So it's a great honor for me to give this Dale T. Mortensen lecture. Dale has been very important for me and my career. I met Dale in the mid-90s when I started to work on wage distributions and wage dynamics, coming from ten years of painful research on demand systems and consumption. I thought that going to labor was simpler because you would go from many markets of differentiated products to just one market of differentiated products. Is it still working? So I started to work on this around 1995 and I met Dale. Dale invited me to the workshop that he organized in Denmark at the time, which was a great workshop where fantastic people participated. I learned a lot in those conferences. So I learned a lot from him and it's very moving for me to give this talk today. I just want to express all my gratitude. So the second thing I wanted to say relates to what Guido said recently. I'm not turning a microeconomist. I was at the Bank de France early this week and it was all about search and monetary economics. I couldn't understand a word of what they were talking about. So definitely this is not where I belong to. I am a microeconomist and I don't intend to do anything else. I'm interested in wage distribution, individual wage dynamics and employment mobility. But exactly what Guido said is true. The more sophisticated our models become, the longer the panel data you need to identify them. Clearly, if you estimate, let's say, a neighborhood Kramar-Margolis model on match employee-employee data, you will need 20 years of data. You can control for a business cycle by adding dummy variables or any other sort of features. If you want to estimate structural models that build a theory of wage determination and treat the models seriously and estimate those models, then if you need 20 years of data, at some point you will need to worry about the interaction between aggregate shocks, the environment and the amount of heterogeneity that you want to put in a model in order to fit the data. That's why recently I became interested in this project. So the paper I'm going to present today will have lots of heterogeneity and aggregate shocks at the same time. The other thing I wanted to say and I'm going to move to the paper is about estimation. The difference in the way we estimate the model today from a macro paper and the way we estimate models on match employee-employee data. Not really because the models we estimate have become so complicated that the only method that is available to us to estimate them is the simulated method of moments. What you do, you calculate moments from the data and you try to match those moments. So whether the moments have been calculated by the BLSP people or by yourself from the raw data doesn't make a big difference in the end. So what I'm doing here is not essentially different than what I've been doing until now. So that was the initial remarks that I wanted to make before turning to the paper which is joint work with Jeremy Lis. And it's about the micro-dynamics of sorting between workers and firms. So in this paper we want to ask two questions. The first one is what is the role of worker and firm heterogeneity in explaining the micro-dynamics of unemployment? And the second question is how does business cycle affect sorting? That is the joint distribution of worker and firm types over time. So in order to do that we're going to develop a sequential auction model which is the model we developed in the paper that Guido referred to a moment ago. I should say that the sequential auction model is a great name for this model. I'm not the one who proposed its Dale Mortensen. So we didn't invent this name. It's Dale. So it's not going to be the Burden-Mortensen model. It's not going to be the Mortensen beside this model. This is the sequential auction model and I think it's much better this way. So it's a sequential auction model with heterogeneous workers in task and aggregate productivity shocks and then we are going to estimate the model from US aggregate labor market data spanning the period 1951-2012 because at the time this is the latest date that we had. So a word before moving on about the sequential auction model. So what is the main idea? The way we thought about the sequential auctions was we start from the Mortensen beside this framework. We keep some sort of frictions as a source of frictions in the economy but we get rid of Nash bargaining. We keep the main idea in competitive models. The reason why wage is equal to marginal productivity in the viralizing economy that's because if you're not you can find another job and Bertrand competition is going to, in one way of thinking of viralizing economy is through Bertrand competition you move your wage up to marginal productivity. So what is the effect of frictions? The effect of frictions is such frictions is the way we think of it is in this way. Workers when they are unemployed they have zero bargaining power and so when they leave unemployed they leave at the minimum wage that they are willing to work for that this is the reservation wage. But it's not so bad for them, they can search on the job and when they find would be another employer willing to hire them then that triggers Bertrand competition and they get a wage rise. So this mechanism allows to span all the models between the monopsony model to the pure viralizing competitive model. But for this particular work it happens that this wage setting mechanism is very useful because you'll see whether employed or unemployed workers will always be paid the best remain option that is the second best option. And the second best option is going to allow us to simplify the Bellman equation a lot and this is the technical reason why we have been able to introduce a lot of worker heterogeneity and a lot of firm heterogeneity. So this so abandoning moving away from Nash bargaining is going to give us a lot of simplification in laying off or solving the equilibrium. The other thing is that because of poaching workers are going to move inside workers wages are going to move inside the bargaining set so exposed workers are going to be paid somewhere inside the bargaining set so exposed the wage allocation is not going to be very different from what you get from Nash bargaining. So this paper indeed builds on several previous work so I did a first attempt at pushing in the direction of today's paper in a previous work of mine that I published a few years ago in which I had only worker heterogeneity and aggregate shocks. Of course there was no firm heterogeneity. We started to think about sorting and production complementarities in a paper with Jeremy Lees and Costas McGeer that recently got published in red in the special issue edited by Guido in honor of Dale Mortensen. So this current paper will have exogenous worker heterogeneity and do genus firm heterogeneity will have sorting or workers and firms and would have aggregate shocks and sorting is going to move along the business cycle. The reason why we are able to do that is that again because of the simplification in the Bellman equations you see that the equilibrium model that we get has a recursive structure which allows us to solve the equilibrium exactly and not an approximation. So there is a huge literature. We are not the only ones doing heterogeneity and aggregate shocks. There are some competitors in the room. I don't know how we are going to share the cake in the end. I hope co-operatively instead of... I hope we are going to vote competition. So of course there is the directed search with which posting approach by Guido and Shuyong and others. Then there is a random search and which posting that Josep and Fabien recently developed. Dale and Merville Coles have a follow-up work on this. Then this work is related to all the work on let's say the unemployment volatility puzzle.  Then there is work about sorting. A lot of many papers, very important papers that I'm not going to refer to extensively. But I must say that there are very few little work with two-sided heterogeneity and aggregate shocks and you see that's what I'm going to talk about today. Now the model. So time is discrete in index by T. There will be a continuum of workers indexed by type X which is between 0 and 1 with an exogenous distribution L of X. There is also a continuum of potential jobs indexed by Y also between 0 and 1 and the aggregate state of the economy is Z, X, Y and Z. At the end of period T minus 1, the distribution of matches is that is passed on to period T as a state variable is denoted as HT of X and Y. And this is prior to the realization of the aggregate shock for the period. Prior to the realization of ZT. And UT of X is the distribution of work types in the population of an employed worker. Knowing HT is enough because you have this accounting equation that gives you U given H. Timing. So at the beginning of period T, the aggregate shock is realized as a draw from Markov transition probability Pi of Z prime. So you move from Z, you go from Z to Z prime with probability Pi Z Z prime. Then the timing is as follows. First, separations occur. Then workers search for a job and firms post vacancies and then meetings occur. All right. So let me go through all these stages one at a time. So first, following the realization of ZT, job separations occur. Here we are going to assume that there are two reasons for a job separation. So let me denote for the moment very loosely as P sub T XY, the present value of a match XY. Given the aggregate state at time T. So it includes ZT but it includes also all the distributions of types that I mentioned earlier. And let me denote as BT of X the value of unemployment. Okay. So there is the value of a match and there is the value of unemployment. So take a match XY. You see ZT, you calculate the value of the match PT of XY. If the value of the match is less than the value of unemployment, of course, there's no point in continuing and the match is destroyed. We call that endogenous job destruction. Otherwise, if the match is still valuable, then we assume that there is an extra possibility of job destruction with probability delta. There is exogenous job destruction. Why do we have something like that? It's very easy to understand from the beginning. When you look at the dynamics of unemployment over time, you see that unemployment goes never below say 4%. So you need something that's going to give you at least 4% of unemployment in every period. That's this delta. And the rest is going to be driven by the interaction between types and the macro environment. So right after job separations, we can calculate the new distribution of types in the economy. And we are called HT plus of XY. All those matches of type XY which have not been destroyed. So you need PT to be greater than PT and you need not to be destroyed for exogenous reasons. So 1 minus delta times the indicator function that PT is greater than PT. And then you can calculate the new stock of unemployed of type X.  So starting from HT, you calculated HT plus. Now following the realization of the T and job separations, workers search for a job. So we assume that workers search both when unemployed and when they are employed. So I defined here the aggregate search effort of all searching workers in the economy. That's the sum of all unemployed workers plus a fraction of matched employees. S is the search effort of employed workers relative to unemployed workers. You can see it as a fraction of them or with a probability S less than 1 you search. At the same time following the realization of the T and job separations, firms post vacancies. So there are searching workers on one hand and there are firms posting vacancies on the other hand. Here we assume that there is a cost convex function of the number of vacancies posted. And each firm of type Y or all firms of type Y are going to post VT of Y vacancies so as to equate the marginal cost of a vacancy to the marginal return of a vacancy. What is the marginal return? That's QT, the probability of meeting a worker. I will explain in a minute what it is exactly, times the marginal value of a filled vacancy which will be also derived later. And from this equation by aggregation you can calculate the total number of vacancies in the economy. Then workers and firms meet. So for that I assume a meeting technology M over T and VT giving the total number of meetings in the period. And from this matching meeting function I can derive the probability for an unemployed worker to contact a vacancy which is MT over LT. The probability for an employed worker to find a job which is S times lambda T and the probability per unit of recruiting, per unit of vacancy VT Y the probability for a firm or for a vacancy to meet a searching worker. So that's QT which is MT over VT, so standard in such matching theory. Now values. So let's start with the value of unemployment. So we assume infinite horizon. What is the present value of unemployment? That's going to be the expected discounted sum of future earnings. Conditional on being employed, unemployed, unemployed. Conditional on being unemployed in period T and given ZT and given all the distributions HT, given the distribution HT plus. So in period T unemployed workers receive some payoff, instantaneous payoff that we assume is a function of their type and the aggregate state of the economy ZT. And what's happening in period T plus one? We're going to write by many questions. So what's happening in period T plus one? An unemployed worker can meet a vacancy or not. If they don't, they continue with the value of unemployment BT plus one X. If they meet a vacancy, because we assume that they have zero bargaining power, whether they find a job or they don't, they continue with the value of unemployment BT plus one of X. So that means that it's very easy to work out the Bayman equation in this case. BT is B over XZT plus one over one plus R times the expectation given information at time T. One minus lambda T plus one, that's if they find a job, but if they find a job, they're going to be paid the value of unemployment. If they don't find a job, they are paid the value of unemployment. If they find a job, this job is of type Y drawn from distribution BT plus one Y over BT plus one. But you don't care because they have zero bargaining power, so they receive BT plus one X. So it's the same here and there, and so lambda T plus one doesn't matter. And that's the only parameter through which you can have dependence to distribution. So there is no dependence to distribution. It's just BTBXZT plus one over one plus R, expected BT plus one X. So that means that there is a solution, a very simple solution, which is BTX is a function of X and ZT, where B over X and Z solve this linear equation. And it's contracting, so numerically, just have to discretize as you want, and it's going to simply iterating the standard algorithm, the forward algorithm, will give you the function. So we can calculate this function, B over X and Z, X and Z. The value of a match. So how do you calculate the value of a match XY at time T, so PT over XY. What is it? That's the expected discounted sum of worker and employers' future earnings. So together or separately. So how do you calculate it? How do you calculate it? In period T, we assume that a match XY in environments ZT earns P over XYZT. What happens in period T plus one? Very many questions again. The employee may be contacted by some alternative employer or not. So the probability of being contacted by a firm of type Y prime, that's S times lambda T plus one, the probability of emitting if you are employed, times what is the probability of doing a firm of type Y prime. So that's the number of vacancies of type Y prime divided by the total number of vacancies. Now remember, we assume that firms are going to engage in Bertrand competition for the worker. What does that mean? It means that if Y prime generates a match value that is higher than the value generated by match XY, the worker is going to move to Y prime, but it's Bertrand competition. So it's like an auction. How much does Y prime have to give the worker? The maximum value that Y is able to pay, which is the firm's reservation value, is P of T plus one XY. So that's P T plus one XY. So the worker leaves, but leaves with this contract that is this particular value, P T plus one XY. Or Y prime doesn't beat firm Y and the worker stays at Y. So the match continues in period T plus one and generates the value of the match at time T plus one, P T plus one, X of Y. So it's exactly like for the unemployment value, whether the worker is contacted by a firm or not, it gets the best remain value, P T plus one XY. So that means that when you calculate the value of the match, P T of XY, you have to start with the current, the flow value of the match, P of XYZT plus the continuation value.  And in that case, the continuation value is P T plus one of X. If you're not laid off with probability one minus delta indicator that P T plus one XY is greater than the value of unemployment, P T plus one X, then you continue with the value P T plus one XY. Nowhere you see lambda T plus one. So again, the only reason that would make the distribution be part of the state space vanishes is because there is no dependence to the meeting rates in period T plus one. And so if you define now the surplus of the match as B T minus B T, P T minus B T, then you can get rid of these B T plus one here and show that the surplus, given the state at time T of X one, at least there is one solution. That is a simple function of XYZT that solves this quasi-linear equation. It's not linear just because of this plus here, which is our notation for the max of X and zero. But it is still contracting and we can still solve it finger in the nose by iterating the forward equation. That's a French expression, yes. So again, you can calculate the surplus X and T without solving for the equilibrium. Last thing, you can calculate the expected, the value of a field vacancy. I will pass on this for the sake of your sanity at the end of this long day. The bottom line is that you calculate it given the initial period distributions and given the surplus that you have just calculated. And finally, you can drive the law of motion for distributions and they also only depend on the aggregate surplus and the number of vacancies and the distributions that you got from the previous period. So at the end of the day, it's very easy to compute the stochastic search equilibrium of this model. First, you solve for the fixed point of S of X, Y and Z. It's a function of three variables. It's easy to do, enough. You can even afford discretizing X, Y and Z quite a bit. Then, once you have done that, the model is recursive. So given HT, you calculate HT plus one, HT plus two, VT, VT plus one, etc. So it's very easy to solve. So it's a model with a lot of worker heterogeneity, a lot of firm heterogeneity, aggregate productivity shocks and an exactly calculated stochastic general equilibrium. So what is the aggregate productivity shock? It can be something that you get from the goods market and that we don't model. So one possible extension would be to try and plunge this model into a general equilibrium model which would tell you what is that T, whether it's a demand shock or whether it's a supply shock. At this stage, we are totally agnostic. Okay, now in the last few minutes that I have, I'm going to turn to the estimation and the data. But for estimation, we need a specification. So we adopt a very standard parametric specification, a copper-glass specification for the meeting function. So we don't even bother estimating the elasticity. We assume that it is 0.5. The only parameter that has to be estimated is the meeting efficiency, alpha. Then we need a specification for the cost of V vacancies. So it's a simple power function with two parameters, C0 and C1. For P, the match output, we make something that we believe is relatively flexible. So first, we assume that it is proportional to the LVH shock. And then it's a simple quadratic approximation of a general function of X and Y. So it's a quadratic in X and Y. And you see that, importantly, you have some complementarities there that are going to be quite important. For home production, we tie our hand by assuming that home production is a fixed fraction of aggregate output. And we take the universal constant 0.7 of P. You can choose whatever you want, in fact, it's going to work. But it's not 0.95. So for the worker type distribution, we assume a simple beta distribution. It's nice beta. It only has two parameters. And the density can be like this, can be like that, or can be like this again. So it's extremely flexible and very sparse in parameters. And then for aggregate shocks, we use a simple AR1 process with two parameters, the auto AC parameter, rho and the volatility sigma. So we write it in this way so that sigma is the variance, the volatility of the ARH shock. How do we estimate the model? We first, nothing extremely original here. I mean, we HP filter the log transform data. We calculate moments, means, volatilities, correlations. And we use the method of simulated moments to estimate the parameters. For identification, the idea that we have is that in order to estimate alpha as the relative search intensity, alpha is the meeting efficiency. As the relative search intensity of employees. Delta is exogenous job destruction. You're going to need data on transitions between employment and unemployment, and job-to-job transitions. So in order to estimate sigma and rho, you just need data on aggregate output. We use GDP instead of GDP per head productivity, for some reason it happened to be easier to do it this way. Vacancy costs, so the parameters C0 and C1, they are identified from vacancies. Beta worker heterogeneity, that is, so that's important. I mean, in order to identify worker heterogeneity, we're going to use the series of unemployment by duration. So the number of an employee at a given point in time, the number of an employee with more than five weeks of unemployment, the number of an employee with more than 15 weeks of unemployment, and the number of an employee with more than 27 weeks of unemployment. That's duration dependence that is going to identify worker heterogeneity. And then for the match value-added function, the idea is to use cross-sectional data on firm value-added, calculate the dispersion of firm value-added in every period, and look and create a time series of this, and correlate it with aggregate output, et cetera. We don't use our own series, we take one that has been constructed by Nick Blumen and Corfers recently. So moments, we use the method of moments.  So first, I mean look at the data, so that's the volatility of GDP, log GDP. It's 0.03. Look at the volatility of unemployment, it's 0.20. So another of magnitude bigger. So that's why you need the model to generate an amplification mechanism in order to amplify the small volatility of aggregate shocks to the level of unemployment. But now look at the volatility of unemployment more than five weeks. It's much bigger. The volatility of long-term unemployment is even bigger. What the model does? My pretty good job is at matching those moments, the volatilities. But also when you look at transitions from unemployment to employment, employment to unemployment, job-to-job transitions, the volatility is well matched. Tightness, it's okay. The cross-sectional variance or dispersion of firm value-added, and the volatility of this across time, it's also well matched. The only thing that is not as good as what we would want is the volatility of vacancies, which we predict much lower than what we see in the data, but we all know that vacancies are very hard to measure, so I can live without. We also try to match correlations with one shock that we are going to generate a lot more correlations between aggregate output and between the series than you see in the data, but there is a fair amount of correlation. You see in the data, a correlation between unemployment in GDP minus 0.86, vacancies in GDP 0.72, et cetera. So all the data correlations are very high and the model predicts the right sign and values which are much higher. The only correlation that is very low is the correlation between the cross-sectional dispersion of firm value-added and GDP, and the model gets it right too. Now we do another exercise which is to show that, because I mean moments, you could have the right volatility, but it's not clear that you have the right value. So what we do is we filter out productivity shocks so as to match exactly the observed GDP series. Okay, so in every period, you observe GDP. We ask ourselves, what is the value of ZT that we need to put in order for the current distributions of worker types to generate output that is exactly equal to the observed GDP? So in this way, we can calculate a series of aggregate shocks in order to match exactly the series of GDP. Question, is this series of ZT hat that we generate, does it satisfy the year one process that we assumed in the first place? That's something that you have to check? Yes, it does. So the series of GDP values of ZT that you have to generate in order to match exactly the observed series of GDP is approximately an year one process with the right volatility that we have previously estimated. Then, given ZT, you can use the model to calculate the next period distribution of types and calculate aggregate unemployment by duration, et cetera. Here, we show the actual series of unemployment, unemployment more than five weeks, unemployment more than 15 weeks, unemployment more than 17 weeks. The green dotted line, that's the data. The blue, that's the one-page ahead prediction. You see that why the volatility and the correlation is right? It's because the R square is quite good indeed at all frequencies. So that seems to be working well. You can do that for unemployment-to-employment transitions, employment-to-employment transitions and job-to-job transitions. Scale is a bit misleading, but you see that the dynamics is exactly where we produce. The level is a bit off, but not so much. And for job-to-job transitions calculated from the job, so we don't have them for the whole period, it's also pretty good. The only thing that doesn't work as well is the dynamics of vacancy data. The help-wanted vacancy that we have glued with the Jolt's measure somewhere here. So we have the right dynamics, but not exactly the right volatility. We have a smaller, half-volatility with respect to the tool. Parameter estimates. So what we do is we do a simulated method of moments that is we estimate the parameters. And if you estimate the parameters, there is one thing that it is buying you. It's buying you standard errors. So why is it useful to have standard errors? So one thing we do is we use the new real-estimator for the moment variance, and then we use the delta method to calculate the standard errors of the estimates. So why is it useful to calculate standard errors? It's because it's telling you about identification, at least local identification. Think of an OLS estimator. The variance of the OLS estimator, that's the variance of the error term, times x prime x minus 1. You have two components. The variance of the error term, that's the signal-nose ratio. So in order to have a precise estimate, you need to have a good signal-nose ratio. And then you have x prime x minus 1. You cannot have a good estimate if you have multicollinearity if the model is not identified. So having good estimates frees you of doing any other calculation in order to show identification. It proves here that the standard errors, which are very good, already prove by themselves that the model is at least locally identified. That means if you move away from those parameter estimates, you're going to decrease the GMM criterion. Doesn't mean that there is not somewhere another set of values that would do as well. So for that, you need to try many different initial values and make sure that this is the one that is better. This is something that we did, by the way. So we are pretty confident that those estimates are indeed the ones that minimize the sum of the GMM criterion, maximize the fit. So now, what does that give us? So this is the form of the production function that we estimate, p of x, y, z. Here we show it, you know, it's z times a function of x, y. So it's just the quality part. That's quite interesting. What it says is that if you are firm here, you want the best worker. I mean, it increases along the worker type dimension. If you are a worker, it's different.  If you move up, you see that at some point you reach one that is tangent to the iso-client.  You want the best y.  In the data, nobody is here and nobody is there. Because the distribution of worker types that we estimate is this one. So basically, there is no worker with a type above 0.5. And the distribution of vacancy types is here. There is no job type less than 0.1 and more than 0.5. So this function here is a bit misleading because we should restrict it to this segment here and this segment there. So basically, these books are here. Anyway, that's the idea. There is a lot of action along the worker type dimension. Not so much along the firm type dimension. Firms all want the best workers. Low-ability workers are picky. Then that's the distribution of worker types that we estimate. The beta distribution nicely behaved. And this one here, that's the distribution of worker types among unemployed workers. And what you see is that if you have a low x, you have much higher probability of being unemployed than if you are a high-ability worker. So that's what... This one is endogenous. This distribution here, that's v of y. It is endogenous. And we showed... So there are two curves because one corresponds here to a high z. Let's say the ninth-design that we have here in the data. And this one corresponds to a low-agreed shock, the first-design. What you see is that you don't have a shift. As if when z is better, firms of a higher y enter the market. It's more like... You have more jobs, more vacancies that are posted, but roughly with the same distribution, a bit more concentrated in the middle. This is b over p. So what this shows is that it's not a small surplus economy. B over p is not close to 0.9. So this curve corresponds to a bust. This one, so a recession, and this one to a boom. And what's happening is that b over p becomes lower, or p increases with respect to b, in booms vis-à-vis recession. So you have two modes. This one corresponds to workers coming from unemployment. So for those workers coming from unemployment, b over p is higher. But because of the job search, they can move progressively towards a match which has a higher p. They keep the same b as before. So b over p becomes lower. And you see that you have more employed workers than unemployed workers. So this is... There is more concentration in this region here than there. This is the region of feasible matches calculated for different states of the economy. This dotted line here, that's the optimal matches. So b care. That's where if you could perfectly sort workers and firms, if you could be a planner and remove all frictions in the economy, this is what you would do. You would associate this y to that x. But because of frictions, you have a lot of mismatch. And mismatch sorting changes with the business cycle. And what's going to happen is that in a boom, you can afford to be less picky. So the matching set is wider in a boom than in a recession. So that corresponds to a boom. This frontier here corresponds to a recession. Surprisingly enough, I don't know exactly why. But here it moves more than there. I don't know why. That's the distribution of matches, h, that we estimate at two different points in the business cycle. So what you have to take, it's like in one dimension, you would have something like this, like an exponential. So that's why you have this sort of wall here. It declines starting from this frontier here. But what's happening that is interesting is you see that the bump here is more pronounced than this one. Which means that in a boom, workers move faster to the point of optimal matching. Sorting is stronger or the force towards sorting is stronger in a boom than in a recession. So that's interesting because at the same time in a boom, you have more mismatch. But the force towards perfect matching is stronger in a boom at the same time. So conclusion. So we have developed a sequential auction model with heterogeneous workers in task and aggregate productivity shocks. The model fits the US time series data from C-51 to 2012 reasonably well and exactly propagates the technology shock to unemployment rates. In boom, workers initially accept worse matches on average than in recessions and once employed, they move more quickly to better matches in booms than in recessions. What about wages? That's the last slide. So yes, I mean we haven't used any wages. So the next step is of course to go to wage data. So what is the ground project? I mean what is it that we want to do now? We want to take the match employee employee data over 20 or 30 years and estimate this model on the match employee employee data so that we can have a model in which you will have wage distributions that depend on worker ability, firm heterogeneity and the environment and a model in which each worker faces its own wage trajectory. So the problem is can we keep the recursive structure of the model? I was going to do like in my 2011 paper and the model would not have been recursive. Jeremy has this great idea. Why not forcing wage contract to be negotiated in this way? So I will leave it to you to think about it. I hope that you think it's not a crazy idea. What is the idea? The idea is that instead of negotiating about a wage, you negotiate about a value and what you negotiate about, so values, if you negotiate about wages then you have to worry about whether the wage is going to remain in the bargaining set after the productivity shock. A simple way out of this is to assume a peace rate wages like Gadi Barlevy did and like we did in a paper with Jesper Bagger, François Fontaine and Fabien Bostéviné. But if you do that, if you steal your model, it's not recursive. But you can keep the peace rate idea and the peace rate on the value. Basically what you do is you negotiate on Sigma and once Sigma has been negotiated it is fixed forever and this is the wage that's going to adjust. What you get if you do this, you get this very nice wage equation and I'm done, this is the last one. The wage corresponding to a particular contract, that's a weight average of the match for activity and home production minus a discount and this discount is all the greater that you can expect better wage negotiations or contract negotiations in the future and we are able to calculate it in a very simple way, that preserves the recursivity of the model. So I think that at this stage we have the model that we wanted which to bring to the micro data. Thank you.


Deshmukh Sachin, working as an assistant professor in Walsh and Storpe technology in civil engineering department. Today we are going to learn about what is a metacenter and what is a metacentric height and what is its importance. At the end of this topic, you are able to calculate the metacentric height of a ship model which is very important and all the construction of the ship models are totally depending on this and you can classify the equilibrium conditions so that you will come to know how to stabilize or how to make the ships in stable conditions and how to construct it. Now first of all, before starting this metacenter, we must know what is the center of gravity? What is the center of buoyancy? Center of buoyancy, here the upward force is acting. When the body is immersed in water, there is upward force is acting and that force it is located at some place. Here just go through this figure, you will come to know. And the point M which we call now, it is a metacenter. It is located above that center of gravity if it is in a stable condition. Metacenter, it is a theoretical point at which an imaginary vertical line passing through the center of buoyancy intersects the imaginary vertical line through a new center of buoyancy created when the body is displaced. What body is displaced? As you see in the second figure, body is displaced or tipped in the water. Just concentrate on this figure. This is a water and this is a body. This is the center of gravity. G is the center of gravity. This is the original vertical line passing through center of gravity. Now this is a buoyancy, center of buoyancy. You might have remember the Archimedes principle also. This is the center of buoyancy, the center of gravity and this is the M metacenter. Now this particular body is just displaced or tipped. We have written in its definition, it is just displaced. Somehow it is displaced like this. Now this G is over here. Now this B is the center of buoyancy. It is shifted to this place. It is shifted from this point to this point. And from this point, again you have to draw a vertical line. And this vertical line where it intersects to this previous line, this one. Center of gravity M and B which is passing through. This is the previous line where it cuts, where it cuts. That point is a metacenter. That point is called as a metacenter. Now what is a metacentric height? The metacentric height, it is a measurement of the initial static stability of the floating body. And it is the distance between the center of gravity of the ship and its metacenter. That means G and M, that means G and M. A larger metacentric height implies always greater initial stability against over turning. Here, another model I have drawn for you. This is the B, the center of buoyancy. It is the force of the buoyant or I can say buoyant force is there. G and weights, the weight of the body which is acting downwards side. B is displaced over here. This is the M. And this G and M, this G and M is a metacentric height. This G and M is metacentric height. See here, the action over here in the side, body is dipping in the side. So that to make it in a stable condition, we have to go like this. The force of buoyant force is acting over here. And it is going to meet over here M, M and G. The distance between M and G, metacenter and center of gravity, it is called as metacentric height. Which is again a very important word in the ship model or construction of ship model. Now, what are its applications actually? The metacentric height and metacenter, actually these words are used in ship construction. And also to measure the stability of the vessel which is kept in water. Now see, this figure is an old ship model. This is an old ship model. We will come to next figure afterwards. This is an old ship model. And all these strings are there, these strings to make the ship stable. Here, probably here, when the ship is in a stable condition, probably the M will be above G and the buoyant force will be here. It is acting through this axis. And we know that as the metacentric height will be more, more stability is there. The same concept from ancient days to the new modern technology is coming in, providing the metacenter and metacentric height. Just go through this figure. Observe, a multi-storey building is there on a ship. 3-4 floors are there which are constructed on one side. Never matter. If you are keeping the metacenter above center of gravity, it is in a stable condition. It is in a stable condition. Just go through it. Here, you can observe, no such more weight. But here, on the backside, there is a building, small building. And here, more weight is there. But it does not matter if you are going to keep the metacenter above center of gravity and maximum metacentric height. It will give you a stable condition. Metacentric height is determined by two methods, analytical method and experimental method. Here also, one figure I have kept. Here also, you can see, there is a building. These big ships, they are traveling in the sea for passenger traveling and also for cargo, also for wars. The metacenter is maintained so that there is no question of sinking. So metacentric height can be determined by two methods, analytical and experimental method. We will just flash on both the methods. Now pause the video and give the answer for this. What is the proper explanation for the metacenter? A is point at which line of action of force meets the normal axis of body when it is given an angular displacement. B, intersection of line passing through a new center of buoyancy and center of gravity. Point about which body starts oscillating when it is given a small angular displacement. The answer is all, all, all the choices. Here, point at which the line of action of force meets the normal axis of body when it is given an angular displacement. It is a phenomenon where you can see the line of action of forces meets in the normal axis. Then the intersection of line passing through a new, the center of buoyancy is shifted. So from the new center of buoyancy, again you are going for a vertical line which is going to meet that previous one. And point about which body starts oscillating that is m. The body starts oscillating and again coming to its original place when a small angular displacement is given. So all these choices are correct. Now we will shift to this analytical method. This is the analytical method. This is a shift model and this is as m is given over here. And here in this figure we are concentrating on this particular prismized shape. That is o dash to, q dash to q and n dash o and n. This particular small prism. This b is shifted to b1. This is angle. Pb is a buoyant force, center of gravity. Again when it is tilted, the center of gravity is over. This weight of the body is going to act. This is w. This is center of gravity. Now see it is to find the metacentric height. Consider that element is strip, q, q dash and portion of n dash o at a distance x from o. This is the x distance from o. So calculate the volume of this elementary strip. Then the upward force, that buoyant force we can calculate. And the moment of this buoyant force we are going to calculate about o. For the total portion of that n o n, we are getting this particular integration. Because we are concentrating on a small strip, there are different many strips are there. So we are going for the integration of this. And we can find this where i is moment of inertia of the sectional area about the water line. Put these values. Put these values. And finally, bm. You are getting as i upon v. That is moment of inertia upon volume. So once you relate bm, gm is our metacentric height. So bm plus or minus bg. b that is buoyant force where it is acting and g is the center of gravity. So positive sign when g is below b and negative sign when g is above b. Keep this in mind. M must be always above when it is below. It is unstable. Experimental method is also there. From experimental method we can calculate this gm by this formula. Reference books are there. Thank you.


Alright. So hi. I'm Jeff from Vancouver, British Columbia, Canada. I do a few Dribble modules. A few of them are up there, a couple of which I'll be mentioning today, one I'm talking about today. If you want to find me online, I'm on Dribble.org as Gapel or you can find me on Twitter as well. I work at MyPlanet, which is from Toronto, Ontario, Canada. It's a pretty cool place. Talking about headers today, I figured I'd start with a couple simple ones. This one is X content type options. Since it starts with an X, it's actually not a standard header, but this addresses an issue in the past of what browsers try to be pretty lenient in the content they accept. So if you write a script element on your page and link it to something that's not JavaScript, the browser will actually try and still execute it, which might not be a good thing if it's not JavaScript. It might not be something that's supposed to execute. But the browser is going to try and do that in trusted anyways. This is one that Dribble actually handles for you by default. It sets a value to no sniff, which tells the browser to say, hey, if you get a script element or you get a style element that's supposed to link to a style sheet, and the server doesn't tell you that that's actually the content you accept, don't run it. That protects you from a few different options, a few different things. Like I said, Dribble helps you out by default. Make sure that you're kind of doing a safe thing. And I think browsers are actually trying to pull back this behavior so that this header won't be needed in the future, but it's safe to start with. Another one that Dribble gives you by default is frame options. The risk here is something called a click-jacking attack, where if another site puts your website in an iframe, the user sees your website and can try and interact with it, but they can potentially be interacting with an invisible layer on top. So this could be fairly innocuous if they're trying to click a button on your website, think they're doing one thing, and the website that wraps your page is actually doing something else, or it could be something like they think they're typing in their username and password, and that allows them to steal credentials. So there's a few options to kind of restrict this. The default that Dribble goes with is same origin to say your site is the only site that's allowed to have itself in an iframe. You can be more strict. In a lot of cases today, you don't use or don't need iframes, and you can say outright, my page should never be in an iframe. But there is other options. In some cases, you actually are providing an iframe that should be accessible to other locations, and you can target that to say this is the only website that should be able to include my site in an iframe, and this can be done per page. So if you're providing a service to another website or to different service providers, you can say each one is only allowed to iframe the own specific page. So Dribble sets this by default to same origin, but when it sets it, it does it so that it's overridable. So if you want to make this more restrict or not, it lets you do that. Another browser feature is cross-site scripting protection. This is built into Chrome, Safari, and Internet Explorer. Firefox doesn't do this, but it has a couple heuristics to detect, you know, is there a potential cross-site scripting attack on this website? So the default is one, where it goes, okay, if I think something might be running that's bad, I'm just not going to execute that portion of code. That can potentially cause a few problems, though. Maybe it's actually blocking something legitimate, or the other challenge is it's silently blocking it by default. So if something's not executing, you or the user might not be aware of it, but it could actually break some functionality on your website. So a lot of cases recommend that you go to the stricter mode with mode block, and that means that if the kind of the browser heuristic detects that, hey, something weird is going on here, it actually blocks the entire page, which makes it a lot more obvious that something is going wrong and you need to fix it. You might not necessarily be aware of that, though, is the problem. So Chrome adds another option where you can actually send kind of a log of, hey, this browser blocked something, send it to the server, and the server will have a record of, like, hey, content is getting blocked, you probably need to look at this page, whether it's something just, you know, injected innocuous, you need to clean up the page, or the browser is detecting something that shouldn't, and you need to make a larger change. Refer policy is a little bit different, because it's more about the information that you share. Whenever you link between pages on the website, each request says, hey, what sent me here in a refer header? And that also includes if it's a linked request like an image, or you're calling out to a content delivery network for your styles or your scripts. Each of those are going to be able to tell what pages on your website are sending information. And if your URL contains something that maybe should be private, you might want to restrict where that gets sent.  So this header gives you a few options. From the completely restrictive no refer to say, never send a refer header at all, to the most permissive of unsafe URL of any time you're sending a request, if it has a refer, that is my site. Send the full information. And various ones in the middle. The default, if you don't set it, is basically equivalent to a no refer when downgrade. So that if you're going from a secure web page to an unsecure web page, no refer is sent. But as long as you're going from unsecure to unsecure or secure to another secure web page, then it'll include that header. One of the ones that I think is most interesting example is strict origin when cross origin. So that if you're going within your own website, it sends all of the information. Page two knows that it was sent from page one. But if you're linking off site, it hides that path. So if you link to Google or anywhere else on the website, they know that your website sends a request to them, but they don't know which page it is. And then because it's strict, there's the two options, strict or not. The strict one says that it has to be done over the same protocol as well. So if you're linking from a secure page to an unsecure page, it goes, I don't want to expose this information over an unsecure connection, and it completely excludes it. To implement any of these headers, the best case is probably you want to do it within Drupal itself. Since the request is in Drupal 8 is now the responsibility kind of the symphony components, you have to use an invent subscriber as opposed to a hook. But they're fairly easy to implement. First you just register it as a service. The important part here is tagging it as an invent subscriber so that Drupal knows I have to ask this when I need to act or when I'm doing certain things. You can pass it arguments and here I have the example of you're passing it just general site configuration to make some decisions. But any Drupal service can be included here to give it information. And then the actual class is pretty simple as well. You're implementing the invent subscriber interface, which you can see from the use statement is from symphony component. You're telling it I want to act whenever Drupal is sending a response. And then I want to run a particular method. In this case, all it's doing is adding a header. And this is strictly setting that header. It will overwrite any previously one. So for example, Drupal setting the frame options header. This is the way that you can say I want to have the most strict frame options header and Drupal core will respect that won't overwrite it. So one of the other big things that's happening is the internet in general is moving to kind of a secure by default policy. Users should be able to have the assumption that their information between their browser and the website that they're looking at is private. No one else can listen to it or intercept it. Chrome and Firefox are being most strict about this, Chrome especially. Right now, if you go to a website that doesn't have a secure certificate and try and type in a password, they give you a warning to say, hey, this is information you probably don't want to share to anyone in between. And you should probably be concerned that anyone can listen in. If you're typing this in in a coffee shop, someone might be aware of what your password is and could then access your account. And they're bumping this up. Next month, Chrome is actually going to give a warning on any form input on your website. So if you just have a search, users should be able to expect that no one can listen into what they're searching on your website. And so Chrome will pop up a warning as well within Drupal if you have a view with an exposed filter. That's a form input. It sends additional information back to the browser and people probably don't want that able to be listened into unexposed. So there's a couple of options. You know, for securing a website, Let's Encrypt is a free automated service that provides domain-validated certificates. So if you have control over your server, if you run it on a VPS, for example, they provide a command line script and Chrome tools that will perpetually keep your certificate up to date. A lot of services are starting to integrate it. Pantheon is one where you can get a free certificate just by clicking a button and turning it on and through the very interface. And some hosts like Dreamhost, which is a shared hosting provider integrated as well, hopefully more in the future. Or Cloudflare is a service that can wrap your website and they provide free certificates as well. So where strict transport security comes in is that when someone first goes to your website, they just type in your domain. They have no idea whether it's unsecured or secured. And you can do a redirect, but that first request of the website is always sent unsecured because of the browser by default puts HTTP at the front and that's it. They get the redirect to the secure connection and then their browsing session is fine. But when they go to the website again, they type in the domain name, the browser adds it without the pass at the beginning, and they're sending another unsecured request. So the strict transport security is a way for you to add a header that says, if you ever come back to this website, expect that it will have a secure certificate and don't make any requests that aren't secure. And then in addition, if there's a problem with the certificate, if you don't use something like Let's Encrypt that automatically renews it for you and it expires, the browser goes, hey, something really big is probably wrong. And you can't just go, hey, I want to skip this warning. Because the browser knows this is probably something that shouldn't just be skipped. It's pretty easy to set. My recommendation, if possible, so like on my own servers, I run this, I put this directly in the virtual host configuration right alongside where I set the certificates. If that's not an option for you, depending on your host, you can also set this in your HD access files or directly in Dribble itself. I just like to put it next to the certificate because they are related. And then I get to the big one, is content security policy. One of the most common security vulnerabilities on the web is cross-site scripting, as I mentioned earlier. And it can be pretty innocuous. The basic test of it is, can you put in just an inline alert onto your page? And does it pop up my message? You know, this doesn't risk much, but you still don't want to allow this. If an administrator is on your website that has an inline JavaScript, that JavaScript can act as that administrative user is or similar to the click-jacking attack if any user goes to the website and there's inline JavaScript that was put there maliciously on your login page, someone can extract credentials from those users, learn their passwords, get access to your site, or if they reuse that password, they should get access to more from that user, log into their email and other things. So content security policy gives you the option to say, I don't want to allow that. This is a screenshot of the browser console that's saying, this browser knows that I shouldn't be able to run inline JavaScript so that it just skips over it. And it gives a warning to say, hey, there was invalid JavaScript on this page. I'm not running it. It's a little bit more expansive than that. There's actually quite a few options. In the case of the previous example, it's script source where you can say, hey, I only want to allow JavaScript from a certain location to be able to run. You can include that for CSS, which also has some attacks that are possible. You can restrict images to say, well, I only want to allow images from my own domain, like I believe Drupal.org does this, where it doesn't allow links to external images. Connect source actually deals with APIs. So if your site connects, makes an HTTP request to an external service, you can restrict where a browser is able to send any information or make any requests. And frame source is basically the standardization of that earlier frame header, where you can say, what sites are allowed to put my site in a web frame? And then there's also a child source one that says, what sites are allowed to be in an iframe on my own website? So there's a bunch of different options here to give very specific ones. And then there's kind of a generic wrapper around it that is default source. To say, by default, I only want things to be valid if they come from my own website. It also allows a few other options that are pretty helpful. Upgrade insecure requests. It's less common today, but in the past there was mixed content warnings. If your secure website linked to an image on an unsecure domain, the browser would go, hey, something's weird about this. There's a bit of a warning. In the past, you could opt in to allow those or not. Some browsers blocked them. Upgrade insecure requests says to the browser, I want everything to go over to a secure connection. So automatically change it to an HTTPS request, even if it's HTTP. And that applies whether it's a link to your own domain or any other domain. There's the option, there's the possibility that that can break things if it's linking to another site that doesn't enable security. But at the very least, it doesn't ensure that everything goes over a secure connection. And then the last one that I've got up there is report ERI. Similarly, as I mentioned before, with the XSS protection is, what if something is blocked? How are you going to potentially be aware of it? Report ERI tells the browser that if anything is blocked, it should actually notify you by sending a JSON object to a location on your website so that you can actually log and process those to know whether someone is trying to inject anything on your website or alternately if just something is misconfigured and you're blocking something that you do actually want to allow. There's a few keywords that you can apply. You can outright block things. So for example, if you don't want to allow JavaScript at all in your website, you can add this header and say, I want no JavaScript at all. Some of the other ones, maybe that's more appropriate for iframes to say I don't want to allow my site in an iframe or I don't want any iframes included on my website so that content editors can't add anything. Self goes to the same domain, so you're saying I want to allow JavaScript as long as it comes from the same domain as the page itself. The star is basically and everything is allowed. So any domain is allowed, but the one restriction is that doesn't include inline scripts. So if someone was able to add some sort of random JavaScript into a text box on your website, even if it's inserted, that's going to be blocked even if external requests to any content delivery network are allowed. So you have to specifically opt in to say, I want to allow inline JavaScript or style sheets, or I'm going to leave that off and they'll be blocked by default. And then the other one is eval, especially for JavaScript, where it's kind of dynamically created code in JavaScript itself. So that's something that is maybe less used today, but gives you a little bit of protection about certain kind of JavaScript attacks just even if you're limiting to allow inline script as well. You can specify domains. So for example, if you're linking to a particular content delivery network for external JavaScript on your website or linking to certain locations for style sheets and images, you can use wild cards for subdomains. So if you have a network of sites, you don't have to list every single domain in it. You can just list your main domain with a wild card. And then you can actually limit protocols as well. So this would be less important if you were using that upgrade in secure requests property. But in here you can say I only want to allow connections to a website if they go over a encrypted connection, or I just want to allow requests in general with just the protocol in the colon to say that they have to come from a secure connection. This obviously can get a little long. This example is from Drupal release state.com, which I built before I understood this header, so it has to allow unsafe online still because I didn't refactor that out. It needs to include the content delivery networks to load jQuery, Bootstrap, a Google API to be able to connect to Google Analytics. But it doesn't always have to be that complicated. And then again this header is only set on your HTML pages as well, so not every request is going to have to send this additional information. And then hopefully with HTTP2 your browser can reuse connections, and it's actually only setting this header once, and then on subsequent requests it's saying hey, I just want to send this header again, and it's actually only like a single byte each time. As I mentioned with the report URI, there is a risk that you're going to block something that you don't want to. So there is a report-only version of the header, so we can start out with a very lenient one to say I want to allow JavaScript to link to anywhere. I'm going to allow inline because I know I have some stuff, but I'm trying to get rid of it. Do a report if anything is actually blocked, and then you can have a more restrictive one that's in report-only mode. So in this case I'm going to restrict it to self, and then any time the web page loads it's going to apply the lenient restrictions and then report on the less lenient restrictions. So if anything else comes up it's going to give you a report but not actually block it from executing so that it doesn't affect the user or the functionality of your website. And then one of the cool things that I think that you can do with this is that you can actually start to segment your things. So for example on a Drupal website your files directory both has your aggregate files and user uploaded files. And you don't want your user uploaded files to include a JavaScript file that can be included on your website because that's essentially a cross-site scripting attack as well. So you can actually start to separate it out to say I have specific domains with vetted JavaScript, vetted style sheets, and I only want to allow those to execute from a particular domain. And as well I've got an example here. If I only want to allow files or images to be linked if they load directly from you know core or a module or their user uploaded file I don't want anything off my website. So integrating this with Drupal. Drupal 8 does a couple of important things. One is that core doesn't do any inline JavaScript itself. Previously in Drupal 7 the Drupal settings was added through an inline function. That's actually changed in Drupal 8 so it isn't. So out of the box with Drupal you can do a default source self and it won't block things, won't restrict things. And then the other component is that everything is added through a library's definition. So when you're building your module it has to prespecify these are all of the JavaScript and CSS files that I'm going to load onto my website. Which allows to make an automated policy to say I know beforehand everything that should be valid on my website restricted to only those things. So once I'm giving a presentation on it I figured I have to actually build this. So I have an alpha version of the module that applies a report only header and actually does do that pull it in from libraries. Which is a great start. Unfortunately parts of the web don't like this. Google Analytics is one example. This is their recommended JavaScript and they tell you to just paste this into the head of your website. And then the other problem is like you can wrap this in Drupal, add it into a local file that's fine. But it dynamically loads its own separate JavaScript file and the library system has no way of knowing that this exists. Thankfully in this case they actually do provide you with an alternative. You can wrap the inline script here into something local to Drupal and then you can include the file within JavaScript. The first version really only exists to support Internet Explorer 9 and previous which aren't supported anymore. So hopefully more services move to this structure where they provide snippets and direct links to be able to create content security policies for websites to make them secure. This is one of the reasons why I decided it was a good idea to rewrite one of the top 25 Drupal modules to make a version that actually does work with content security policy that does use that second set that define it in the libraries so that you could turn on an automated content security policy module and not have to worry about your analytics just breaking. It does have some things that are probably important to continue on. In finish right now it doesn't have any way to handle that logging. It doesn't expose whether it's automated policy is failing in any means. The other problem is that it only works for script and styles. So hopefully it needs an API so that other modules can say I need to be able to load an iframe. I need to be able to connect to an external service. Don't block me from being able to do this. And then the last one is manual configuration for things like the image sources. The module is never going to be able to make a decision of does the administrator of this website want to be able to link to external images or not. So that's something that's going to have to be a configurable option in the interface and I just haven't had the time to do that yet. So I know I ran through a lot of things quickly. You can see my presentation online. It does have a bunch of resources for each of the sections that I went over. Links to where you can find out the headers and some articles to learn more about them. As well as some extra slides that I had cut out. Contribution sprints are tomorrow. And I would love to hear what you think about my session. So if you have any feedback, please go to the event website and let me know what you think. As well as for DrupalCon itself. Thank you. I think I have probably a minute for questions, but I know I'm running late here and I don't want to eat into the next presentation's time. Hi, a while back I was reported that opening a new window of new tap gives the new window or tap a partial access to the DOM of the previous page. So it can replace for instance the location. Are there any things right now available to combat that? Or would you just push the no opener into the link in the HTML? So yeah, there is the no opener property on HTML links and that's part of content security policy itself so that you can actually specify through the policy that the page should disown any openers as well. So that works from the header and you don't have to put it in the HTML anymore on the HREF, right? Yeah, because if you're linking to another page and you want to exclude the opener, it's the responsibility of the linking page, whereas content security policy allows to move that responsibility to the target page to be able to restrict that. Thanks. So there's definitely a whole lot more options in content security policy. Not all of them are available yet. It's actually on its third version. CSP2 is largely implemented in Chrome and Firefox, but there's additional options that are going to be enabled in the future to restrict more things like that as well. Yeah, so basically for still supporting IE11, you will still have to put it in the HREF, probably. Yeah, that would be an example of Internet Explorer 11 and potentially Edge, but hopefully Edge gets updated in the same manner of... Thank you.


Don't you ever get the feeling that China are aware of something the rest of the world don't know about? The industrial revolution in China is still very much in progress. Within the past 50 years or so they have went from a centrally planned closed economy to the second largest economy and will be the biggest economy on the planet within 20 years. They have risen out of the ashes in the late 20th century and now dominate Asia as the top major superpower in the region with huge global influence. So when we say don't you get the feeling China know something we don't that is literal. They have even went as far as to lift three-quarters of its population out of a state of poverty and they branch out into every country in the world. Chinese people are everywhere. There are 81 million Chinese people living outside China and that only accounts for 6% of the total number of Chinese. Have you ever heard the expression of why are there so many Chinese? Because they were here first on earth that is. Anyway guys, we wanted to tell you about the famous Dropa stones said to be at the very least 12,000 years old. They have hieroglyphic inscriptions that can only be read under a microscope and these enigmatic discs are one of the weirdest things ever discovered on earth concerning alien visitation. Wait, do you hear this? Is it possible that China has deciphered ancient knowledge as their rise continues in modern times? A Chinese archaeologist discovered these stones right around 1930 near inaccessible mountains. Very close to the then independent nation of Tibet. They were found in a system of artificially carved tunnels and pantries that are said to have been home to a very small group of beings that grew to around 4 foot tall with heads larger than the average human today. There was mass scattering of bones of these tiny beings that have been kept under lock and key by the Chinese since the Communist Revolution of 1949. As the archaeologists excavated the site with students from Peking University they began to come across these Dropa stones. In fact, it is thought they discovered close to 800 of these things which all had holes in their centers. The walls of the cave system were adorned with carvings of the rising Sun, the moon, stars, the earth, mountains, and dotted lines linking the earth with the sky suggesting that this site is in fact a crash site of extraterrestrial beings who got stranded in this region in the very distant past at least 12,000 years ago. Who were these mysterious beings? What were the enigmatic disk and where did the star maps carved on the cave walls lead to? The disk were examined by Dr. Sum Um Nu in Beijing around 1958 who concluded that each groove consisted of a set of tiny hieroglyphs of unknown origin. According to the doctor, one of the hieroglyphic lines read, the Dropa came down from the clouds in their aircraft. Our men, women, and children hid in the cave 10 times before sunrise. When at last they understood the sign language of the Drapas, they realized that the newcomers had peaceful intentions. Another section reads regret of the inhabitants of the mountain because the aliens had crashed their ship and could not build another to return to their planet. They knew their existence was doomed and therefore they wrote down their story for others to read. They wanted to tell us who they were and what brought them here. They left a message for future generations, but the alien artifacts they left behind were hidden from the public. Physically, the granite stones were a very hard stone indeed. It would have made it impossible for the primitive people to carve the lettering, especially with such minute characters only being visible under a lens. When testing a Dropa disc with an acycograph, a surprising oscillation rhythm was recorded as if they had once been electrically charged or had functioned as electrical conductors. Have any of the Dropa people survived? At the time of the discovery, the cave area was still inhabited by two tribes known as the Cams and the Dropas, both extremely odd in appearance. Experts have been unable to categorize either tribe into any other known race, as they are neither Chinese, Mongol, nor Tibetan. Said to have yellow skin, very reminiscent to the founding father of the whole of China, one of the first emperors, the Yellow Emperor. Ancient Chinese records talks of a very special being described as a God like King, a son of the heavens. He is credited with having invented Chinese medicine, various religious practices, including worship of the sun, moon and five planets, and technological inventions like the compass and calendar. It was believed that he lived in the Kunlun mountains, which are in the heart of Tibet. Close to where the Dropa stones were discovered, it is also said that his wife was a woman from the skies. Now, isn't it strange that this emperor has relations to this area and similarities to the people that lived there? It is possible. You have to wonder that Chinese people are descendant from a completely separate group of beings who just happened to crash land on earth and the emperors were a direct line from this event. Is 12,000 years enough time for the numbers to get to one billion? Who knows, guys? Perhaps the Chinese government is aware of this today. And this is the reason there is so much being hidden in China from the rest of the world in terms of the ancient history surrounding the Chinese people. As for the Dropa stones, no one knows where they are now, apart from being in China somewhere. They are part of ancient history that China does not want the rest of the world to know about. Why do you think this is, you have to wonder? What do you guys think of this anyway? Comments below and thank you for watching.


It's Redam Sulya on Fever 104 FM. Dr. Ajay Esshetty, he is lead consultant urologist with Manipal Hospitals, Yashwanpur and Hebal. Thank you for joining us, doctor. Say, doctor, if not for a doctor, what would you be? What would be your profession? What line of work would you be doing? Probably playing gully cricket. As a kid, I always wanted to be a bus driver as well. I felt that was the coolest job ever. But you were talking to us about a few passions that you picked up during the pandemic. What were they, any hobbies that you took seriously? Yeah, I picked up a musical instrument just to prove myself wrong that I had absolutely no musical talent inherent. But I think I still agree, I don't have any musical talent. But I did manage to, you know, learn the guitar. And I am a rhythm guitarist now and we have a small band. And we often play maybe, you know, whenever we have time to catch up. Yeah, that's amazing. Hey, guys, you want to see doctors on stage performing and playing music. I managed this band just letting you know this happened right now. You can get in touch with me and we play at weddings as well. Yeah, we do never say never. Never say never. Okay, let's talk about some serious health related matters now prostate disorders. This is a term that we have been hearing very, very a lot of recently. I wanted to speak to you about what are some common conditions affecting prostate health? So for everyone out there, anybody, any male less than the age of 40, you know, typically in the 30s to 40s, if there is a prostate condition that is affecting you, it would be what is called inflammation of the prostate, a condition that you would read up in Google as prostatitis. Beyond the age of 50 is when the prostate starts to enlarge. And that is typically when one would come into the domain of benign prostatic enlargement. Again, the term is BPH. That's a very common term. After the age of 50, one would expect that. We would consider and even consider a diagnosis of cancer in somebody who is beyond 55 or 60. And we will talk about prostate cancer going forward. But these are the three common conditions, prostatitis, benign prostatic enlargement and prostate cancer. How does one go about diagnosis of prostate cancer, doctor? So, prostatic problems, I think the most important thing is don't disregard the signals that the body is giving you. So if you start having symptoms like urinary frequency going up or you suddenly find that the urine flow is slowly starting to get lesser and lesser, that's the body trying to tell you that there's a problem with the prostate. And most people often neglect these early symptoms and don't make a visit to the doctor. So whenever you have a symptom like that, just go meet your friendly local neighborhood urologist who may consider certain tests and pick up the problem and start you off on medications at an early stage. That's when they're most likely to work. Right. It's not necessary that everyone needs surgery. Medication can also solve the problem. It will. It will as long as the problem is diagnosed early, which again is in our country, given the fact that people don't come in early. The ones that end up on the surgical table are people who have come so late in their disease that medications will not work or they've come so late, they've already developed complications.  Okay. Can you give us a fair understanding of how the surgery actually works in case of benign prostate surgery required? So benign prostate hyperplasia, VPH surgeries, you will read of two common surgeries being done these days, both of which are minimally invasive. There will be no external cuts on the body. The names of the surgeries are bipolar resection of the prostate, which is by far the commonest surgery that is advocated for prostate. And the second technology which is now becoming very popular is laser enucleation of the prostate using either Holmium or Thulium lasers. What I want to tell everybody is laser is the new kid on the block, but that doesn't mean that that's the best for everybody. Laser is ideal only when the prostate size is huge. Anything between 80 to 100 grams or above. Yes, laser has an advantage. It also has an advantage in patients in whom they are on blood thinners for a heart condition or a brain condition that you cannot stop. The risk of bleeding is high and that's where lasers have an advantage. Otherwise, anything other than this, a bipolar resection is more than satisfactory. Lovely. In terms of prevention, how can one go about it and what would be a few tips that you can probably share with us? Yeah. So again, prostate growth is controlled by genetics and that is nothing that one can do anything about. So more than prevention, I think it's important to detect the problem early because genetics is not in your control. Lifestyle here has no role to play in prostate. It's purely genetics. So I would focus more on early detection so that you can start treatment early so one can avoid surgery and all the complications of the disease per se in the future. Dr. Ajay Shetty, he is lead consultant urologist with Manipal Hospitals. We will be talking about cancer when we come back. Keep it tuned right here and thank you so very much for watching.


Popular youth sports, such as baseball, gymnastics, and soccer, often require complex and repetitive movements involving turning, twisting, and squatting. These movements can lead to conditions such as femoral-acetabular impingement, which is characterized by painful rubbing of the femoral head against the acetabulum. Surgery is a common treatment, but success is not guaranteed. Understanding the factors that lead to repeat operations could help surgeons make more informed treatment decisions, ultimately reducing the need for secondary surgeries and improving patient outcomes. A recent study published in the American Journal of Sports Medicine evaluated whether certain anatomical characteristics of the hip bones could help predict surgical success. Researchers examined pre-operative standing antroposterior pelvis radiographs collected from adolescent patients who eventually underwent surgery to correct femoral-acetabular impingement. Specifically, they measured the femoral-epiphyseal-acetabular roof, or FEAR index, the alpha angle, the lateral center edge angle, or LCEA, the tonus angle, and sharps angle. These measurements and patient-reported outcomes were then compared between patients for whom surgery was considered successful in alleviating impingement and those needing secondary surgery within two years after the primary operation. Among the 81 evaluated patients, 11 underwent re-operation within this two-year timeframe. Many of the pre-operatively measured parameters were found to be significant predictors of surgical success. Patients were considered at increased risk of re-operation if they had a FEAR index value greater than negative 8.7 degrees, an LCEA less than 22 degrees, a tonus angle greater than 6 degrees, and sharps angle greater than 44 degrees. These values are often associated with a relatively shallow acetabulum and hip dysplasia. Patients who did not require a second operation also demonstrated significant improvements in all patient-reported outcome categories during the follow-up period. These findings are based on a relatively small dataset collected by three surgeons working in a single clinical center, which may reduce their generalizability to other patient populations. They nevertheless demonstrate that radiographic imagery could be an important tool in identifying adolescent femoroacetabular impingement patients at increased risk of re-operation after surgery and in developing more effective treatment strategies.


Hello and welcome to the course on dealing with materials data. In the present sessions we are working with random variables and its expectation. And today what we are going to work on is little different from that. Anybody who has a data or is dealing with a situation or an event always has a question as to what proportion of data would be larger than certain value or what proportion of data would lie between these two bounds or what proportion of value data will be more than or less than certain value. So these kind of questions are being answered in statistics by several inequalities. In today's session we are going to talk about two such inequality and one such law which is called a weak law of large numbers. So in outline let us see, we would like to introduce the estimation of proportion of data larger than the given quantity. We would like to do this through Markov inequality, secondly with Shebyshev inequality these are all improvement on one or the other. And finally we will introduce what is known as weak law of large numbers and let us start. So Markov inequality is defined as let X, if X is an random variable such that it is a positive random variable and there is any number a which is positive then probability that a random variable takes value larger than a that probability itself is smaller than expected value of X divided by a. The proof is very simple expected value of X is minus infinity to infinity X fx dx. So you can break the integral from minus infinity to a and a to infinity which is fine. Now because all the quantities are positive here each of these summation is positive therefore if you drop one of the quantities it will be smaller than the given quantity expected value of X. So you get expected value of X is larger than integral of a to infinity X f of X dx. Now here you are considering all values of X which are larger than a and therefore if you replace X by a the quantity becomes further small and therefore from minus infinity I think I have made a mistake here this has to be a to infinity. So please make the correction I will make it right here let us do that this should have been a to infinity just as this case and therefore and therefore we have expected value of a is equal to probability that or is equal to a multiplied by probability of X greater than or equal to a I hope I said expected value of X and not expected value of a. So it is expected value of X which is greater than a times probability of X greater than or equal to a and which proves the inequality. So what it really says is that how much of data can be expected above a given value a this bound is given by this it cannot be larger than expected value of X or the it cannot be larger than the ratio of expected value mean value of X divided by a quantity a this is called Markov's inequality. We move to another inequality which might be known to you in other cases also which is called Shebyshev's inequality again X is a random variable but now we are not assuming that it is a positive random variable so we are generalizing the case it has a mean mu and a variance sigma square then for any value k we are again not putting a restriction of k being greater than 0 as in the case of Markov inequality this is for any value k probability that the absolute difference between the random variable and its mean value is greater than or equal to k is smaller than the variance of the random variable divided by k square. This can easily be derived as shown here from Markov's inequality because X minus mu absolute value is a positive value you assume k to be greater than 0 because otherwise if this inequality does not make any sense and therefore for any value of k you have this. So probability of X minus mu square is greater than or equal to k square and then you put that expected value of this quantity and k square and which is this so you derived the Shebyshev's inequality I think here instead of saying any value of k, k is implicitly coming out to be positive so that may be noted. So both these inequalities provide bound on the probability when only mean or mean and variance are known to you for any random variable. In Markov's case it is only a positive random variable in the case of Shebyshev inequality we do not put such a restriction. Please note that no distribution assumptions have been made it is a normal distribution of course these distributions are to be introduced later but no distribution assumptions are made but we should know that if you know the distribution these bounds can be further refined and can be exactly computed. And this we move because this inequalities will be useful for us to prove a weak law of large number. What does a weak law of large number says? It says that if X1, X2, Xn are independently and identically distributed random variables we call it IID. So they are independently identically distributed random variable with expected value of Xi is mu for all the Is and for some epsilon which is greater than 0 probability the absolute difference between the arithmetic mean of or the average of the random variables X, X1, X2, X3, Xn and the mean value mu the absolute difference is greater than a small value epsilon tends to 0 as n tends to infinity this probability tends to 0 as n tends to infinity it means that the difference between the average of these random variables X1, X2, X3, Xn and its common mean value almost vanishes as n becomes large and large as your sample in future you are going to X1, X call X1, X2, X3, Xn or sample of size n. So from a random variable X you take a sample of size Xn which is your data. So as your data becomes larger and larger the arithmetic average the average of these sample is going to be very close the difference between this average and the mean common mean value is going to diminish as n becomes large and large. The proof is rather simple we have to make one assumption that there is this random variable variables have a variance sigma square which is finite. See there are cases in which you have infinite variance is also. So here we are defining that assume that variance of all X is sigma square which is finite then we apply the Shebyshev's inequality to this and then if you apply the Shebyshev's inequality it is obvious that as n tends to infinity this quantity tends to 0. So this once again this is a weak law of large number. Let me tell you why it is called a weak law because it is the probability which tends to 0 and not actually the difference which tends to 0. If therefore you call it a weak law of large number we are going to have a central limit theorem which is a stronger law of large number we will come across when we move further in this course. So what is the implication? What it says is that as I said before the sample average under the stated condition by stated condition I mean that the common variance of X1, X2, X3, Xn is exist and it is finite then it differs from its mean value by more than epsilon or rather the difference between the sample average and the mean value as n tends to infinity it eventually diminishes. So if it is more than epsilon that probability goes to 0 as the sample becomes large and large. So let us summarize what we have learned today. We have introduced some measures to find bound on the proportion of data being larger than given quantities. The first inequality we introduced was Markov's inequality in which we assume that the random variables are positive. In the Chebyshev's inequality we removed that restriction of random variable being positive. We said that it could be any random variable with having a mean value mu and a common variance sigma square and then we gave an inequality in which we showed that the difference between the mean and the arithmetic average actually the random variable X actually is smaller than the ratio of variance and the quantity k above which you are looking for it. Looking for the value to be larger or let me clarify very specifically it means it tries to say that the random variable X minus its mean value the absolute difference is larger than a value k. This proportion is smaller than the variance of X divided by k square. This is the bound it gives and finally we introduce a weak law of large number which indicates that under the assumption of finite variance the sample average differs from its mean value more than any small value epsilon it tends to 0 as sample size becomes sufficiently large. So, as sample size is large the difference between the sample average and the mean value diminishes. With this we cover up the complete session on the random variable and its expectations and next we will move on to the special distributions. Thank you.


On Tuesday, June 6th, the Southeast Kentucky Chamber of Commerce held a membership meeting with special guest Lee Balaclaw. Balaclaw is a cost reduction expert visiting the Pikeville area to assess local businesses and help them understand better ways to manage their finances. Mountaintop News spoke with Balaclaw for more details. Today's topic was about cost reduction and how businesses can benefit from reducing their costs in multiple different services, including telecom, waste, merchant services, small parcel shipping, and a bunch of other categories. Local businesses need to know that they have a consultant who will be self-funded based on a share of savings and we don't charge a commission and we guard our clients' interests vigorously with vendors so that we make sure that they are getting the best deal and that they have the best services for the price. Cancer, it's a very scary word, but an outstanding treatment facility was here at home. I was led to the Lawson Cancer Center. As a nurse practitioner at the Lawson Cancer Center, we are champions for our patients. I am so happy for Robert. The treatment worked. Businesses in Pikeville are growing every day and more pop up every year. Balaclaw is positive that by working together, growth for local businesses will no longer be an issue. I didn't think that being in eastern Kentucky was going to be a competitive advantage, but every different town has a different set of vendors and so we had to learn a lot of different vendors very, very quickly, which has been a tremendous advantage to us. We've now worked with more than 90 telecom companies and we've done work on clients in 19 different states. We are available to clients in the area. Our cost for an analysis is free. We're happy to help out local businesses. They should reach out to us because we can absolutely help them. In 10 years in this franchise system, we've only found two clients that actually didn't had all of their costs completely optimized. Reporting from Mountain Top News, I'm Nick Collum.