potential in red here it triggers the opening of the voltage gated calcium channels which are the blue channels on the on this picture and this will trigger the entry of calcium ions within the terminal the orange dots and those calcium ions can go to bind to specific receptors localized on docked vesicles the docked vesicle are the one which are just opposed to the membrane and if they find those docked vesicle and the specific receptors on those docked vesicle it will trigger the release of neurotransmitter within the synaptic cleft and then it will they can bind to the pink receptors specific receptor for neurotransmitters and the chemical cascade and everything will trigger the will create an electrical signal in the post-synaptic neuron so it's a very complex phenomenon I'm just today interested in what's happening in the presynaptic part when calcium calcium ions enter through the calcium channel and have to find the very small receptors located at the docked vesicle okay so just a zoom on this part so the dot vesicle are really attached to the membrane through the snare complex which is the complex of protein and on the snare complex you have the receptors for the calcium so calcium enters through the blue channels then they diffuse and if few calcium like 4 to 8 find the receptors then the synaptic vesicle will fuse with the membrane the membrane of the vesicle with the membrane and then everything will start for the transmission so the model here that we did is calcium ions are bronion particles that diffuse freely in the terminal we know that particles that calcium ions are charged particles but we will neglect this at the first step and the docked vesicle is just a sphere tangent to the plane okay here you have the sphere in green and the tangent plane in blue and the binding on the snare complex is when the bronion particle will find the red cylinder you can find here so this is our model of these ions finding the complex find the small cylinder here which is the center of the cylinder is the center of the in the tangential point between the vesicle and the plane okay so we are now interested in the time and in the further step of the project the probability that an ion starting from this channel will find this small cylinder okay so I will present now the asymptotic analysis we did for this narrow escape time so the narrow escape problem we have here is the following a brilliant particle is described by a stochastic equation x dot equals square root of 2d w dot d is a diffusion coefficient of the particle and w dot is white noise and the first time to it did domain here on megabar which represent the domain we are interested in through the small hole in red the cylinder in red in this picture is given by this so the first time the particle find the domain okay the particle is reflected everywhere on the border of the domain except at the red cylinder as it's absorbed so we are interested in the mean first passage time to this cylinder which is u of x and we know it's very well known it's dinkin that this mean first passage time follow the solution of the mixed boundary value problem which is here d laplacian u equal minus one d is diffusion coefficient d u dn equals 0 is a classical reflection at the boundaries and u equals 0 is a classical absorption absorption at the red cylinder here so we are going to to try to find the asymptotic analysis of the of this time okay so the the the first tough we can look to see when we look at this this domain that it's invariant rotation around the axis delta here which is very easy to see and according to the equation we have we know that this problem is independent of theta if we consider the cynical coordinates around delta so we can just study an equivalent problem in domain omega which is a 2d domain the projection of the domain on theta equals 0 for example so this on this domain you see the blue is going to the blue the the red sphere is here the red the arc of circle the small cylinder is now just segment okay and the equation becomes the following equation where you recognize here the laplacian in cylindrical coordinates very simply okay so I'm now in a 2d domain with a 2d problem which is equivalent to the problem we had in 3d you notice as well that I put the diffusion coefficient on the right and that we have reflection on the blue black and green boundaries and absorption at the red segment we are interested in the asymptotics of u when epsilon which is the length of this segment goes to zero very small goes to zero is very small in front of the rest of the boundary so the problem we have here is that we have a singularity because when epsilon goes to zero the point here is not regular so to desingularize this singularity we we will have to okay the problem of this singularity is that it prevents us to use a classical method which are for example the green function on this domain because we don't know the order of the green function in epsilon and desingularity this it depends on the domain and we don't have access to this the other method which is very classical is matching asymptotics so we try to find a solution near the cusp near the hole we try to find a solution in the domain we try to match and then we can obtain something but here because of the geometry is not possible as well so the idea is to desingularize the singularity and we are using conformal maps so here because we have tangent circles we will use the inverse map which comes very easily when you start to think about it because it will transform these domains into the main tilde omega we have here because the inverse map will transform the sphere tangent in zero into parallel straight lines you notice that the small hole here in red is going to a straight line here and you know that inverse maps are putting spheres circled into straight lines and straight line into circles so in reality the the hole here is not a straight line it's a knock of circle part of the circle but the radius of this circle is 1 over 2 r a which is here the the abscissa of the hole and if you maybe don't remember because I didn't tell you this before r a is in all those quote of epsilon okay it's a simple computation so sorry this mean that this at the first order we can consider that this part is a straight line okay the first order is straight line so putting setting v of st equal u of r vd we can now consider the equation in the map domain which is much simpler domain because at the first order it's like rectangular domain the equation is much more complicated because it captures the geometry of the problem in omega but still the domain now is much easier and we get this this equation we have the reflection dv dn again on the blue and black and green boundaries and the absorption on the red boundary so to solve this equation we will now use a scaling property sorry a scaling method so we put zeta equal s square root of 2r epsilon square root of tilde epsilon okay which means that which means that we are going we are taking your our interest is in the region very close to the hole okay so very close to the red boundary so by setting this using the scaling we can put big y equals of psi t equals v of sts very simple and then we can do a regular expansion of big y in power of epsilon tilde tilde and injecting this regular expansion into the equation and expanding the equation now we obtain here the asymptotic of the equation in power of epsilon and we are we will now take care of the terms of leading of much interest leading order terms of the equation the first one is in one of a tilde epsilon square then the second one is one of epsilon etc etc so using this expansion now we are looking because we are looking for asymptotic analysis we are looking of the leading order term looking for the other term sorry we will first consider the first term which is the t the second derivative of y0 over t equals 0 so using this equation and the boundary condition we have we have on the blue and green boundaries we can show very easily that y0 is not is independent of t okay this is what we get from the first term the second term the second order term gives us this equation here and integrating over t again we can show that y1 is as well independent of t it's simple computation and using this we obtain a complete an equation for y0 in zeta and using the boundary condition now at the whole which state that in zero in zeta equal 1 solution equals to 0 we obtain the form of the leading order term of the solution big y0 near the whole going back into our first parameters we have that v of st take this form okay so it's equals to 0 near the whole this solution is an approximation is not an approximation it's the leader order term of the solution near the whole okay our problem is we have to compute a so usually you use the rest of the parameters but this approximation of the solution is not good far from the whole we cannot use the reflection the last last boundary condition we get so to compute a we will use the divergence theorem which state that the integral of bar omega of laplacian u it's equal to the integral of the border very classical equation so this the laplacian u equals minus tilde the volume of tilde omega over d just comes from the equation d laplacian u equal minus 1 and the other part because we have reflection everywhere except at the whole say that this integral on the border is exactly the integral of the solution at the whole it's good because we have a solution at the whole so we can then using our first order term of the solution at the whole give this equation and then find a and we now have another first order term the leading order term of the solution in epsilon for the the whole domain so to get toe to get the mean first passage time sorry we just put the value of a in v of st and then consider when s is equal to zero when we are far from the whole s equals to 1 at the whole equals to 0 for the whole and we get the mean first passage time for a Bernan particle to the small hole and in the boundary layer we also have the leading order of the mean first passage time and we know as well the way is behaves okay so we computed the leading order term of the mean first passage time to a small ribbon located between two tangents first and we could show that this mean first pass time is constant outside of the boundary layer as we just noticed and is well this tells us that this mean first pass time is well approximated by a Poisson process so this is a result we already know so it's mean that we can we can consider that the arrival of this particle to the small hole is Poissonian and the first approximation the law of arrival is an exponential this is very interesting because using this analysis in further development of the project that I don't have time to present here we could compute as well the probability when the particles start inside the boundary layer because here it's we have the mean first passage time to go to the whole when you are far from the hole because we set s equals to 0 so it means we are far what's happening when you are close the problem is still a problem so using the same kind of analysis what we have here we could compute the probability to reach the cylinder before escaping the domain okay it's the same kind of computation and using this we could build a model of the active zone which is the place where vesicle are located and the calcium channel are located as well to investigate the influence of the position of the channels on the crowding of vesicle or not crowding of vesicle etc etc on the release probability which is the probability to have the fusion so the probability to have four ions that are coming to this vesicle or not and using this we could build a model of the prescine optic terminal which bigger with the whole stuff we have over there and the fact that this mean first pass time is Poissonian is really what is important here in our study because if you want to model the prescine optic terminal you have a bronyon particle you you can do bronyon simulations if you want it's very simple not that simple because the domain is not that fun but okay you can do it but you will wait for hours because of the very small hole you have here and because of the very long time you have to find this small hole the fact that it's a Poisson process allows you to use simply Gillespie algorithm to say okay it's Poissonian I can at least use Markov chain for what's happening because it's constant it doesn't depend on the position so it doesn't depend on the time and it's what we did in the following of this project and I wanted to show you this because it's a very first step but it's everything is is going after that because we could show that the mean first pass time is independent of the position and that this time is Poissonian time so this work was published in the Siam multicore modeling simulations so I want to thank just my PhD supervisor David Altman and my lab mates and the organizer of this conference for giving me the opportunity to present my work today thank you I was just wondering what do you mean by it's well approximated by Poisson process I mean the first passage time is approximately exponentially because of this because it doesn't depend on the position in fact so it doesn't depend when you start so it's yeah you have the mean and the variance is the same and it's well approximated there any other questions if not let's send the speaker again


Within you placed there by the Holy Spirit is a desire to pray, is a desire to connect with God, but the flesh is weak. The flesh fights your commitment to prayer. Why? Because prayer is the death of the flesh. The flesh seeks distraction. The flesh seeks entertainment for entertainment's sake. But the spirit desires that which is of the Holy Spirit. And so within you is this desire to pray. It's up to you to either act upon the desire of the Spirit or the desire of the flesh. It's up to you to say, I'm going to choose to pray rather than go after that which the flesh desires.


One of our personal favorite ancient sites is the ancient fortress of Saxe Huaman. We believe this site was built an unimaginably long time ago, yet it would still be a daunting proposition for any invading party. One of the most impressive features of the site, and the reason why it is ranked as one of our favorites, is the inexplicably baffling stonework that makes up the fortress' maze of outer walls.  Although many other sites within Peru undoubtedly contain incredibly precise stonework, Saxe Huaman is the jewel in the crown when it comes to the evidence for a lost advanced civilization. The largest stones in this boundary being 28 feet high, regularly academically estimated to weigh over 120 tons, with more enthusiastic estimates placing the largest stones at around the 300 to 400 ton mark. Located on the outskirts of the ancient Inca capital of Cusco, it rests on an enormous artificially leveled plateau. Deconces of three outer barriers, gargantuan walls, 1,500 feet long and 54 feet wide, created in a strategic zigzag shape.  As recently mentioned in another video, there is overwhelming evidence to suggest two phases of building was undertaken at certain sites within Peru. We feel that the constructors of Saxe Huaman are the same people who indeed built most of ancient Peru. This group were the ones who utilized the enigmatic protuberances even found upon the casing stones on the Great Pyramids. However, interestingly, there was another later phase, and although not as complex, still far more advanced than any academically studied ancestor who are currently claimed as the actual builders. This means that more than one ancient civilization must have called ancient Peru home. A later group, re-inhabiting these sites, flourishing to a point where they were clearly inspired by the site's original builders, becoming highly capable stone builders themselves. How old is Saxe Huaman? Who could have possibly built it? And why did they not utilize the mysterious protuberances found on much of their other stonework throughout Peru? It is undoubtedly one of the most incredible ancient sites still standing on our planet. And thanks to the incredible capabilities of its builders, it will remain standing for many more years to come. It is a site filled with inexplicable features, which we find incredibly compelling. Osaka Castle is one of the most intriguing of all of Japan's forgotten wonders, a place we have covered in the past. It was, we believe, like so many other inexplicable sites around the world, re-inhabited by our most recent of ancestors, placed within an academically permitted timeline of events. A chronology that if one wishes to succeed in the mainstream must toe the line of. For if one goes against the grain and explores the site with a critical mind, one can clearly see it contains a number of surviving features, which not only displays lost knowledge, thus the work of a lost civilization, which at some point in the very distant past built ruins all around the globe. Building countless polygonal ruins, which have, due to their incredible construction technique, fortunately survived into the modern era. However, it is not just its polygonal foundations which show clear evidence of these elusive and consistently denied lost ancestors. Octopus rock, for example, also sometimes known as the drum stone, is the largest megalithic stone found within the walls within the castle's grounds. This giant stone, just like those of Baalback, is enormous. Estimates for its weight range from 100 to 300 tons, although it could, of course, be far heavier. However, even at these conservative estimates, any explanation of how ancient man accomplished such feats remains elusive. For the fact remains, the stone is of an incredible size, and to this day its placement, along with many others found throughout the world, remains unexplained and unknown. So for one to conclude that this stone's use, its quarrying, transporting, and placement within this wall, was done by our less capable, more primitive post-Ice Age ancestors. Yet all these methods of building and lifting, the knowledge of how to do such tasks, somehow simply vanished through the ages. All of which now remaining a mystery even with computer technology, an explanation still evades us. Thus to conclude this to be anything else than that of a relic, left by a far older, now lost civilization's work, we believe, would be highly illogical, and should appear illogical to anyone with a capacity to dissect the purposes for these actions, taken by an academia claiming to hold all the answers. All the while, actively concealing or ignoring any conflicting controversial evidence, truths that due to their belief in their power, laying within their reluctance to ever admit an incorrect hypothesis for the origins of species or the timeline of man, thus this doubling down on fallacy merely makes their persistence at sticking to said posits not only a damaging conspiracy, which robs us all of our heritage, but can also be perceived as an attempt to conceal anything which could alter the status quo. The octopus rock is an incredible feat of ancient engineering, and one, just like that of the polygonal masonry techniques that can be found at countless other sites the world over, is clearly a relic of a forgotten past, accomplished with the use of forgotten technology and knowledge. Just how big is octopus rock? How old is it for that matter? And how did our ancient ancestors accomplish these feats? Because our research deepens and our studies widen, our target, that of a currently hidden lost civilization, becomes clearer in the mind every day, and it is only a matter of time before they are fully rediscovered. To deny such facts will eventually become too ludicrous. It is a journey of discovery which is undoubtedly highly compelling. In the country of Ethiopia, some seriously old megalithic ruins can be found. Many of unknown age. For example Tia, located in the Sado region of Ethiopia. An archaeological marvel, which is a UNESCO World Heritage Site, remarkable for its large stone pillars. But imagine the surprise of initial explorers when they stumbled across an entire church, in the shape of a Templar Cross, completely carved out of the ground. If a type of volcanic tuft, I'm sure its initial rediscovery would have come with considerable archaeological interest. Who could have carved such a structure, straight out of the rock, or indeed why? It is known as the Church of Saint George, and is largely thought to have been constructed around 1200 AD, yet, alas, no one really knows. The Church of Saint George is one of 11 monolithic churches in Lalibela, a city in the Amhara region of Ethiopia. Originally named War-War, the historical and religious area was named Lalibela after the King Jeb and Miskail Lalibela, of the Zagatid dynasty. Who supposedly commissioned its construction. Although like the pharaohs of Egypt, he may have just laid claim to the impressive ancient structures, which resided in the region, long before himself. He may have also been attributed with the act due to him being regarded as a saint by the Ethiopian Orthodox Tuhito Church. No one can really explain how he could have built it, and many religious followers believe he received instruction from God. With many ancient sites upon Earth, if researched heavily enough, reveal evidence that they predate their modern-held suspected builders. For instance the amazingly designed ancient site of Puma Punku, which contains stones created in weight-bearing shapes, with no mortar ever being used, yet the structures were earthquake-proof. These structures were said even by the Incas to have been there before them, they believed they were constructed by the gods themselves. The only conclusions that can be made from such structures including the church of St. George is that the builders were highly sophisticated. Enlightening artifacts may vanish, but thankfully, the ancients built structures to last. And a temple church carved into the stone ground, in the middle of Ethiopia, of unknown origin, is a very curious structure indeed.


Maxime Wachir-Lagrav beat women world champion Ju Wenjun in round 5 of the Gibraltar Masters. Let's find out what happened in this exciting game. Maxime, it got exciting very early on. You took a little time and went G4. Were you trying to recall lines or over-the-board inspiration? It was more like over-the-board. I felt like I want some tempi, so I should be able to try it. But I wanted to be sure it doesn't lose by force because it very well could. And then since it got heated, I'm not sure about the evaluation. I didn't actually check, so we know what it was. Right, now Wenjun continued to play pretty fast while your clock went down. What was going on in your mind at that point? Well, I thought it was doubtful. She was still in a prep, so I just went for it. And of course, I needed a lot of time for my first 20 moves or something because there was a lot of things happening. Right, now give us some insight. What happens to an elite player of your level when you're sort of caught off guard in the opening so early on? What goes on? Well, I guess I caught myself off guard, so this was sort of the plan to get a fresh position for maybe both of us. I'm not sure. I mean, she was probably at some point in her preparation, but then, you know, it was just an ads-up game. And could you point us to the critical moment in the game? I have no idea. I mean, there were so many. I guess when I got Qg4, it was already close to winning for me with this idea of Qg4. So I thought Qg7 was too slow. I wasn't sure if she could have played some B5 instead of Bd7 that looked very critical as well. Right, now tonight is the Battle of the Sexes and you just beat the woman world champion. Feeling confident? Unfortunately, I have teammates. That doesn't show a lot of confidence in your friends. Well, am I supposed to show confidence for them? Okay, now you're quite irregular at this event. Give us some idea. What's the team strategy? Generally, we play something off-beat. We get outplayed and then sometimes we save the day. So I hope we understand that they can play and we go less off-beat this time. All right, well, it's going to be fun and all the best for it. See you soon in our studio. Thank you. Thanks.


I'd like to welcome to the stage Alice Richardson from the ANU College of Law and the title of Alice's three-minute presentation tonight is Judging Portraits. We have two portraits of Justice Michael Kirby. Now, when Justice Kirby walked into the Archival Prize and saw this first portrait, whether it be a wrinkle and blemish and wrink and will everything to see, his first reaction was, well, that's a bit ugly, isn't it? Money-Clark will say, yeah, right? Tell me about it, mate. But when Kirby looked at this for a second time, he started to like it, and I'd like him all to raise one hand.  And I want you to cover one side of his face and then the other directly down the nose. What do you see? You'll see that one side of his face looks evil and the other side looks good. So he started to look a little bit like Two-Face of Batman. What could this mean? Now, this other portrait of Kirby shows him alone in a crowd. What could that mean? And it also shows him without a wig on. Is he just trying to show off his good head of hair? That age? Or is he trying to show himself unmasked in the law? Ladies and gentlemen, my thesis is on judicial portraits, and in particular, I'm looking at what portraits can tell us about the legal profession. My hypothesis coming into this was that portraits were used to glorify the legal profession and to highlight the virtues of judicial power. But I was surprised to find the portraits that aren't only used from the top down, they're also used from the bottom up. Portraits are used to question the law, to challenge the legal profession, and to subvert judicial power. And so here this portrait of Kirby shows one side of his face evil and the other side good, because the law isn't only about justice, it's also about injustice. And that a judge is a party to that injustice necessarily, and this can have a toll on the individual. This other portrait of Kirby shows him alone in a crowd, because that's what he is.  In fact, the artist went to some of Kirby's contemporaries and said, hi, would you like to be in the background of a portrait of Kirby? And they said, no! One of them even said, I wanted him writing that I would not be in this portrait. And so what the artist did was quite clever. He painted Kirby not amongst his contemporaries, but amongst two judges. So there's two faces you see in the background, the Sugarman and Wallace, two former judges. And this, I think, is a much more powerful message. It questions the role of a dissenter, not just within their own time, but within all time. Ladies and gentlemen, every picture tells a story, and these two portraits tell quite different stories about the same man. And these two portraits are just two of many that make up this beautiful mosaic that is our legal history. And this is a legal history as painted by artists, not written by lawyers. Thank you.