Nico is a professor in plant physiology at the Scuola Santana in Pisa, of which he was in the past also the director, and he will talk to us about innovation through DNA and RNA technologies. Thank you for your new income. Thank you. Thank you very much for the invitation. I'm glad to be here. And as soon as my slides will be on, I will try to be fast because I realized that we are already late. The good news is that I tend to be fast. The bad news is that I have a lot of slides. So let's see which will be the final result. Okay, so I'll skip the first one because this is just the title, and I will move to the obvious. We already know all this, the world population. I'm trying to get this working, but no, no, I'm trying to have a pointer. Ah, okay, okay, okay. Okay, okay, okay. Thank you. Thank you. Okay, so the world population is is is increasing and we are heading towards the rewarding numbers in terms of world population and you see around 10 billion people in 2100. Okay, we will not be here probably, but it will be a problem for those who will be here. This will lead to the need for more food. There is no doubt about this. There are a number of estimates online. So I don't know how reliable are all these estimates. But some of these say that we need 70% increase in food production, which is which is very worrying because it's a lot. Okay. So we need for sure to change something in the way we produce food. And the other important point is that we know that all this is happening in the context of climate change. So not only the world population is increasing, and we will need more food, but we will need to produce this food in a context which will be more difficult that in the, than in the past. We will have less water in some places more water in other places, higher temperatures. So we will need to change a lot in the way we do agriculture and reproduce food. So we will need to choose among different scenarios. We have we have to do some something of course we cannot stand and see, but we need to choose among different scenarios and I found an interesting publication which came out very recently which is the result of a European project, which presents four different scenarios. One is the plant innovation scenario. The second one is your food health choice, the food emergency and the reject tech, we will see rapidly now, which each of these scenarios propose. One is financial means growth and tech technological options unlimited so what we can use all the available technologies we can, we have unlimited the financial resources to reach the goals the scientific goals, the innovation goals to produce new technologies to innovate at the fastest possible speed. The second scenario is is is what Giovanni carada described us is the consumer driven market. And when I say consumer driven market I do not only mean something which is of interest of the supermarkets because the consumer will decide what they will sell, but the consumer decision. What influences the policy makers and the policy makers will influence science in the end, and therefore will impact the in the direction that research will be taken will take. We have a food emergency scenario, which is something that to me reminded the COVID emergency. Okay, so we had a health health emergency where we have a pandemic situation worldwide, and science was alloyed to go faster. Because we needed the vaccines, we need therapies. We need monoclonal antibodies, we needed the RNA based vaccines which were never used before, and all this happened very fast. So that scenario demonstrates that it is possible to face a specific emergency route. Here's an example by applying an emergency scenario in which we will provide unlimited resources, but which are focused to solve an emergency. I don't consider this good because we, we, unless the emergency is a real emergency something which cannot be predicted. I just showed you that we can predict that the population will increase, that the climate will change, so it's not really a scenario which we can apply to what we know. We have something that again was described by by Giovanni, which is the reject tech scenario. So, there is a general mistrust in science policy makers and the agri-food system, and we want agriculture to get back to the past. We don't want innovation or we don't want anything which is new, and we want to keep things that not as they are, but even to go back to the past. So technology is bad. We have to reshape agriculture, but based on ecosystems and needs, et cetera, et cetera, not using technology. So the big difference in this four scenarios is this. So the fact that all the technologies that involve DNA modification are not desired or not accepted by many of these scenarios. So what makes the real difference between these scenarios is whether we can, we will, we will be able to use or we will be hampered to use technologies that influence DNA. And this leads to the first part of my talk, which is DNA technologies, so which technologies are available to modify DNA so that we can produce more, better food or, you know, we're using a sentence which is very popular. We to produce food in a more sustainable way. So, and this leads to a new genome techniques as they are defined, which are exactly the technologies described by Giovanni, so the new technologies of DNA manipulation. I'm very worried when I use these words because DNA manipulation is not fantastic. Okay, but I know this is the way it is used generally. And in order to identify what they are, I show you this, sorry, these two covers of science and nature, they date back some years, and they presented the technology of CRISPR-Cas9 as the breakthrough of a year. So we are not, when we talk about something new in science, we do not necessarily talk about something that happened yesterday. It might be a technology, a science advancement that happened five, six, 10 years ago, but that is now ready, the technology is ready to be used in agriculture to produce new food. But if we have new genome technologies, there should be all genome technologies. Okay, it is nonsense to say that we have something new if we don't have anything old. So let's see what they are, the old genome technologies. But, well, this was already said by many of you, also in the questions. So, breeding, human beings have been improving crops since millennia. And this was done by modifying genomes, because if you cross two species, what you will end up is a mixed genome of it over two parents. So it's a big, this has a, breeding has a huge impact on the genome, which is an impact which is even stronger than transgenesis. So if we speak about which is the impact, the actual modification on a genome by simply talking about breeding, breeding, inevitably has the biggest impact, because it's two genomes, possibly of two relatively unrelated species, but which were compatible or made compatible by the breeder that are mixed together. So we have mutations, plants have been improved by mutations since centuries. And one way to mutate a genome is to use radiations, which will impact on DNA at random. It will modify at random the genome will lead to 100 of the negative effects and possibly to a few positive effects. In this slide, you will see the radiation field, which was in near Rome at Vienna, where a source of radiation was in the middle of the field, and all the crops grown around where irradiated to get to increase variability could be picked up evolution in a way in a very strong way. Okay, harsh way. And this, this, this approach led to many, many crops which are which are actually used and consumed. One example is the pink grapefruit, which is obtained which was obtained by by mutating the genome by radiate by using radiations. And you see that this Ruby grapefruit obtained by radiations is sold as a jam, which is organic. So we have, we have a paradox here, in which we have two scenarios together on one side we have the your food health choice which is for example, which is organic. And on the other side, the radiations used to produce the crop that was used to produce this jam. So it's a, it's an example of how these scenarios might be in conflict, and the consumer might not always realize about this conflict. This is genesis course GMOs GMOs are perceived as a kind of failure. Okay, especially in Italy. Okay. Well, GMOs we don't have them. We survive we had no problems. We forget that we import GMOs from Brazil from other countries, and they are not really zero kilometers crops if we import them from Brazil. And this is the surface of the actors, which is currently grown with GMOs. And, well, saying around 200 million actors that does not tell you much. Okay, how big is the surface. Okay, well, let's compare it to the surface of Italy. So this is the wall surface of Italy, which is around 30 actors, million actors of course. So the surface which is cultivated with GMOs is huge. Okay, and we are talking about corn, soybean and cotton. No, no, no, no more. So GMOs were a great success technology which had a great success and a success which Italy did not take any advantage of, because we are paying the costs of this technology by having to import from other countries that GMOs we are not allowed to cultivate. And this is the scenario. Okay, so here I put together a number of claims that are used to convince the consumer that that product is better. Because it's GMO free, because it's a non GMO, a natural product, etc, etc, etc, etc. So this leads to the new genome techniques so with this part I, I hope I convinced you that human beings have modified genomes since ever. So we are not talking about now these crazy scientists are starting to modify the genomes with something new is simply that we take the technology is going ahead. So, and we are talking about gene editing. And which is the, the characteristics we wish for gene editing to be safe, precise and predictable, because not even breeding is inherently safe, precise and predictable. So we are talking about more, we cross to plants and we hope that the new plant will be better, will be safer and and and showing the traits that we want. Okay, the reality is that we cross and we cross and we cross fingers as well, because we hope to get the desire result because it is not true that you are doing genetic engineering, because you have a project and then you realize the project is based on trial and errors, the transgenesis process. So we need something better. Okay. So what is genome editing and what is CRISPR, because the technology which uses genome editing is called CRISPR. So it's something that was discovered by a manual sharpened engine if I don't know, which we're working on on a bacteria, a useless bacteria, where we're studying an apparently useless process biological process in an apparently useless bacteria, and they discovered by chance. There is a mechanism that is happening in that bacteria, but that can be translated into a very powerful technology. And for this discovery, they got the Nobel Prize a couple of years ago. So the technology is based on this protein, which is cast nine, I will not go to the detail but you can recognize here a double elix of DNA. So this is how the system works. This protein will cut DNA and will be directed to a precise position by the RNA sequence so we can use RNA as a sequence we will find the complementarity in DNA and will then act at that specific position. So this will allow what is a site specific in a way we can say mutagenesis or editing of DNA. Well, CRISPR means this I don't even try to read it. Okay, so it's a it's a forget it. Okay, you know that it means something about you will never be able to remember better CRISPR means clustered regularly interspaced the short palindromic repeats. It means that this is not very friendly terms of communication. Okay. Cas9 is easier. It is a CRISPR associated protein number nine. Okay, so just just because acronyms are puzzling. I wanted to show you that there is something behind the name, but is is something that you can you can forget you know that it happens. Well, Cas9 is a molecular system. So it cuts DNA, but it does not cut DNA in any places it cuts DNA exactly in a position. It cuts DNA of course, and it cuts DNA following an RNA guide sequence so you get a site specific DNA cut. This site specific DNA cut is followed by a repair of DNA, which might modify DNA in that specific position so you will, you will get variants. You may get a knockout. If you choose the right position so you switch off the gene, or you can modify the gene, you can get the gene to be more similar to a wild relative. And this is how it works. Very simply Cas9 is this light blue molecule. It opens DNA. It uses, which is the orange double elix. It utilizes the purple RNA guide. You can design it in the lab. And this RNA guide is used to define the exact position where DNA will be cut and then repaired. So it's simple and efficient. Okay, in my lab we started using it and it worked the first time we tried. It did work. It is faster, more efficient than transgenesis. Great. So this technology can be used to modify plants and to modify plants in specific traits because now we know thanks to the genome projects we know the genome exact sequence of the genome of many crops. So we can identify the genes which are responsible for the specific traits, which is still difficult. It's not an easy job. And we can modify them for getting better food and better agriculture. One of the very first CRISPR, which is not a plant, which is a fungi, which was produced is this mushroom which resists browning. And immediately it led to this. So, and this allows us to say that, yes, we are using a new genome technology, but the perception is simply that is a new generation of GMOs. And with all the easy terminology that can be used by Greenpeace and all these organizations which are against, which are for the reject tech scenario. Because this is exactly the reject tech scenario. So we have a new technology, but if we adopt the scenario number four, which is reject tech, it will stay in the labs and will never reach the supermarkets. And it will never reach the developing countries. It will never reach any place where it can be used to solve food related problems. Now, many companies predicted that we could have CRISPR plants in our dinner plates in five years. Usually, it's always better not to make predictions because usually you fail. Okay, but in this case, it was not too bad. So we should have had the first CRISPR dinner in 2020. But we now have the first CRISPR modified crop, which is on the market in Japan. So there is at least one CRISPR based product in Japan. And this is interesting because Japan was one of the country which was against GMOs. People in Japan didn't like GMOs and they were no GMOs in Japan apart from some blue colored flowers which were initially produced in Japan. And the second point which is of interest is that this is improved in nutritional value because it's a rich thing, GABA, which is supposed to lower your blood pressure. Okay, so it's a nutraceutical product which is aimed, if you consume it, to improve your health.  This is the oversimplified scenario. And this is more recent, well, 14 February is very recent, is wheat which produces less acrylamide. You will say, why should wheat produce acrylamide? Well, all food that produces contains good things, but it might contains also bad things. Okay, so usually bad things are here and good things are here and bad things are here, but are still there. So we want to reduce the amount of acrylamide which can be produced by wheat and this was obtained by genome editing demonstrating that we can use this technology to produce better food. Of course, we will need also more food and of course plant more resilient, etc, etc, etc, but this is feasible. The European Commission is discussing how to regulate these new technologies. We have two scenarios on the table. The plant innovation scenario of the reject tech, who will win, we will see. Politics will decide actually and then the consumers will be important in this decision and this will set the direction that Europe is taking for the use of this technology. Remember that Europe is not the world. Okay, that is China, that is the US, that is South America is Africa, so there are other continents that might take different decisions than Europe, and we will see. The point is that CRISPR-Cas9 leads to permanent genome modifications which are different from transgenesis. We are not talking about inserting foreign genes inside the genome, but they are permanent genome modifications and this might be one of the reasons why we have a very jet tech approach and perceptions. Okay, it was said there is also something religious, so God created that DNA, why, how they are modifying it. So the permanent genome modification is perceived as possibly dangerous scientists playing God, etc, etc, etc. So let's go to RNA technologies, which are something newer and which are different from DNA technologies, although CRISPR-Cas9 in a way is partially an RNA technology because it utilizes RNA as a guide to cut DNA. So let's remember that RNA is the first product of gene expression, which will lead then to a protein and finally to phenotype. Okay, so if we are talking about RNA technologies, it means that we are going to modify the way RNA is present in the cell, so we are not touching DNA, we are playing with this molecule. The DNA, the genome isn't touched, but we can act downstream. So why should we modify the genome if we can modify the expression of a genome and more specifically the expression of a specific gene. In this case we can get a transient modulation of gene expression. We'll steal this be rejected by people who reject technology, so we do not modify the genome, we modify the way the genome is expressed. Okay, and the genome, the way the genome is modified in its expression happens every day. We have sun, the genome is expressed in one way, if it rains, the genome is expressed in another way, so we are simply exploiting the ability of the genome to adapt to something. And we can do it because there is one process which is very important, which is the RNA process, which means RNA interference. Again, scientists are not very good in finding terms. Okay, because if I tell by this new tomatoes produced by RNA interference, it doesn't sound so it is not friendly. Okay, the word interference at least. But the concept is that you can have a sequence of smaller and a smaller and a can enter the cell and will recognize a sequence of RNA and will destroy it. To make it simple. Okay, so you can use a small RNA sequences to destroy messenger RNA so to destroy the message messenger in it so you can you will block the expression of that gene, or you will strongly reduce the expression of that gene. This can be done. This can be done to to to kill insects, for example, if you have a plant, which contains this small RNA, which encodes a gene or better encodes a sequence for an RNA in the insect, which is an housekeeping.  Okay, because the RNA will down regulate the expression of one gene, which is essential for survival. Of course, you can design RNA for that specific insect. So only if that specific insect, having that specific sequence of RNA is targeted, then it will be the only one to be killed bees will not be affected.  You can treat and the insect will eat that sequence and simply by eating it works. So the insert eats this small RNA sequence and it is killed because inside the cells, the process of our interference will block the RNA and RNA, which is essential for life. Okay. So by spraying. So you simply spray the plant with this double stranded RNA, it will be uptaken by belief, and depending on the sequence of RNA you utilize you can kill some insects, fungal pathogens, viruses. And it has been demonstrated that you can block viruses because you can target RNAs which are viruses, many are many viruses implants are RNA based chewing insects, etc, etc, etc. RNA technologies, which are most promising are based on double stranded RNA foliar spray. So it's not, we are no more talking about modifying plants, we are not in the city industry producing a new variety of plants, obtained by gene editing or by disease or by breeding, but we are talking about something which will be exploited by companies usually selling fertilizers pesticides because it's an RNA based pesticide in this case. But we can, and it has been demonstrated that this happens in a trans kingdom way so the RNAs of the plant can interfere with the fungal RNA, but also the fungal RNA can interfere with the plant RNA so you can interfere with this mechanism in a way that the plant wins the battle with the pathogen. And even more recently my lab demonstrated that this is also possible in nature. We have a plant which is over expressing one specific small RNA. It will be released in the soil, and it will be uptaken by a nearby wild type plant, and you will modify the way the genes are expressed in the target plant by simply growing it nearby a plant which is producing that specific micro RNA. You can simply add a synthetic micro RNA which is identical to the natural one to the soil, and you will modify the expression of the gene in the receiving plant. And even that micro RNAs are important for a number of traits which are important in agriculture from stress biotic and a biotic stress develop development, etc, etc. You can utilize an RNA spray to modify plant development to modify plant resistance to stresses to modify plant resistant to insects. The RNA spray for transit modulation of gene expression is a new technology that might be more perceived as more friendly RNA is non toxic. Of course, we eat RNA every day we will have RNA for lunch. I'm pretty sure we will have also DNA for lunch. And we eat normally so it is not supposed to be dangerous for for health, and it will be transient. It will be like any other agrochemical product which is preyed on plants, but it will be more specific. And it will act on specific insects specific traits, and it will be able once developed to improve the plant productivity and food production. There is not one single technology that will save the world. We will need an array of technologies and many of them were mentioned that we need precision agriculture we need artificial intelligence. We need the DNA and RNA technologies we need better pesticides. We need a better farm management technologies, etc, etc. But if we use all these technologies, we will able to save the world and the human beings will be still here in a heavily populated world, but possibly living well and healthy and possibly more than 100 years in good health. Thank you very much for your attention. Thanks a lot periodomenica for the very interesting talk. We have time for a couple of questions online. Thank you for the great talk. I have a question concerning the Chris mechanism. So when say you want to change the color of that mushroom, so that he doesn't get brown if I remember correctly. We know that you can associate this property with a specific site that you target with RNA. But I mean, once you cut I have two questions. The first one is, can you also manipulate the way it's reformed in that specific place. And the second one is, how do you know that the specific site doesn't correlate also with other properties that you didn't want to change. I have answered it to the last question. You need to know very well the process. Okay, so the genes involved, of course the gene involved in calls for enzyme which will oxidize one compound which will become brown and so you want to kill that gene. You can do it by the knockout approach of CRISPR. So one approach of CRISPR is simply you target the gene to make a version of the gene which is no more functioning. Okay, it's the easiest way of using CRISPR to get the knockout gene. You can also do what you proposed, so you can repair the DNA by either hoping that it will be a new sequence will be in the repair process. Okay, a sequence will be slightly changed in a way that the protein is more efficient. So in that case we will have a mushroom that get more brown okay undesired about just to explain what what happens, or you can use a guide to, you can even use the guide to insert a new trait, a new piece of DNA, but in that case, the technique is used to make a GMO. Okay, so I'm not talking about that. The problem of GMOs that one problem GMOs is that you cannot predict the site, the site of insertion of the trans gene, the foreign gene you are inserting the genome. You can insert the foreign gene in a precise site, but in that case, it's a GMO. Okay, so it's not the new genome technology I'm talking about. The new genome technology I'm talking about is a technology that does not leave anything in the plant that is or can be called as transgenic. And this has an impact on regulatory regulatory aspect, while you can trace any transgenic plant that very easily with this technology, you will not be able to trace it. Okay, so if the country. I think that the country of your preference will start producing seeds modified with this technology, and we'll start selling the seeds to us. And no one explains how they were obtained. There is no way we can discover it. And we will use them. Okay, so, and you know that to enforce any law, you need a method to detect the people that are not respecting the law. And in the case of Cas9, it's reasonably easy to hide the modification, it could have been happened by chance in nature as in a laboratory by using CRISPR. And this has a big impact in terms of the market. Okay, because a country which is not regulating this process carefully can very easily have a variety that are superior. While we are discussing about, should we do it? Should we, how do we regulate it? We might start receiving this plant. There is a nice story about an orange petunia which was on sale in Italy for a while. It was transgenic, it was just by chance entered by error, and people were very happy because usually petunias are not orange. And we're buying them and then someone discovered that were a transgenic plant that were not illegally, it was by error probably imported in Italy. So if you don't have a method to detect the modification, it's very easy to alter the market. Okay, thanks to like everything is very clear. I just have one remaining curiosity, which is, I mean, once you use CRISPR as saying the easiest way that you say it, so you just remove that, you deactivate or remove that gene. I mean, I'm not an expert in genetics, but one gene is coding for more than one property, I guess, right? Well, I'm not a geneticist. One gene is encoding. The dogma is one gene, one protein. We know that this is not true. Okay, there is one gene, and there are, and there is the possibility that that gene produces different variants of that protein. Okay, but usually, let's say usually one gene encodes for one train. Okay. Okay, no, I just want to reiterate it like in the most naive and simplest way possible, my question. So isn't there the risk that once you change the color of the mushroom without being knowledgeable about that you're also changing other properties that you don't want to change and you make it poisonous. Yeah, it is possible. It's the same when you cross two plant species. You cross two plant species and you mix two genomes. Okay, you don't know how the interaction of the two genomes together will be expressed into a new plant. So you might, and there are examples of breeding leading to toxic, for example, to a higher accumulation of alkaloids in some plants. So it is not the risk is inherent in any technology. Okay, but it's not, but it's not the new technologies which are also the old technologies are even more dangerous. What you need to do, of course, is to evaluate carefully the final result you get something which is not done with breeding. Okay, so my lab produced a tomato which is black. Okay, it is on the market. No one asked us to prove that it is not toxic. As far as I know, nobody died. Okay, but this is the only toxicological result I can, I can, I can discuss with you. So no one claimed that relative died after eating our black tomato. So it's nonsense that on one side that you have to spend two million euros to prove to carry out toxicological test on GMOs or any modified plants. And on the other side, you can cross anything, obtain anything weird. Okay, because a black tomato is weird. Okay, and that's the reason why they're selling it. It's weird. People like it. But in theory, you should check. Okay, it's the same. We don't have time. Sorry, but it's we are very short. No way. Otherwise, we cannot have lunch. Choose between question or lunch, because we have to be here are too sharp because the speaker or two has to start at two so sorry about that.  So just in case you need to ask questions. Sorry to have to interrupt, but we are very late. So our last presentation of the morning is from a speaker who will be connected online. Leo Violini who


Hi everyone, Joe for jaspeaskasewrakes.com coming at you with a 2019-2020 Panini Mosaic basketball celo pack rig number 864 with the final seven illusions basketball spots being given away. That's going to be in a separate video. A very big thank you to this group here for making this happen and all the teams are here and let's roll it, randomize it, two and a six, eight times for names and teams and then a second dice roll will be for the giveaway part. One, two, got Brian down to Matt and then two and a six, eight times for the teams. One, two, all right so I'm not going to read off the whole list but here's the first half of the list right here and no trade windows and filler breaks. There's the second half of the list right there, let's just print this out and pop open that pack. Good luck. Let's see, could be some surprises here. Was there an auto here? Hey, Damien Jones. For the Atlanta Hawks, an auto out of a celo pack, not too shabby, Joel with Atlanta. Pink camo, it's exclusive to this pack, Dwight Howard, Alonzo and Tremont waters. All right, not too shabby. Let's flip back over here, let's gather everybody's names again, Joel down to Tim and everyone in between, new dice, new list and top seven after seven, four and three, seven. That's right, he was with the Lakers for a second, right, and he's a current king. He's bounced around a little bit already, four and three, seven times, top seven after seven, one, two, three and seventh and final time. So from eight on down it's sad times but thank you everybody for giving this a shot. Happier times though for the top seven because you're in the break, Joel you're in, Carlos, Steve, Kevin, Brian, Tim and Brian, Brian Frank and Brian Croft. So congrats to the top seven, thanks everyone for watching, for breaking with us, we'll see you in the next video for that illusions break, bye bye.


The human intestinal microbiome is composed of over 100 trillion microorganisms, mostly bacteria, which outnumber the host's own cells by a factor of 10. These microbes reside in the gastrointestinal tract, which contains up to 80 percent of the body's immune cells. This complex relationship between the host and their microbiome is essential for maintaining healthy immunity and preventing disease. When this balance is disturbed, it can lead to inflammatory diseases such as cancer. Recent research suggests that alterations in the gut microbiota can contribute to the development and progression of certain types of cancer. Therefore, understanding how these microbes affect the host's immune system could provide insight into novel therapeutic strategies for treating cancer. This article was authored by M.R.H.Assary, M.R.H.Assary, Tahani Baksh, and others.


The last 3 modules sub modules in fact we talked about finite vector space matrices tools for multivariate calculus. There is yet another topic which is basic fundamental to pursuing data simulation that is called optimization. Optimization in finite dimensional vector spaces I keep referring to finite dimensional vector space because all the computational problems in numerical analysis and all the applications where we use computers to compute the solution the basic mathematical framework is finite dimensional vector space. In practice we can we can do only finite things we cannot do infinite things. Therefore finite dimensional vector space is the appropriate background on which the entire theory of computation has been built around. And to emphasize that I keep referring to the importance of recognizing the role of finite dimensional vector space. Now why optimization? We earlier saw in module 1 a broad introduction to an overview of data simulation. The data simulation can be thought of as curve fitting. Data simulation can be thought of as regression analysis. Data simulation can be thought of as identification. Data simulation can be thought of as estimation. So let us take the point of view of estimation. Whenever we want to estimate we want to be able to estimate optimally. What does it mean? We want to be able to get the best estimate. Best optimum optimization. So optimization theory is fundamental to pursuing estimation theory. Estimation theory and optimization theory are interrelated to the fact I use principles of optimization in estimation. Estimation theory is a topic within statistics. Optimization theory is a topic within multivariate calculus. So it is the interaction between the two that provides the ability to optimally estimate. So we would like whenever we do whatever we do, we want to have the best prediction. We want to have the best estimate. We want to have the best way to tell what the temperature in Bangalore would be tomorrow afternoon. So on and so forth. So we are always seeking for the best. Best means optimum. So we need to be able to have a clearer understanding of the notions of optimality when is something optimum and the properties of optimum. Optimum can be maximum or minimum. When you try to talk about cost functions I would like to be able to minimize the cost. When you try to talk about profitability we want to maximize profits. So in economics the aim is to be able to maximize profits. So in economics most of the problems are posed as maximization problem. In engineering sometimes we talk about minimization of energy to be able to accomplish a particular task. In the case of estimation we would talk about minimizing certain magnitude of errors. So maximization, minimization are parts of the optimization theory. Maximization and minimization are truly interrelated with each other. So in this sub-module we are going to be reviewing principles of maximization and minimization. So a classification. Let F be a scalar valid function. You can see the notion of a scalar valid function comes into play right away. Let F be C to Rn that means F is a function which is continuously differentiable in Rn. At least twice continuously differentiable. If F is twice continuously differentiable functional. So if it is a scalar valid function it is called a functional. What is the relation? Minimum of F with respect to X is the same as maximum of minus F. Therefore it is enough I study either maximization or minimization without loss of generality we will consider minimization. So that is the general idea in the start that we need to understand. So you do not have to do maximization and minimization separately because of this intrinsic relation between maximum and minimum. It is sufficient either to do maximum or minimum. We will do minimum. A classification of minimization problems. Minimization problem occurs in various shapes and forms. The first classification is with respect to modality. A minimization problem can be unimodal or multimodal. In a unimodal minimization problem the problem has only one unique minimum. For example if you have a cost function which is parabolic which is a quadratic function this is a unique minimum. But if you have some non-linear problems you may have a function which may be like this in this case there is multiple minimum. So unimodal function versus multimodal functions unimodality multimodality who creates this the cost function that we use is the one that creates unimodality multimodality. It is easier to do unimodal minimization as opposed to multimodal minimization but at the outset we would like to be able to distinguish between the existence of two types of minimization problem. Now let us describe mathematically what is the minimum. Let F be a function. Let X star be a point at which the function attains the minimum and what do I say the how do what is the property of the function of the minimum. If I consider the value of the function at the minimum if I consider any point which is in a small neighbourhood of the minimum so let us draw a little picture. Let this be the minimum point X star if I consider a small neighbourhood around that this is why the value the function at Y in a small neighbourhood on X star is always larger than X star. So in this case X star is called the local minimum. So for example in this case this is the local minimum. So this is X1 star this is X2 star in this case this is X star. So X1 star is the local minimum X2 star is the local minimum in the sense that if you go in any direction away from the minimum the value the function is going to increase that is the basis in here.   A function has a unique minimum is called uni model function otherwise called multi model function. The function X times X square minus 1 is multi model the function X square is uni model I would very strongly encourage to be able to plot these functions and see where the modality occurs where the minimum occurs where the maximum occurs. So if there are going to be multi model there will be multiple minimum and multiple maximum too. Multi modality is always a headache optimization problems are man made. So when you are trying to create a particular problem do not create too much of trouble for yourself choose the cost function such that it is endowed with unique global minimum. If you can arrange the problem such that it is endowed with a unique global minimum your headache will be lot less. But if you formulate the problem such that it happens to have multiple minimum you have to scratch your head finding the global minimum will be a much more difficult problem. Of course this is easily said than done for a given cost function some problems may be endowed with one minimum some problem may be endowed with multiple minimum. If the problem is endowed with we have a duty to find all the minimum to be able to pin down who is the global minimum what is the best minimum. So uni model versus multi model the next classification is constraint versus unconstrained. Again those of us who have done little bit of meteorology or data simulation should be able to appreciate. Minimize f of x that is an unconstrained problem I have no constraint on x but I would like to be able to insert a constraint now. Let C be a subset of Rn defined by a set of equations or inequalities for example let C1 be the set of all x such that x1 plus x2 is equal to 1. Let C2 be set of all x in R2 x1 is greater than 0 x2 is greater than 0 x1 plus x2 is less than or equal to 1. So let us understand those constraints now the first constraint C1 is given by this line maybe I will use the arrow the arrow. So in this problem x1 plus x2 is 1 so what does this mean even though there are very many points in the 2 dimensional plane I am interested only in those points that lie on this line the line is the constraint. This the second one on the other hand x1 must be greater than 0 x2 must be greater than 0 x1 plus x2 is less than or equal to 1 and that essentially tells you the region is inside the triangle. So these are the so constraint could be along a line along a curve it could be a sub region. So what is an unconstrained minimization problem an unconstrained minimization problem is stated like this given f of x minimize x with respect to all points in x square in R square there is no constraint you can go anywhere wherever it leads to that is called unconstrained minimization problem. Minimize f of x not over all x but over x belonging to C1 that means I am not interested in every x but I am interested only those x that lie along the line say that is a constraint minimization problem. This is a special form of constraint minimization problem because the constraint set which is the line is given by the equality constraints so this is an equality relation x1 plus x2 is equal to 1 is an equality relation x1 plus x2 is equal to 1 there are infinitely many point that satisfy the that equality. So I am interested in minimizing f of x not over the entire x but along that particular line C2 I would like to be able to minimize f of x constraint minimization problem this is called inequality constraint because x's have x1 is greater than equal to 0 x2 is greater than equal to 0 x1 plus x2 is less than or equal to 1 so that is called inequality constraints. Most of the problems in meteorology are either constraint or either unconstrained or constraint with equality constraints in operation research they all often deal with constraint optimization with inequality constraints of these 3 problem constraint optimization inequality constraint is the most difficult one but these problems are now very thoroughly understood this body of literature represents one of the most thoroughly understood disciplines within optimization theory. The theory of linear and non-linear programming deal with minimization under equal inequality constraints you may have heard of linear programming linear programming what is linear programming linear programming deal with they deal with minimization under inequality constraints in this course we will deal with only with unconstrained and equality constraint minimization problem why we try to formulate the problem in such a way. So equality constraint is easier than inequality constraint further classification so we talked about unimodal versus multimodal constraint versus unconstrained now I am going to talk about universal multi objective functions there is only one objective there are multiple objectives let f if f is rn to rn is the only function to be minimized then it is known as unie objective when f is a vector valid function if I have m components where we want to minimize some component maximize some other component it is called multi objective minimization optimization let me give you an example let us take an example of an automobile design it is one of the hot problems I want to maximize the fuel efficiency I want to minimize the price the cost I want to maximize the safety and comfort so an automobile designer if you tell him I want you to give me a car with a maximum efficiency he will give you but there are no safety no comfort I want to give you a car which is best comfort but it is very few mile per gallon the real automobile design is there are multiple objective that do not that are consistent with each other and automobile engineers have come up with strategies to be able to solve this multi objective optimization problems fortunately in meteorology we are always dealing with one unie objective so operation research people dealing with multi objective optimization and the top of the inequality constraint wow that is some of the toughest minimization problem one can deal with so the conceptually the optimization problem that often occurs within the context meteorology oceanography dynamic data simulation are the easiest of the problems but we say it is difficult it is not because conceptually difficult is because of the size of the problem in meteorology the course of dimensionality we are interested in solving large problem but simple problems in operations is on the other hand they may be solving small problems but are much more complex when compared to problems in meteorology so that is the difference I would like to be able to I would like to be able to bring about so if you meet with the automobile design engineer talk to him or her as to what kind of problem how do they optimize so that we can learn from the kind of methodology they use so multi objective multi so you can think of all the things now unimodal multimodal constraint equality inequality and then unie objective multi objective if you stack all of them together you get a broad overview of this discipline called optimization theory and that is what people in operations resources research there are two groups one develops the fundamental theory others talk about applications of this theory to various problems of industry of engineering and industrial interest the next one is the notion of convexity convexity and optimization are intertwined and I would like to bring about the beauty of the role of convexity the notion of convexity in an optimization so it takes a little bit of a definition so let us be a subset of Rn I call yes a convex set if for every pair of point X and Y and S if I join them by a line the line segment joining any two X and Y completely lies in X for example in the case of a circle if I pick a point in the case of a circle if I pick a point here if I pick a point here the entire line within this if I get this the entire line within this but if I pick a point here if I pick a point here part of the line is outside the set so this is not convex these are convex sets the notion of convexity essentially includes every point is such the line segment joining them includes so you can think of that a sphere is a particular a circle is a perfect example of a convex set a convex object I have to define what is called convex functions but before I talk about convex functions I am now talking about convex set when is a set convex that is the definition of a convex set when do I say a function is convex I will tell you pictorially I am sorry the picture is not perfect but you get the idea I have a function ffx you take a point x ffx y ff y ff y you draw ffx and ff y join them by a line that is a chord in this case the entire function lies below the chord. So what is an example of that if you have x square if you took two points any two points on a parabola if you draw the parabola the parabola is always lies below the chord any function that has this property in general called a convex function x square has a unique minimum so convex functions in general have unique minimum that is where the notion of a convexity comes in we are interested in quadratic functions all the cost functions that are interesting in data simulation are all quadratic functions why quadratic functions has cost quadratic functions appropriately formulated is convex function I have unique minimum I do not have to pull my hair trouble myself to be able to perform minimization so that is where the notion of convexity comes in. So s is a let s be a convex set let x and y be point in s a function from s to r so the underlying set over which the function is defined as a convex set are you all in place so there is an underlying set which is convex there is a function defined over that if I take any two points in the convex set and evaluate the value of the function and draw a chord the function lies below the chord what is an example x square.  So if f of x is convex minus f of x is called concave so for you how would I imagine a convex function f of x is a typical example of a convex function x transpose x is a typical example of a convex function x square is a typical example of a convex function concave functions for maximum convex function for minimum maximum and minimum are dual of each other concave functions and convex functions are dual of each other so within the context of minimization we are in generally interested in convex function convex sets. So x square is convex x cube is not convex what is the what is the what is the plot of x cube that is x cube. So if I took a point here if I took a point here some part is less some part is above. So x cube is not convex x square is convex so that is the model by which you can go with your notion of convexity convex function. So we have defined convex set we have defined convex functions. So there are very many different ways of characterizing convexity let me quickly run through them in the previous definition of convexity I did I simply assumed that there is a function I did not assume any differentiability or anything f is a function I defined it to be a convex. Now suppose I know a little bit more you say in addition f is c1 a c1 function is said to be convex if for any 2 x and y f of y is greater than or equal to this the curve lies above the tangent that is an equivalent definition. If on the other hand if f is in c2 twice differentiated continuous functions the that f is convex if and only if the Hessian is positive definite positive in fact it can be called positive semi definite it is a strictly positive definite do you say the distinction place. So any f in c1 f in c2 for a c2 function if the Hessian is positive semi definite it is convex if it is strictly positive definite it is called it is called convex for example let us take a straight line is it convex secondary derivative is 0 a rhythmic place is so this is convex but this is strictly convex a straight line is simultaneously convex and concave because it is the separation between convex function and convex on the straight lines so you have examples of convex functions. So what is the why are we interested in convexity you earlier talked about unimodality unimodality and convexity are close cousins of each other unimodality refers to functions with unique minimum global minimum unimodal problems are easier so unimodality and convexity are intimately associated with each other so let us talk about this now let f be a convex set sorry let f be a convex set f be a function from s to r so what does it mean f is a real valid function defined over a convex set then f has a unique minimum hey that is the theorem I am not going to prove this theorem is the theorem in convex analysis f is on the other hand is in c2 then at the minimum the first derivative is 0 second derivative is strictly positive definite at the minimum first derivative is 0 and second derivative strictly positive definite means what that point is a minimum so what is a typical example of a convex function f is equal to x transpose ax minus b transpose x is a typical function that is in c2 when ax is symmetric and positive definite now you can see all the tools that we have developed in optimization theory in in in in in matrix analysis all comes into a hue now beautifully so this is a quadratic form this is a linear function this is a general quadratic form so if you look at all the functions that 3d bar 40 bar all talk about they are all functions of this type they are they are typically convex they are also typically in c2 they have a as a Hessian Hessian is symmetric and positive definite so by definition by design all these functions are unimodal they are convex functions everything is beautiful so the role of convexity in inducing unimodality is one of the fundamental beauty of the underlying mathematics that one needs to have a an appreciation to be able to see why when we develop problems when we develop objective functions we always think of objective functions as quadratic forms or quadratic objective functions and that is where the importance of convexity unimodality comes into play so with that as a background now I am going to run through conditions for existence of minimum please understand algorithms tend to compute the point where the function are trying to the minimum but before you start your computation somebody has to guarantee that there is one that exists there is unique so unless I know something exists I cannot go and find it so mathematics helps the first level of mathematics helps you to prove existence and uniqueness of minima once you establish the existence and uniqueness of minima then you develop algorithms to be able to seek it so characterizing the properties of minima and maxima and then algorithms to see the minima and maxima as fast as possible as efficiently as possible these are two complementary aspects of the optimization area so condition for the constraint minimum condition for the constraint minimum again most of us know from basic calculus but in calculus we talk about univariate function here I am talking about the corresponding results for the multivariate function a multivariate function means it is defined over a vector the value scalar f is in C2 twice differentiable twice continuously differentiable a necessary condition for the minimum to exist is that at the minimum the gradient must vanish a sufficient condition for the minimum is that at the minimum the second derivative must be positive definite that means the Hessian is a symmetric positive definite matrix Hessian is in general symmetric it need not be positive definite every positive symmetry need not imply positive definite but when you consider positive definite matrices you need to consider only symmetric matrices that comes essentially from the theory of quadratic forms so that is where the whole thing comes into play that is why Hessian is very important the tool from multivariate calculus that characterizes the second derivative so what do I mean by saying this Hessian is positive definite and around the minimum the function looks like a bow a punch bow so the minimum is a valley so how do I characterize a valley at the minimum point in the valley the function is convex the function looks like a parabola so parabola x square parabola is a model for such minimization process which is related to the quadratic function now I am going to talk about once we have talked about the conditions for the minimum I am now going to talk about equality constraint problems this is simply an algorithmic process I am going to illustrate that by an example let us suppose this is the problem we generally do in univariate calculus I am sure every one of us would have done I would I am given a rope of length L feet I am going to I am asked to enclose an area with this let A be the length B be the width 2A plus 2B is equal to L so I am given a rope of fixed length what is the idea here I am going to have to use the rope to enclose an area the area A is A B A is a side B A and B are 2 sides of the rectangle so what is the idea when if when 2A plus 2B is fixed as L how do you maximize the area A times B suppose somebody says I am going to give you a rope the area that you can enclose by that rope is going to be yours free so humans are built in greedy so you want to be able to say hey with this rope I want to be able to enclose the maximum area that you have to that I can so that is the problem now so maximize A is equal to A B when 2 times A plus B is L so now you can see it is a constraint problem A is the variable B is the variable A and B are not independent if A and B are independent variable when is this maximum infinity A is infinity B is infinity but A cannot be infinity B cannot be infinity because A plus B is L by 2 or 2 times A plus B is L so I have to solve a problem with a fixed length rope so that is the constraint so this is the equality constraint so I have to maximize the equality constraint what is the simple way I am sure every one of us if you cannot have gotten your B as degree until you have solved this problem once in your life I am sure every one of us have solved so what is that we do we first eliminate B from this constraint you can simply say B is equal to L by 2 minus A so if you substitute B in the A A becomes this now A becomes a quadratic function in A you compute the derivative of capital A with respect to little a this is the derivative you compute the second derivative it is negative the second derivative positive means minimum second derivative negative means maximum so the A obtained by solving D A by D A is 0 so when L by 2 is equal to 2A or A is equal to L by 4 so the first derivative is 0 means L by 2 is equal to 2A or that implies A is equal to L by 4 when A is equal to L by 4 B is also equal to L by 4 so at which time the area is maximum the maximum area is L square by 16 so this is the method for solving minimization problem under constraint so what is that you do use the constraint eliminate one of the variables you convert the two variable problem into a univariable problem apply the principles of calculus you solve the problem method of elimination that is the illustration for solving equality constraint problem this is easy for small number of variables but in meteorology you have tens of thousands of variables you cannot do this but again it is essentially an example so what is the general method for solving equality constraint problem the classical Lagrangian multiplier so I am going to quickly run over the framework for classical Lagrangian multiplier so equality constraint minimization problem Lagrangian multiplier method let G be a vector valid function I want to be able to minimize f of x under the constraint that G of x is equal to B what is B B is a m vector G x is a function is a vector valid function so G refers to G m G 1 G 2 G m B refers to B 1 B 2 B m so what does this constraint refers to G I of x is equal to B I for I running from 1 to n so each of this is going to constraint so I would like to be able to minimize this under equality constraint fx a nonlinear function G is a nonlinear equality constraint in the previous problem whatever the equality constraint a plus B is equal to L by 2 that is a linear function a is a variable B is a variable they occur in the first variable first degree here G of G 1 of x G 2 of x I do not know what it is it could be any function so in general is a nonlinear function so define a Lagrangian which is a sum of f of x B minus G of x that is the constraint you lambda is a vector lambda transpose B minus G of x is a scalar add that scalar to f of x so that becomes a new Lagrangian function now x is a vector belonging to R n lambda is a vector belonging to R m because G is a m vector B is a m vector lambda must be a m vector so I have now defined a function where this is n long this is m long so the total number of variables is n plus m I am expanding the space over which I need to do the minimization this is the technique that Lagrange designed number of years ago what did he say he said the following what is the theorem the theorem is as follows the minimum of x when G of x is equal to B the constraint minimum of f of x is equal to the unconstrained minimum of L he converted the problem of constraint minimization to an unconstrained minimization unconstrained minimization we know how to solve constraint minimization are difficult so what is the method you convert a constraint minimization problem into unconstrained minimization problem but what is the price we are going to pay the constraint minimization problem is a n dimensional problem because x is a n vector but the resulting unconstrained minimization problem is a m plus n variable is a larger space so by expanding the space over which I am going to minimize I can convert a hard problem into easy problem so that is the fundamental idea lambda is called the under demand Lagrangian multiplier so what is that unconstrained minimization problem how do we solve this you compute the gradient of L with respect to x equated to 0 gradient of L with respect to lambda the second one must be lambda I am sorry this must be lambda so you compute the gradient with respect to x gradient with respect to lambda equate them to 0 the gradient computation I have already talked about when I talked about multivariate calculus how to compute gradient of various types of functions now you can see why we do what we did all of it may that is right so this gives you a set these two give you a set of necessary condition a necessary condition for the minimum is that at the minimum the gradient of f of x so what does this essentially say if b is equal to g of x so if this constraint is satisfied this is trivially true so if the constraint is trivially satisfied what does the first one say the first one essentially tells you gradient of x with respect to f is simply summation of lambda I gradient with respect to x of gi i is equal to 1 to m so each g has a gradient lambda I are the constants this is the linear combinations of the gradients of the components of g f of x is the gradient f of f so at the minimum what does Lagrangian theory say is one of the most beautiful results in applied mathematics it says a necessary condition for the minimum is that at the minimum the gradient of f of x must be a linear combination of the gradient of the constraint functions in a unconstrained minimization what must be the gradient value delta f must be equal to 0 that is unconstrained in a constraint the gradient must be equal to the linear combination of the of the constraint functions the coefficients of the linear combinations are the lambdas so by solving these two equations simultaneously you not only find the minimum x star but also find the value of lambda which are used in this linear combination so you kill 2 birds in one stroke you kill 2 birds in one stroke so either you solve by minimization or a constraint minimization by elimination as we did in this simple example which is feasible only for small dimensional problem if the problem is a large dimensional the only recourse to solving equality constraint minimization problem is Lagrangian multiplier method Lagrangian multiplier method the Taylor series expansion these are very fundamental tools in in in doing many things that we do in in in optimization theory we can also talk about a certain sufficient conditions I am I am not going to go over the details of this but I want to I want you to recognize the following I am going to talk about the need for sufficient condition in an in an unconstrained setup in a in an unconstrained setup what is that we have we have we have talked about the gradient of f must be 0 the Hessian of with respect to x must be spd this is the unconstrained characterization of of of is that I am sorry this is the uncut let me I made a mistake I have to erase this part good that the Hessian must be spd so in the previous slide we only talked about the necessary condition first derivative I have not talked about the second derivative condition are you in place there is a first derivative condition and second derivative condition first derivative is necessary second derivative is sufficient both for constraint both for unconstrained so the sufficient condition for equality constraint problem is that the Hessian of L so that should not be surprising that is the reason I went into this in the case of unconstrained problem the Hessian must be symmetric positive definite what is the analog of that if you consider the Hessian of L with respect to x which is given by this that must be positive definite in an appropriate set of space so with the with the with the with the necessary condition and sufficient condition we have shown the conditions for existence and uniqueness of minima when there is equality constraint that is the fundamental talent of this I am I am not proving the derivation of sufficient condition as I have not proved several of the claims I want you to remember all the theory that we have covered in matrix theory is the half course in linear algebra all the topic we are covered in finite vector space is one third of a course all the topic I am covering in optimization literature optimization literature is about one third of a course in optimization theory so these are parts of several courses pulled together in a hue to be able to develop an appreciation for the underlying mathematical background needed in doing what we do now I am going to illustrate by a simple example let n be 2 let f be given by this that is a non-linear function you can readily see I want to be minimized this I am considering inequality constraint problem I am considering a Lagrangian multiple Lagrangian function I compute the first order necessary condition so first order necessary condition gives rise to these two equations I solve these two equations and I get this optimal solution to be this so that is the optimal solution I am going to leave the method of solving this to get this as a homework problem you can readily see I also compute the Hessian and I show the Hessian and an appropriate definition is also positive definite and hence I demonstrate that x1 is equal to 4 and x2 is equal to minus half is the constraint minimization problem for this which is a very typical homework problem that is that one has to do why I would like you to emphasize the following the function is a quadratic function look at that now first degree second degree second degree the constraint is a linear function so objective function is quadratic the constraint is linear simplest possible case you have to have an aha here you have to be able to do this to be able to do anything else in life in this area so this is a very nice example that illustrates the power of the Lagrangian multiplier by expanding so in here there is only one lambda because there is only m is 1 n is 2 m is 1 so I find both the lambda x1 x2 we solve the problem and that is the constraint minimum now I am going to talk about another class of function which called penalty functions which is again very well used in this is very much in Vogue in data simulation literature in data simulation literature Lagrangian multiplier technique is called strong constraint formulation so let me let me let me go back and so do that tell you that Lagrangian multiplier technique within the context of data simulation is called strong constraint problem because I am I want to be able to console the satisfy the constraint at any and every cost because the constraint is sacred I cannot afford to not to satisfy constraint so the constraint is very strong there is no way there is no way out of it but in some cases I have constraint but I do not want to enforce the constraint strictly but you should be very constraint you cannot you you can deviate from the constraint but not too much so that is what is called weak constraint formulation this weak constraint formulation is done by a class of method called penalty function method say people in in geosciences they are very clever people if they call penalty function they will say oh yeah it is already exist in operation the literature so they give a different name by whatever name you call the row smells the same so the same idea comes in different areas by different names it is very easy to get lost that is why I am trying to develop this bridge between the terminologies that are used in different disciplines strong constraint Lagrangian weak constraint penalty weak constraint means what I want to respect but not to the verb of the verb and word of the law it is like speed limit you say somebody says the speed limit is 60 miles if you go 60.1 are they going to give you ticket now if you go 70 definitely they will give you ticket so when when does the police catch us somebody when there is when when when the speed limit in this highway 60 60 miles are 60 kilometers well plus or minus 5% if you go too slow they will come and ask you why are you going slow if you go too fast they will say hey I will give you a ticket you are so you are allowed to break the rule but within certain limits so speed limit is an example of a weak constraint the example of a weak constraint so f is a function so let us look at this now again f is a function g is another function I want to be able to minimize f I want to be able to minimize under equality constraint so I am trying to solve equality constraint problems that is where that is interesting so instead of a Lagrangian multiplier of Lagrangian function now I am going to talk about a penalty function what is the penalty function this is f of x plus alpha times g transpose gx so this is the alpha is called the penalty parameter alpha is a fixed large number alpha is a fixed large number because I have a 2 here I think I must add a 2 here 2 otherwise it is not necessary you have it you need to have a 2 if I have a 2 here you should have a 2 below so what is g transpose gx it is simply gi square sum of gi square alpha is called the penalty constant or a penalty parameter alpha is chosen alpha is not a free variable there is only one free variable which is x what is the difference between this and Lagrangian multiplier in the Lagrangian multiplier lambda was a free variable x is a free variable here it looks as though alpha plays the role of lambda it looks as though alpha plays the role of lambda but the difference is alpha is fixed it is not a free but x is free so I have 2 free variables here one free variable and another free parameter but I have to choose and fix it this is the difference place now that is right so alpha is called a penalty parameter generally penalty parameters are supposed to be large so the gradient so what is this you solve this constraint minimization constraint minimization problem by solving this unconstrained minimization problem p alpha so what is the gradient of p alpha it is gradient of this plus that now you remember when we talked about multivariate calculus h transpose h g transpose g the gradient of this is Jacobian transpose tan g in order to be able to do that you must have known the knowledge from multivariate calculus that we did in the last lecture that is why we are trying to make it as complete as possible where d is a Jacobian so x star the optimal solution is obtained by solving the gradient is 0 this optimal solution x will always depend on alpha so the optimal solution is a function of the penalty parameter alpha it may place so given a problem I can solve the problem in a strong constraint fashion given a problem I can solve the problem in a weak constraint problem that prints is the following question how are these solutions are related it can be shown I am going to show in a minute if I took x star alpha and let alpha grow to infinity it reduces to x star alpha of the Lagrangian multiplier technique in other words the weak constraint solution converges to the strong constraint solution when the penalty parameter grows unbounded alpha goes to infinity you say in other words a problem is the same problem you solve it do different ways you formulate it by two different ways so which solution do I take I want to be able to talk about the difference or a relation between the two solutions and that is the final solution the weak solution converges to a strong solution as the penalty parameter goes to infinity so what does this tell you if you believe strong constraint population is difficult weak constraint problem you can solve it and you can simply change alpha or plug alpha to a large value then you will know you got a solution which is as close as possible to a strong solution so what is alpha in terms of speed limit in some police department they are very strict if you they will not allow more than 2 miles above speed limit in some police department they will allow 5% above the speed limit that is the value of alpha in different departments and why do they do a structural limit they want to make money if I give you a ticket the city gets money out of you so what is one cheap way for cities to be able to get good money from public put speed limit if you put speed limit there are people who will test it and if you catch them when they test the speed limit you can find them you get money so alpha is the parameter by which you allow you vary the allowance above speed limit so that is where the role of the parameter alpha comes into being so it can be shown that the solution the weak solution tends to be a strong solution as alpha becomes large I saw there are other properties I am sure you can follow this but that is the main result of this page is this result convergence in is the fundamental result I am going to illustrate the weak solution and strong solution again by example so I got an ffx I got an ffx I got a gfx is a quadratic problem with a linear constraint you can easily see this problem let us look at this problem now this is x1 this is x2 ffx is the parabola you can see a bow sitting on that but I am interested that line so I am now have to define the parabola over this line alpha is my place so instead of the parabola being located at the origin now I have to think of a parabola defined over the line where will the parabola be a minimum a little reflection tells you it must be half half so the constraint solution is half half unconstrained solution is 0 0 so that is what we have shown we have formulated this problem as a penalty function problem p alpha alpha by 2 we have computed the optimal solution by penalty the optimal solution by penalty is given by this now when alpha goes to 0 1 over alpha goes to I am when alpha goes to infinity 1 over alpha goes to 0 therefore 1 over 2 plus alpha inverse 1 over 2 plus alpha inverse tends to 1 over half 1 over half everybody with me please therefore you will be able to see and if you solve the same problem we have already solved the half half is the strong solution the weak solution converges a strong solution as the penalty parameter grows and now it is a beautiful illustration of the relation between the two so strong versus weak constraint formulation again there are two choices mathematicians have provided us so which one we are going to choose in our analysis that is the question minimize f of x with respect to g of x is equal to b so what is the one standard condition that constraint condition that comes in meteorology barotropic if the atmosphere is barotropic there are there are constraints geostrophic constraints so when you when you recover the u v velocity it cannot be anything it must can satisfy geostrophe so geostrophe is a constraint that comes from physics u and v are the velocities that you may recover from other means the recovered values of the velocity if they do not satisfy the geostrophe constraint the recede value of the velocities of no use so what is that you would like to be able to say recover the velocity with the constraint the recovered velocity must satisfy geostrophe constraint do you want exact geostrophe or you want approximate geostrophe if you want exact geostrophe strong constraint if you want approximate geostrophe we constraint in meteorology all the equations are approximation from Navier stokes from primitive equation so when your model is an approximation there is no point in requiring something to be stronger so everything has to be consistent therefore we constraint formulation is a beautiful formulation where you allow for variations from the equilibrium or conditions but only by a very small percentage so it fits in so this mathematical concept of strong versus weak jives well with our concept of geostrophe is that atmosphere which is perfectly geostrophic no is the atmosphere is always barotropic no is always baroclinic no in some cases barotropic in some cases baroclinic there are different situations so we would like to make different approximations so depending on the nature of the approximations we can impose different kind of constraints to be able to handle problems that is that is so mathematics provides you the facility to be able to handle different parts of analysis and different kinds of assumptions you want to make and that is where the fit between physics and mathematics comes into a beautiful hue and that is what I would like you to appreciate when we do this so Lagrangian multiplier method is a strong constraint formulation which forces exact equality constraint penalty function method is called a weak constraint formulation which only forces approximate equality depending on the values of alpha the solution is more closer to the constraint when alpha goes to infinity when the when alpha goes to infinity the constraint is exactly satisfied we will use both the formulations in most of data simulation problems with this we come to a set of exercise problems again I want you to go over these are very simple exercise problems I also would like to recommend that you do these exercises both with pencil paper also on a computer one particular medium of my choice my favorite choice is matlab for example when you say plot the function it should be f of x I am sorry not f of alphas this should be f of x not f of alpha I would like you to plot this function what are the quick way to plot this function matlab in two lines you can you can you can you can do so I would like to recommend use of either matlab or mathematical if you have good facility in programming in either in mathematical or matlab you can do these exercise of pencil paper and you can verify them by doing in a computer and that will make your understanding rather complete so I have given exercises covering most of the topics that we have covered in this in this in this arena some of the standard text books on optimization these are my favorite text books I have copies of these things in my library in my personal library Luenberger optimization vector space 1969 is a classic book Luenberger introduction to linear and non-linear programming in 1973 is another classic book on constraint minimization nation so for linear and non-linear programming problem published in 1996 is again another classic so any one of these all these books are very similar you can read these books based on the notes to further expand on the proves and deeper understanding and I hope with this you come to realize how what are the what is the extent of the mathematical ability that one needs to have to be able to pursue and do good work in data simulation this involves concepts from finite vector space concepts from matrices concepts from multivariate calculus and concepts from basic optimization theory that is another part which I am not included in this discussion is probability theory when you go to stochastic aspects of estimation you need to understand reasonably good you need to have a good background in probability theory and basic statistics we will try to fill in some of these things as we go by through the lectures so with this we will conclude our overview of mathematical polymerase for doing data analysis thank you.


Miki boot to kimu Prazi siineh såhuifan, owed maq Gardens Terima kasih ni kuh tapeh Pati ni ni k то ביט These are two different kinds. These are two different terms. If we all go to discuss one at a time, the security guide companies, those are companies that hire the security guides. And the security guides, these are personnel that will be contracted to protect people and their property in whatever case they will be at a given period of time. But remember, in today's video, we are mainly focused, we are looking at the UAE. Remember, security guides in the UAE and security guides in the other Gulf countries, the other Gulf countries we are talking about. We are talking about countries like Qatar, Saudi Arabia, Kuwait, Oman, Bahrain are totally far different from this company that we are talking about. Now remember, all companies, much as all people may be security guides, and all companies may be under one contest name, the security companies. But the work, the payments, all the services may differ in one way or the other. At whatever, some companies may share the same services, but the management is totally different from one another. That's why you find at a given situation that the security guides that are working in the Gulf countries, for example security guides that are working in Qatar, are working in Oman, and they are getting salary that is totally different from the guides that are working in the UAE. Why? That is a question that should be asked between me and you. And how do we get it? It is you and me to find out the right answer or the right reason. Why? And this is exactly what we are talking about. So in today's topic, we are talking about the UAE. Earlier on we discussed the salary, we discussed about Qatar, we discussed about the salary in Qatar, but this time we are talking about the UAE. And one of the subscribers asked me what is the basic salary of the security guard in Dubai? Or what is the basic salary of the security guard in the UAE? Remember when we talk about the UAE, we are talking about Dubai and Abu Dhabi. There is a context of the two events that we are talking about in one way or the other. But remember that the security guard salary in the UAE is reliance upon today's two systems. Remember the United Arab Emirates is a nation where two security regulations are working. All the security regulations that are in place. Remember I talked about the two security regulations where I talked about the PAS code, the PAS code which is the private security company organization formerly known as the PSBD. Then we are talking about another one which is called the CIRA, the security industry regulatory authority formerly known as the BDC. By around 2000 in the UAE there are not only four more regulations for the security service provider. That is why most cleaning companies provided both security guards and cleaners at that time. But still today the majority of the security companies provide cleaning services because they have been doing this type of business for many years. But there is a parametic difference between the past and the present. This is what I am talking about and this is what we are discussing. We are trying to look at what is the basic salary of a security guard in the UAE or some people may just term it as Dubai or the way you want to call it but we are looking at that as what we are discussing. Remember that the company had an option either to give the cleaning or security guard to their staff. Therefore it was a very big problem for some companies because you would find that the security operator or the person who is contracted to work as a security guard will not perform his duty to the expected. So remember that it was very essential after too much complaints to the clients. It was very essential the UAE government to address the issue. Thus a new security regulation was announced in 2002 in Abu Dhabi which was followed by the Emirates after then. After forming the PSBD for the private security company the basic salary was defined by the government. Since then all security guards working under the PSBD that is the private security business department started getting the same basic salary but remember when we are talking about the salary don't forget we talk about the basic we talk about the minimum wage all those things are also discussed under what we call salary but remember in Dubai the largest province in the UAE did not follow what we call the PCBD security regulation rather it created its own department that is the result of the BPC was created and the salary also remains low compared to the PSBD now that both the departments have changed their names their names the PSCOD and the serial respectively we want to see how much salary a security guard get paid in the UAE by the way don't forget to subscribe to this channel it is mixed from the Malkom mixed from the mixed creation TV even the basic salary among the PSBD guards from any company remains equal but overtime pay and other allowances are different it depends on the company how good it is for the employees remember the seller and the DPC guards are allowed working only in Dubai they also have the same pattern of salary as PSBD guard the basic salary is equal but overtime and allowances are huge differences from company to company both in PASCOL and the CIRA guard when other states followed the PSBD rules but Dubai could not afford the salary to the security guards as much as the PSBD the main reason was the financial crisis in Dubai in 2008 set it back in 2017 Dubai also increased the security guard's salary and rewrote the security regulations as the result CIRA was formed just like any other countries UAE private security guards also work 8 hours plus 4 hours overtime per day and 26 days per month overlook the salary structure of the security guard in the UAE remember we are going to look at what you call the PASCOL guard security guard and what does this person get at the end of it all remember if you have a PSCOD certificate your basic salary for 26 days 8 hours will be 2000 your overtime 26 days 4 hours overtime will be 770 dirhams and work on off days 4 days per month will be 692 dirhams meaning that if a PASCOL security guard will have a total of 346 dirhams i think that is very clear because we are looking at you having that license and remember for you to work in Dubai you must have what you call a CERA license this license you can either have it by yourself or pay by yourself or the company can pay for you then it will keep on deducting from your salary every end of the month it just depends on what you call the contigio argument between the two of you you and your company but remember for a security guard who has a security license the CERA license will be entitled to a higher salary compared to a PASCOL with no CERA license and it is just estimated that a PASCOL a security guard who has no CERA license will get between 1800 to 1700 dirhams compared to a PASCOL with the license will be a much more higher figure of the salary at the end of it all so what you need to know what you need to know with Dubai is that you need to have what you call the license you have to have the CERA license and normally this license depends it depends on the kind of training that you took at one or the other we shall try to look at that in another video and what I have to give a hint what I have to let you know is that each training has a different amount that you are supposed to pay as its fees so the amount that you pay that means even your salary after getting your certificate or your training certificate at the end of it all that permits you to deliver your work which you call the license then it will be the same amount that you will have a figure that will be even higher than compared to people without a license at one way or the other so that means that the basic average total compensation will be around 3000 dirhams per person and in this average total compensation we can look at in case the basic is 90 cias maybe 60 cias 9% and housing allowance is 14% transport allowance will be 8% other allowance 9% remember that most companies provide housing allowance to their girls they provide the transport allowance that is to and fro and other allowance that may agree by the company that is part of this so for the total security guard can make around 3000 salary at the end of it at the end of it all the matter if you have the pistol or the passcode or the serial license at the end of hope thank you so much for tuning into my video hope I have answered your question someone was asking from me and that was from Ghana Malkunse is called Ogoda Bain from Ghana hope I have answered your question thank you so much for tuning in my video hope to see you in the next video it's mixed from the next patient TV don't forget to subscribe support me we are looking at a road to 1000 subscribers see you again in the next video


What's good YouTube? This is your boy Chihuahua back at y'all again with another art video man. If you're new to this channel Go ahead hit that like button come in subscribe makes you click post notifications So you will be notified it tell you what y'all some heat in today's video. We finna Turn that boy KSI into a robot, so I'm gonna do a full walkthrough on how to make a robot cartoon here So without further ado, let's jump right into this video Okay, let me go to the new The art the artboard. I'm using this 18 by 18 inches Don't get that out the way Just for the people who want to know Okay We're gonna drag and drop our picture And I'm gonna let you know too. I got like Um for different display strings, so on this other string what I'm looking at is a reference of The robot face But I'm sitting that on the other string. That's what I'm looking at. Okay Drag and drop our picture in here that we finna use I'm holding shift as I grab the corner so I don't Distort the picture Okay, I'll put it in the center We're gonna bring the opacity down Right here lock that layer Then we're gonna create a new layer right above it I'm finna come up here and finna Go to new brush and you cannot get this option unless you're using a digital art tablet I'm using a ycom centique 22 inch So you cannot get this option unless you're using a digital art tablet So let me hit okay Go to pressure And I'm gonna change these two bottom numbers to three I thought I'd do that Now the first thing I like to do when I'm doing the robot head or the transformer face. I like to trace The eye socket And it kind of show you What a pocket is let me on make this brush a little bit wait. Let me see. Okay.  We got this little eye socket going Bring this cheek bone like this Right with his nose right here. They're too high So you gotta make it make sense. You gotta make the little bone structure make sense Okay, that's uh Bring this up here Cool is good I need I want to bring this up a little higher Yeah, so we pull that right there Let's go ahead a little nose socket right here Yeah, I'll see it coming together man.  Okay, cool I'm trying to do the half robot half regular face. Come together y'all. Good to go. Good to go Also, let's go to our circle tool We gotta add the robotic eye go shift Make it a little bigger move it down some probably right there Make a copy by holding off now we finna do the effect like the skin getting peeled back So I'm gonna draw that is That's this copy of this little clamp we just created and then we got The little clamps to hold the eye We're gonna select all that We're gonna go to expand the pins And then we're gonna go to expand because we gotta remember we use the shape That's why you gotta do it twice when you're using the shape Hold hit okay And now you want to go to Your path finder. So let me pull out my path finder and you want to click divide After you click divide we can come up here Right click Isolate isolated group And we can delete the lines that We overshot See I'm saying see how that line going through it And we delete it what I like to do To not make this look so negative like just open All this free open space some extra little wires So it seemed like it's a lot going on even on my color artist I like to just add it local parts go to our pencil brush a pencil tool Move this color black to the top make sure the bottom one stayed locked And we're gonna do this eyebrows Cool, it's perfect Now what we can do we can add little cut marks Inside this metal area Just to give it man if y'all would like to see me coloring this In and adding shadows and all that as a full walkthrough tutorial Get this video to 300 likes and I'll drop part two with the shading and the shadows and all that good stuff, man Thank you guys for watching may she stay tuned because more heat is coming soon and I'm out this thing


You asked and now it's finally here. Appalachian Wireless now offers unlimited data on the best network in the region. See store for complete details, better service, bigger savings. That's today's Appalachian Wireless and East Kentucky Network Company. Lawrence County native Tyler Childress has been making waves in the country music industry with his new LP purgatory. Tyler says growing up in these mountains played a big part of who he is today as an artist. It's foundation for just me as a person you know and the way that I've grown to see the world around me and you know it's influenced the characters that I write about. It's influenced the sound what I want to hear out of my music you know how other people's music you know what I think's quality and what's not. Rolling Stone magazine describes Tyler's sound as a raw look at the darker regions of modern-day Appalachia where bluegrass is in the soul but cocaine is in the blood. However Tyler describes it a little differently. The sound I'm trying to go for is it's a it's a combination of a lot of things but it's like Marty Stewart says we're doing a little thing called the Hillbilly Rock you know I mean grew up listening to a lot of Southern Gospel and a lot of bluegrass you know growing up in this region country music was a was a big influence early on you know listening to a lot of Ricky Skaggs and Larry Cordell and pretty partial to D White so all that you know just welded together with some drive-by truckers and I don't really know how to explain it other than that. Those who knew Tyler early on knew right away he was something special and was destined to do big things. I teach at Lawrence County High School and I teach freshman and I had Tyler several years ago in my freshman government class a little broad-eyed red-haired kid and I play music and a lot of people know that so me and Tyler connected pretty early because he played music didn't take long to figure out that Tyler wasn't like most the other children he was he was already writing songs and was interested in some pretty esoteric stuff.  If you miss Tyler's show at the Mountain Arts Center you can catch him this week on December 2nd and 3rd at the V Club in Huntington West Virginia reporting from Prestonsburg I'm Sean Allen for EKB news.