Good morning to everyone who are appearing in this virtual summit. The other men of innovation who are participating in this unique hackathon, including Professor Kannan Mogul of Indian Institute of Technology Mumbai. Founder CEO of the climate Small Technologies is based in Guaimattur. Chief Operating Officer of the Derby Foundation based in Bangalore. Dr. Anthony from the Department of Social Entrepreneurship and the Incubation Centre of the Madras School of Social Work Chennai. My enthusiastic and passionate colleagues from the BIT campus of the Anna University who are the prime drivers of this unique hackathon including Professor Senthil Kumar, the Dean of the campus of BIT campus. Professor Putrajit Kukodi, the Head of the Pharmaceutical Technology Department of the BIT and the University campus. Professor Annapurna, Head of the Computer Science and IT Department of the BIT campus and the dedicated band of colleagues and students. First of all, I am very delighted to participate in this virtual meeting and also to inaugurate this COVID-19 National Bioinformatics online hackathon for full status. This is a unique event organized by several stakeholders who have been concerned greatly on this pandemic. In fact, on behalf of the Anna University, I thank all these guests who have been enthusiastic and crafted this entire hackathon program for the benefit of this nation. This event has been carefully crafted by my BIT campus of the Anna University with a very unique and productive partnership of the eminent innovators both in the academic and entrepreneurship world from different cities in this country of the country. In addition, I am extremely delighted that this hackathon has drawn the very overwhelming support of almost all the government departments in the country involved in higher education, skill development, innovation, innovation promotion and everything connected with the skills and innovation and all the other things needs to enhance our capabilities of our Indian students. In fact, we are all aware that few weeks ago, United Nations declared the coronavirus disease 2019 pandemic to be the greatest test this world has faced since the World War II. As of this morning today, more than 3 million people have been affected and more than 2 lakh people have been killed by this deadly virus. It's unfortunate that in India we have lost more than 900 people due to this COVID-19. Clinicians, pathologists have been struggling to understand the damage wrought by this coronavirus as in 3 years to the body. It is now being realized that although the lungs are ground zero, the virus reach can be can extend to many organs including the heart, blood vessels, kidney, gut and the brain. So this disease can attack almost anything in the body with devastating consequences. Its ferocity is breathtaking and very humbling. This kind of unprecedented globally pervasive virus calls for intensively cooperative and normal efforts at global, national and local levels from all friends. Practice clinicians, vaccine developers, drug discovery scientists are leading this challenge from one of the main friends. Scientists, engineers, innovators, technicians might have given up all over the country including India to fill this crucial gaps in the nation's response to this deadly and cruel pandemic including these teams of scientists, engineers across the country, across various institutions and the government bodies and even private startups. They are very immensely and immensely involved in the design, manufacturing and distribution of large quantities of PPEs including ventilators and sanitizers, masks, face sheets. So in addition, there is an imperative need to develop a behavioral-centric solutions based on the local habits and the culture of the masks of our people which are different across the country and especially the people living both in the rural and rural areas have different habits, different cultures. So this needs a solution which people can understand and easily follow. And the solution for this kind of issues in mitigating this coronavirus 19 as of this sector of the people can come from the hackathon that we are launching today. This hackathon throws great opportunities for the app developers to come out with responsive apps, web-based apps which will enable health authorities to take measures to contain this pandemic as well as the public to protect each other from the virus in a very simplistic and novel way. India being the powerhouse of the software skills and apps development and expertise there is this great opportunity, this is a great opportunity to our skilled and talented students in all disciplines to team up and give shape to their intuition and innate abilities. More on this perhaps since I am not an expert on the apps, I have no little bit about it and it will be spelled out by my other experts who are actually your partnering in this sector and they will give you in more detail what should be done by these talented students. And I wish to take a two minutes of my time how Anna University, a leading technological university in the country has responded to and risen to the challenges thrown by this pandemic. And in the last few months Anna University's technological technologist we have played a very significant role and mentioned a few the roles of Anna University designed, fabricated and manufactured and designed and tested by our faculty members led by the Centre for Aerospace Engineering for the last 15 days five of our drones have been put into the service of the request of the Corporation of the Chennai to carry out the disinfection on the houses and buildings which are not easily accessible and in the last 15 days the drones of the Anna University has covered about 40-40 lakhs kilometers of the areas in the Chennai City Corporation and our people, the experts in the biotechnology department have come out with new sanitizers which can kill not only the proteins of the RNA of this virus and our people in the textile engineering department have come out with a washable mask and the department which has said to our department to the remote sensing department have helped the state government in mapping out the zones, what we call the red zones as in terms of concentrated people, concentrated and infected people in the entire city of Chennai, Chennai and the entire Chennai north to take appropriate measures of dealing with the kind of measures that replace the best zones and my NHHID team has helped in coming out with helping in repairing the ventilators in many of these hospitals and they have been doing a great job and my manufacturing department has helped in producing what you call the split type ventilators and provided to the hospitals along with the Shastra University and so this is a, an university is contributing its might in all friends in this hover of need for the nation and we have joined with many departments in the state government and we are being very happy and we will continue to challenge our responsibilities and to mitigate the effects of the coronavirus to the full extent I will assure you and I am glad that all the people, especially our chairman for Shastra Buddha and all the stakeholders have been intensively involved in designing this kind of a hackathon so that it can bring out a novel solution and for the people they need which will, people they need the solutions based on this kind of an approaches so with this one, I again thank all the members especially my team at the Anno University BAT campus is one of the campus is doing extremely well and having designed, taken initiative and taking a drive with this one, so with this one I again welcome all of you especially my other stakeholders, important stakeholders who are gracing this occasion including Professor Anno Shastra Bodhi and taking off his time with a busy schedule and helping and giving up all the importance, all the support that needed to drive this kind of an institution to rise to the highest level and to meet the challenges posed by this unprecedented crisis such as the state which has currently worked across the globe and across the nation Thank you very much once again for all of you


I wanted to talk to you about a woman, actually, that I am trying my best to model my life after, to be honest. When I read her story some years back, I just, I don't, you know, when you have that, you know, when you read something or you hear something about just like one particular person and you're just like, I just want to be her, right? Like, I just, even if I, even if I recognize that I can't be all of that, right? I just like give y'all, just give me a piece of it. And this is the great Nana Asma'u. So Nana Asma'u is the daughter of Shehua Uthman Danfolio, who was a great, a very great scholar, basically in the late 1700s. And long story short, he was not only, you know, he wasn't only a scholar, subhanallah, when the West talked about him, they say he was just, he was the, he was like a fighter, that he was a strong fighter. But in reality, it was what is that he's, that he was the, the caliph basically of a very large Islamic empire that had been an Islamic empire, actually, at that point for hundreds and hundreds of years. And so we don't actually talk about Islamic empires inside of Africa. That's just a whole nother, you know, we just got to work on that. That's a whole nother thing. But what happened was, is that at that particular time, the, the base of the Sankhat Empire, or the Caliphate, sorry, was actually closer to West Africa. But the encroachment of slavery, literally the, because slavery was introduced, of course, it was coming down through North Africa into West Africa, through the coast, entire, basically entire villages, if you can imagine, like entire towns, we think about villages, we think small. But in reality, some villages are very big. They're biggest cities that we know them today would be completely disappeared, right? Would be completely disappeared. So if we were to look at, let's say, in one year, over the course of slavery, there's more, it's, it's recorded somewhere, somewhere into the tens of millions, right? Tens of millions of people came up missing. And one particular year, basically, let's say out of Gambia, about two million people came up missing. Now the entire population of Gambia is only 2.5 million people, right? So when we talk about the encroachment of slavery, what we're saying is, there are people who are stealing folks, kidnapping people in, in mass amounts and, and bringing them to the States. So at this point, there was also, I want you to, to understand what's happening. I want to give you a little bit of that historical context, because as a result, it's something that the Islamic Caliphate said, we actually have to move the capital of the Caliphate because of the level of, of harm and war that we're fighting on an ongoing basis. Sometimes we think of slavery, we think, oh, they disobeyed people, that was it. We don't know that there were actually people who were fighting on the forefront to do their best to kind of push back against it. And so they moved the Caliphate, and then there was also an internal conflict, to be honest, between, between the Muslims. And part of the internal conflict and just, you know, we have to tell that, is it okay if we tell ourselves the truth of our history? Is that okay? Okay, because that, you know, it's not usually my way to sugarcoat things. But so I want you to understand that the Muslims in West Africa are in a war against basically the Europeans from the Portuguese to the British that basically because of the encroachment of slavery. And then there's a war that's happening. We'll just say with some of the Northern tribes, not all, but some of the North African tribes against some of the West African tribes because they were some of, we'll just say there were groups of folks that were, that were saying, well, you know, we were warring with you guys, it's okay to say, to sell you into slavery for a number of reasons. The details of that, we can talk about later if you, if you want. But the point is, is that he moved the caliphate and there is a war on two fronts, right? Like we're trying to solve an internal conflict, right? While at the same time, we have a very large enemy from the outside. And the daughter of the, basically of the caliphate, once shehua with mandem who was growing up and when she began, she was in her young twenties. Basically, she herself was also a half of the Quran. She was considered someone who was a master of Maliki Fiqh. She was also a poet, but she decided basically the way that these men are behaving and fighting amongst themselves. I've got no time for it. She literally started a woman's movement of her own. And this movement basically is, she decided, you know what, because inside of that, so you've got this political war going on, inside of that, the Muslim community of some, not all, are debating whether or not women, because of, because of what's happening, should women go out, maybe we should shut down the girls' schools because at that time there were very large institutions where women, when girls were memorizing Quran and learning Maliki Fiqh, there was like a, a push. It always happens during conflict, political conflict. It becomes a question, maybe we, in order to protect our women, we should keep them at home, right? That we shouldn't let them go out to the institution out of fear. Nana Asma'u, may Allah Subhanahu wa Ta'ala continue to just elevate her rank and expand her, decided I'm not having that. So basically she began with a group of women in her area and she said, what is that feedback? Right? That far? So basically she started with a small group of women and she brought these women together and she was like, listen, this is what we gotta do. There are number one, we have to make sure that women, no matter where they are, understand their Dean, that they understand their personal relationship with Allah Subhanahu wa Ta'ala, that they don't become disconnected from the Quran and their spiritual tradition. We have to make sure that these women know their Fiqh because this is also, we're in spiritual warfare. This is not just a political issue, we're in a matter of spiritual warfare. We have to make sure that these women, that their prayers are accepted. On top of that, SubhanAllah, she said that what happens in the midst of war is that SubhanAllah, the people that are most affected are women and children. So she said, we have to make sure that these women also have their own means of economic empowerment and they have to know how to do it in a halal manner. They have to know how do they start their own businesses and have their own businesses and they're going to do it according to Fiqh, not according to, we just gotta do what we gotta do, but they were going to know how to do it so that those women would have a tofiq inside of their affairs. She also said, we know that SubhanAllah, she said, in some of these areas that people don't have, you know, people don't actually have access to water. We have to make sure that people always have access to water, that we want to make, we have to still take care of our people because when the caliphate moves, right, then basically it's like the capitol is going, her fear was like, now the capitol is going to be that place where people, you know, the elite can also move, but everybody can't move. Everyone can't afford to move. Who's got a tissue for me? I don't have a tissue. Somebody have a tissue? Does that get okay? We know what's happening. Thank you. So she understood that everybody can't move, but also she understood that because of the encroachment of slavery, I want us to think about it for a minute. If you go into a region and you steal the most, you steal, basically let's say those that could be the labor and the ones who were going to be able to do the work. And we're not just talking about the farmers, right? We're also talking about the muscle. We're also talking about the stealing of the army. We're also talking about the stealing of the teachers. We're talking about the stealing of the builders, of the craftsmen. We're talking about those who do construction. We're talking about the doctors. We're talking about the Quran teacher. We're talking about, we're not, sometimes we think it's just one class. If we say we're going to steal, right, majority of this place, who's going to be left? The weak, the vulnerable. And so what she says is, you know, what happens in these situations is sometimes they won't have, they won't have proper access to food. We've got to make sure that these populations are still taking care of. And lastly, she said, of course, in these situations is that if, you know, if women are having babies, if people are getting sick because of not having clean water, they've got to have access to healthcare. So basically she started with a small group of women. And to make a long story short, every time she would go into a village and she would make sure that the, that village would have those five things. She would always come and teach sacred knowledge, making sure that they knew their Dean properly. They knew they studied Akida. They would study Maliki Fiqh. She would make sure then that they had some kind of economic arm by which those women would be able to sustain themselves. She would, so then she would also build a school and she would build a clinic. And she didn't train a group of women who were in that village that she would train them to the point that now I can hand over this project to you. So you don't, if they tell you, you can't come into the masjid, you don't have to worry about it because your job is to make sure that these women, the women in this particular area, know their Dean fully intact and that they are not dependent upon anyone economically because they know how to sustain themselves, that they have established their own businesses. When it comes to, she looked at, okay, who are the midwives and the conveyors one, right?  Then your job is to train somebody else and to get an apprentice. So then we're taking care of our own healthcare. She did that in over 800 villages.  So I'm like, wait a minute, first you didn't just train and in every, in every village she went to, she made sure she left a group of women who were basically who were at a scholarly level that they could then train the other women, that they then became responsible to date. We still have the, we still have that definitely throughout Senegal, definitely throughout places in Nigeria and Gambia and Mauritania, you have places where women have their own centers, their own Quran memorization centers. They study Maliki Fiqh, they have their own, what they like, they call it, even they call it a susu in terms of the way they support each other. I tell us this to say that a lot of times as women, I give you this story to, it's exactly what we're talking about when we talk about having a level of faith, right? And resilience and knowing what is, you don't actually need to know it all and you don't actually need the support of every man in the Masjid. I know, please, maybe, you know, so I'll close the doors because I don't want nobody to get mad. But in our, you know, sometimes we're so focused on, well, the men won't let me or, you know, the men are holding us back or the blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, blah, right? Whatever it is as opposed to let them run their affairs and let us run ours, right? That they are not basically look for the path of least resistance.  So if you want something different, then you make something different, right? You want a different reality for the next generation? You're the one responsible for that. Trust me. Trust me.


Tim says, a month ago, an external company invited me to view their SharePoint folder. I accepted and not having 365 in the company yet. I created a personal Microsoft account using my work email. A month later, we all know where this one's going. A month later, well, because we're all reading the same question, because we also know the story as well. A month later, my company moved to 365 and I gained a Microsoft business account still with the same email. Now, whenever that same client shares things with me, I can't access it with my new business account. Their tenant seems to be tied up with my old personal Microsoft account. Yeah. This has been the non-going thing. Some of the first questions when I joined this group came up, and I could relate to this personally, because I did this exact same thing prior to a prior employer joining Microsoft 365, I use their domain-based account for creating one. You have to understand there's two, and this is what I learned. It was like three months of going back and forth with the support people. Nobody can answer my question, and I finally figured it out. The fact that I had to go into the Microsoft admin and I figured out that was one of my big feathers in my account, because that's not my space. But there's two ruling entities for Microsoft accounts, and that's why when you log in, it asks you, is this a personal account or a work or school account? Those same emails can live in both of those spaces. You can create your Microsoft account just like you can use Google or Yahoo or any other email account, and create a Microsoft-based account for your personal use, and then they have the one when somebody creates a tenant using that, and you log in, and that one's in the enter ID space. The trick to this is I had to go in and try and delete my personal account, and it kept reverting, and it deleted the registry out of the business-based account. You have to be really careful. The first thing I'm going to tell you to do is change the, if you're using the same password, change the password on the personal account, so you know which one you're using. When you log in, always log in using that. Now, there's another new change that's putting another spin on this. If this was a Teams folder, it's saying it's a SharePoint folder, but I'm wanting to give it a side to Teams. The new free community Teams automatically redirects to live.teams.com instead of Microsoft. Teams.Microsoft.com instead of live.Microsoft.com. See where it redirects to, and that could be the other problem, is they're trying to share a Teams-based folder with you, and it's redirecting you to the other, again, it's like the personal version versus the business version. You're not the only one. This has happened a lot. We get this question all the time. Yeah. I'll go ahead, Dow. I was going to say what I've heard from others is, if you have a case where you've got the same email address, know into the personal account, add an alias. Make that the primary. That's a good one. Then you're no longer sharing. Then you're no longer sharing that the email address. You still got the personal account. It just has a new alias, and that's your primary, and it takes care of the problem. That's a result of people who have, again, going back to the Microsoft world, have got a business account and a personal account with the same IDs, and they logged into Teams, and Teams can't really figure out which one's which. It's improved a little bit. Yeah. Because it's interesting, so I have four different emails, four different tenants, and the logins there. There are some other problems. Again, there are personal issues with my primary account not logging into the new outlook, the new Teams, except through the browser because it's having difficulty there. But what I've noticed is, what I've noticed is when I log out of one by one out of those profiles in the new Teams client, when I remove those primary tenants, it then defaults and switches over to the new community Teams. It opens up, and then the final thing, and I've got an old hotmail account that I use for that stuff, it will then, I can log out of that community-based Teams product with my hotmail. So it's just interesting that it, so you can, you should be able to be logged into multiple tenants. It should be able to reconcile between them and the free version, and the benefit there of being logged into all of those, except of course in my case with my primary environment, which was the first one, which has been in existence before all of the others, but somehow gets rejected from the new Teams and new outlook. I'm not bitter or angry or anything. Anyway, it's interesting. It does a decent job, except for that of switching in between them. When I, this is an improvement. Microsoft has had a lot of feedback, so if I get five meeting invites, and when I click on them, the old way is that it would just not work or not work properly with the full features, because you're logged in the wrong ID, in the wrong tenant, kind of all those things, where now it asks you, do you want to switch tenants? Do you want to go to the place with the best experience? And for the most part, I won't say in all cases, that works pretty well. Yeah. There's some work you've done. Different profiles. Yeah, the profiles. I had actually messed up my profile with Office, like completely with trying to do the switching and it just got a real mess, and eventually I had to completely log out of, just everything, like it's just everything everywhere. And eventually I got to the point where it had got all such a mess that I had to recreate a profile on my laptop, and actually go in with a new laptop and blast away the whole other profile, because it had some real issues between the two. I was gonna say the exact same thing. I log into my computer with those separate profiles with no space, but you also have to purge the credential manager, because it does cache all those web-based and machine-based credentials, and I put links for that in the spreadsheet for you. We were just talking about this earlier this week, Sherry and I, about that issue specifically, but it's a, look, and again, I'll just re-emphasize that there's still work to be done by Microsoft on that. They used to think it was an edge case, this scenario, and a lot of MVPs were like, no, this is much more common than you think, and it's pretty standard.  Yeah. I have, I think, a last count, 14 different logins between my own, my son's business, and then also all of my clients. So I've got eight different logins on my computer. You're just trying to show us all up, Sherry. You've got more friends in all of us. We get it. Oh, it's crazy. Well, and the whole Windows Hello doesn't work for me because it's the same face going to all these different profiles that are on my computer. I can't, you know, I've still got to use passwords or pens to get into those because it's the same face. It's just which hat am I wearing today? Okay, can you, would it work if you have for each of your profiles, make a different face? Put glasses on, different glasses for each. This is my, the Superman, Clark Kent, yes. Clark Kent, Superman. Because he doesn't look exactly the same without the glasses. Really? I look the same. That's the same for me with that make up. No one recognizes me. I got some Yammer glasses at the MVP conference. So did I. Yes, I did. The official Yammer glasses. There you go. We'll have to get a screenshot at the end or something. Go find our Yammer glasses. If you're logging into a profile that's specifically to work on social stuff or get into Viva Engage, you have to wear the Yammer glasses. And Viva Engage won't let you log in with the personal account anymore. Hasn't for some time, which is unfortunate because I've got two or three different teams, channels, whatever, I've been at a bit abandoned because I can't get in there with my personal account, with my MSA account. Yep. I've understood and I heard this morning though that that may be changing. But they're going to be wonderful. That would be wonderful. Yeah. That would be fun. Well, I can't access the community questions because it's to my personal account instead of my business account on the same email address. So that's how I have to access all the community questions. Well, I made the mistake of when Microsoft offered the MVPs like please confirm which email that you want to use as your primary. I had the same thing. You respond in the time frame to get it away from my hotmail and move over to my collab talk email, which I should have. So I continue to have issues where I'm doing work and oh, there's a PGI call and then I can't get into it because I'm on the wrong ID. And anyway, stuff happens. Yeah, that's interesting because on that as you were suggesting there, I have one in this case. It's an outlook.com account that I use. And that's the only place I use it for is as authority to get into my MVP stuff. And teams, well, no, not just the MVP stuff and the various forums that I go and answer questions at. The idea being is that that email account doesn't get used for anything but just an authentication. It doesn't receive or send email. The one that I list as here's how you communicate me is the other one, the adlive.com account. And you get into the same thing. You'll be doing something in the MVP world and they'll say, give us your email account. Well, which one do you want? Yeah, I switched one from a hotmail outlook and it broke everything because hotmail is just a garbage dump. I get probably 200 spam messages in there a day that can't Microsoft do a better job of understanding. This is not a really hotmail. Well, that's why my hotmail is only for my MVP. And so I get all the notifications that I can't turn off. All of it goes there. I know I don't read it. So I could get it and I could access the mailbox and I look at it maybe once or twice a year and I go in and just delete everything because that's all it is. It's my login. And so in some ways, and I use my other garbage account as my Gmail, that's where I, if I have to give an email to sign up for something, it's Gmail. It was MVP related, it's hotmail.  So it kind of works out.


Welcome to a captivating journey exploring the profound depths of Yin and Yang. In this visually stunning video, we will unravel the essence of this ancient concept, revealing its intricate meanings and profound symbolism. Our journey begins in a serene garden, where Yin and Yang are beautifully manifested. As the camera pans across lush greenery, we witness a magnificent Yin and Yang symbol meticulously crafted with colorful flowers and stones. Its contrasting halves, one dark and the other light, gracefully merged together, capturing the harmony of opposites. Look closely at this exquisite symbol, for it holds the key to understanding the interplay between Yin and Yang. The dark side, representing Yin, symbolizes the feminine, the mysterious, and the passive aspects of the universe. Its color evokes the calmness of the night, the nurturing darkness that conceals profound wisdom. On the other hand, Yang, portrayed by the bright side of the symbol, represents the masculine, the active, and the transformative forces in our world. Its radiance embodies the vibrant energy of the sun, illuminating the path towards growth, action, and change. As we contemplate the natural world, we recognize the eternal dance between Yin and Yang. Observe this majestic river, meandering through the landscape, its currents, at times gentle and serene. Embody the Yin, while the dynamic and forceful rapids represent the Yang. Yet, within this apparent dichotomy, both elements coexist, harmonizing their energies to shape the world around us. In the heart of a vibrant city, we witness the human expression of Yin and Yang. Tall skyscrapers soar into the sky, symbolizing the ambition and progress associated with Yang. Yet, amidst the hustle and bustle, we find serene parks, tranquil retreats where individuals seek solace and harmony, representing the Yin within the urban chaos. Elements of nature further embody the duality of Yin and Yang. Behold the fiery passion of a crackling bonfire engulfing all in its warm glow. It embodies the fiery essence of Yang, intense and transformative. And then, witness the frozen stillness of a pristine ice cave where silence and calmness reign. This embodies the essence of Yin, cool and introspective, relationships, to mirror the interplay of Yin and Yang. We witness a joyful family gathering, a tableau of connection and unity. The parents, with their nurturing and gentle qualities, represent Yin, while the children's boundless energy and curiosity embody the Yang.  As our journey nears its end, we find ourselves in a tranquil Zen garden. Here, the essence of Yin and Yang is distilled to its purest form. Raked gravel, carefully arranged stones, and serene water features create an oasis of balance and harmony. It reminds us that Yin and Yang are not just external forces but also reside within ourselves, waiting to be discovered and embraced.


Yes, I'm leaving, leaving. Hey, welcome back YouTube to week seven of my AMD challenge. This challenge is that I'm gonna track one company for the next 52 weeks to see if keeping track of the news, the price action, doing technical analysis in earnings report on if I could be a successful trader by the end of the year by just keeping track of one company owned. Now this week in AMD a lot has happened. They have their first red day after about a seven or eight day run upwards. Their new seven nanometer CPUs are testing almost at five gigahertz. And the most impressive thing of all is that AMD finally reach a hundred billion dollar market evaluation, like that's crazy because I remember investing into AMD back when it was like $14. And now it's at a hundred billion dollar market evaluation, that is insane. But before we dive into Robinhood, the news in the market analysis of AMD, make sure that you stick to the end for the market evaluation. I got a little something special for you guys. But before we get started, make sure that you scroll down and hit that thumbs up button and kind of look like this. And then take about half a second to just hit that click button on the thumbs up. It helps out this channel more than you guys can even imagine. Like just hitting the thumbs up button that take one second literally helps out this channel tremendously and allows me to have the time to do the research to bring it to you guys. So now that you guys are hit the thumbs up button, let's go ahead and dive into my Robinhood account to show you the moves that AMD has made this week. Okay, here we are on my Robinhood account. I'm sitting at $22,441 on the week I am up $630.55 up 2.89%. So I had an amazing week for week seven for my portfolio. So I have a free stock available from Antonio. Thank you Antonio. Let's open that up right quick. Let's click the right one. There you go. Oh, I thought that was gonna say Amazon. All right, AMRS is worth about $3.86. Thank you Antonio. Make sure you leave what you got down in the description to let everyone know what kind of free stock that you got. Also, if you guys want a free stock, make sure you click the link down in the description, sign up for Robinhood and you get a free stock. Also, we bulls down in the description. If you sign up and deposit $100, you'll get two free stocks value up to $1,200. All right, here we are on AMD, the first red data head in a very long time. It is at $84.76. On the day it's shot down 2.15% on Friday. But on the week, it's up 8.44%, $6.60. So it started out around $77 and shot all the way up to $84.76. Somewhere along the line, I say around the $86 price point, AMD had broke above the $100 billion market evaluation. If we scroll down, I am up $2,412.65 on AMD. Now, this week since AMD was so expensive and overpricing, I say I was gonna wait for the pullback a little bit. I didn't buy any extra shares of AMD. I'm gonna wait for the price to pull it back just a little bit more and then I'm gonna dive back in. So my total gains for AMD is still around $31.62. So let's scroll down a little bit more. The market cap is at $99.62 billion and I believe AMD is gonna be a $100 billion company for the foreseeable future. So if you think that AMD is gonna be $100 billion for the next five years, you could go ahead and invest into it right now and don't have to wait for a pullback. But I don't have that much money to invest. So I'm gonna wait for a little bit pullback so I could get the most value out of each stock. The 52 week highs at $87.29 and the 52 week low was at $27.43. If you can invest into AMD at $27.43, you came up. You did a phenomenal job at getting in at the dip and riding it all the way up to $87.29. Congratulations to you. Not everybody is as lucky, but AMD is probably gonna keep surging up in the foreseeable future. Now if we scroll down just a little bit more and take a look at the news, they did hit their $100 billion market evaluation three days ago. And now they dipped just under $100 billion to $99 billion, but I do think that they're gonna stay above $100 billion for the next couple of years or so. But that's all that's going on in my Robinhood account at the moment. Nothing too crazy. If I see a good buying opportunity this week, I'm gonna go back in with about three more shares and buy some more AMD so I could continue to gain some gains from AMD. But enough of the Robinhood account. Let's dive into the news. There's some great news coming out. And then we'll do our market analysis. All right, here we are on the news. AMD Next Gen, their CPU Zen 3 has reportedly been spotted almost hitting a five gigahertz boost clock with 4.9 that's been tested with 4.9 boost clocks, which is insane to have a CPU other than Intel go so fast at 4.9 gigahertz. I'm pretty sure once the consumers get their hands on it, they'll be able to overclock them to over 5.0 gigahertz. Now these tests are coming from the models with 16 cores and a CPU that's at a 5.0 gigahertz. That is insane speed.  The seven nanometers are just destroying the market right now and they're the only ones on the market with seven nanometers chip. So Intel is falling, falling, falling far behind. Okay guys, so AMD might continue to surge over the next couple of weeks because they have a monopoly over the CPU market at the moment. Also Apple did cut their ties with Intel. So Apple computers are no longer gonna use Intel CPUs. They're gonna design their own CPUs. So that's another dagger in the heart for Intel. Now the next news that we're gonna look at has to do with AMD and Nvidia. So Nvidia they're gonna announce in September their RTX 3000 series, which should be announced on September 9th. They're gonna announce it. They're gonna do all the specs and then they're gonna announce the price point of their 3000 series. Now if that price point is super high compared to AMD new GPUs that are gonna come out, then that could be very helpful for AMD. We know AMD GPUs is not gonna be better, faster or stronger than Nvidia's. But when you compare the price points, AMD is gonna be able to say, okay, they're pricing that top tier GPU at $799. We're gonna make a GPU that is just 20% less as strong as your top tier, but it's gonna be half the price. So AMD is gonna have to price point their GPUs at a much lower price than Nvidia's top GPUs in order to compete with Nvidia. So hopefully AMD new GPUs can be stronger and faster than Nvidia's last series of GPUs at a much cheaper price so that people don't go out and buy Nvidia's used last gen series other than AMD new GPUs. So piggybacking off of that, the graphics cost is about 25% cheaper than the 2070 so that RTX 2070 series, but it comes close in terms in performance. So it's gonna be even cheaper than Nvidia's last 2070 series, but it's gonna be just as strong. So just like I said, they're gonna have to make sure that price point is at a great price point in order to compete with Nvidia. And the last bit of news we're gonna look at is Ryzen 7 Pro 4750G review, the 7nm CPUs. Right now it's going crazy out there with that thread performance. It offers a 7nm chip that offer up to 25% increase in single threaded performance and up to 2.5 times increase in multiple threaded performance using different applications. That is insane for the new gen CPUs, a 25% increase. AMD is killing it right now with their 7nm chips. So that's a bit of the news that coming out, a little bit of Nvidia news, a little bit of AMD news. Now let's bounce over to the market analysis. So here we are on the 180 day for our chart. We've been talking about this over the last seven weeks. So let's zoom in towards the upcoming weeks. AMD is still way overvalued for me to get in but it's shot up from around $58 to $87 for a percent gain of around 48%. It's just a couple of weeks. And the news do say that their price should be at their price point. So it might not be so much overvalued as I think it is. So let's zoom in on the one hour 20 day chart to draw some new trend lines. Okay, clearly we can see here there's a little resistance line right here at around $87. So let's draw that line out right here and extend it out. All right, so I mean bounced off of here once, twice and kind of rolled off the resistance line and came back down. Now AMD could do two things this week. It could trade within this channel using the 180 day simple moving average as this resistance line. Or it could get some more news and bust above the resistance line that we're looking at right here. Do I believe it's gonna fall below $77, $76? I think it could use this as support. I don't think it's gonna fall all the way back down to $59. If it do, I'm gonna buy a whole bunch more money. But I do think it's gonna stay in between these channels right here for the next week until around September when more news come out on the GPUs that are gonna get released. Now, like I said, other than just looking at AMD we're gonna look at their competitors. Let's take a look at NVIDIA, N-V-D-A. All right, taking a look at NVIDIA let's zoom out to the four hour 180 day chart. Now NVIDIA is straight up killing it. Let's draw this trend line and then draw one more trend line right here. All right, so we're looking at NVIDIA. It's been trading in between this up with channel for the last couple of months. It's been trading in this up trend channel and right now it's at the top of this channel. It could come back down all the way to this channel to around $416, $420. In this channel right here. So if AMD falls, I might see AMD rising if AMD falls but who knows? I'm gonna keep track on both companies. If this company, if NVIDIA do fall a little bit and AMD is at a good price I'm gonna go ahead and get in with a couple of shares to get a quick scalp on AMD and then take that quick profit. But I don't think NVIDIA is going to fall below the 180 day simple moving average. They could also continue to rise above and break above out of this trend line. I don't think so, but I think it's gonna stay in this channel. I think AMD is gonna stay in this channel and hopefully everything next week is smooth sailing. All right guys, and that's it. That is week seven of AMD. I gave you guys some good news, some good news from NVIDIA and some bad news from Intel. I didn't go in with any shares this week from AMD but hopefully this week if it stays within that channel and pull back just a little bit I'm gonna go in with a couple of shares of AMD, buy some and then try to sell it at the top of the resistance lines that I showed you in my marketing analysis to get a quick profit from AMD. So I do have a grip on my plan for the week. That's the good part of tracking this one company for the next 52 weeks is that I'm going in with a plan and not just buying anything and everything off of a whim. So if you guys wanna keep up with this challenge make sure that you scroll down and hit the subscribe button and while you're down there go ahead and smash that thumbs up button. But other than that, I'm Zeke bringing you the Dream Green Show and I'm out, peace.


Okay, can everyone hear me? Okay, so let's start now You know, I've always been sitting out there. This is my first time on this side of the room and it's quite scary Anyway, I guess I can't say welcome anymore because by now hopefully you're settled in but it's really been a pleasure to meet Most of you I still haven't met all of you So hopefully in the next week I have the chance to talk to all of you Yesterday you had a presentation about ICTP by Stefano If you have any questions about ICTP or you'd like to chat about the diploma program, especially I'm more than happy to talk to you about it I am not not from the perspective of a student But as I'm a postdoc here and I at least can help a little bit with maybe the application Process or some of the things that I know about it and the experience of students with whom I've talked anyway Okay, so today I'm going to do an introduction to Ergodicity so probably many of you have seen most of what I'm going to say Tomorrow Davide will do ergodic theorems but ergodicity is something Extremely important in dynamics and also in other fields like for example even in probability theory. So Okay, but I will do it mostly from a dynamics perspective. So I would like to a little bit motivate Why we care about this concept of ergodicity And then I would like to define it and hopefully work through some examples to show Some various techniques that are used to prove whether a system is ergodic or not. So Okay, so just to I guess it's almost happened at the beginning of every class but to remind you our setup We have some space some set X We have the Borel sigma algebra the measurable sets of X We have a transformation from X to X and we have a probability measure and I'm going to assume that Mu is T invariant so I'm going to assume now that we're always talking about a measure preserving Transformation and I'm going to write NPT so that I don't have to write measure preserving transformation every time Okay So, okay, so let's suppose suppose. Suppose. There's a set Suppose there's a set a Such that a is a T invariant set so such that T inverse of a equals a and Suppose that it has positive measure, but strictly less than one so Something like this X to X Let's say I have some so a that's T invariant so I can decompose X like a union a compliment Okay, let me consider a conditional measure mu a defined by mu a set intersection a over mu of a and I can do the same thing with respect to a compliment side mu a compliment the set Intersect a compliment here and one minus mu the measure of I so I can do this right Yes, okay, it's clear to everyone that these are probability measures still Maybe it's not so obvious, but they're also still T invariant measures So let me show that I'm assuming that a is T invariant so I can replace a by T inverse of a So I have mu T inverse of a and I can pull out T inverse inverse of the intersection and Mu is T invariant So this is the same as mu of b intersection a over mu of a Which is exactly mu a of b Okay, and this is the same for mu Restricted to a compliment. Yes So now I have decomposed mu into two P invariant probability measures Yes, so if I think of restricting T to a and T to a compliment Then I have it can decompose this measure preserving system into two separate measure preserving systems this Characterization that we would like to find is one when a system cannot be decomposed So there's an analogy drawn sometimes between Ergodic systems and prime numbers So you decompose every integer into the prime numbers, right? It's factorization because the prime numbers are things that you can't really decompose further So we think of these measure preserving ergodic systems as the units the building blocks of other things the things that can Not be reduced anymore Okay, so that's one motivation So we want to find a characterization for when this cannot happen And maybe you already have in mind which property here, but before I actually Introduce the definition. Let me give a The same but a slightly different characterization of this so I'm going to denote by M Xt the space of T invariant probability measures on X Okay, so one thing about this space is that it's convex So Mxt is convex mean so that means that if I take lambda between zero and one Any two elements, so if I take mu one mu two and M Their linear combination is also still an M So mu one lambda mu one plus one minus lambda mu two is still an element of that so this space has this very nice property and Extremal points of a convex space. So an extremal point. So mu and be Written as a non-trivial linear combination of other elements in the space, right? so whenever Mu equals lambda mu one plus one minus lambda mu two For lambda strictly between zero and one then mu equals mu one equals you too Okay, so there is a Characterization as well as the extremal points of the space of T invariant probability measures are the ergodic measures Okay, so I haven't proven that it's probably clear from this decomposition that extremal points are Ergodic measures, but the other way needs to be shown too I think the proof goes if you're not an extremal point then you're not ergodic But the proof requires a little bit more than I want to discuss here. However, I'm happy to talk about it later in the exercise session okay, so if I would like to Prevent this decomposition from happening. What is the property here that I would have to change or what is the property here? That allows me to write these conditional these conditional probabilities So I I want to keep I will have invariant sets so I I mean I want to keep a Comment about invariant sets here, but what's the property of the invariant set here that allowed me? Yes, right okay, so that it's between zero and one so if the measure of a were one then the measure of its complement would be zero and I would have a problem here, right If the measure of a were zero then I would have had a prop problem here. Yes Okay, so this is kind of the motivation for the first definition So a measure preserving Transformation is ergodic Reset so if for every set that's T invariant so for every set a First of a equals a The measure of a is zero Or one Okay, so There are other ways of Characterizing rigidity or perhaps using this definition to come up with equivalent statements for different objects So let me Introduce that well, let me give you a claim as you're preserving so sorry MPT Doddick every am I writing large enough? Can you guys see on the back? Yes, okay, thanks if for every Measurable from X to R such that F composed with T equals F F is constant almost everywhere Okay So you can see that we have gone from a characterization in terms of sets to a characterizations in terms of functions Okay, I'm going to prove this claim as Written, but just to make a comment you can replace measurable or L2 here I should put this is me almost everywhere And this invariance Can also be me almost everywhere Then you can extend it Pretty easily, okay, but for now the statement in white is what I would like to prove So we go from a characterization of sets to a characterization of functions These are kind of the two that I'm going to work with today But I would like to say that you can also go further to a characterizations in terms of operators So if you look at this composition as an operator acting on L2 It's a linear operator. It's an isometry. It preserves the L2 norm and the characterization of ergodicity is that Any eigenfunction corresponding to the eigenvalue one is a constant function almost everywhere so it may be unclear what you gain from that but Once you introduce the setting where you can use functional analysis. It becomes extremely useful So actually the third characterization is also very important, but I won't go more into that today Okay, so let me prove this claim Okay, so let's go this direction So I suppose my measure preserving transformation is ergodic And I want to show that any t invariant function is constant almost everywhere. Okay So let me take a Function f composed with t that equals f and I want to show that this is constant. Yes Okay, so let me consider the following sets T is the set of all x's and x Such that f of x first of all, is this a measurable set? Why do I know it's a measurable set? Yes, it's a pre-image of the interval t to infinity, right? I've been assuming is measurable. So this is a measurable set Now just a comment if f is not constant over at almost everywhere then it takes at least two different values Right on some positive measure Sets right so for some t if the function is not constant For some t this is going to be a positive measure set that doesn't have full measure, right? But if I want to show that f is constant almost everywhere I need to show that every such set a t has either measure zero or measure one Okay, good because I'm assuming ergodicity. So the only thing I have to show is that these sets are t invariant sets And I you know I use this definition one So let's do t inverse of a of t Well, this is such that t of x I can write this also x and x such that f composed with t of x is greater than t Well, I'm assuming that f is t invariant. So this is just The set of x such that f of x is greater than t And now we've returned to it just being a t Okay, so these are indeed invariant such which is good news for us because that means that they have only So mu of a which implies f. So we have proved the first direction. Is it clear? Let's prove the other direction The other direction being I'm going to assume that any at t invariant function is constant almost everywhere And I want to show ergodicity Yes, okay So let me take it t invariant set a so let now a good way always to go between Set and function is to consider Characteristic functions right of the set. So let me think about composing the characteristic function of a with the transformation t I get the characteristic function of which set the inverse of a right I want all the points that would be mapped into a under t Under one iterative t right so this is the indicator function of t inverse of a now I chose a to be a t to be t invariant set So this is just the indicator function of a now I'm assuming that any t invariant function is constant almost everywhere the indicator function can only take two values right zero or one So either so either it's Equal to zero almost everywhere Which means that the measure of a Which I can get by integrating over the space the characteristic function of the set d mu is going to be zero or I get that This is one almost everywhere Which then implies that the measure of the set for the same reason? So that proves ergodicity So We have now just proven this claim is it clear so let's do a few examples to actually see how we use these Characterizations and definitions in practice okay, so The first example. I'm going to do is an example. You've been seeing a lot about so I'm just going to do circle rotations So example one of the only example. I will work through fully So rotations so recall that the rotation we I guess we say it maps from our mod z to our mod z and For now, let me assume that we are talking about the levain measure and I'm going to use I'll use additive notation for now. So I have x plus data mod one Where we can have e to the 2 pi i x x plus data Okay, and so let me consider first the case where theta is rational and to do an absolutely explicit Example, let me take theta to be one fourth. Let me construct this set a in the following way So I'm going to take zero to one eighth going to take one fourth to three eight going to take one half To five eighths, and I'm going to take three fourths to seven eight If I draw this on my circle Okay, so under the rotation with theta equals one fourth What happens to this first interval? Where does it get sent? So the next one right and this one gets sent to the next one and this one gets sent to the next one Okay, so what can I say about a under t? Yes, in terms of in terms of the of how I'm saying a set x under t What does that mean? For the whole set It's invariant right because I'm Staying within here at the iterate. It's a t invariant set. Yes. So t inverse Of a equals a Now what's the measure of a One half right i'm considering the big measure It's one half. Yes. What does that mean? Is this rational rotation ergodic with respect to the big? I found a t invariant set that was had measured One half so neither zero nor one so it's not it's not ergodic and in fact for any Theta that's rational so any theta that's p over q you can always think of the set a i goes from q minus one i over q One i over q plus one over two something like this So you can always construct the construct the analogous set for the appropriate rational number And uh, this will be invariant, but it will have Positive measure and not measure one. Okay, so rational rotations are not ergodic with respect to the big I have a question though Can you think of a measure for which this transformation is ergodic? Delta measure on what? You're close. I so I want to okay Think about so think about what you are saying with periodicity instead of considering sets here Let me consider. I don't know for example points in these sets. Let me take zero Let me take one fourth. Let me take one half. Let me take three fourths, right This is an invariant set right what if I take a measure That's supported on this orbit I need to ensure that every point has positive measure in here, but let's say the Full support of the measures here What do you think do you think that's ergodic? Yes? Yeah, maybe you could I don't know you could put a measure one fourth one fourth one fourth one fourth Okay, I want the full measure to be just be supported on these points, but I want them to have positive measure each Okay, so what about this example? Yes, right and invariant set must contain all of these points or none of these points If you have only two of these points in a set or three of these points in a set Then its pre-image is going to have different points. It's not going to be invariant Okay, so in fact you can have you can think of rotations as ergodic with respect to singular measures measures that put positive measure on sets that are measure zero in the bank okay, so You wouldn't be losing that much in the rational case in general though if you think of a system That has dense orbits As well as many periodic orbits and you consider such a measure Yes, you might have ergodicity, but you also will be losing a lot of the interesting dynamics that are going on because you're kind of Giving the rest measure zero So I guess my point is that first are considering probability measures Then we say okay, but important measures for us will be invariant with respect to the transformation And then we say okay, but we don't want to reduce we won't we don't want to be able to decompose our system further So then we're considering ergodic invariant measures But even ergodic invariant measures aren't necessarily all important for us So there are still further characterizations of measures that are more relevant or less relevant for the system that you're considering I don't know if anyone will talk about this in the rest of the school, but Anyway, just to keep that in mind Okay All right, so let me just say That I could show this using the claim by thinking of a function that's not T invariant I mean a function that is tan variant that's not constant. So for example, let me take the function f Of x equals e to the 2 pi i x q Okay, so if I do f composed with t of x I get e to the 2 pi i x plus theta Which is p and this is e to the 2 pi i q of x and e to the 2 pi i p which is 1 So I just get f of x back So I can also find an allegesly to a t invariant set That has positive measure between zero and one I can find a function That's t invariant. That's not constant. I guess also I should mention Sometimes we oscillate between saying a measure preserving transformation is ergodic or a measure is ergodic, right? So this is not a measure of preserving transformation if I consider the vague if it's rational, right? But it could be if I considered the measure that we discussed so if you have If the Transformation is clear and you're trying to choose a measure sometimes people just talk about ergodic measures So you'll hear it phrased in different ways Okay being irrational so theta not being in q Yes, so I was talking about the vague measure Good. Thank you. Yes But almost everywhere here is large, right? I mean it's small So yeah, so anyway, but yes, I don't want this right now. That was just a comment. So let's forget about this now. I'm back to the vague Okay so Let's consider the irrational case I would like to use the invariant function characterization. I'm going to need the Fourier expansion of a function Does anyone want a quick explanation of Fourier series? Or can I just use it? Okay, I'll just use it. Let me then just say Briefly a few words just in case it's the first time you hear it. So I have here a function from let's say R mod z to r or I consider consider any function from r to r if it's periodic let's say one period one for now And I want to I can decompose this function into its harmonics. So I write it in terms of Basic oscillatory functions like cosine 2 pi and x sine 2 pi and x and I look I write it as a linear combination of these Right and they have varying frequencies and you add these up and you can represent your function in this way Okay, and if you write these using in in the complex way, you get a very nice Concise way of writing your function as a sum So I'm going to take write it as n and z a n G to the 2 pi i and x so I'll look something like that Okay, so this is a way that I can represent my function so um And something that you're going to need in one of the exercises exercises I give you today is the Riemann Lebesgue lima So if you have an l1 function l1 periodic function on r Then uh the Fourier coefficients go to zero and modulus as n goes to infinity Okay, so these guys the norm of these guys go to zero as n goes to infinity Will be useful. I think for one of the exercises later, but I'll write Riemann Lebesgue lima to remind you guys Okay, okay now suppose That this f came from choosing so I want to take an f That's tn variance right I'm taking an f. That's tn variant under my irrational circle rotation And then I write its Fourier expansion like this So let me write then what f composed with t of x looks like e to the 2 pi i and x plus theta This is just e to the 2 pi i and theta e to the 2 pi i and x And I chose a t invariant function. So this must be equal to f which means that this must be equal to e to the 2 pi i and x So I have a property of Fourier series That if these are equal then the coefficients are the same for every n. It's uniqueness Okay, so I have that this Must be the same as this For every n Okay, so that means a n e to the 2 pi i and theta has to be equal to a n for all n equals zero. I'm in good shape Trivially yes, that equals zero Well, unfortunately e to the 2 pi i and theta It would have to be one for this to hold. Well, that's only true if theta is rational Can only be true if theta is rational So if I'm restricting theta to be irrational, this is never one. So that means that all of my Coefficients for n not equal to zero are identically zero. So that means that my function is really just A not so that means that's constant, right? Okay, so then by the claim I've shown that Irrational circle rotations are ergodic with respect to the Lebesgue measure So Fourier series are really a crucial technique for proving ergodicity So today in the exercise session I will ask you to prove that the doubling map that you've also been seeing a lot about is ergodic with respect to Lebesgue And I would like for you to do it Showing that invariant sets have measure zero or one and I would also like for you to try to do it showing that Invariant functions are constant almost everywhere and you will use The Fourier expansion and you will use Riemann Lebesgue lemma Try to do it in two different ways so you get used to the different techniques Okay, so if f is in l1 I'll say of x mu yes then I look at then I can write it like this so I want this let me It has to be periodic in r or it has to be from r mod z to r. So I I'm taking x Let's just say for our purposes. It's going to be zero one Okay So I function l1 Let me just put that here since this is what our example will be to x mod one is zero one Lebesgue measure mu then I write its Fourier expansion and Then you have the property that the modulus of the Fourier coefficients go to zero as n goes to infinity Not you not always Maybe I mentioned things about lp spaces at the end and containment and things Yes, I'm mixing between using measurable l1 and l2. This is a claim. That's true for l1 functions, right? Sorry say again. I didn't hear you. Yes. I am Yes, okay. Yes. I am using a stronger claim, right? So let me introduce a third type of example So I'm going to talk about the shift space that you've already seen defined in a particular setting by hana. I think yes You remind your example to Full shift Okay, so I like this example And this proving our goodicity for this will be the harder of the two exercises. I think it's really tricky Maybe for some of you it's easy But I like it because the invariant measure that we consider is not Lebesgue So we leave a little bit the world of Lebesgue and we consider a different type of measure So consider the seek the set of sequences at sequences everything I say Is also true for one sided, but I'm just going to assume we have two sided sequences And each coordinate of the sequence comes from some alphabet of k letters I'm just going to denote them by numbers one through k And remember the shift map Sigma little sigma moves everything to the left, right? So the image under sigma of a sequence I have A decimal or something marking at the place here This will look like so in the case of one sided sequences I Kind of don't I don't have a left hand side before the decimal and I get rid of the left most coordinate. Yes Okay, so you're familiar more or less with this map If I want to define a measure on this space, so I think you saw a metric For this space. I want to just define a measure on this space So I'm going to go back to what Oliver said and to what Irene said You know we have these sets that we care about we have the braille sets And we really can because of we have all these nice extension theorems We can really just say things about the generators of the braille sets And define things on the generators and then it nicely extends to the whole space, right? So I want to Do this because it will be easier for me to define the measure on just the generators of the of the of all the sets But I need to find what these are so in r or in zero one The generators are intervals, right? But I need to find the analogous concept here. So what are my generators here? So generators in this space are cylinder sets. So these will be generators of the sigma algebra And what do they look like? Well cylinder sets are Sets of sequences that are formed by fixing finite strings of symbols. Okay So you say from this point to this point. I want it to look like this and then you're free outside of that Okay, so let me write this I have y m This is the set of all x in sigma such that x i equals y i for all i Between m and n. So these are my cylinder sets. These are my generators. I'm going to think of everything in terms of this So if I asked you to prove ergodicity of the measure I defined Then you're going to have to look at sigma invariant sets Is that well The things we have to work with that we can say a lot about are the cylinder sets So try to always approximate sets by cylinder sets or unions of cylinder sets Okay, okay, so now I need to define a measure on these So let me take a probability vector okay So think of this like the probability I get one the probability I get two the probability I get k So you can if this is on two symbols You can think of this as flipping a coin if it's on six symbols. Maybe it's like throwing a die So these are independent, right? It doesn't the probability of getting One of these symbols in a place doesn't depend on the place Each of these are positive and their sum is one So with this I'm going to define the product measure. So the measure of a cylinder will just be given By the product of the probabilities of each of these symbols, right? So this is going to be p of ym Multiply it all the way to p of ym So this is my probability. This is my measure. Sorry And Let me start off by at least showing That it's sigma invariant. So claim sigma invariant So let me consider mu of sigma inverse of ym Ym what is the inverse image under sigma of this cylinder set? Yes, so let me just write it as a sequence. So I have ym To ym fixed and you're saying okay since sigma moved to the left sigma inverse is going to move it to the right So then I'm going to have an open spot where I had ym and everything was shifted to the right And what can I put here anything in the alphabet, right? So this inverse image Is sigma as mu of the union from i goes from 1 to k Of now the new cylinder sets i Ym I have full freedom once I shift it over I can have anything there All of those sets are in the pre-image of this cylinder set Now what can I say about each one of these cylinder sets? Do they have overlapping elements right because If I put if I consider the sequences where I put one here And then I consider the sequences where I put two here Well, they can't be on the same set none of none sequences with one here are going to have two here So all of these cylinder sets are in fact disjoint So I can write this as the sum of the measures Of each of these new cylinder sets have a probability For each one of these they're they're independent so I can pull this probability out. I get the sum i goes from 1 to k of p i mu times the probability of my original cylinder set Now because I have a probability vector I said all of these guys add up to 1 So when I actually do this sum this part goes away And I'm just left with mu of my original cylinder set So it's indeed sigma invariant Yeah, but it's a union of more cylinders other cylinder I mean is the union of two disjoint intervals an interval necessarily I mean I'm considering I'm considering Maybe so maybe so I Need to think if there's something that pops up I really want The cylinder sets to be I want you to think of the cylinder sets of strings that are Connected strings that are fixed Not that you have one string fixed here and one string fixed here So I just it's it's enough to consider this probability on The cylinders that have this the the string fixed in one place I'm not I mean and then I can extend it for sure But so maybe there's another way to do this but I wanted to do it with the basic building blocks It's just M can be negative M and N are integers So M could be minus 100 and N could be two Yes, so And so cylinder sets have fixed strings of different lengths As long as you want as short as you want Okay Okay, so your task today is to prove. Yes. Ah, well that So the measure of that will be the probability of y m Times the probability of y m plus one blah blah blah all the way to the probability Is the product So my claim and what I didn't show you but what it follows from all these extension theorems That we're saying if I define the probability the measure on these generators This extends to a measure on the space. Okay, I'm not showing this but I'm claiming this from things that we've heard before as well so This is all this is the information you need to know to show ergodicity in the exercise session It's not an easy task. I think but hopefully it's fun Okay, that's all I have for ergodicity. Let me very briefly just tell you what LP space is because it was We realized that we're using these functions and we haven't defined them The spaces at all So I think davide will use l1 tomorrow certainly So I promise I will be very quick So I have a measurable space here and I take a measurable function for now Let's say it's a real value function and I take p between one and infinity So I define a norm on this function Which looks like the integral over the space the absolute value of the function raised to the p Integrated with respect to the measure mu to the one over p So this is a norm And the space of functions the LP space of functions are all the measurable functions on x Such that the LP norm is finite But this is what we mean by an l1 function or an l2 function. In fact, they think really all we're going to need is p equals one or two in general uh I don't think we'll need Okay, I don't think we'll need l infinity functions um One thing I think that's important. Well, these are vector spaces and one property Nice property that we have because we're dealing with probability measures. So if mu is finite And for one less than or equal to p less than q less than or equal to infinity Lq is contained in LP We have containment. So This is nice for us. Okay Want to proof of this? Okay Okay, that's all so those are LP functions. I'm done and I will see you at two o'clock. So thank you


Hello everyone, welcome to theCUBE's presentation of Women in Technology's Global Event, Celebrating International Women's Day. I'm John Furrier, host of theCUBE. We have Rachel Thornton here, VP of AWS Marketing, CMO of AWS. Rachel, great to see you.  You've had a great career. Thanks for coming on. No, thank you for having me. I'm excited to be here. You know, I'm super impressed with your super inspiration to a lot of people, your career, Microsoft, Cisco, Salesforce, Amazon, you worked in amazing companies that had great growth, great transformations and business success. And all the employees that have all grown since then, you've been part of these great success stories. And you've had a great career. And the theme here is mentorship, which is a super important topic.  Everyone needs a mentor. Most people don't know how to do it and how to be involved. It's almost like a secret dark art of success that needs to be opened up. What's your thought about mentorship? Hopefully people don't see it as a secret dark art. I actually am a huge proponent of mentorship, both mentoring folks and actually encouraging people to seek out a mentor for themselves. Early on, you know, when I started working, I really thought about how can I navigate a particular situation or what do I wanna learn more about? And even though I may have been nervous or a little shy at first to ask, I always thought just ask, because really being able to have a mentor, someone who you can ask questions of, someone who can help you with questions or help you with situations you're navigating or give advice I think is critical. As a mentor, I would just say as a woman in tech over the years, I've realized the criticality of sort of finding your voice and using your voice. And so I look at mentorship as a great way to help individuals, every individual that I mentor sort of find their voice and use it. And then ultimately advocate on behalf of others, advocate on yourself, on behalf of yourself as well. And I think it's just really, I think it's a great thing to mentor and I encourage everyone to do it by the way. And it's also ask yourself, hey, who would I wanna be my mentor? What do I think I wanna get out of it? And then go forward. Well, let's start with the mentee side. When you were coming into your career as you grew through with mentorship, a mentor, how did you find a mentor? How should people think about asking and finding? What's your thoughts on that? Because asking is great. People might be nervous. I mean, I know I'm nervous whenever asking people, am I interrupting them or confidence? It's a hard thing. How do you find a mentor? What I did and what I encourage other folks to do when they think about it is kind of write down what you're looking for in a mentor, what are the things you would like to ask or get help with or get advice with? Is it career progression? Is it learning how to navigate maybe collaboration with different teams? Is it, hey, you have a couple of great ideas and you'd like to figure out a way to get them surfaced in the organization? But kind of write down what you're looking to get. And then what I did and what I encourage other folks to do is really look around not only just kind of your immediate team, but what are some of the other teams you're engaging with? I would even ask people in your organization, I did this early on, like, hey, I'd like to get some more info on this or some help with this. Who do I think would be or who do you think would be a good person? We have a leadership principle at Amazon, learn and be curious. And I think it dovetails so nicely into the whole mentor mentorship, mentee relationship because if you're looking for a mentor, it's good to sort of think, okay, what do I want to get out of it? Who would I ask? If I don't know, start asking people that you do know and I think that's going to lead you to the right person. But on the mentor side, I think as you're working with the person, keep asking questions. What do you really learn about them, learn about what they're trying to do and help them learn about themselves, their opportunities, where they can grow more. So I just think that's a great leadership principle for the whole construct of mentoring. It's a relationship too. The mentee mentor relationship is one that's a give and take but also there's gains from both sides. How have you gained from your relationships with your mentors in the past? And how should people think about that? Because it's just human, it's a human thing, but it's also kind of a, it's a cool thing and it helps everyone both sides. Can you share that relationship, give and take and what people can gain from a good relationship? I think the biggest thing for me has been just the different perspective. I find that so valuable. I love the chance to get a completely different take on something, a completely different perspective, one that I maybe wouldn't have considered because I think if you are, and we're all like this, we all come to a decision or a situation with our own set of understandings, our own biases, if you will, our own frame of reference. And I think it is a powerful thing to work with someone else and have them give you a completely different lens on a situation because it opens up, not only how you think about something or how you react to something, but just how you would learn or maybe think about information or that situation going forward, right? And maybe probably do an even better job with handling it or processing it or considering it. Support is a huge thing in life, right? Having someone to support you and your career, same thing.  I'm sure you get a lot of requests to be mentored. I mean, I'd love to have you mentoring. Hey, can you mentor me on this? So I'm sure you have your share of requests, but you're also mentoring. Now you're the mentor. How do you view your assignment? What's new? What are your tricks? Is there some secret trade? Is there a way that you handle it? How should people think about being a good mentor? Is there a common vibe or practice that you see successful for you? I think on both sides, mentor or mentee, when I take on, when I work with someone in a mentor capacity, I spend sort of the first time getting to know them and also what it is they want, it's kind of what they want out of it. Ask a lot of questions in the upfront, find out kind of what they're hoping to achieve. Like I think I said a few minutes ago, there could be folks that are like, hey, I want help with sort of career progression over the long term. I've also mentored folks who are like, I have a great idea that I just want some help with sort of packaging up and maybe positioning and then helping me navigate who would be the best team to take it to. So I think that's good to know kind of upfront, is it ongoing or maybe it's just in certain cases, it can be a very time-bound thing. But I think ask questions, on the mentee side, I always sort of come at it when I have a mentor, like here's what I want to get out of it, here's what I'm looking for, here are the three things I want to make sure I engage with you on. And then it's really clear on both sides. If I do have someone who comes to me with a mentorship, with a discussion around being a mentor, I will always ask, hey, have there other people that you've talked to because it could be that they're looking for, input on a project, for example, and there could be a better person I think, that hey, this person could be even better than me on helping you with this. You're navigating too, you're providing a little path and direction and the key is really to help someone in mentoring, it sounds like. Now let's have a look at the Amazon and AWS culture, you mentioned leadership principles. Is there programs within AWS, is this part of the culture, I know being a good manager is mentoring too as well, but is there formal mentor programs within AWS? Yes, there's actually several different ones. Women at Amazon, which is an amazing group that we have, they have Amazon Circles, which is a great mentor program. We have programs that are by country even, so as you can imagine, Amazon's a global company. One of the programs that I was really excited about because I worked with the team that started it, but in the UK, we started a Get IT program and it was interesting because we basically wanted to make sure that we were encouraging and aspiring girls between the ages of 12 and 15 actually to be interested in careers in tech. And we sort of thought, how do we do a good job with that? How do we get those girls excited? How do we get the mentors? How do we get them sponsors? That was the other thing we thought about a lot of. So what we did was we aligned teams and individuals inside at AWS to schools and then within the schools to grades and then to individuals in the grades, girls in the U.S. grades and over the course of a year, they would meet with their mentor, a team would have a specific school they would sponsor and then members on that team would be mentors to the girls in that school. And then at the end of it, there would be sort of a project and an assessment and it was really exciting to see girls who were sort of, they were thinking about it, but maybe they weren't sure. And then by the end they were like, I'm really excited about it. And I actually know kind of the next steps if I wanted to continue on with university with kind of a tech job in my sites for my future career. That's a great segue into the breaking the bias, which is the theme this year of International Women's Day is getting that as bias broke, getting people in early and also creating a culture of inclusiveness where there's no bias and we see it. And then this is a good way to call it out this year, specifically, and it's been a theme I know in this area, but this year they're calling it out. How do you know when bias exists and how do you know when it's gone, when we're not talking about it anymore? I mean, that's the scene would be to me, but this is a big deal, share your thoughts on this bias piece and what we can do together to help aware and solve it and break it. I think we all have bias. I think that you really do have to, I always in my head, I think, whenever I'm meeting with teams or just meeting with people one-on-one or meeting with customers, I think I sort of ask myself, what's my take on the situation? If I weren't me, if I was someone else, what would their perception be? What am I bringing to this situation that's sort of based on my context is sort of who I am or my background and how is that different if I were to sit with someone that has a completely different background, a completely different set of context or a frame of reference? I think that's so important across not only the teams I have here, I have a global marketing team. So always asking myself, I know I'm going to look at this one way. It's not the only way. So how do I make sure I have a great cross-section of leaders, a great cross-section of team members to bring to bear on a situation? Because the more I can do that, the more diverse I can make those conversations, the better off we're going to be with whatever solution we come up with for our customer or solution to an internal problem is just not just looking at it through one lens or two lenses, but how do I get a group of people, a group of different frames of reference, if you will, to come to think about it and then say, okay, I've seen it this way. How are you seeing it? And that just opens up so much more, I think great ideas, great conversations and ultimately great innovation. The more diverse those conversations are and the more diverse the audience is with the group is I'm having them with. That's a great take on how you feel and how you looked at that. And I think that's to me a great call out because you get to be self-aware and that's hard to do. You just basically walk through the mindset of stepping back and looking at perspectives other than your own. And I think to me that is hard for some people I've seen. And so that's one self-awareness, right? How do you do that? And then how do you maintain it? I mean, can you give some examples of how you've seen that in your career where it was just people weren't thinking before they were speaking or maybe driving too hard through conversations. And then the ideal scenario that you just pointed out, which is, okay, zoom out and understand and think and then align with at least, and you can do that in a debate. That's your philosophy at Amazon debate and align, but can you share some experiences where you've seen people just drive through too hard or didn't do that and scenarios where it did work? I definitely think that it's true. You can get folks in a meeting or in a conversation who are like, oh, I think I'm right on this. I know I'm right on this. Let me explain to you who I'm right on this. And sometimes it's just, it's important that you take a moment and say, okay, but if we had someone in the room that wasn't you or didn't have the background, would there be different? Would it be a different answer? And I always try to frame it. I think when you get sort of locked into there's a right answer, that's not always the way it is. I think that there's, depending on the situation, there's definitely answers that, yes, if we're trying to solve this problem, we've looked at it a couple of ways. We think there's a couple of different answers or a couple of different scenarios in which we can get the best outcome. But the more you can kind of move away from, at least I think move away from, hey, there's a right here or there's only one way here, the better you're gonna be ultimately on, hey, actually, there turned out to be a couple of different ways that we could have addressed this issue or that we could have built this program. And so I do think that's important is not to come lock yourself into one way, but think, all right, let's take a beat and say, hey, could there be another way we could have thought about this?  I think both different perspectives. What's come out of a lot of these interviews is that diversity, inclusion, and equity brings more power functions. It's a step function in value, right? It's a competitive advantage too. I mean, if the data is becoming clearer and clearer that more diversity, more inclusion, more equity brings more power to the conversations, more, and products. And this is proven. How do we get there? As you're a senior leader now, you've got the helm at AWS on marketing. You got a lot of influence as you go through your career. How are you going through that progression of keep driving that positive mindset, that change? Mm-hmm. I'm really, I love my team. When we sit down and talk about conversations, what I always try to think about it is, let everyone else speak first. Like, I don't wanna be the first person to comment on something, right? I always say, hey, let's hear from everyone else first. Because then I think people feel free to kind of share what they think. And I always do kind of look around and in my head just think, okay, have we got the teams here that we wanna make sure we're including in the discussion, right? So kind of just saying, oh, we're gonna roll out. Hey, we have a new idea for our marketing program. Who's gonna, for all of our customers, great. It's a global program, great. Do we have global representation? Great, if we don't, hold on. We need to pause for a second. We're thinking about new messaging positioning. Okay, great, for our customers. Who's here to talk about it? And we have marketing representation. How about PR? How about the engineers to your point? But just again, I think the more diverse we can make that conversation. If I'm in a room and I'm like, oh, there's only a few of us and we all are going to have the same frame of reference for this conversation. Let's make sure we get some other folks in the room. So it's not just us with one set of context.  You guys have been so successful at AWS and Amazon. AWS in particular, its results. You look at, just go back to our first Cube event there in 2013, just enormous success. And you've got such a diverse customer base. It is global.  That's the statistic in the customer base in general. So super important. And this is really a big deal. So I have to ask you, as you're the leader out there of AWS, you're an inspiration to many out watching. For the young folks out there, the young girls and young women out there who are going into their careers and thinking about tech, whether they're in early school or getting into the career path, what advice would you give them around how to be successful, how to find mentors, how to be a good citizen in the community and how to contribute and how to move forward in a very positive way? When we started the conversation a couple of minutes ago, I mentioned finding your voice. I think that's really critical. I think find your voice, use your voice. I know that sometimes, you know, early on, you know in my career, I was maybe nervous about asking questions but ask the questions. I think that the more questions you can ask, very oftentimes you'll ask a question and someone else, a bunch of other people in the room are like, oh yeah, I would have asked that question. I think that, wait, you know, I'm super proud of my leadership team. It's a 70, 30 split women, yay. But I definitely think look at who you're surrounding yourself with, think about your mentors, think about your team, think about your community and just kind of, you know, ask yourself, hey, how can I, you know, have this be an even broader community and even more diverse community? Because having that, I think, is just gonna help make whatever comes after it that much better. And so I think that would be my big advice is just, you know, learn and be curious. Like I said before, ask a lot of questions but definitely find your voice and share that voice with your community and make that community as sort of as broad as you can. Rachel, thanks, that's great insight. The word community resonates as all my interviews here on this International Women's Day all comes back to community and being part of something super important. Thank you so much for being part of our program and our community. We really appreciate it. Thank you for your time and insight and your mentorship and also your insights here on theCUBE, we really appreciate it. Thank you so much. Oh, thank you, John. This was really great. Thank you for having me. Okay, this is theCUBE's presentation of Women in Tech's global event, celebrating International Women's Day. More content coming. Stay with us for more. I'm John Furrier, host of theCUBE. Thanks for watching.


Hello everyone, this is Amit Dan and on this channel you can find financial travel and more videos if you like what you see Please do the thumbs up and consider subscribing. Thank you Hello everyone, this is Amit Dan of amitdan.com. In the past I have done several videos on Chromebook and today I'll show you how to do screenshot on Chromebook. So the first thing you're going to do. So let's say You'd like to take a screenshot from a website. So I'll go to amitdan.com website. So once we have that website up or You can take a screenshot of anything basically what is on you know, what is on the screen or visible So there two ways you can do the screenshot Let's say you want to take a screenshot of the full screen You don't want to select anything then hit the control button which is right here and then hit the window Selection key which is right here So let me just show you this for buttons again. I'll keep the Chromebook a little bit closer So here's the control and here's the window switch or window selection key right here Okay, so here's the control and then you hit the window selection key And then it took a screenshot right away It was very fast which is right here and then if you want to open up the screenshot Then here's an option a show in folder. You just click on here or you can click Copy to the clipboard. So I'll show you just where show in folder. So let's hit show in folder And then this is going to take you the your downloads a folder where all your downloaded stuff And then if you just click on it Then you can see that, you know, it took a screenshot of the screen. You're looking at which is right here Okay, so I'll close this and then I'll actually delete this one from here and then I'll show you The next one where you want to select Some parts of the website or the window. You don't want the whole thing. So you do Very similar but instead of just control and window selection you have to hit control shift and Window selection button all together. So again here control shift Together and then window selection and then you'll see that the Screen became slightly darker. Now it's giving you the option to select So what you do is on your keyboard you press on the left side and then you just select The part or parts you want to Take a screenshot out. So here it's selecting only this part. So I'll just let it go From the keyboard. So I was just in holding it here to select that part. Then once I remove my finger, then you'll see that you get the same Smaller window showing the screenshot has taken and if you go back to the folder again Then you'll see that It's located in the downloads folder and if I open it up Then here is your screenshot So I'll just go ahead and delete this one too and Basically, that's how you take Screenshots on Chromebook If you like what you see, please give it a thumbs up and subscribe. There will be more videos coming up On this channel. So I'll see you shortly. Thank you