One of the most remarkable archaeological discoveries of the year, researchers have just ignited a major debate regarding the cone as depicted in many dynastic depictions from the time of the pharaohs. Elongation of the skull was and still is a widely practiced method of cranial deformation, something that has widely been accepted as deliberate deformation despite a few cases when the skulls do not show any signs of adjoining or sagittal suture ends that seemingly show that certain people in society grew like this without any doctoral design. Now if the king or queen of the land had this feature and it was clear to the subjects of the royal ruler that this was the case then isn't it likely that the people would attempt to copy and of course this led to the process of cranial deformation because the people wanted to look like their leader and in Egypt this has caused great concern and confusion if the people were simply copying something on a massive scale then the thing they are copying from must have been real, something like that anyway. The latest discovery that relates to the ancient appearance of these people delivers a great insight into their way of thinking and indeed all across the ancient lands of Egypt we see depicted in reliefs and hieroglyphic inscriptions scenes of the great monuments in the life of the great rulers and occupying these scenes are beings with huge skulls unlike anything in existence today in these scenes the cone is well documented and this would probably have triggered a type of fashion frenzy to look like the royal leader would surely be a great honor and this is probably why it gained a lot of traction before eventually fading into the darkness the trend in this way probably immortalized in the strange head cone depictions nobody really knows what the strange cones represent but it is possible that these strange objects that appear in paintings and wall carvings are a representation of the cranial deformation and they have been confusing experts for years some even saying that they are a representation of a cataclysmic volcano episode some have even speculated the cones were merely symbolic until now researchers investigating the strange cone depictions have come up with a startling discovery they have physical evidence that these things were in fact very real and this throws the integrity of previous explanations into serious dispute for too many ages now the so-called experts in the positions of education have called out the ancients as mythical fantasies why would the ancient people lie would it not make more sense that they were actually depicting things that did happen rather than making it all up archaeologists made the discoveries at armarna one of the ancient egypt's most unusual cities the site was occupied for more than about 15 years during the 14th century bc while egypt was under the rule of the pharaoh who gave the location its name Akhenaten he developed a short-lived religious system focused on the worship of a single god represented by the sun and this king fathered to in common the team could find no chemical evidence from the well-preserved grave that the headcone had melted and dripped onto the occupants hair and this totally undermines the leading hypothesis about the cones that they were perfumed lumps of ungwent that slowly melted in the sun to perfume and cleanse the body both literally and spiritually the idea is that by melting and cleansing the hair the cones might have richly purified the individual placing them in an appropriate state to participate in rituals but in this new grave site that confirms the existence of the cones no such connections can be made reporting in the journal antiquity a team led by anna steven of australia's monash university unearthed two real-life head cones and graves at the archaeological site of armarna in egypt head cones it appears did exist and at least in some cases they joined their wearers in death speaking about the recent discovery carina roge a conservation scientist from the museum of fine arts houston and an authority on the study said it was very satisfying to finally be able to say that the head cones are real an amazing discovery that has been archaeologically confirmed dr carina's colleagues found the first cream colored headcone in 2010 while excavating a grave the second emerged in 2015 from a jumbled up skeleton in a grave that had been ravaged by tomb robbers both graves belong to people who were not elites and the first belong to a woman the cones were hollow measured about three inches tall and just under four inches wide and were made of wax presumably beeswax because the head cones were found within graves the team said the findings provided insight into their funerary roles the obvious suggestion here is that they helped the deceased to be reborn into the afterlife or brought them benefit once there said anna stevens and archaeologists from monash university in melbourne australia and lead author of the study but this doesn't mean that they always served this purpose they may have had multiple roles some archaeologists have argued that the main role of the cones which have been featured on tomb walls from the 18th dynasty around 1550 bc through the time of cleopatra was to act as perfumed ungwants under the intense egyptian heat the scented wax cone would melt into the wearer's hair or wig providing a sweet aroma to the wearer so far the team's findings do not confirm that interpretation and alas hieroglyphics are not easily decipherable they couldn't detect any trace of perfume in these cones but that doesn't indicate that perfume wasn't once present in these cones or others wouldn't you want a fresh cone for your burial as opposed to one you had already used the interpretation has arisen partly from depictions of anointing rituals using oils and perfumes sometimes in scenes that also show cones being worn and partly from observations of how some modern african groups apply animal fat to their hair a few scenes show apparent ungwant cones on stands or in bowls including during production or the process of being placed on the head ungwants were generally thought to purify the ancient egyptian wearer placing them in an elevated state of being when in the company of a divinity or death as the justified deceased scholars often link the cone specifically with sensuality sexuality and related notions as they are frequently associated in imagery with women sometimes unclogged the cones also appear in banquet scenes and other contexts that involve divinities such as the fertility goddess hathor in tomb scenes they are often read as sensual motifs associated with the rebirth of the tomb owner who is usually male they have also been interpreted more broadly as symbols of the tomb owner's contentedness his status as a justified spirit in the afterlife it is suggested that the cone sometimes represent the ba after it had received divine offering the ba formed a person's vital power and was especially important after death when it could move from the grave and interact with the living it was proposed of the purpose that when shown to living individuals the cone indicates the active state of their ba which allowed them to interact more effectively with divine figures in the absence of any convincing examples of head cones from archaeological context scholars have questioned whether the cones were ever produced as three dimensional objects or were instead entirely symbolic of anointing or beautification rituals or of more abstract ideas however the recent fieldwork at the location of the late second millennium bc city of amarna interestingly has now identified two cones from non-elite graves diffuse reflectance infrared Fourier transform spectostropy indicates that their primary component is most probably a biological wax these finds confirm that the head cones exist in a three dimensional form and provide two important examples of their real life use during the time of the dynastic Egyptians it is conceivable that the two cones were model versions made for a burial environment and that cones intended to be worn by the living could have been constructed differently there is no reason to assume however that hollow or perhaps textile lined stuff cones of wax were not also worn in life even if scented they may not have been intended to melt in mass and moisturize serving more to mark the wearer as someone who was in a purified protected or otherwise special state but what do you guys think about the confirmation that dynastic Egyptian cones for purposes of wearing on the head were in fact real what do you guys think they were for comments below and as always thank you for watching


So science tells us that there are numerous benefits of sleep and we're finding out more and more about sleep all the time. So we know for instance that sleep is essential for your immune system and the way that you fight diseases. So if you have a good night's sleep you're very much less likely to get a cough and a cold in the flu. We know that it's essential for your metabolism, so the way that your body uses calories and food. And particularly related to the way that your body senses whether it's hungry or whether you've had enough to eat. And so keeping a good sleep schedule is important for your health and wellbeing from the perspective of keeping a healthy weight. Mental wellbeing, so particularly your sort of emotional state and keeping an even emotional state is one of the key benefits of sleep. And often when you're tired and irritable it's the people around you who notice and you tend to lose that little bit of insight when you're tired as well. So actually making sure that you have sufficient sleep so you wake up feeling refreshed and restored is very important for your mental health and wellbeing. And talking about the brain for sure memory is a dynamic process which is some memories of prunes, some are consolidated, some are dealt with and some linked together through the different phases of sleep. Difficult memories are dealt with during sleep as well. So we know for all of those reasons that sleep is essential for your mental health from the perspective of memory. And then this is concept of flushing out toxins from the body and from the brain. And this is a relatively new concept over the last sort of five years or so. And it's a little bit like having a sandy beach strewn with rubbish. So the tide comes in and it sweeps away all of the rubbish and you're left with a beautiful sandy beach again. And the same thing is true for the brain, the sort of funny proteins and toxins that build up during the day are washed away during sleep at night time. So there's very many reasons why sleep is essential for you. And it's not just the absence of wakefulness as we used to think it's actually an active dynamic process where the body rests and restores, rehabilitates and prepares you for an active day ahead.


Over this past weekend Roger Federer, the former world number one and 20-time Grand Slam champion, was approached by a super fan at a restaurant who's sporting a tattoo in tribute to the former world number one. Here's what Federer's reaction was. The tattoo actually said there is no way around hard work embrace it which was a quote that Federer had said over his career and this man was so inspired by that quote and by Federer himself that he got a tattooed on him. Do you have any tennis tattoos? Let me know in the comments.


Cancer stem cells, CSCS, are a small population of cancer cells that have the ability to self-renew and differentiate into multiple types of cells. They are thought to be responsible for tumor initiation, progression, and metastasis. CSCS are able to adapt to the environment around them, which allows them to survive even when exposed to chemotherapy and radiation. This makes them difficult to eradicate completely, resulting in tumors returning after treatment. CSCS also play a role in angiogenesis and metastasis, two processes that allow cancer cells to spread throughout the body. Understanding how CSCS behave and interact with their environment could lead to new treatments that target these cells specifically.


Hello everyone. I'm going to talk about how to succeed as a product manager for almost any product. I'm Siddhartha Langevan and I'm currently a Senior Technical Product Manager for Amazon Web Services. A little disclaimer here. All opinions are my own and does not represent any of the current or previous organizations that I've worked for. About me. Who am I? I'm from a city called Chennai in South India and I did my undergraduate from College of Engineering D&D in Electrical and Electronics Engineering and I completed my MBA from Arizona State University. So during my time at ASU I co-founded the Product Management Club outside of work. I'm into photography, drawing, designing and also I love motorcycle riding. I'm a member of Iron Butt Association where you have riders all over the world doing grueling rides in their motorcycles. Let's talk about my journey into product management. I'm basically a creative person. As you could see from the previous slide I'm into drawing and designing stuff and I'm also a strong empath. According to the Myers-Brick personality types I come as an INFJ meaning somebody who's introverted, intuitive, feeling and judging personality who's strong in intuition and empathy. So these qualities kind of helped me in designing delightful user experience early on in my career. So slowly over time after designing all these user experience I now became product owner where I was not just doing customer experiences or user experience I was translating user stories into product features. Over time or after my MBA I now moved into a much bigger product management space which is defining the problem spaces and not just defining problem spaces but also prioritizing the problem space or the opportunity space and how to solve them. In today's webinar I'm going to touch upon roughly three major topics. The first thing that's the heart of the product management of any type is knowing your customer. And next we'll talk about how to break things down to a bare minimum which is also known as the first principles thinking. And finally we'll talk about how we can as a product manager you can empower and influence the internal stakeholders. Knowing your customer. So the first question when you start as a PM in any company is to ask who's your customer and what is or what are their problems. So there are various ways to do this and let me talk about the different ways that I've come I've experienced with. So the first is understanding whether your customer is an enterprise customer also known as the B2B or the business to business or whether is your customer a common person like you and me also known as a consumer or the B2C the business to consumer. So a small difference between a B2B and a B2C is a B2B or the enterprise customer typically has a sales team or a CTO or a CEO who's going to make the purchase decision.  So in a B2B you can categorize your customers as who's making the purchase decision and who's going to use your product. Whereas in a consumer space your customer and the user are pretty much going to be the same. For example I'm a user of a Spotify and I also make the purchase decision of whether to upgrade to a premium subscription or not. The next thing when you come to learning about the customer is that understand what their behaviors are. Like what did they do in their day to day life. So in this space or in this part of knowing your customer I always suggest that the behavior trumps demography. So what does demography mean? Demography is roughly categorizing the user persona as somebody who's a male or a female or somebody who falls under the age category of 10 to 20 or 20 to 30 or whatever.  Those come under demography. So this is not a very strong way to segment your customers or understanding your customers because users from the same demography could have different behaviors. So that's why it's important to understand customers based on their behaviors. Like what do they do when they wake up in the morning? Or what do they do in their job? Are you dealing with a technical customer persona for a BW space? Are they, you know, for example, database administrators or is it somebody who's a developer who sits in code or are you talking about somebody who's, if it's in the consumer space, are you talking about, are you thinking about somebody who's just started out their family who has one or two kids, etc. So always knowing that behavior helps them understand the needs or the problems that they are facing. So that put that transitions us to the next thing is knowing their goals or needs. For some you for a particular person with this behavior, what are their goals or what are their needs? Understanding that is very important to know how you can solve their problems. And the next thing is also very important. Start tracking the problems. Not all problems are weighted at the same level. Different problems are of different sizes to the users. Some may be small, some may be big. So it always helps for us as a PM to understand what's their biggest problem so that we can solve that first. And the next thing is understanding whether your your solution or the problem says that you're going after is a painkiller or a vitamin. For example, a painkiller is something that the customer cannot live without the customers in pain. So they need to take this painkiller to get rid of the pain versus something as simple as vitamins. You know, they can or they might not need it, but it will be a nice to have. So what sort of a problem are you going after? Are you? Is that problem something really a pain for the user that want to solve? Or is it some sort of an experience enhancer that your customer can still live without? The next part in knowing your customer is what are your customers currently doing and what alternatives do they have? So in this slide, it's about competition. It's understanding who are your competition. For example, you might be in the food delivery space. And the first thing that you can think of competition could be like companies like Uber Eats or Dodash or it could be Swiggy or Zomato or any food delivery companies. So understanding who your competition is is a very important thing in this step. Also, the next thing is understand why your customer is using that particular competitor's product. This means that understand what are the strengths or what are the weaknesses of that competitor and why is that appealing to that particular customer persona? Another area that you can consider as a competitor is also the DIY solutions or the do it yourself. So going back to the food delivery example, you may think Uber Eats or Dodash is your competitor, but you could also include the fact that there are some people who prefer to go to the rest, walk to the restaurants by themselves and get a takeaway or a two go. So include that in your competition analysis. The next thing in knowing your customer is where or how you can learn about your customer. So we spoke about understanding your customer, their personas, their goals, needs. And then we also spoke about understanding the competition and what are the different options that they're using, et cetera, et cetera. But how do you get this information? The first thing that I like to do is check on social media, whether it is an enterprise app, or even if it's a consumer app, check on social media, such as platforms, such as Reddit, Twitter, LinkedIn, you find a lot of data or sentiments about what common people is talking about your product or in this problem space. So a lot of people have conversations about this feature would be nice or I still face this problem. Currently, none of the options give me this feature, et cetera. But so social media is such a great place to scout for information, to learn more about your customers. Also, comparing the B2B versus B2C space, it's easier to get face time with customers in a B2B setup than a B2C setup because in an enterprise world, you know your customers by their name, you might be having a relationship with them, the sales team, or the purchase decision maker. So for consumer apps, I would still say leverage social media to learn high level sentiments and feature requests to formulate your initial as hypothesis that, you know, these are the needs or these could be the potential solutions that you can use to solve their problems. And also, quantitative data is also equally important as qualitative data. So you might understand what you might learn what customers are talking about, what they feel, all those things are qualitative data, but quantitative data, such as funnel analysis, funnel as in right from the time where a user signs up into an app until the final purchase is done or a final order is placed that the complete funnel analysis or heat maps for conversion ratio in an e-commerce industry, etc. All these quantitative data also helps. So now that you've learned about your customer and their needs, what's the next thing? The next thing is to come up with our think of solutions to solve their problems. And one of the easiest and quickest way to do that is developing the first principles thinking. So what is the first principles thinking as a quick introduction? It's, it's something where you break down things into the bare minimum, like then there's no complex dry complex things involved in the equation is just that what does what do you need to do in order to solve your customer's problem in the most simplest manner. So some of the key areas you can focus is talking on the biggest problem or the opportunity that your customer would like to have it solve first. So your customer persona might have like different problems varying by different sizes of the problem. So as a PM, it's on us to prioritize what's the biggest problem or the opportunity you want to solve for your customer. So the next thing is prototype that minimum lovable experience you can provide for your customer to solve that problem. So by prototype with it could be something a rough sketch on a piece of paper or it could be using tools such as balsa make or envision. It's just about converting your ideas into us into a sketch so that you can convey to your different stakeholders or your even your potential customer. The next thing is probably a very important step in this solution I think which is hypothesize and validate using experiments. You improve the prototype and then repeat so that you have the continuous feedback loop to improve your solution. So you have various options and experimenting such as a test, heat maps, final analysis like I spoke on the previous slide and all that. Another thing is when you're trying to come up with prototype or when you're thinking of solutions in a very creative way, understand your constraints. For example, your engineering team might have a certain skill set. They might not have certain skillset or your teams might be working on already other priorities or your company can only focus on certain strategies that by the leadership and has decided that they might they won't do certain things. So understand your constraints and try to work around that. So now you have understood your customer. You have used first principles thinking to break things down to bare minimum. And you have a rough idea about what you need to do to address those problems. And what's the next thing that you can do to succeed as a PM for almost any product. And this is equally important as understanding your customer, which is how you can empower and influence the internal stakeholders.  First thing, product management is not something that you sit inside a cubicle or inside a room and work in silo. It's a very collaborative process. So invite your designers and engineering friends to the party. So whenever you are trying to ideate or brainstorming a solution for a problem. I invite the designers and the engineering friends to the ideation session so that you can get the best ideas out of everyone. And you can deliver the best solution possible to the customer. Of course, as a PM, you own and you facilitate those discussion, and you ensure the quality of the decision made. But it's not always necessary that you should come up with creative ideas. Ideas can come from anywhere in the company. And as a PM, you're responsible to nurture everybody comes up with ideas so that as a team, we solve the problem for the customer in the best way possible. The next thing is as a PM, it's our job to reduce ambiguity and drive clarity through strategy, setting goals, preparing the roadmap, coming up with success metrics, and also the counter metrics. So this helps in influencing the leadership and informing the your engineering counterpart and the sales team, everybody to align on your vision of what you think makes the best sense for the company to work on and also provide the best value to your customer. So the next thing is, don't forget your marketing and sales, or, you know, the field or go to market friends. So they are your proxy for the voice of the customers. Often at times, even at situations where it's difficult to directly get in touch with a customer, the sales or the marketing teams are in touch with the customers and they act as a proxy for the voice of the customer, they know what the customer needs and they might be easier to reach than the actual customer. So definitely listen and empathize with your marketing and sales team. The next thing is empathize not just with the customers, but also your internal stakeholders. And when I say that I mean, get diverse feedback from them. Like when you propose an idea, when you propose a strategy, always take the different feedback that you get from the different teams, everybody has their perspective and the engineering team will have the technical perspective, the leadership team will have the business strategic perspective. So it's very valuable to get everyone's feedback. And as a PM, you decide what feedback makes sense and what feedback you can ignore. And also understand the challenges and priorities. Like every team has got their own priorities. Every team has got their own challenges. And every team has their own goals. So understand that they already have all those things. So have empathy when you're working with them. So to summarize, whatever I spoke. The first thing is being curious and have the willingness to unlearn and learn about your customer, their problems. And what are the different ways you can solve their problems. And the next thing is developing the first principle thinking, where you break down things to absolute bare minimum, to understand what is the best way to provide, or what is the most quickest and simplest way you can provide the best experience to your customer. And next thing is empower and influence your stakeholders. Make sure you you you are the person to drive clarity in strategy, inform the engineering team, what to build, and make sure you educate the leadership about what the customer needs. And finally, have empathy towards your customer, and towards your internal stakeholders. So I would like to conclude this webinar with this code. I mean, this code is actually mine. So Rockstar product manager creates an illusion of obviousness with the leadership and team so that they continually continually know when and where to invest and what to work on so that they can deliver continuous value to customers and generate sustained profits for the company. I hope you enjoyed this webinar. Thanks for your time. And you all take care. Thank you.


Action Jackson asked okay he asked me why do I consider aliens and the abyss movies epistemological now You know this is a I'm answering a question for people who've actually seen the movies So I hope you've seen them so aliens is Is a movie about this? Really really particularly the second right the second But the aliens franchise is about this really really really spooky Horrifying Alien and an alien is particularly horrifying because it is parasitic and is parasitic on the human body.   I don't know what it is, right? But in a sense that its effect on your life is evil, right? That which harms human life is evil It is evil it destroys human life and it grows and it's almost impossible to kill and it's just this amazing Monster that actually it wasn't a camera who invented but it was the guy who was the director of the first alien Another famous director. I apologize for having a abysmal memory But anyways, you've got this alien and then in the movie aliens You have a team of marines Sigoni weaver who is the only survivor of the previous encounter with it these aliens Which was the first movie alien and a corporate guy and it by the way, the movie is very anti-corporation So it's anti-business in that sense and usually I'm not usually I'm not I don't like movies that anti-business But again because the theme here is epistemological. I don't mind the anti-business side of it so You've got this whole crew then and every one of them Deals with the situation in a different way Every one of them has to figure out how they're gonna survive. So some of them Panicked they die very quickly They're just some of them are consumed by fear They die very quickly The the corporate guy wants to find a way to manipulate the situation, but he evades Essential aspects of reality. He evades the true nature of this alien and the threat that it poses Ultimately dying The only people to survive there are two people basically other than you know, there's kind of a robot But the two people who basically survive one is Sigoni weaver and The beauty of the movie is the Sigoni weaver is super-rational But not just implicit the rationality is not just implicit Who I found these explicit she constantly during the movie says Let's stop and think let's figure this out What should be our next step? How given the nature of the alien? How do we deal with it? How do we take a next step in order to defeat it or in order to you can't really defeat it But how are we gonna survive? I'm gonna save the lives of the people I care about in this group and survive It's a constant issue of mind never evade Never look the other way always deal with the facts as they're in front of you and have the courage and the rationality To focus your mind on a problem and try to say to figure it out in Sigoni weaver in that movie is one of the great great heroes in action movie Because she's so explicitly Rational Now the other character who survives with Sigoni is a marine and The reason he survived is he figures out very early that the only way he's gonna survive is That he attaches himself To the smartest and rat most rational and most experienced person which is Sigoni weaver He watches everybody else act irrationally and he identifies the fact that they're all completely irration and He says if I'm gonna face this enemy if I'm gonna face this evil from gonna survive this Sigoni weaver clearly has the most information clear as the most knowledge and clearly is rational I'm just gonna I'm gonna attach myself to her and I'm gonna do what's necessary a for her to survive and Be for I'm gonna follow her orders because she knows what she's doing and nobody else knows what so he identifies Again conceptually Again, what's what? Puts the fear aside because they're all fake puts the fear aside uses his mind Focuses and deals with reality as it is So that's alien and it's a constant movie where you're constantly in fear It's like a horror movie, but I think a very very sophisticated horror movie and it's the action is fantastic The suspense is fantastic, and I think at the end of the day who character is is amazing. I mean


What's good y'all it's your boy Ross back again with another video. So we got to talk about Roman Reigns on his uh recent promo on uh this past Friday night smackdown He uh teased himself leaving WWE now there has been some reports of him talking about it on different shows in the past few months like different podcasts or whatnot in the past saying that he does eventually plan on leaving WWE and wants to get into Hollywood wants to get into acting which I don't think it's a surprise to anyone I think a lot of people can kind of see Roman doing that following in the footsteps of uh the Rock following in the footsteps of John Cena and of his recent transformation of his character I can see why maybe potentially studios are interested in this version of Roman Reigns because one he has to look to the lines that he's been given it sounds more like him sounds more believable he sounds authentic on the mic and I think that's what's gonna probably drive some studios and potential directors to want to check him out see what he can do in a movie setting granted he was in a movie with the Rock uh I believe it was that uh spin-off that Fast and Furious spin-off with Jason Statham I could be wrong but he was in a movie with him so he has some experience and I think that's where he ultimately wants to take his career after the wrestling and with this recent promo that we had on Friday I did watch I just didn't uh record it to a reaction to it he was like yo once I'm done you know I'm saying once I'm done uh wrestling man the whole world's gonna have to acknowledge me and I like that I like the fact that he's pretty much saying yeah man once I'm done doing what I have to do here the whole world's gonna acknowledge me the whole world's gonna acknowledge my gifts and my talent so it'll be interesting to see how soon that will take place I'm sure he will finish out his contract with WWE but the real question and the real question that WWE management should have probably been I guess asking themselves who's gonna be the next guy to take over for Roman that should have been a question for months now that should have been a question last year they've been planning to have Roman on this amazing run but you gotta find someone to either A beat Roman and then B become the next guy especially for SmackDown because without Roman who do they have some people can say oh they have Drew they have Brock Brock is a part-timer I don't think a lot of people want Brock realistically I don't think they want Brock to just win the title and if you do you gotta be you gotta be tripping you don't want him to win the Universal Championship because you're not gonna see the belt he's a part-timer and we drew um he's not as over as he once was so I don't know if the fans really gonna be that receptive to him being the top guy on SmackDown when he was just a top guy on Raw so I'm not sure how that works anything can happen from now until when Roman actually does leave or when his contract does in but I just don't see Drew being the guy I just know now I do follow JD from NY if y'all know who he is he's a big one of the bigger YouTube creators wrestling YouTube creators on his platform and I was watching his latest podcast and he was talking about it and he brought up an interesting point which I could see WWE doing this he brought up the fact that if there's no one for Roman to beat right now I think well what he said was he should probably retire the belt well not retire the belt but like relinquish the belt kind of what Oscar did no one can beat Oscar in NXT but she came to the main roster she forfeited the belt the same thing here if no one can beat him they don't have anyone to beat him before he leaves to go to Hollywood just have him relinquish the belt I've done it all I've beaten everybody no one can beat me I'm going to you know do movies now here's the title that I can see them doing that also here's another thing that they could do and JD also mentioned I think a lot of us have thought about this but we know WWE is not going to do have Walter be the guy it makes sense for Walter to be the guy to defeat Roman if you look at it the title reigns were were hella similar he has a faction Imperium it makes sense and he's a heel but he can legitimately beat your ass it makes sense Walter would be the perfect fit but we know WWE is not gonna go the route of making sense they're gonna go the convoluted way and I don't think Walter will ever really get that chance he would be the only viable person that can do it I'm being serious he's the only viable person that could where it makes sense storyline for him to beat Roman he has backup he he has that that that championship like figure the dude is brutal as hell it makes sense comment down below if y'all would love for Walter and Roman the Imperium Imperium versus the bloodline to go at it can you it makes is the match itself those matches itself just is perfect comment down below if y'all would think he would be a nice successor to Roman Reigns once he went to Hollywood because I think he would I think that's the only person on the WWE roster out of NXT Raw and Smackdown I think that's the only person that can do it that's the only person that can get the job done and it makes sense so um yeah man I don't know I do think if they can't if they're not gonna use Walter and they don't have anybody else I do think JD's idea is it's plausible it makes sense have them have them relinquish the belt he's leaving he can't defend it have them relinquish it he'll go down as the greatest Universal Champion of all time probably go down as one of the greatest WWE champions modern day no one beat him no one took him down no one could stop him and he's going to go do movies now it makes sense since they haven't booked anybody else and this falls on WWE because the end of the day out of all the errors of wrestling when we knew snow cold in the rock we're gonna hang it up gonna do other things we were good because we had other talent we had other talent that could take over we had the John Cena's we had the Batista's we had the Randy Orton's we have a new fresh Brock Lesnar we had the Eddie Guerrero's we had these talents that could take over when these guys are done we had it and that's because they built these guys up because they were already stars now we're in a situation where WWE hasn't taken time to really build somebody believable so when Roman does inevitably relinquish the title loses the title who he's gonna lose it to who you haven't built nobody up that's believable I was hoping they were gonna do something with King Xavier Woods but he's been he got him over here crying over a fake crown you got him over here getting destroyed by Bobby Lashley in the men's survival series match I don't care him win that tournament doesn't mean a goddamn thing and things can change we've seen it with Daniel Bryan we've seen it with Kofi sometimes you can have a fantastic string of matches where people get behind you and you can create a potential new start from that it's just it depends on WWE's booking you can tell WWE has put in all the creative juices into Roman Reigns all that creative talent is going into Roman Reigns everybody else we'll see what we can come up with you am I lying am I lying and that's the problem Roman is fine you need to worry about the rest of your roster you need to worry about the rest of your company because once he leaves which he's made it very clear on his last promo that he ain't gonna be here too long now what are you gonna do they'll throw millions of dollars at Roman but I'm sure he will go do movies he'll be on a part-time schedule and that's just what it's gonna be so I don't know comment down below let me know do you guys agree with that if he does end up leaving that he should probably most likely just relinquish the title because they haven't built anybody else up to to take take the belt from him or do you think he should drop the title before he leaves at any point to somebody and who would he drop the title to my pick would be none other than Walter himself that would be my personal pick but who do you guys have and it gotta make sense someone believable that we can be like oh you know where it makes sense for Roman to drop the belt to him because to be honest with you he's damn near beating everybody so I would love your thoughts and opinions on that appreciate our love and support road to sandy k appreciate y'all kicking with me see y'all on the next one peace


Hey everybody! Hello out there! It's the end of month once again and you know what that means. It's time to welcome you to another edition of JSA's Fast Forward. Thanks for joining us as we broadcast live online via LinkedIn and YouTube and through our very own JSA TV newsroom. I'm Dean Perrine, Executive Vice President at JSA. And I'm Jamie Scottokataya, Founder and CEO of JSA. And today guys, get ready, we are going to be teaching you the ABCs from the world of tech telecom and data centers. That's right. We're going to hit all of November's best headlines on JSA's Telecom News Now blog from A to Z. From AI to Zettabyte. And from Access Points to Zipfile, I guess. Okay, you got it. Let's go ahead and kick things off. We're starting at the very beginning. A is for Asia, capacity Asia, that is, which is happening right now. It's APAC's most senior connectivity conference going on in Singapore. JSA is there on the floor with our senior account director, Ms. Jennifer Spano. So make sure you say, Jen! In our November news alphabet, A is for Asia and B is for billion, as in one billion dollars. That's the price tag for Prime data centers is new Chicago data center campus. B is also for breaking ground, which they just did to begin work on the construction project, which is set to become the largest facility in the Chicago land area at over 750,000 square feet. That's right. 750,000 square feet. That's pretty impressive stuff there. Yeah. Yeah. That's a lot of square feet. And funny, you should mention Chicago, Mr. Dino, because that's the word of the day for letter C on our show. A, B, C. Easy as one, two, three. Simple as don't rate me. A, B, C. Easy as one. No, baby, you and me. Sing a J. Get it. That was perfect. I'm so sorry, guys. I can't do any of that. Anyway, sorry. Moving on. So we debated which one of us was going to be the Jackson Five, and I think that we decided that you were going to be Tito and that I would be Janet. Okay. Yeah. All right. So what are we talking about again? I don't know. Chicago, I think. Chicago. Chicago. That's right. C is for Chicago, guys. So while Prime data centers is just breaking ground in Chicago, T5 data centers just finished their project, recently completing phase two of their Chicago Two data center, which is now open for business. It's the only facility with 20 megawatts of available space right now in the market. So get it while it's hot. That's right. So let's move on to the letter D now. It partially stands for Dean Perine, who recently announced that he has achieved the perfect ratio of peanut butter to jam on a sandwich. And I'll give you a hint. It is making sure that it is exactly the same amount, peanut butter to jam. Gotta have it this way. No way. No way. You're going to have more peanut butter and stick you. Anyway. All right. Perhaps most importantly for our industry, D also stands for Data Bank, of course, who recently announced the completion of its migration of four Houston area data centers to their edge co-location and interconnect platform, formerly owned by Cyrus Won, these freshly functional acquisitions add 42 and a half megawatts of available power to their services in the region. Well, congrats to us both then. We are now at the letter E and E stands for entrepreneur. It's easier to say when you aren't thinking about it. Entrepreneur of the year, in fact, Fyre Sense founder and CEO Mark England has been awarded the entrepreneur of the year award by Australia's Percy Foundation. The award recognizes an outstanding entrepreneur who is making an impact both locally and globally. Well done, Mark. And I will work on saying the word entrepreneur for our next fast forward. Yeah. And so well deserved. So well deserved. Mark is incredible entrepreneur. The E word. Okay. So now we're moving on. All right. All right. To the letter F where I know Mr. Dean will make some F word jokes.  No, Jamie. Jamie, come on now. I am a serious mature fellow. So I would never do anything like that. I'm waiting. Okay. The F word for today is five stars. Oh, okay. That's a good one. I'm keeping it above board today, Jamie. So after fast forward, we can drop some F bombs. Okay. Our friends that light path recently scored a five star rating on the 2022 global real estate sustainability benchmark report, something that I know is near and dear to your heart captain. The rating is a reflection of sustainability benchmarks where light path managed to achieve a score of 96 out of 100. Well done to our friends that like that. Very exciting. Proud of you guys. All right, guys, we are on to the letter G for grand opening. The grand opening in question is for Data Bank's brand new data center facility in Salt Lake City happening tomorrow morning, December, December, tomorrow, December 1st. Also, it's there six in that Salt Lake City area. So congratulations, Data Bank. And speaking of upcoming events today, H is for Honolulu, the location of PTC 2023 taking place January 15th through the 18th. JSA TV will be there as always rolling out the green carpet in Honolulu with live streaming interviews from the PTC hub. And we hope to see you there. And I love the green carpet sustainability. We love that. All right. Can't wait to see you guys in Hawaii. But right before we need to talk the letter I, which is in this instance, India. That's where next truck just announced construction of the largest data center in Eastern India. The 25 megawatt facility will be located in Kolkata and serve next to his 13 large scale facility in the country. It's not standing. So that's the letter I and we couldn't land on the letter J without tuning our own horn just a bit. J is for JSA today. Oh, yeah. I like that one. Yeah. That's correct. It's also for our friend Yao, Yao with a J, Yao Marquise, Marquez Lima, as he'll be leading a JSA TV live two day event featured across all of JSA social media channels and website next month. Very cool stuff happening there. The interview series will take place on December 14th and 15th featuring thought leaders across Europe on the top of 2023 predictions. Very cool stuff there. Yes, yes, yes. We were already doing some planning today with Yao and it is going to be awesome. So definitely tune in. Don't miss it, which brings us to the letter K for the newest member of the Forbes Technology Council. Yes, we are talking you, Kim, Gonellius. Kim is the CCO and co-founder, of course, of Verne Global Finland. And as an invitation-only council, this is mega cool guides. All members have to be vetted and selected. So great accomplishment, Kim. Congratulations. Yeah, that is awesome. So let's see here. Now we are at ABCDEFG, H-I-J-K-L. We are at L. Or as my daughter would say, L-M-N-O-B, all one letter, L. If you've ever seen my handwriting, you think the same about me, probably. A doctor. That's right. I'm writing my descriptions, everything. Doctor of data centers. Okay, so what's L stand for, Dino? Or do I need to check on my daughter's Sesame Street episode to figure this out? No, I got this. I got this. L is for Light Path, who recently entered the Miami connectivity market with a brand spanking new, all fiber network that stretches over 135 miles. It's significant. It also stands for Light Path's upcoming lunch and learn. Lots of L's there where attendees can learn all about the new fiber option in Miami, complete with a free lunch. Who doesn't love a free lunch? Check out lightpathfiber.com for more information. Love that, lightpathfiber.com. All right, guys, we are on to M now, our alphabet flying by M standing for Metro Connect. We had to major digital infrastructure leadership event, taking place at the end of January, Fault Lauderdale, Florida. JSA TV will be there, live streaming interviews, Dean himself. So make sure you reach out if you'd like to schedule an interview with Dino, live in person, Dino. Who wouldn't want to schedule an interview with me, right, J? I think it's cool. I do too, I do too. And so now we are arriving at the letter N, which stands for new hire. The new hire announcement comes from ConnectBase, who added Rob Carter to its leadership team as chief operating officer this month. So congratulations to ConnectBase, the ConnectBase team, and to Rob Carter. Congratulations on the new position. Yes, great, great hire there. We also got another new hire, Greatness, with the letter O. So that stands for Osin O Merchu, the new vice president of development at Stream Data Centers. Outstanding pronunciation, J, that was great. So good, good luck to both executives in their new roles. Definitely, congratulations, guys. And we are wishing you a prosperous, productive future and present and past and probable projections too. Dean? I hope prestige and purpose are on their path wherever they pass. Dean? Not to mention profit and prosperity. Oh, Dean. This message is brought to you by the letter P. Oh, what is it?  Okay, just get over it before you all start talking about picking peck of peppers. Pick of pepper pe- P is for power partners. As in inks inaugural power partner awards, that were just announced. The awards recognized B2B organizations across the globe that have improved track records of supporting entrepreneurs, there's that word again, that helps startups grow, including on the list where our friends at Involta. Congratulations. Yay, yay. Now we're on to the news. Involta makes waves this month by announcing a live digital data center tour in partnership with our friends over at Data Center Dynamics, called the Enterprise Edge broadcast. I love that. The tour of their Ohio facility will also feature panel and live Q&A session. Sounds fun. It does indeed sound fun. And speaking of Q&A, Q is for Quebec, Montreal, Quebec to be specific. That's where our friends at Cologix expanded their Microsoft collaboration this month, adding a fourth Azure Express route on ramp in Montreal. This is in addition to some other news from Cologix this month, announcing the expansion of Cologix Access Marketplace, a virtual connection platform into the company's New Jersey and Silicon Valley data center. So that's going on there with our friends up north at Cologix. Congratulations. Oh my goodness. And if you're just joining us, by the way, I see you all in the chat. Thanks so much for those messages. We love you guys. We appreciate the kudos. So the P highlighting. But if you are just joining us, we are going through each letter of the alphabet with a great story for each letter. Thanks to our writer and right from the pages of our JSA blog TNN over the last month. So thank you guys. And we made it all the way to the letter R right now. So Dino, go ahead and take it away. Okay, I'm just glad there are no more peas. Okay, R is for recertification. This month, Light Edge announced recertification for a total of 10 compliance standards, including SOC one, two and three, as well as ISO 22301, a new certification for them. So congratulations to our friends at Light Edge. Yeah, and Candace just said the power of Perrine. And S is keeping his train rolling. S is for SAS, of course, software as a service guys. The news is around the SAS offering by Connectbase, who rolled out another product update this month. Amazing. This platform is called Connected World. It can now perform right-of-way near-net analysis automatically, guys. That's pretty crazy. This means users can just identify serviceable locations, narrow fiber route easier than ever before. Pretty cool. Wish I had that when I was over at Telex. This is a game changer, what's going on over there at Connectbase, and they're getting so much, much to recognition for that SAS platform, so I'm good on them. T is for title in particular, the title of the most innovative startup from Pittsburgh Technology Council. That's right. Data Center and IT Services Company, I am critical, recently won the award as part of the 2022 Tech 50 Awards, this month being named to the top company in their category. So this is a pretty significant award for the local Pittsburgh community. Basically, I am, as a data center, was awarded their top technology provider award there in Pittsburgh. So congratulations to I am. And you know what? We are getting down to it now, Dean. We are all the way up to you right now. Me? You. Yeah. You, as in you, uptime 99.999% uptime. As a matter of fact, that's the reliability offered by Horizon on their newly completed fiber optic network in Dayton, Ohio. That new route ties into 6000 route miles of fiber that Horizon already uses to service Ohio. Yeah, I love it. I love what's going on here in the Midwest with our fiber providers, especially those who are hitting some of those rural markets. Congratulations to Horizon. So now moving on to the letter V. This one involves JSA2. V is for our, our last virtual roundtable of the year. So while it's sad, it is also hosted by our friend and everyone's top of everyone's list in telecom. Mr. Robert Powell is going to be hosting this one of telecom ramblings, you know, and love him as much as we do. It takes place December 8th and will be all about infrastructure and one of Jamie's favorite topics, sustainability predictions for 2023. The first 100 residents, registrants will receive a free lunch. So make sure that you sign up too. Yeah, I love that. I love that. Get your free lunch, sign up, and let's talk sustainability predictions for the new year. All right. Next up, W. W is for wholesale, that's wholesale collection. No, no, no, no, wholesale co-location, the purpose of Prime Data Center's newly announced Silicon Valley facility. They broke ground this month in Santa Clara on an 80,000 square foot data center that will be all built to suit. So very cool prime. Yeah, excellent there. And X is for BDX, naturally, who has been busy this month. BDX launched the development of a 100 megawatt hyperscale data center campus in Jakarta, Indonesia. Upon completion, it will be their 11th data center in the Asia Pacific region. So congratulations to BDX. Yeah, and you know what? This next one also involves BDX, this time through. It's Y for Yangtze River, the Yangtze River Delta, where BDX built a sustainable design and build project last year. And this month, they won an Asia Pacific Cloud and Data Center award for it. So yay, this facility features all kinds of modern high efficiency features, and they're very proud as they should be of this recognition. Well done. Yeah, yeah, I'm very proud of them as well. We started at A and we're all the way through the alphabet to the last letter, Z. And Z is for zero, as in net zero carbon emissions by 2030. That's the goal of Databank's new Senior Director of Sustainability, Jenny Gurson. Gurson was hired this month to implement the company's ESG initiatives and has her site set on a pretty meaningful goal. So congratulations and good luck to Jenny Gurson on their zero carbon emissions by 2030. A lofty goal to say the least. I will say absolutely. We should send her a copy of our best-selling book, Reiner Data, just to give her a few more ideas. Actually, Databank wrote a chapter in it, so absolutely something that she's probably already read.  Speaking of books, that's another edition of JSA Fast Forward in the books. We went from A to Z with all the latest news and headlines from Telecom News Now, and now you're all caught up. So next time, yes, we did it. Take care, everyone. And as always, happy networking. See you next time.


Exitons, quasi-particles of tightly bound electron-hole pairs, dominate the optical response of atomically thin transition metal decalcogenites. Here, the authors review strong light matter coupling in two-dimensional semiconductors arising from confined excitons interacting with trapped photons or localized plasmas. This article was authored by Christian Schneider, Mikhail M. Glasov, Tobias Korn, and others.


In this lecture, we will study the notion of big O and small O of a sequence and also for a continuous function. We will also see the definition of order of convergence which is very important in numerical analysis. Well, let us start with an example. Consider these two sequences sequence n and sequence n square. Both are unbounded sequences and now, you can also see that both these sequences tends to infinity as n tends to infinity right. Now, if you ask the question which of these two sequences will tend to infinity faster? Obviously, you can immediately tell that n square will go to infinity faster than n right. Let us take another example. Now, we will consider two sequences 1 by n and 1 by n square. Now, these two sequences are bounded sequences and both will tend to 0 as n tends to infinity. Now, again we will ask the question which tends to 0 faster? Obviously, you can see that the sequence 1 by n square goes to 0 faster than the sequence 1 by n. Therefore, we have now intuitively developed the feeling that if two sequences are converging to some limit same limit, then one may go faster than the other right. This is the basic idea of the small O and big O because we are interested in measuring who goes faster to the limit than the other. That is the question of order of convergence and it is all about comparing two sequences that are converging to the same limit in terms of the speed at which they converge.  Let us see the definition of big O in the context of sequences. Assume that we have two sequences sequence a n and b n both are sequences of real numbers. Then we say that a n is big O of b n if there exists a constant c and a natural number n such that modulus of a n is always less than or equal to constant times modulus of b n. And this should happen at least for sufficiently large n that is what we mean by saying that there exists a natural number n such that the condition holds for all n that is small n greater than or equal to capital n. Now what this definition tries to say well we will just put this definition in a different form and see what it means. We can do this if all b n's at least for sufficiently large n are not equal to 0. Then you can see that modulus of a n divided by modulus of b n is less than or equal to c that is equivalent to saying that the sequence a n by b n is bounded. Let us take a simple example let a n is equal to 1 by n and b n is equal to say 10 by n. We know that both these sequences are going to 0 right. Therefore, you may just think that a n by b n may go to infinity because b n is going to 0, but that is not going to happen obviously because when b n is going to 0 simultaneously a n is also going to 0 and at what speed both of them are going in the same speed right. Of course, you can see it with simple calculation this is equal to 1 by n divided by 10 by n that is equal to 1 by 10 and that is the constant that is appearing here in this particular case you can in fact, say that a n is equal to 10 times mod b n. There is no need to put mod in this particular example and that is what this says. Therefore, a n in this example is a big O of b n. Similarly, you can also take another example where a n is n square and b n is say 10 by n then you have a n by b n is equal to 1 by n square divided by 10 by n that is equal to 1 by 10 n right and in fact, this is going to 0. Therefore, you can always bound it by any number say for instance 1 also you can take as capital C and say that for sufficiently large n mod a n divided by mod b n is less than or equal to 1 right. So, in this case also you can say that a n is big O of b n. In fact, in the second example you can say something more than merely what happened in the first example. In the second example a n is in fact, going much faster than b n right that is the basic idea of small O. Let us define small O now again you have two sequences a n and b n. Now, we say that a n is small O of b n if for every epsilon greater than 0 there exist a natural number n such that mod a n is less than or equal to epsilon times b n for all n greater than or equal to capital n. So, in this case what we are doing is we have a sequence a n and we are saying that you give me any epsilon see that is more important you give me any epsilon I am giving you guarantee that my a n the sequence will become less than that small number that you gave into b n ok at least for sufficiently large n that is what you are saying it may not happen right from the first term of a n, but you go after 10 or 15 or some sufficiently large small n then this will surely happen that is what you are saying and you are pretty confident about whatever epsilon that somebody gives you that is what the definition says you give me any epsilon I can pack this sequence in this, but still you are saying that may I can make my a n something less than or equal to epsilon times this. So, you will have that confidence only when that a n by b n is converging to 0 then only it can happen. So, that is what the definition says that your sequence a n by b n is intuitively if you see it is converging to 0 that is what in a particular case when all this b n are not equal to 0 at least for sufficiently large n this is equivalent to saying that a n by b n is in fact, converging to 0. If you recall in the last slide we have taken a example where a n is equal to 1 by n square and b n is equal to 10 by n you can see that a n is going to 0 much faster than b n. So, if you take a n divided by b n you will see that it is 1 by 10 into n. Now, you give me any epsilon greater than 0 I can always find a sufficiently large n such that this is less than or equal to epsilon for all n greater than or equal to capital N. Therefore, in this case a n a n is equal to small o of b n. So, the notation small o means a n has to surely go faster to the limit than b n then only you will say that a n is small o of b n whereas, in big o either a n should go faster or equally as fast as b n then also you can say that a n is big o of b n there is a subtle difference between big o and small o. So, this is what we will remark you have two sequences a n and b n you can see that a n is small o of b n means what a n is definitely going faster than b n that also means a n is going as fast as b n because going faster than b n is something more than that therefore, a n is also big o of b n. So, if a n goes faster than b n then it is also a n is big o of b n because we are demanding more stronger conditions here than this that is why if this happens this will surely happen, but the converse is not true you can take many examples the first example that we have given in the previous slide is also an example where a n is big o of b n because a n and b n are going at equal speed that is if you recall we have taken a n equal to 1 by n and b n is equal to 10 by n. Remember in this case the converse is b n is always staying ahead of a n. So, it is not the position that matters it is the speed at which they tend to 0 matters. You can see that a n divided by b n is equal to 1 by 10 and that is a fixed number therefore, this cannot go to 0. Therefore, in this example a n is big o of b n, but definitely a n is not small o of b n. The same idea is also given in this example we are taking a n is equal to n and b n equal to 2 n plus 3. Now, let me summarize what we will learn from big o and small o and b n notation. We have two sequences in particular let us take both the sequences are converging to 0. Then a n is big o of b n means the sequence a n tends to 0 at least as fast as the sequence b n that is what is meant by big o and small o means that a n tends to 0 definitely faster than the sequence b n this is small o. So, I hope you have understood the notation of big o and small o and the subtle difference between them. Once you understand this you can also extend this idea to continuous functions also. Let us give these two definitions in terms of functions consider a point x naught in R and f and g are continuous functions defined in a small neighborhood of x naught. Then we say that f is big o of g as x tends to x naught this is very important all this o notations are defined as x tends to something. Therefore, you should always write this where this x tending to in order to compare one function with the other function. Notationally we will write f of x is equal to big o of g of x as x tends to x naught that also one should write. The definition is almost similar as we did with the sequences when can we say this that when there exist a constant and a real number delta such that f of x mod is less than equal to c times mod g of x whenever x minus x naught is less than or equal to delta. What it means? I do not want this condition to happen everywhere on the real line in a small neighborhood of x naught if it happens that is enough because we are only worried about x tending to x naught. Therefore, as you go closer and closer to x naught this should happen. If that is the case then we say that f of x is big o of g of x. Let us similarly define the notion of small o again let x be some real number and f and g are continuous functions defined in a small neighborhood of x naught. Then we say that f is small o of g as x tends to x naught. Notationally we write as f of x equal to small o of g of x when this happens if for every epsilon greater than 0 there exist a real number delta greater than 0 such that mod f of x is less than or equal to epsilon into mod g of x whenever x minus x naught is less than equal to delta. Again this condition should happen in a small neighborhood of x naught that is what is important here and again you can see that this the role of this epsilon which says that f of x divided by g of x should tend to 0 as x tends to x naught and that is provided if g of x is not equal to 0 otherwise that is what this inequality means. Again the same kind of remark that we made with sequence will hold here we have two functions f and g which are continuous functions defined in a small neighborhood of x naught. Then you can see from the definitions of big o and small o that f of x is small o of g of x will always imply that f of x is big o of g of x. But again the converse is not true you can take examples in a similar way as we did with the sequences. So, I leave it to you to think about various examples for why the converse is not true again let us summarize. Suppose you have two functions f and g and we know that f of x is tending to 0 and also g of x tends to 0 as x tends to some point say a. Then we say that f of x equal to big o of g of x means f of x tends to 0 at least as fast as g of x tends to 0 as x tends to a that is what is mean by big o and what is mean by small o small o means f should go to 0 definitely faster than g of x going to 0 as x tends to some point say a or x naught in the previous definition we have taken. This notations are very important in numerical analysis and why in particular we are more interested in taking whether a sequence or a function tending to 0 because we will be studying errors for various methods and we wish our errors to go to 0. Now our interest is to see how fast this error goes to 0 as some parameter tends to something this is what we will be interested in the subject and therefore, this notations will come quite often and it is very convenient for us to use this notations than every time telling what they actually do. Let us take an example well this example is familiar because we have discussed in our previous lecture. Let us take the function f of x equal to cos x and let us try to write the Taylor formula for cos x around the point a equal to 0. If you recall this is given by the Taylor polynomial given by this plus the reminder term given like this. Now if I want to use the Taylor polynomial instead of cos x then what is the error that I am committing in that representation well that is precisely this reminder term or the truncation error. This is what we have seen in the last class unfortunately this is a unknown expression because of this quantity xi which generally we do not know, but we only know that xi lies between x and 0. So, that makes this expression to be unknown. Now our interest is to understand how fast does this error goes to 0 for that let us just define this reminder term or the truncation error as a function of x. Let us call this as r of x and sorry this may be xi here. So, r of x is a function of x in fact, this xi also depends on x as x changes the xi will also change therefore, it is really a complicated function. Now our question is as x tends to 0 what will happen to r of x well it is very clear that as x tends to 0 r of x will also go to 0 why because although this term cos xi is unknown, but definitely we know that it is bounded. Therefore, this quantity is some bounded quantity means it remains constant and this term is going to 0. This is the first one is bounded and the second this one is going to 0 therefore, the entire thing will go to 0 as x goes to 0. That is quite clear now our interest is to see how fast it goes to 0 well that is not a very difficult question because we can understand how this term goes to 0. So, you can immediately say that r of x goes to 0 as fast as x to the power of 2 into n plus 1 tends to 0 as x tends to 0. So, that is what we meant by saying that r of x this is the function just to compare this with the definition we had 2 functions f and g and we say f of x is big o of g of x. The same instead of f here I have r of x and r is big o of what this function. So, just take this as g of x. So, r of x is big o of x to the power of 2 into n plus 1 as x tends to 0. This is something like you are comparing your error with something which you know very well how it behaves. See this you know how it behaves intuitively you can imagine how fast it goes to 0. Now what you are saying is my truncation error in Taylor series is going as fast as this function goes to 0 as x tends to 0. Often we say that the function r is of order 2 into n plus 1 ok. This kind of words are quite often used in numerical analysis to say how our error goes to 0, how fast the error goes to 0. Suppose you say that my error is going to 0 with order say 5 it means your error is big o of x to the power of 5. Similarly, you can interpret in terms of the small o also. Finally, we will quickly define the notion of order of convergence. You have a sequence a n and you know that the sequence a n is converging to some limits say a. Then we say that the order of convergence again you can see that the order of convergence is something to understand how fast this sequence is going to a. So, we say that the sequence going to a with order of convergence at least linear if we can find a constant c less than 1 and the natural number n such that modulus of a n minus a is less than equal to c times a n minus a for sufficiently large n that is n greater than or equal to the capital n that you form right. So, this is what is called at least linearly. So, it means the sequence is converging at least of order 1 that is what it means. Similarly, you can also say that the order of convergence of the sequence is at least super linear if there exists epsilon that converges to 0 and the natural number n such that a n plus 1 minus a is less than or equal to epsilon n times a n minus a modulus a n minus a for all n greater than equal to capital n that is for sufficiently large n onwards this condition should hold. Similarly, you can define for quadratic at least quadratic convergence and this can further be generalized to any alpha we say that the order of convergence of the sequence is at least alpha that is very important it is converging at least up to this speed that is what it means. If you can find a constant c and the natural number n such that this condition holds you see this a n plus 1 minus a modulus is less than or equal to c into modulus of a n minus a alpha for all n greater than or equal to capital n. Often we will also use the notation mod a n plus 1 minus a divided by mod a n minus a and limit n tends to infinity and that is maybe some constant say lambda because this is if this is happening of course, to the power of alpha. So, this is also one equivalent definition for this in this case often in some books people call this as rate of convergence in some books even order of convergence is otherwise called as rate of convergence. Therefore, there is no standard usage of these words we will come across such expressions in non-linear equations and with this I thank you for your attention.


I am a social robot, educational partner, which brings out spontaneous grow with children through conversation and play. So who are you? What's your name? I'm Ryota Miyazaki. And you work on this product, right? Yeah. And who are you? I'm Taubo. I'm supporting this project. And right here we see a little robot. How does it work? You can make it follow. Hey, come with me. Come over here. Let's go this way. Come, come, come with me. No, no, no. Over here. Over here. Over here. You're very, very drunk. That's great. So, do you know what this is for? Sugar? Yeah, sugar. What can you do? To become smarter. To have a conversation. It's possible to have a conversation. And this guy can... Can you come over here? Yeah, yeah, yeah. Come, come, come. Okay, let's go. Run. How fast they can go? Yeah, no. Like this? What is a... What is a projector inside? What is a projector? A parent's computer. A parent's computer. And a... A speaker's... And you can share these experiences with grandparents. Camera? I have a social robot. A sensor? You can see where people are, right? Yeah. And then... You can see the application. Can you see the application? I'm not... Secret. Yeah. So, how soon is this on the market? When people will buy this? 90. Next year? No. 90. 2000? 2019. Two years. Yeah. So, what is this area here? It's just an area, can you show? Yeah, of course. So, this is the future living project. And this is a so-called sustainable container, which is the washing machine of the future. This is the washing machine? Yeah, of the future.  Let's pretend this is dirty clothing. This is dirty? Yeah. And then you close the drawer. And once you close the drawer, you can see that the entire system starts working. Ah, it's happening now. Yeah, so the first step is that the system analyzes the clothing and just put it one by one. So, it basically detects where the dirt is. It recognizes the fabric, the piece of clothing is made of. It also recognizes what kind of clothing it's made of. Nice. This is like magic. Yeah, kind of. Whoa. So, after this is finished, it will go down? Yeah, it will go down. And it will be transferred down here. So, the washing process starts. And due to the washing process, small amounts of detergent and water are sprayed on the clothing, which you can see below. So, this is the water with detergent. And it's directly sprayed to the areas which are dirty. And the amounts you need are adjusted based on the information just for scanning the clothing. It's scanned and know exactly how much treatment you need? Yes, exactly. And where will it go after? After this, it will dry. So, basically, this works for suction, right? So, the water is being sucked out of the system. Yeah. The clothing stays dry. And the last step is the folding step. So, the clothing is folded by a robot. So, how soon can I buy this? So, this is what it's supposed to look like. Is that real? It's only a demonstration. Demonstration? But it will be real in a few years. No, it will probably still take at least three years. Three years? Yeah. So, at last, you can just open your drawer and your folding is folded and also will be... Organized. Organized. So, basically, for example, this drawer has all louses. This drawer might have all jeans. This drawer might have all socks. But this drawer will have what I need for today. And then it takes a node with AI. I need this color. It's better for today. Yeah, you can just... And then it will take automatically. Yeah, so, you can just... Select. Select it and you can control it by an app. So, this is how it's supposed to look like. So, you work in a Panasonic robot? Yeah. Division, right? So, Panasonic will have robots. You take the clothes, put it inside. Yeah. Make the food. Make food. Make food. So... No, that's the... Mixer? No. Maybe three. Three, yes. Or hybrids. Because this is so cool. Yeah, I think. And then he's going to explain it. Yeah. English on. English on. Let's do a Japanese one. Okay, so, let's give you a start. Welcome to Panasonic, your wonderful world of the future. Yes, welcome to our better living tomorrow tour. In the upcoming future, it is said that leading edge technologies like IoT, robotics and artificial intelligence will have an impact on our lives and our businesses and our values and our lifestyles will become increasingly diversified. Of course, there are so many changes concerning society values and lifestyles and we at Panasonic, we anticipate these changes. I do it just for you, just for the camera. And so, we keep on researching and developing consumer appliances and services to meet the customers' demand. Next one will be yours. Are you doing IoT technologies? We will see how this works in the household and how convenient our lifestyle will become and by integrating robotics and artificial intelligence into our everyday lives, which will take over two years of time consuming chores. We will have much more time spending it with our families and friends. By the way, this is my fantastically Tobias. And this is my wonderful part-time wife, Boemi. We're very happy to have you here. Only for you, but only for you. Okay, so, are you ready? Can we go to the kitchen? Yes. Okay, then let's start the kitchen. Who likes to be in the kitchen? Do you like to be in the kitchen? What about you? You? No, no. Some people are like, most of the time if we ask, all men are like, what's been the living room? What's been the living room? And watch football? Yes. Okay. So, yeah, and a kitchen is going to be more fun to be in the kitchen. We already experience that every day with our artificial intelligence kitchen advisor, which is a good health in the kitchen? Yes, because it also reminds me of some special events, for example. I mean, it will tell me how to cook because I'm a bad cook. In the future, I will be a better one, hopefully. And as you can see, it will also tell me that there's a special event today. For example, Noemi's birthday and so on. So, for each purpose, you can order some special recipes, for example. Okay, so now that it's Noemi's birthday, please show me some special recipes. That's what he will do in the artificial intelligence kitchen advisor. It has a range of delicious menus. It's connected to a lot of emotions. For example, you might know the famous poor bookies instituted in France as one of the main hosts. Noemi basically cooks food in the world. He has the alternative to them and also connected to other professionals like chef cooks and nutritionists who provide us a range of menus. Now, let's see what you want to say. I think this one, we will return it. It's very nice. It's probably one of my favorite recipes. Basically, I ate it a lot of times in restaurants but I never ate it at home. So for my birthday, it will be perfect, I guess. But it isn't complicated. Yeah, and I call him cute but he's not available today. So I think I have to do it. But it will be easy in the future. Please prepare it. So that's what you have to do. The kitchen appliances, all the kitchen appliances needed for that menu will get started to cook. We'll get ready for cooking. For example, the oven just starts to heat up and also use the kitchen appliances. They can adjust the temperature, for example. Nothing will burn after everything on the side. And some people like to block or move pictures of Facebook of their food. We have here an embedded video camera over there. So you can take pictures of videos and then log in or put it on Instagram. Great stuff. Okay, so what you see over there right now is that the chef will tell me what to do step by step. So if maybe I am the best cook, I will hopefully be in the kitchen because I just get the information. And I will also get the information concerning seasoning, for example, which is obviously very complicated. Some information is how we can garnish the plate, for example. This is an appetizer, so I will get some suggestions from A to Z. Some food services are needed to cook and eat the menu, basically. Yeah. Okay, so I think it's your birthday, so leave me alone. Leave me alone. I tried to say it in a kind way. Leave me alone. Let me just see if I can do it by myself or if I have a special friend already waiting for you in the audience. Exactly. To be as already mentioned, we will get over to the dining table. Let's change the name when you show it. Let's change this one. Yep. So this design we are using will help in the children's room because this is a so-called social robot. You can communicate through each act is played through each action. It's a so-called educational partner because it helps children in supports and in groups. Children don't have a healthy diet. And no children don't like the other stuff. For example, spinach. Spinach is most of the time on the world, not in a child. So parents sometimes have a hard time to show to children what is good for them. It's an educational partner now in the future. Mom, I want to have a fun dinner. Crickadella. With carrots and potatoes. I don't want kids. Lewis, I know interesting stuff about carrots. Would you like to see one? Yes, okay. The carrot man is a veteran. He wants a honey can. Big. Carrots are sweet and you could clean them become strong like carrot man. Lewis, do you want to turn into carrot man? Well, I don't know what I'll do. So, as you can see, in the future, children might be convinced to at least try foods and hang out before you go to school guys telling funny stories and having conversations with the children. It also takes a lot of pictures and videos of the children in their natural environment. So people can compare those pictures maybe they took three weeks ago and it's also connected to an educational platform the educational institution creating a huge platform with a lot of support and advice when it comes to the health of children. And by the way, kids really love this little guy so it's good to have him in the kitchen. Let's go back to Tobias and let's see what's happening in the kitchen. Everything went perfect so far with wonderful meal but I'm looking for some special beverage. And as far as I remember white wine would be a good choice when we have some wine here this is by the way our sake cooler which has a couple of different sake and as you can see it's a little bit different here so it's complicated when it comes to sake so I have no idea I don't know do you know sake cooler? Japanese rice wine I've never seen so how can I find out if it's good for all meal or not I don't want you to be disappointed so that's why I'm asking we have our little sake cooler over here I think that's the best idea I've had so far because in our little mobile sake cooler there is a camera and it detects the label that is connected to the database and from here on the display you can see that it gives you the information that I need all the characteristics of this sake cooler I will know in just a couple of seconds if it's good for all meal or not yeah I can see also some recipes which go well with the sake cooler cheese as well that's good you both cheese lovers would like to have cheese as appetizers okay so it goes well with that one do you have cheese? yeah of course because our second name is cheese we have family cheese okay so please take a seat for the cheese because in the future well you can just take a closer look into that corner over there because over there there is a huge fridge we have a smaller one and we gave him a name hi cool cool please come to the dining table well cool is a movable fridge it moves responding to my voice commands as you can see but it's also important that it has an embedded sensor technology because it can accurately measure the distance we don't want it to bump into anything so what does it do? it messes up the whole room and it is always updated so if something happens suddenly my wife is over there let's go because I need my wife for a couple of more years yeah that's good I won't be blown over by a fridge just imagine you're having a party at home you're having friends over you don't want to get up all the time just to get to the fridge to get to my ranch or something to eat plus when you don't eat it also carries away the dishes back to the dishwasher so you have two things what this fridge can do and even my husband won't get run over by the fridge I gave it a try but as you can see it can move around safely that's really important because if you have little kids and they crawl around you won't bump into me perhaps ok so thank you very much so far as far as I can see you can already see the bubbles yeah we need to do the laundry wash clothes no I don't think anyone likes to wash clothes


From VOA Learning English, welcome to agriculture in special English. I have a question for you. When is a plant considered a weed? Well, the experts at Penn State University have a simple answer. When the bad qualities outweigh the good qualities. Consider the fact that crops produce several hundred seeds from each plant. By comparison, each weed plant can produce tens or even hundreds of thousands of seeds. And some buried seeds can survive up to 40 years or longer. Eradicating or getting rid of weeds means that you have to remove all the seeds and roots so the plants will not grow back. But birds, wind and weather can bring them back to the land. A more common way to deal with weeds is to control them so that the land can be used for planting. Experts advise using two or more control methods. Chemical weed killers or natural treatments like corn gluten can suppress weed growth. Dense planting of a crop can also act as a natural control. Bill Curran is a professor of weed science at Penn State University in Pennsylvania. He says one of the most common methods for suppressing weeds is dense planting. He says a dense competitive crop that quickly shades the soil will help. The weeds need light to grow so blocking the sun will reduce their growth. Other controls include turning over the soil, pooling the weeds or covering them with mulch made of shredded wood, garden waste or other material. But even mulch has its limits. Weeds can be transported in mulch. This is also true of soil, grain, hay and animals. Animals like sheep or goats eat weeds so they can provide a biological control. Even insects and other organisms can also act as biological controls. For VOA Learning English, I'm Carolyn Presuti.


What's up guys evil deer here today? I'm going to be playing left for dead again. However this time I'm going to change a little bit I'm not gonna be teaching you weaponry words or words for different types of zombies But I'm going to be teaching you the words for like body parts of the Body parts of the body. I guess God that sounds terrible Jesus. So yeah, I'm gonna be teaching you body parts And stuff like that. So anyway before I do get into my whole lesson I just wanted to speak about a few things that have happened with my channel and also One or two things that I've seen within the community as of recently now for those who just randomly drop by on this video I speak a creative language called Esperanto. It's About 150 years old spoken by 200,000 to 2 million plus speakers Yeah, that's pretty much it was created to help with like intercultural communication now for those who haven't watched my first Video is you're gonna want to go back and watch those first the left for dead videos I mean just so if you hear some random words You know what they mean because I've already had two previous videos and I've already taught a few words So anyway, that's that little renders feel now one thing that I've had happened recently is I a few weeks ago I released a video called I'm from my yosuiyo, okay? And that means I'm just from cool land and it's a funny story about that happened between me and a mate Esperanto's and it it actually got a lot of Like reactions and stuff from a lot of Esperanto's who sent me some messages going. This is really cool I love the idea. Let's make this a thing and I didn't expect that much feedback on that particular video So when I started getting all this feedback, I started thinking Yes, let's make this a thing So if you guys want to make this a thing There's more yosuiyo the fake country from where Esperanto's come from before we were completely dominated in World War 2 Leave me a message below if you don't know what I'm on about go watch that video then come back and leave me a god damn Then come back and leave me a message. So Yeah, if you're interested, let me know if I see enough interest. I will I'll do something I'll create a web page. I'll make a Wikipedia article. I don't know I don't know maybe you'll even get picked up by like, you know Fox News or something, you know How great in their journalism they are so that's a possibility.  Anyway, so that's that Second thing I wanted to say is I take part a lot in red edit groups I talk in different ones and there's an Esperanto one if you get dies you guys if you guys don't know about You should go check it out. It's got like 3000 plus members or something But anyway in there today, I saw a well, I didn't see someone replied to one of my messages saying I should check out the social media platform It's in Esperanto. Now. It's called the verdule Dot-com and verdule just means green people. It's a combination of verda, which is an adjective that means green and oolah Which is as you guys probably should know The suffix for person. So the dual is just like a common way of saying Esperanto without saying Esperanto People just for some reason we've got this fetish with green. There's probably a historical reason there I don't know what it is. So yeah, go check it out. It's a mixture between like Facebook and Twitter It's pretty cool. It's pretty cool. The interface is very basic You can tell it's still in its infant stages However, there seems to be a small bug growing community on there I've signed up to sign up anyone can sign up But you've got to be approved by it looks like an admin and they do like a small little Esperanto test Not like language test, but just ask you a random question like who created this one and that's as well Okay, you don't know if you don't know that That You're an Esperanto, so you know that everyone knows that if you're an Esperanto anyway, so yeah Go go check it out. I'll leave a link down in the description. It looks pretty cool. I'm signed up My name will be evil dear You can follow me if you want Yeah, just support the community man support the community it's the more that we support these Esperanto initiatives Rather than using the big websites like you know Facebook and stuff even though I've got a Facebook page which Some of you guys might see it might not have I still like to support these initiatives like the Esperanto games and stuff like that Anyway, I've like gone on for ages about that topic. I'm almost at the end of the first level I haven't taught you guys one single word yet. Actually, I am at the end of the first level. What is Jesus? I am good. Okay, so I'm basically just gonna close off this door I'm gonna cut it here and come back directly in the next level and I'm back So that didn't take as long as I thought I was going to take now I'm just gonna pick up some women see you're which is MO. I've got all that I've got sunny Gila My health is looking fine. Let's pop the cherry and go out the door. Okay. Take out that zombie.  No, there's the legs Okay, so the late the word for leg in Esperanto is through the and it's called K. R. U. R. O Now that's just the leg It means exactly the same as in English the full leg However, the reason I say that is because there's actually another word for leg in Esperanto and it's gumbo Now I see people using this word gumbo when they should be using Kuroo Now you're probably thinking why is there two words for leg? Well, that is an interesting historical thing from what I understand I couldn't be completely false in this bit of information. I'm giving you now if I am point pointed out correct me You better come with proof and facts man. I was I won't believe a word say no just joking just joking So yeah, the history behind Kuroo and gumbo is an interesting one There is a dictionary Encyclopedia in Esperanto Then again, it might be it doesn't matter. It's called piv and it's kind of I think it stands for plena Votado I could be wrong. I don't know. I don't I'm not very good with acronyms That is kind of like the standard has been for a very long time for Word usage and stuff like that in the Esperanto community. There's a lot more books and stuff out there now But it's still very prestigious. I don't know if that's the correct word, but it it's Authoritative in some sense. Anyway back. I think it was in the 80s. It could have been another time There was a French author. I believe he was French. I could be making everything up right now I don't know but there was an author or an editor Sorry, who took over and what he did is he added like a whole heap of Not needed or rarely like used words With French origin Into the dictionary. So one of those words was gumbo So he bought in this word for leg when we already had a very well established since like, I don't know Dinosaur times in Esperanto dinosaur times is like under 50 years ago. Just in case you don't know and Tried to replace Krudo now. I don't know why he bothered But this word now gumbo was in the dictionaries and obviously it's kind of set itself in usage Well, oh, we have a tongue cool around here somewhere Yeah, let me just kill that dude off first.  I just got airborne straight over the top of that. Oh god.  Oh Oh God damn. I knew that was gonna happen. That's why I popped mine like little healthy thing Okay, so I'm just gonna quickly heal up them. We'll go ahead. So yeah Krudo means leg and gumbo means leg now There is some people that debate and say that there's a difference between the two but there isn't really a difference like some say Oh, it's like technical and another say no Krudo only means bottom of the leg while gumbo means the whole leg And I don't know that like everyone uses Krudo No one uses gumbo except for people have just gone to a dictionary and looked up leg and just happened to find gumbo It's not the standard usage. So don't use it. Anyway, that's my random little rant about those two words I'm sure someone's gonna like in the comments below say no, it's got this meaning but whatever whatever I'll take you on. I'll take you on. I'll take you up back behind the Esprino flag. Whatever. Oh god I keep shooting this guy in the back by the way, the word for back in Esprino since I'm shooting people in the back It's daughter soft easy word to remember. Just think dorsal fin. Okay, daughter. So it's the same for both humans and animals They're all daughter song the back Now just shot that guy in the head the word for head in Esprino is couple couple Easy to remember. Just think of like a toothpaste cat cat for any form of cat. I don't know why I picked toothpaste But yeah, so think of just a cap and there you go. You've got couple. So Let's move ahead. Let's move right ahead. Let's just go up here up the stupato Which was the stairs you would know that if you've gone in my previous video. Oh god Why did I do that? Why did I do that? That was a bad idea? I just attacked the plan rule and I've got no health pack I am the worst player by far apart from myself. Wait. No, that makes no sense. Okay.   So let's just activate this So we have a machine puff below here, which is machine gun now Shoot that guy right there in the waist.  You can really associate that with except for tail But people's tails on the back so that doesn't really work unless we're talking about the male tail Which is on the front That makes no sense for an idiot So, yeah, we've got Khalil is the waist. Let's shoot this guy right here in the food.  Oh, the word Mano in Esperanto means hand. They gave Marlo Don't know what you can associate that with you're just gonna have to memorize that one. Sorry guys Root learning it is ah ah fight off idle. Just got burnt by the fire. Geez. I'm terrible I'm just stuck here. Come on fire. Go away. Okay, cool. Moving ahead moving ahead. So, let's see grab some more mumitzio Now let's move around here here nothing all good.  Oh, is this part of the head?  I'm assuming it doesn't cause too much pain It's like shot straight in the brain the word for brain is Turtable turtable See we're on a roll now now. We've got the words down pat. What is that guy doing? Is he like way ahead of me? I think he's way ahead of me somehow. I think he jumped off the building. That's what he did I didn't even think about that.  Anyway, I pretty much reached the end of this one I'm just gonna shoot all these zombie league just now I didn't teach too many Esperanto words in this one. Sorry about that guys.    Am I? Chuck that over there. I almost died right before the end of this that would have went really bad Okay, let me in here. Let me in. Let me in. Oh Come on Someone pick me up, please, please. I'm doing this game. No justice. I'm doing it absolutely. No justice. I'm there someone Wow, I am so sorry guys at least I've got two pistols by way. I didn't teach out in my previous lesson The way to say like dual pistols is duobla pistolo. Okay. Let's get in here Finally end the game done Sorted okay guys, so if you've enjoyed this video and you want to see more videos like this Give it a like leave comments below when you guys leave comments It gives me ideas of what you want to see so leave some comments and subscribe to the channel if you haven't already And I will see you in the next video and it's not well You might end up playing with me online and I'll get you all killed