Network Dynamics is the study of how networks change over time as new connections and structures are formed or removed. With the study of political network dynamics, we're asking the question of how do socio-political networks form, mature and eventually disintegrate? In this analysis, we're interested in such questions as how do things spread across the network as a function of the structure of the network of connections and various questions of network resilience and robustness to outside influences? The study of network dynamics is used as a tool to study the formation of many different kinds of socio-political networks such as criminal networks, terrorist networks, political movements, innovation networks or changes in culture etc. This approach is particularly relevant when dealing with informal political processes and organisations, where the organisation may have no formal structure but consist of purely functional connections, as would be the case in the early formation of a political protest, a new belief system or the workings of various criminal organisations. A primary factor to note is that networks are a very organic form of organisation. They typically emerge or grow out of the local interactions made by actors without global structures being imposed. Connections are typically made by individuals on a functional basis according to some cost-benefit analysis of the individual. People exist within some environments and they wish to do certain things such as move around, communicate, form acquaintances, exchange goods etc. All of these activities create connections but which connections are made and which are not made are a function of both the individual's propensity to make those connections and the limiting constraints within that environment. Most connections both have some advantage for the individual but also cost the individual something to make those connections. Thus there is both an outward force to create connections that is driven by the individual's motives to access whatever it is that is on the network but there is also some limiting factor requiring them to expend some resources to make that connection. For example we can think of a criminal network what we call a dark network. Dark networks are illegal and covert networks such as drug cartels, hacker networks, illegal flows of arms and money, terrorist groups etc. Dark networks are particularly interesting to study with respect to socio-political networks because their central defining characteristic is that they're trying to achieve something without being detected and this makes them different for most formal organizations in society which have both a manifest formal structure and an informal network structure. These dark networks in country are purely functional networks.  You have to reach out to your informal network and find someone there. Individuals in such networks often do not trust each other and thus each link in the network can be seen to cost the individual and the more links an individual has the more exposed detection they are. Thus we can see here the two forces that are relevant in most social networks. The outward incentives driving the individuals to make connections but also the counter force that places the cost on every connection they make working to reduce the overall number of connections. For a network to form then the benefits to the individual must in some fashion outweigh the costs being imposed on them for forming part of that network. As an example we could think of the socio-political network forming a movement to try and change an oppressive political regime. Individuals are motivated to form the connections out of a desire to change the political order and the need to band together with others to do this. But also they face a potential cost that the regime imposes on the network by threatening them with arrest and persecution. In such a situation we can identify a number of key parameters to the development of the network. Firstly the individuals internal desire for change. This motivation can be seen to be driven by the emotions of anger and hope which are emotions that drive people into action but also we can identify the level of oppression that the individuals experience as another important factor. Oppressive regimes are maintained through fear which is an oppressor of behavior. Most social structures that regulate political systems are based on fear which works to dampen down change and maintain the system within its existing configuration. In order to overcome fear people's anger has to be strong enough and their vision of an alternative future has to be strong enough but added to this they typically have to be connected with others. Revolutions happen when people are no longer able to control their oppression and outrage any longer. One example of this being the self-immolation of Muhammad Barzizi a street vendor in Tunisia who set himself on fire on the street in response to the confiscation of his wares the harassment and humiliation that he said was inflicted on him by a municipal officer in her aides. An event that is seen to be a catalyst that ultimately led to the Arab Spring Revolutions. Most control is maintained by controlling the means of communication within a society so that those who are resistant to existing structures cannot connect and communicate with each other at large. Throughout history the control over information and communications has been the key element in regulation because they are the means through which people connect and can form counter movements. Ultimately humans are governed by the neural networks in their brains and the sociopolitical structures of a society and its operations are determined by the neural networks of the individuals and how those individuals are interconnected within the overall system. If the neural networks of the individuals conform to that of the authority and if they do not have the means to connect with each other through unregulated channels then change will not happen. Change happens when people's neural networks diverge from those of the authority creating a desire for change from within the individual and when they can connect through unregulated peer-to-peer networks. This is why the internet is potentially such a powerful political force in the world today. Not only does it provide alternative narratives that can diverge from the dominant ideology but also it gives people the potential to connect within unregulated environments. Historically in virtually all processes of political change people come together and collect in public spaces and if they can do that then they may experience a sense of solidarity that strengthens their resolve to overcome their fear of the regime. With the rise of information technology increasingly this public space where people can connect is on the internet. What we see with many movements today is that they are born on the internet and then move into public spaces. Networks are non-linear systems that means they have non-linear dynamics and typically grow or decay at an exponential rate with tipping point dynamics. Social networks like Facebook and WeChat have grown at such a rapid pace because of the network effect. Like dark networks protest movements are also informal functional networks occurring spontaneously without formal organization which can grow or decay rapidly. Many revolutions of the modern era have happened rapidly and unexpectedly including the French Revolution, the Russian Revolution of 1917 and the Iranian Revolution of 1978. These revolutions all took the people by surprise. In the example of the Iranian Revolution none of the major intelligence organizations like the CIA or the KGB expected the regime to collapse. Right up to the revolution they expected the incumbent leaders to weather out the movement. The Shah's fall came as a surprise even to the Ayatollah Khomeini, the cleric who from abroad in exile coordinated the revolutionary process that was to install him as the future leader of Iran. In a recent paper on the subject the authors illustrate the non-linear dynamics behind this process of change. Their model hinges on the observation that people who come to dislike their government are apt to hide their desire for change as long as the opposition seems weak. Because of this hidden preference a government that appears unshakable may see its support crumble following a slight surge in the opposition's apparent size caused by events insignificant in and of themselves. Unlikely though the revolution may have appeared in foresight, it will in hindsight appear inevitable because its occurrence exposes a panoply of previously hidden conflicts. Networks have thresholds, tipping points and feedback dynamics that make them subject to rapid and unpredictable change.  A network's resilience and functionality are closely related to the flow on that network, without any flow we do not have a network and no capacity for the system to operate as a whole and achieve certain ends. Our bodies function because there is a flow of blood and other resources around the whole system, likewise the community can form a functional unit when there is a flow of social capital through the interconnections within the group. As we integrate the system creating more connections and pathways for resources to circulate and potentially for the system to operate as a whole its capacity to realise work and resist change may go up, the inverse is also true, removing links reduces the flow and robustness of the system. Connectivity is one of the basic metrics of graph theory, it asks for the minimum number of elements, nodes or edges that need to be removed to disconnect the remaining nodes from each other. The connectivity of a graph is an important measure of its resilience as a network. A graph is connected when there is a path between every pair of vertices. In a connected graph there are no unreachable nodes. Connectivity reduces the path length on the network and makes people feel closer to each other and thus perceive that they form part of some common organisation. Resilience is one of the characteristics that is often associated with networks. We see time and again how small terrorist networks can persist, adapt and innovate in the face of an opposing security force that may be thousands of times their size. For example, the provisional IRA, a small terrorist network in the Republic of Ireland, managed to survive for 25 years while under continuous pressure from the British security services. There was a continuous interplay between them as the dark network of the IRA would conduct an attack. The British security services would reverse engineer them with the network then adapting. There would be many attacks conducted using a particular set of methods and technology before the security services figured it out and the British adapted to resist them before the IRA would adapt new strategies, again attacking with a new set of methods. Not all networks are resilient though, particularly centralised networks suffer the same vulnerabilities that hierarchies do. If the central hub is removed then this can drastically reduce the overall level of connectivity in the system. Centralised hubs are effective at rapidly connecting systems but the opposite is also true, they are single points of failure for rapidly disconnecting the system. When we talk about a brittle dictatorship like that of pre-war Iraq we can understand this as a network with a dominant centralised hub holding it all together with limited distributed networks connecting the whole of civil society. When the centralised hub is removed and without matured distributed networks of civil society the system can fall into the kind of chaos we saw in Iraq. This dynamic relates to how the network was formed and the distinction between connections made under rules of preferential attachment or the fitness model. With preferential attachment people connect to those who are already well connected thus irrespective of their merit those who are central will become more central making them over time too big to fail while at the same time those major nodes can be inefficient leading to a critical state in the system. A fitness model to the network development would though be room for others of merit to rise where the system may still be centralised and vulnerable but instead is dependent upon hubs that are more efficient with the rule structure that is better able to select for new more efficient nodes to rise. A key question for many is in how one intervenes to foster the development or disintegration of a social network. Policy makers may want to foster the development of innovation clusters by looking at the network structure or securities may want to disintegrate a criminal network. How one intervenes and tries to affect the development of the system changes in fundamental ways as organisations go from linear and well bounded to non-linear networked organisations whereas with traditional centralised hierarchical organisations we have one or few large nodes in the centre at the top who push out instructions to the rest of the organisation and it is seen that we just have to affect the central location to affect the mass of the organisation in the same way that we traditionally see the potential for change as lying with the president of a country or equally the way that mass marketing has tried to influence the mainstream of members within society by affecting the middle of the distribution. They do not look at how things are interconnected, they simply look at the characteristics of the individuals and aim for those characteristics that are most prevalent in the population thus trying to speak to the mass of people and in so doing hoping to affect the whole system. Whereas when dealing with linear systems of organisation you can only really affect the whole by affecting those large components near the centre of the mass. This changes though when dealing with networks where one can have much higher leverage by being strategic in one's intervention by analysing the network according to different metrics to look not only at what elements are most connected but also at other metrics such as between the centrality and how irreplaceable any given node in the network is and then affecting the network in a specific place. For example in attempting to break up a cannabis network the law enforcement agencies in Holland use data mining and network analysis to map out the dark network of the cannabis group and traders consisting of data on 30,000 members even though the real network was actually much larger than this. Traditionally the police had an approach of focusing on the kingpins in the network but they were finding that this approach did not break the whole network in fact it appeared to make it stronger. They combined hard data from criminal reports with soft data to map out the different functional roles within the cannabis network and various other attributes the members and how they were interconnected. It became apparent from this network model why the network did not fall apart when given the arrest of so many key actors each year. The police had thought that these networks were organised in a top-down fashion like the mafia but that turned out not to be the case. If it had been the best way to destroy it would have been through removing these centralised nodes however when the data was combined it was shown that the interactions were not top-down but had a different structure that was more functional and dynamic. The primary network had over time spawned other criminal and social networks. When a node was removed it was able to adapt and find replacements within those tangent organisations. The police decided to adopt a different approach looking at the specific roles that people played within the network to try and find those with functional roles that might be most difficult to replace. Over time they came to identify those doing the electrical work on the cannabis growing rooms to be scarce and difficult to replace. This model showed that every time an electrical worker was taken out the network's efficiency greatly dropped. The bosses were only coordinators and managers they were not so difficult to replace. The key was in looking at the specific roles and identifying those that were hard to replace. Those who could insulate rooms or install irrigation systems along with the electrical workers were the hardest roles to replace. When one of these were removed they were replaced by another freelancer but if the police stayed targeting those specialists the supply of such skills would run out and the network would fall apart over time. This is a good example of how in non-linear systems and complex systems the details matter. If you remove them through statistical aggregations then you remove precisely what it is that you need to succeed in your modeling or interventions and likewise this is why you need to use computational methods on real data. But we are of course not always trying to destroy sociopolitical networks just as often people wish to find methods to foster their development. Distributed networks cannot be controlled in a traditional sense through centralized control systems but they can be developed and modulated altering the costs of making connections in order to influence it to develop in a particular direction. This is the essence of managing complex systems. You cannot control all the parts but you can influence it based upon its evolutionary potential because power becomes diffused out within distributed networks. The whole system becomes greater than any of the parts. No one's in control or have the capacity to affect all the parts directly. The only option for affecting the whole system is to understand the current potential of the system and then create platforms or connections that facilitate the system to evolve in a particular direction that is possible given its past evolutionary history. Complex systems are path dependent meaning the set of possibilities available to the system now are contingent on the historical trajectory that brought it to this point and which conditions the current set of possibilities going forward. If you want to influence the system in the most effective manner you have to understand its history which tells you its current potential and then develop connections that facilitate to evolve within one of the current possibilities.


Hi everyone! Welcome to Kids in the Kitchen. My name is Camden. My name is Ansley. And today we're going to make mini hamburgers. Here are the ingredients you'll need. Red frosting for your ketchup, yellow frosting for your mustard, mixed together shredded coconut and green food coloring for lettuce, vanilla wafer cookies for your buns, and chocolate mint cookies for your burger. Let's go back to the kids and they'll show us how to make them. And we first start off with making the mustard. And we squeeze it really hard in a circle on the sides. And then the next one we do is ketchup, which is the red frosting. And then we do it on the other one. And we do it right on the sides again. And then add some of this. And then you put these chocolate cookies on. Also, get the cookie, put it on top and then this. And then this is what it's supposed to look like.


WHO defines four dimensions or domains in data quality, which you see presented here. Completeness, internal consistency, which means do the data agree with each other. External consistency, does the data reported by health facilities agree with data from other sources such as a health facility survey? And finally, a review of the consistency of the denominators of the population estimates that are used to calculate coverage. So I'm going to review each of these four domains in turn. You see here a chart that is showing the trend over the last 12 months in the reporting completeness for two different data sets. It's possible with a single chart like this to show the trend for multiple data sets. Completeness, reporting rates, this is the most fundamental aspect of data quality. And before you attempt to interpret any trend in the data themselves, you have to look at what is the trend in the percentage of completeness of the data. Internal consistency, what do we mean by that? Well, you could think of this internal consistency as the apparent accuracy of the data comparing one aspect of the data with another aspect of the same data set. And there are several different ways of measuring this internal consistency. A way of measuring is here referred to as a metric. There's one metric which is the consistency over time that is our data that consistent from month to month. B, the second metric is consistency between indicators that are related and the commonest example of this is to assess what we refer to as the DPT dropout rate are the reported numbers of first doses of pentavaccine consistent with the numbers of third doses of pentavaccine. And we'll provide some other examples of related indicators. And finally, there's a form of internal consistency which can only be measured by visiting the health facility as I've referred to. And that is the consistency between clinic registers and reported data. And in that way, we can measure something called the verification factor. This is an example of the type of chart which we can use to look at month to month consistency of data in this case, the number of reported third doses of pentavaccine. And each of these lines represents the trend over the 12 month period and the pent of three doses for one region. The blue line is region one. And the blue line in particular has this hump here which unlike the data from the other regions suggests there's a certain inconsistency from month to month. This has jumped up in a way that we don't quite see with the data from the other regions. However, when we're looking at data at the level of a region, we can't be sure is this due to a data quality issue or does it represent an actual increase in services? But look what happens when we actually look at these trend lines for individual districts. So here we see the data from the same country and from region one. But in this case, there's one line for each of the districts of region one. And there's a certain amount of instability from month to month in the indicators. But look at this line for district number 12 where in the month of June, the reported third doses of penta has more than doubled and then it drops back down again. This is highly suspicious. And the lesson here is that when you're looking for month to month inconsistency, it's best to look at the data that are disaggregated to the level of the district and then you're more likely to pick up these quite suspicious numbers and have confidence that it is a data quality issue. In fact, with DHIS-2, it's possible to drill down, to go down to an even lower level and identify the specific health facility which has reported the suspicious number. And I think you would agree with me that when we look at these lines for each of the doses of vaccine for this health center number two of the same district of the same region, we see that this jump in the value for the region is actually due to a single number reported by this health center in June. And we can also see that this is almost certainly an error. This is due to a data quality issue. Not only has the typical value of less than 100, of the typical value of penta three jumped to 3,749, but we see that this health center in the same month has reported normal consistent values for the other data elements. So here we see an example of an erroneous value that has been reported for one health facility. This slide shows you the table that is generated by the WHO data quality tool to automatically identify facilities and values like this that are extremely suspicious and which are almost certainly due to errors that have been entered into the DHIS too. In this case, it has sorted these values and put up at the top of our table, the 12 months of data for Coway dispensary data on penta vaccine doses given in females under one dose three. And it has found that this number is the most extreme and most suspicious value of all in all of the immunization data sets. And we'll practice with this WHO data quality tool and see how it can be used to rapidly and automatically identify such outliers. The next type of internal consistency that we will be reviewing is, as I said, consistency of related indicators. And here's some other examples of related indicators in addition to looking at the dropout rate between penta one and penta three. We could also compare the values of the first doses of penta to values of the first doses of OPV vaccine. Both of these are typically administered on the same visit. So we expect the values of these two indicators to be roughly the same. And then a final example, the data on confirmed cases are frequently reported both in the monthly outpatient department report and reported in the malaria lab test report that is submitted each month. So we could compare confirmed outpatient cases to the total number of positive RDT and microscopy tests that were reported in a given month. The slide here shows how the WHO data quality tool analyzes for the dropout rate between DPT one and DPT three. And it generates this type of chart showing that there's one particular district which had a negative dropout rate, which if reported for a full year is usually a sign of a data quality problem. External consistency, I'll just quickly review these last two dimensions which aren't a major focus of this workshop. Here's an example of how the WHO data quality tool has compared the values reported on a household survey. In this case, this was a demographic health survey. The values for antinatal care first visit coverage reported on the survey versus what was estimated based upon the data reported by health facilities. And in this case, there's a striking difference between what is called the routine estimate of coverage, that is calculated with health facility data and the estimates based on the household survey. And finally, consistency of population estimates or denominator estimates. There's a couple of things that should be assessed about the denominators. One is whether they are consistent from year to year. And the second is whether related denominators such as the number of pregnancies, the number of live births, the number of infants are consistent between each other. So here's a chart giving an example of a country which has not had year to year consistency in the growth rate of the number of surviving infants, the population under one. In fact, that estimated number of population under one is seen to have dropped from 2015 to 2016. And then it increased dramatically from 2017 to 2018. So this estimated value is not showing year to year consistency. And similarly, if you think about it, it is a bit unusual that we would find that the estimated number of infants, of surviving infants in 2018 and 2019 was estimated to be actually greater than the estimated number of live births. That really should not happen at national level and suggests that we have some errors in the denominators used to calculate coverage.


Hey guys, welcome back to my humble abode. And the last time you were here, we did a smart home video talking about how we can use voice to control the home. Now in this video, I'm gonna show you some of the cool places you can have smart home devices that are just not lights within the home. So let's check it out. Okay, so you guys are wondering why I am in bed. And if you are, definitely hit the subscribe button and notification icon to see more videos of fun things I do on the channel. Now we're talking about different smart home products. This is a smart mattress from Aidsleep. And what I like about it is that the Aidsleep pod, which is what I have here, comes as a full system that does, of course, your sleep tracking as well as also regulates temperatures of your bed. So this is a queen size mattress. It's got two sleeping zones and two tracking zones, which means for me, I like my side warmer. I can keep it warm with the pod. Now the pod has distilled water in there, which allows you to regulate the temperatures. You can keep one side cooler, which board fam likes. And I like my side warmer. And you can have two separate accounts within the app to do that, which is great. Now in terms of the sleep tracking though, that is the best aspect of this because it does a really intense job. I've got my sleep report for pretty much the whole year. And you can see my sleep fitness, how well I sleep, the times I go to bed. You can also see the times I fall asleep, how long it takes me to get out of bed, which February was one of the worst months because it's really cold and I take my time. And also you can check out my heart rate, how well I get into deep sleep. Tons of metrics that honestly makes it superb.  I can do this on my phone and I can also use voice controls with Google and Alexa. Now speaking of voice controls, there's something else I do have in this room. Now I've got shades behind me and these are from a company, Lutron. Now I want to give a big shout out to my boy, Quinn from Snazzy Labs because he is the one who put me on to this. Now the Lutron shades are great, simple and easy to install. I don't want to change the installation process here. What I like about them is that you've got full control. I can use Google or Alexa to basically open up my blinds and I can say stuff like, hey Google, open up blinds. And it's going to open up the blinds behind me and you're going to see that whole process. Now I can also use the physical controls which are right here to open up the blinds and that's also really nice with the peak of controls. It's simple, it's easy to use and it makes it quite easy to have shut out blinds in your room and also work with your whole connected ecosystem. All right, so I did say I wasn't going to talk about lights but I will talk about light switches from Lutron. Now I love them because you can install them anywhere within your home, they have a regular light switch. And it works like a regular light switch but it also has Wi-Fi connectivity and this is done through the Lutron bridge which I have connected to one of the routers within the home. Now I like it because, look, as I mentioned, easy to turn on and off through the switch but you can also do it through the app and that's where I can control all my Lutron and evil devices like the Serena shade that you saw earlier, as well as also my lights. I can set it at different levels. It is simple, it is easy to use and honestly it is fantastic. Now I'm in the living room and honestly this is where I spent a lot of time and the air quality here can get stuffy because I don't have the windows open a lot of time which is why I use an air purifier and the one that I like using it in my house is the Samsung cube air purifier. I like it because it's got one really cool functionality which is about location awareness. It checks the air quality outside and also what you have inside, matches if it is poor or good and it turns on to improve the air quality you have at home. Now the location awareness is great because as you're getting closer to the house it knows you're getting close and it turns on to basically get you the right air quality that you're used to. Again for me that is simple and it's easy and it's honestly no fuss. You can control it on the app but that's not why I really like it. All that location awareness is great. Now I have mentioned a ton of applications and a ton of devices already before even going through the rest in the video and this brings you most to our sponsor Qualcomm with Wi-Fi 6C and why it's so important because my next device which is a router, a mesh router is Wi-Fi 6C compatible. This is the Linksys Atlas. Now what I love about the Atlas is that it is a mesh Wi-Fi router with Wi-Fi 6C support and what does that mean for you in general? It means that you have a dedicated six gigahertz lane for connectivity for any device that supports Wi-Fi 6C. So I do have my Galaxy S21 Ultra which does. I do have my PC upstairs which also and more devices that support that basically will use that dedicated line but that's not the only benefit. Now this system can support up to 195 devices. Now I've got a channel lights connected. I've got my smart TVs connected. I've got all the devices that you see in this video connected to this. So that brings in the real importance of what Wi-Fi 6E can actually do and what Qualcomm brings to the table for higher speeds, better connectivity, connecting more devices and again, better coverage across your home. So I've got three of this mesh Wi-Fi hubs around the house giving me connectivity from my door to my yard outside and having full coverage all the way. So honestly, this is probably one of the most important things you wanna add to your smart home to ensure that all your devices as we continue stay connected and while I'm sweating underneath the lights, let's go ahead and check out the most important thing we have in the house, which is our air conditioner. Stay cool in the house. We've got split AC units in different rooms and they are from LG and why I like LG here is that they've got Wi-Fi connected units that connects through the ThinkU platform, which is great, which means I don't have to use this cumbersome remote or look for the remote. I've got voice controls which I can easily use but I can also jump into the app on my phone which I have handy all the time to change the temperature, to change the fan speed, to look at air flow even just schedule when my air conditioning turns on. Now, as you can clearly see here, we have a few other appliances from LG that have taken up our smart home in a whole different level. ForwardFem here and I am going to be talking about some of my favorite home appliances. Now, everything for me is about speed and efficiency and I love everything in my home to make my life super easy. And today I'm going to show you the LG wash tower. Now, I absolutely love this thing because it makes my life so much faster. Now, historically, if you are going to put your clothes in the washer or the dryer, you have to select through a bunch of options. So what's the cycle speed? What's the, what kind of water do you want? Hot water, cold water? I love this thing because I don't have to do any of that. So I pop my clothes in there and I click normal speed and it actually detects the material and how big the load is. Now, that is such a time saver. The same thing goes for the dryer. You no longer have to guess how long the clothes need to be in the dryer. You just click start and it detects it for you. So when the clothes are dry, the washer knows and you are done. So the cool thing about the application here is that you've got all the things your device is in and I can jump into my wash tower here and see what's going on with my wash. So my dryer, there's nothing in there. It says it's normal. Does the auto detect, which is great. And I can see all the things that I want to do in here. I've got pre-wash off and all that stuff. I can't change anything because it's actually running. But if I had something in the dryer, I can also go ahead and set that. I can go in and I can also download different cycles as well. So you've got different things you can download. And as Boar Femme says, it does most of the work for you. So this is just me checking to see what it does. All I wish is that LG puts a robotic arm so you can move my laundry from washer to dryer and I'm good. Now, this is the final piece of LG smart hardware that I actually have and this is the LG Core Zero all in one. Now, what I like about this is it's got its own tower and that tower serves multiple purposes. Number one, I can put all the accessories and extension to it. It also houses the second battery which it has two batteries for this and it has an auto dump feature which means when you're done vacuuming with this bad boy you don't have to open it up and mess around.  And you now have a nice vacuum to use. Now, speaking of just vacuum functionality, this thing is great. Great suction, great power, works on hardwood, carpets. Like, you know the standard drill there, which is great. Now you're going, okay, what is the smart functionality with it, right? You've got Wi-Fi connectivity. You can see the charging. You can see if your collection area is actually full. And also you can swap this out to mop. It also has a mop attachment which you can see here. Allows you to do more than just vacuum with this bad boy. It's absolutely amazing. And check this out. It's got this compressor tool here so as you're filling up dirt, you just press it down and it presses it and compacts so you can do more with the 120 minutes battery lifetime. So it's awesome. And speaking of things that serve you time, let's talk about the Brava oven. This is one of my favorite things in our home because it saves you so much freaking time. So this oven actually cooks with light. And it's sort of like a mix of everything in your kitchen. You can use it as an air fryer. You can use it to reheat your food. And you can use it as a type of conventional oven. Now how this works is it works with light and it has these different sections and comes with these different trays. Now I don't know if you can kind of appreciate it from here, but it has these one, two, three sections which means that you can actually cook your steak. You can cook your vegetables all at the same time. And the oven, it's smart enough to recognize the amount of heat it needs to apply to cook your food perfectly every time.  So if you want it medium, if you want it well done, the app will do that all for you. If you wanna know more, I will leave a link below for the full review of the Brava Oven that I did a few weeks ago. We're going way in the bathroom, Thunder E. No, this is not only fans. This is a place that a lot of people only think about having smart or connected appliances.  Yes, I do have smart lights, but I'll start off with the Sonos Roam. And I like the Roam because it's small, it's portable. It is connected via Alexa or Google.  Now, I also have this nice cabinet that I picked up from Amazon, it's got built-in lights, which is great, especially if you wanna do your makeup or you are flossing or whatever you're doing in the bathroom. Now, for me, the biggest thing here is the shower. That is the shower from maybe a by moment. I've been using it for almost a year now. And I've gotta say it's been a great experience. Now, the version I have here comes with the wand, which has the attachment on the side. And I like it because it is not connected in any form or fashion, but it's smartly built. The reason is that this thing is easy to install. You can install it by yourself. You also have adjustability in terms of height. So if you're shorter or taller, the shower will work for you. But the greatest thing is that it uses 45% less water. So it's great for the environment, number one. Number two, it's great for my pocket because now that I own a home, I have to pay for my water supply and I'm using less water, which is great. But overall, using the shower and the wand together is a great experience in the shower. It's comfortable. You've got adjustabilities all around. And honestly, look, this is something I would definitely tell people to go pick up and check it out. They have different models to pick from and something that might have fit your style and look within your home. All right, so you guys have clearly seen that you can have smarter appliances and smart things around your home that are not just light bulbs. And no, there's no only fans edition for the bathroom section. Sorry guys, I apologize. Anyway, if you guys want to pick out any of those devices or those appliances, I have the links for you down below. And if you wanna see how you can control your smart home with just voice, check out my next video with of course controlling my smart home with Alexa. Otherwise guys, thank you very much and always enjoy your entertainment.


N. The Tiger. Financial News Network. T.F.N. News Update. Welcome folks, we at The Down Industrial finished out on 1.40 and Aztec up 42, S.P.S. Flat. Gold gold contract trade down $7.50 at $19.92 an ounce. We had Silver down $0.29, $23.77 an ounce. Light sweet crude up $0.44, $71.99 a barrel, notes and bonds. A 10-year note. 1.5 ticks trade in $113.13, the 30-year down $13 at $126.24, and $King Dollar up $68 ticks trade in $103.267, the euro is at $108, the yen is at $138 and the British pound is at $124 to $1 U.S. We get over and take a look at the spy folks, bottom line you have no buyers out here. We got a flat market up $0.17, you did volume of $56 million, bottom line is that you know last two days we did $97 million. This is all waiting about the debt ceiling talks all this week. This is going to go all week. So you have President Biden and Speaker McCarthy at 5.30 speaking tonight. I'm sure they're going to come out with a statement and if you go look at the S&P okay we'll go back to the S&P. You're going to see inside this S&P mini futures that you have two high volume lows. So that tells me whatever they say we're going lower tonight. Right now the futures to trade at $4206 and the low that I'm talking about out here is $4191. That's going to get hit. I suspect it's going to get hit overnight because I can't pitch them coming out of those meetings not saying something. That would be almost unheard of. We go to the dollar, we take a look at the dollar. The dollar is looking for $106 and the $106 in general is going to bring markets lower. So if we take a look at the dollar right now you're at $103.268 and bottom line the last swing point out here, highest swing point is laying out there at the $105.83. I'm getting where I'm getting the $106 folks is that that's a .382 retracement of the leg down. That's that's where that is. You know you got to remember the dollar had a nice expansion all the way up. The dollar reached what's that $114. So if you take a look at that from the highs to the lows the $106 area is that .382. Have a great night folks. Have a safe night. Come back and visit Tommy tomorrow morning. Kicks us off 9 a.m. Great show folks. Look at him folks.


Sometimes, we use different formulas for different input values. For example, maybe shipping is $5.99, but free for orders over $100. Or maybe tuition costs $3,000 for up to six credits and an additional $300 per credit over six. And your bank might extort a convenience fee if your balance is under $25,000. Now it's important to recognize that in all of these cases there is still a function defined for each input, but the formula used depends on the input value. And this leads to what's called a piecewise function. Our notation for piecewise functions looks something like this. Here we have our function, and it's equal to, well in this case, three different formulas depending on the value of x. So if x is less than 100, we use the function 10. If x is between 100 and 150, we use 50x, and if x is greater than 150, we use x squared. We can still try to find function values as we have before. So for f of 10, we have x equal to 10, and so this means we'll use a formula for x less than 100. One way of looking at it is that for this particular value of x, these other two lines don't exist, and our function is just 10. So f of 10 is equal to 10. For f of 125, we have x equal to 125, and so we use the formula where x is between 100 and 150. And again, it's helpful to pretend that the other two lines of this function definition don't exist because we don't have x less than 100, and we don't have x greater than 150, so we'll cover them up. And our function definition says that f of 125 is 50 times 125, which gives us our function value. For f of 500, we have x equal to 500, so we use the formula for x greater than 150. And again, these first two lines aren't applicable because x is not less than 100, and x is not between 100 and 150, so we can ignore them. Our formula says to square 500, and so we get. Now if a piecewise function drops out of the sky and hits us on the head, we're probably walking in the wrong neighborhood. More likely, we're going to need to write the piecewise function, and we can also write a piecewise function by writing a formula to compute a function value and then identifying where the formula applies. For example, suppose a company charges $5.99 for shipping, but offers free shipping on orders over $100. Let s of x be the total cost when you order x dollars of merchandise. So a helpful strategy here is to try some examples to familiarize yourself with the problem. So suppose you order x equals $50 worth of merchandise. Then the total cost will be the cost of the merchandise plus the cost of shipping. Now the cost of the merchandise is $50, and since we have to pay for shipping on orders under $100, we have to pay that $5.99, and so our total cost is $50 plus $5.99. Now again, since we're trying to do the algebra, it helps NOT to do the arithmetic. So remember, equals means replaceable. Saying x equals 50 means that any place I see x, I can replace it with 50, well I don't see it anywhere, but also any place I see 50, I can replace it with x. And the important thing to remember is that because there is a change when our orders hit $100, this formula only applies on orders less than or equal to $100. And so when we write our function, we'll include the formula with a note that this is only good if x is less than or equal to $100. What if you order more than $100 worth of merchandise? So again, we can try some specific examples. If x equals $200, then again our total cost is the cost of the merchandise plus the cost of shipping, and so that's going to be $200 plus our shipping is going to be free, so it'll cost $0. And again, since x equals $200, we can replace $200 with x and get our formula. And so our formula, but this only applies on orders more than $100. So we can write down our formula with a note that this only holds if x is greater than $100. Or let's consider tuition. Tuition for our college costs $3,000 plus $300 per credit over $6. So write a function t of c, giving the cost of tuition when c credits are taken. And here we might notice that the formula changes when you go over six credits, so there's going to be two rules. A rule when the number of credits is less than or equal to six, and a rule when the number of credits is greater than six. So again, we can try some specific examples to see how this works. Suppose you take c equal to five credits. Then our tuition formula is $3,000 plus $300 per credit over $6. And since the number of credits we're taking five is less than six, then there are zero credits over six, and so t of five is equal to $3,000. And again, equals means replaceable. Since c is equal to five, we can replace five with c and get our formula, t of c is equal to $3,000, which is the rule for c less than or equal to six. What if you take more than six credits? So suppose you take eight credits. Then again, our tuition is $3,000 plus $300 per credit over $6. And this time, there are eight minus six credits over $6. Again, it helps not to do the arithmetic. What are we going to do with this amount? Well, since it's $300 per credit over $6, that means we're going to multiply this eight minus six by $300 and then add it to our $3,000. And since c equals eight, everywhere we see an eight, we can replace it with a c and get our formula, which applies wherever c is greater than six.


Today I want to talk about artificial life something I've worked on for a lot of years and it sort of underlies a lot of research I've done more recently This is another New Mexico CS for all video for the past. We're doing on computational thinking and programming All right that very idea of artificial life is is kind of a weird because we normally think of life as is natural Nature is full of life But we need to come up with a definition broad enough so that we can see other kinds of things as being life or Life-like and in fact, that's the distinction that we'll talk about Immediately after though we claim is that these systems are merely life-like Strong claim is that these systems are actually life Whether it actually makes a concrete difference in any particular system is unclear But it does make a difference in our expectations We'll take a look at some demos and then try to wrap up as quick as we can This is my big area. So I like to talk about it The the meaning of life Not just a movie by Monty Python Here's a dictionary definition the state of being which begins with generation birth or germination ends with death Anything that happens in the middle This is sort of a catch-all. It's it's not completely satisfying. It's a description of what happens during a life rather than some Sort of necessary and sufficient conditions for what it means for anything to be a life Many people have taken cracks at Coming up with such a definition here's to a self-sustaining chemical system capable of undergoing Darwinian evolution a Self-organized non-equilibrium system such that it's processed governed by a program stored symbolically and creeped itself Now both of these talk about systems. They both talk about them doing something on their own sustaining organizing They have slightly different emphases Gerald Joyce is a chemist perhaps not surprisingly Least moment as a physicist When I as a computer person See program and particularly see things like symbolically Those are little red flags to me That's there's a lot of stuff that has to be explained when someone invokes program symbolic representations and so on I want to boil it away and make it as simple as I possibly can my favorite definition Now I Got this from my dad the internet seems to think that this is maybe from doctor who I'm not sure if anybody actually has any references to this and print I'd be interested to see a citation The key point of this is the preservation preserving so a big umbrella definition life is a system that Dynamically preserves pattern Okay, now you might think you'd be able to preserve a pattern without being dynamic about it like Mount Rushmore You know you just make it big and you make it out of rock and the pattern will persist the pattern will be preserved But in fact even the mountains come down eventually and it turns out Mount Rushmore Every fall the National Park Service gets out there and repairs it, you know plaster's up Lincoln's nose or whatever it is what they do so the larger system of Mount Rushmore plus people Dynamically preserving that pattern, but the lifelike part of it is really the people more than the Mount Rushmore Okay, so this is clearly extremely general and we're gonna have to admit that there might be Some things that aren't really as lifelike as other things. I mean even a little eddy whirlpool in a stream That you know if you moved one pebble it would disappear it has a Dynamically preserved pattern the water flows by and you see it it lasts for some period of time That's gonna have a little bit of life according to this view according to this definition So this fundamentally is sort of computational paganism Wherever you look out in the world if you see a pattern being dynamically preserved that is a little bit of life That is a system. That's a little lifelike and then it's a spectrum Okay, this is plenty of room for what we need Okay, so now we can build computers computer programs whatever that will display this kind of property that will dynamically preserve their pattern What are those? Computer systems that we build well that depends on the stance that we want to take to them We could take the weak claim And say that this computational system is a model of some living system and when we do that Our goal is to understand something about life Or understand something about whatever system we're claiming it's a model of and ideally we'd like to be able to make predictions About whatever it is that it's a model of Okay, let's take a look at an example. All right Here is a model of the world everything It's been running for a while here a day 2,400 and something What it is is a 100 by 100 grid with mountains All around it that nothing can get through and Spaces inside that can hold things You may see these little flashes every so often Those are I'm imagining lightning bolts on any given time step any given square has some probability of just zapping whatever is there and that's our model of stuff happening that Whatever else goes on in the system if it's going to be a realistic model at all it's got to have some process of tearing down decay Time-passing, okay, so let's dynamically preserve our pattern. Well, let's just draw a man first here Okay, this guy He's now setting in one of these squares and all of these little creatures that I've implemented The way they work is they look at once their turn to go We're scattering the turns around into every square in random order and then doing it again when this it's this guy's turn to go he looks at one random spot in his neighborhood and does something about it Maybe he moves there. Maybe he destroys and eats whatever's there. Maybe he has an awesome Whatever we want to do this particular guy does nothing. Okay, once his turn. He just says I'm done All right, and he's preserving his pattern Fine, right, but we know that sooner or later the odds are gonna catch up with him and He's doing pretty well Yeah, but he's the only Instance of the guy so down here. We have the list the amount of time that we've got the total number of living things We're calling this guy look he I call him type s because he just stands there. He's the standing guy Well, we'll even let him live but sooner or later. He's gonna get zapped by lightning and then he's gone Hmm So how do we fight against that we fight against that by Reproduction we fight against that by building a system that can make copies of itself. So Here is such a thing This is little green square is like a plant that just grows under the influence of sunlight or some resource That's generally available and it goes from one to two now. It's four. Well, one of them got zapped It would have gone for oh we lost our standing guy. Okay? He wasn't very satisfying anyway, he was Mount Rushmore Mount Rushmore just got you know lightning hit it On the other hand, it's very very very unlikely at this point that Enough lightning is going to hit all of these little type P plant guys To wipe them out their pattern is being preserved by copying and that's the basic living trek We start out with one guy then we had two then we had four and it's often used as an example Let this speed up a little of An exponential growth process one times two is four times two is two times two is four and so on It's worth noting that this growth process that we're watching right here Time thirty eight hundred Thirty nine hundred four thousand coming up. This is not actually growing exponentially Why not well because very quickly the plants are not limited by their ability to reproduce the way I program these guys They can reproduce fast They're limited by the ability to find empty space put an offspring in these guys never actually move when they wake up They look at one of the randomly picked neighbors and if it's empty and if they have enough energy They split they give some to they create a new plant in that position and then they Reduce their size by somewhat more than what they gave All right Let this go even faster All right and and what we end up with is this you know ocean full of plants That are Occasionally zapped By lightning and that creates an empty spot and then one of the neighbors fills it in that regrows and so on Okay The basic pattern preservation idea of life. It's about Amplification it's about reproduction and it's doing great Obviously we could have other things show up in this world like in particular a Urbivore whoa So what happened there we sort of missed it was so quick The Urbivores when they get a chance to move they look at a random square if it's empty They move into it if it's occupied by a plant they eat it if they have enough energy They might create an offspring where they used to be And that's basically it so they just sort of move around randomly and if they happen to have a plant next to them They try to eat it And what happened well, we had an absolute explosion in the population of these Another extinct the Urbivores the H's They're gone. So if we let this speed up the plants regenerate themselves and Now if we look at the classical mathematics governing predators in this case The prey is the plant and the predators the herbivores like if the plants had lookouts they'd be go, you know look out here come the vegetarians In the classical mathematics of it the continuous mathematics of it It's not possible for anything to actually go extinct. So the Urbivores become very small in number that would allow the plants to rebound and then there'd be plenty of food So the Urbivores would reproduce and eat them up Here of course, there's always that possibility of the last guy dies and in fact that's what happened here Let's try it again. We'll stick in a Urbivore He eats he reproduces they reproduce 200 300 400 reproducing very rapidly and Basically a plague oh my I'm just sweeping across it eating everything and Once again, they will all start to death now You can we actually if we can get lucked out Let's see what happens here We will get a system which this might do it Yeah, I think well. Yeah, I think this might do it If we can get a system where there's enough small patches of plants That have a few of the Urbivore sort of scattered around in them then in fact we can get to a rather stable Circumstance and this this will do it. Let's go to full speed here All right So the Urbivores are chasing around after the plants the plants are getting eaten But then the Urbivores are having famines and starving plants are regrowing. This is quite stable for As long as I've been watching it as I've been setting setting up this video it's only a small piece of what we would normally consider a living system if the Standing guy wasn't very realistic because he just sat there and tried to preserve one single pattern flawlessly The limitation here is that whenever the plant Reproduces itself. It's offspring is always absolutely identical down to the every last teeny bit of behavior and every possible parameter Same thing with the Urbivores The copying process is absolutely faithful Let's take a look at another example All right, so we've got our stuff happening again Let's put in and one of these evolutionary plants which you can't really see there The idea here is this plant has some genetic information that tells it one Two tells them what kind of color he wants to be all right, so this is sort of a pale blue green And now we're going through the exponential growth phase one two four which will quickly give way to a Quadratic growth phase in this case because our world is two-dimensional, so the periphery Only grows that fast But the difference here is that every time one of these plants has an offspring the offspring's color either It's it's you or how intense it is May shift slightly. Okay, and you can you may already be able to see that off on one side here The color is a little different if we let it speed up It should become more apparent Yeah, so now we're sort of getting some blue purple stuff and we're getting some sort of green or yellow stuff and It's kind of starting to look like a clown wig or something like that now. Why are these colors changing? They're just changing because of drift Because the only way that these plants move is by having offspring the offspring have little mutations So the further we get from the center where we started the guy with the more Generations down in terms of the plant lineage that we are all right. We've got a evolving herbivore Let's get one of him going And the idea with him is whoops he has a Particular color that he'd most like to eat so the the main color of his face this guy would you know sort of like to eat a sort of light Cream color so the the food that's around in the plants around not his favorite food That means he has a lot when he tries to interact one tries to eat it He won't succeed as often. That's the way I've made this work that when you get a good color match Yum, you chump it down when it's a bad match You're more likely to just not be able to swallow it and you don't get any energy that day But once again when you have a kid the kids Preference for what color and what amount of saturation how intense the color slightly modified compared to yours Okay, and these guys are starting to Reproduce and spread a little bit Speed this up All right, what's going on here the 200 to 50 There they're they're spreading now unlike the original herbivores which just ate everything these guys are more selective It seems like I'm here anyway. They kind of like the greenish stuff And they're sort of leaving the bluer purple or stuff behind And as a result the green stuff is starting to disappear from the world and the blue and Purple or stuff is filling in the empty space left behind We now have an evolutionary system where the plants are evolving under the pressure of the herbivores and The herbivores in turn are evolving under the pressure of the food sources provided by The Plants, okay, so what's gonna happen in the long run here? Maybe maybe we should let this cook for a while and talk about some other stuff and then come back and see what's happened here all right, so Was that model? All right, is it a model of a living system? If so what living system is it a model of it was that was that green stuff supposed to be algae or these little white dots They're snails. It was not actually a model of any specific system and one of the terrible problems With you the weak claim of artificial life is that it's really hard to make a Specific accurate model of an actual living system because actual living systems are so sort of gnarly They kind of depend on all sorts of different things and because they have that amplification step because they have that reproductive step with a System that has amplification Small differences at one time become big differences later on they can become big differences And as a result the small details of the living system may in fact Make a big difference how the system works over time so To make an accurate artificial life model of any natural system a specific species interaction What have you is very challenging. There's a lot of parameters that have to be set I mean, you know, how fast do these plants grow how fast they gain energy? How well when do they try to split how much energy do they give to the offspring? I just sort of made up parameter values for all that stuff in order to make a demo that showed some effect So coming up with predictability is the challenge But on the other hand if you sort of back up a little bit and say well I'm not trying to model algae or any specific living system in the natural world I'm just seeking to understand how living systems act in general According across many different systems. They act a lot like this They have Reproduction with amplification and so on Okay Well if we're not talking about the weak claim that this is a computer program Which is just a model as we've been talking about all through this class Then the alternative is making the strong claim the strong claim is that a computational system can be Literally be a living system and that we need to Bend the definition of living system and or computational system until that can actually be true The difference between taking the strong claim and the weak claim again is a matter of emphasis With the strong claim we don't necessarily care about modeling any particular system It's the difference between trying to model a flight by making bird wings and modeling flight by making jet engines and aluminum wings With the strong claim for artificial life the focus is up just on building systems that actually do something That potentially is useful or at least useful to somebody So do we have examples of this? Artificial systems that are out in the world doing work That are reproducing Maybe you know Well, here's one example This is data from 2001 kind of old now from use DSD Showing the infections of the code red computer virus and we can watch it over time At midnight there was a few hundred by noon well by 6 7 a.m. There's Thousands by the afternoon. There's tens of thousands by the evening. There's hundreds of thousands all over the globe What we end up with essentially is a map of Microsoft software usage as of 2001 on the entire globe This will go around one more time So unlike the demo that we looked at first The world in a box This it's confined to being inside computers. Yes, but it's all over the planet and Since then there have been many other sorts of these things out in the wild getting transmitted by Internet or floppy disks or picture frames all sorts of things USB keys and They actually do stuff They may do stuff just to computers the Stuxnet virus last year Did stuff in the physical world that caused physical machines to wobble and destroy themselves? How real do you need it to be? Before you say well that thing went out It worked its way through the communication channels reproducing itself found its target and Destroyed stuff in the actual world So I think there's some pretty strong basis for the strong claim that Computational systems can be living systems Since I think I am a computational system. I need the strong play you do too all right Let's check back. Oh, whoa What has happened here? Well, the blue stuff has sort of got eaten up And look at this now we've got these Red guys in the red patch. We've got some blue guys down here and All kinds of things. Oh, there's some green guys down here. There'll be some Well, okay. All right, so so it looks like what's happening now is Yellow plants seem to be kind of spreading out of the Southeast Because there isn't anybody who's really eating them But we know what'll happen soon enough The it looked like they were red guys here They're already getting lighter up here So where we used to have sort of big solid blue Monoculture of one type now we've got lots of little patches of quite different colors near each other And what looks like a endlessly churning, but if you step back Kind of stable ecology okay so Let's mop it up if we take the strong claim that Computational systems can be living systems These days we can start and well, there's a new area called living technology Which is focused specifically on the strong claim. It's saying we can build living systems that are lifelike in some way We can build them out of hardware That's like robots and stuff like that. We can build them purely out of software It's the kind of stuff that we just saw here We can build them out of wet wear that sort of carbon-based chemistry water solvents the stuff that we are made of and Hopefully We can do something useful with them for society It drives me crazy That if you look at artificial living systems today the example of Strong the strong claim of a life that I picked is a bad one It's it's one that is tearing stuff down the code red virus Stuxnet It's difficult not impossible, but it's difficult to find really decent examples of using reproducing systems for good For the for the overall benefit of society and I think that's got to change and so my current research area is focused on How can we re-engineer computing? How can we rethink? computing to take advantage of more of these lifelike principles and Oh, and so now it looks like the plants are cycling back towards white to some degree I mean, you know the important point well, there's a lot of important points But one important point about life is like what Woody Allen said, you know 90% of success is just showing up Life fills space wherever there's enough resources to support it and that means it can be there when the extraordinary event just Happens to happen somewhere That's it. Thanks for watching


Hello and welcome to the session. In this session we discussed the following question which says sketch a graph for the function y equal to x square minus 4x. Let's proceed with the solution. The function given to us is y equal to x square minus 4x let this be equation 1. Now we have to sketch a graph for this function. For this we will follow certain steps. First of all let us see the symmetry of this function. Now the function that we have is y equal to x square minus 4x. Now in place of x if we put minus x we get y is equal to minus x whole square minus 4 into minus x. This gives us y equal to x square plus 4x. That is on changing x to minus x in this function our function is also changed. So this is our new function which is y equal to x square plus 4x. This shows that the curve is not symmetrical about y axis. Now let's see if the graph is symmetrical about x axis. Our function is y equal to x square minus 4x. Let us now replace y with minus y. So our new function would be minus y is equal to x square minus 4x. So on changing y to minus y our function is also changed. This shows that the curve is not symmetrical about the x axis. Now we change x to minus x and y to minus y to check if the curve is symmetrical about the origin or not. So on doing this we get minus y is equal to x square plus 4x. So on doing this operation that is changing x to minus x and y to minus y our function is also changed and thus the curve is not symmetrical about the origin. Now we can check if the curve is symmetrical about the line y equal to x. For this we will interchange x and y. So on doing this we get x is equal to y square minus 4y. So the function is changed on doing this. So this curve is not symmetrical about the line y equal to x also. Now we will check if the curve is symmetrical about the line y equal to minus x. For this we change x to minus x and y to minus y. So we get minus y is equal to x square plus 4x that is the equation is changed on doing this. So it is not symmetrical about the line y equal to minus x also. And so we can say that the curve is not symmetrical about any lines. Now let us check if the curve passes through the origin or not. For this we will put x equal to 0 and y equal to 0 in equation 1. So we get 0 is equal to 0 square minus 4 into 0 that is we have 0 is equal to 0. So we can say the point 0 0 satisfy the given equation 1. Therefore we say that the curve passes through the origin. Now in the next step we find the points of intersection of the curve with the axis. First of all putting y equal to 0 in equation 1 that is in this equation we get 0 is equal to x square minus 4x that is x into x minus 4 the whole is equal to 0 which gives us the value of x as 0 and 4. So thus we will get two points of intersection 0 0 and 4 0. Thus we can say that the curve is the x axis which coordinates 0 0 and 4 0. This point that is 0 0 is also the point of intersection of the curve with the y axis. In the next step we find the intervals in which the curve is increasing or decreasing. For this we need to find dy by dx. So differentiating the equation y equal to x square minus 4x with respect to x we get dy by dx is equal to 2x minus 4 that is equal to 2 into x minus 2 the whole. Now for finding out the intervals in which the curve is increasing we take dy by dx greater than 0 that is 2 into x minus 2 the whole is greater than 0 which gives us x greater than 2. Now for finding the intervals in which the curve is decreasing we take dy by dx less than 0. This means that 2 into x minus 2 the whole is less than 0. So from here we have x less than 2. Thus we can say that the function is increasing for greater than equal to 2 and decreasing for x less than equal to 2. In the next step we find the turning points of the curve find the turning points of the curve we take dy by dx equal to 0. We have dy by dx is equal to 2 into x minus 2 the whole. So here we have 2 into x minus 2 the whole is equal to 0 and from here we get x is equal to 2. Now x equal to 2 in equation 1 that is this equation y equal to x square minus 4x we get y is equal to 2 square minus 4 into 2 that is we have y is equal to 4 minus 8 which is equal to minus 4. So when we have x equal to 2 y is equal to minus 4 from this we can say that the tangent at the point 2 minus 4 is parallel to the x axis. Then in the next step we find the minimum point on the curve for this we find d2y by dx2. Now as we have y is equal to x square minus 4x so from here we have dy by dx is equal to 2x minus 4 and from here we have d2y by dx2 is equal to 2 and this is greater than 0. Now from dy by dx equal to 0 we have x equal to 2 so d2y by dx2 x equal to 2 will be equal to 2 only and this is greater than 0. So this means that y is minimum when we have x is equal to 2 and for x equal to 2 y was equal to minus 4 so we can say 2 minus 4 is a minimum point on the curve. Now in the next step we prepare a table of values to find few points on the curve for the function y equal to x square minus 4x we will find different values of y by putting different values for x in this equation like when we put x equal to minus 3 in this equation we get y as 21 for x equal to minus 2 the value of y is 12 for x equal to minus 1 the value of y is 5 by putting x equal to 0 we get the value of y as 0 by putting x as 1 the value of y is minus 3 by putting x as 2 the value of y is minus 4 by putting x as 3 the value of y is minus 3 for x equal to 4 value of y is 0 for x equal to 5 value of y is 5 for x equal to 6 value of y is 12. Now we will plot these points first we have the point minus 3 21 so this is the point which coordinates minus 3 21 now our next point that we have to plot is minus 2 12 so this is the point minus 2 12 next we have a point minus 1 5 this point shows minus 1 5 next is the point 0 0 this is the point that is the origin which is 0 0 then we have a point 1 minus 3 1 minus 3 is this point next point that we are supposed to plot is 2 minus 4 this point represents minus 4 next we have 3 minus 3 so the point this represents 3 minus 3 next point that we have to plot is 4 0 this is the point that represents 4 0 then we have 5 5 this point represents 5 5 then next we have 6 12 so this point shows 6 12 now we will join these points by a free hand so we will get the shape of the curve this is the curve for the function y equal to x square minus 4 x now this curve is not symmetrical about any lines and as you can see it passes through the origin then it cuts the x axis at the points 0 0 and 4 0 this curve is increasing for x greater than equal to 2 and it is decreasing for x less than equal to 2 now if we draw a tangent at the point 2 minus 4 that is at this point we get that tangent parallel to the x axis the point 2 minus 4 is a minimum point on the curve so this completes the sketching of the curve for the given function so hope you understood the solution of this question


ClickFunnels, ClickFunnels, ClickFunnels. What is it? And how much does it cost? And why do over a 100,000 people use ClickFunnels around the internet? Why? Well, I'll be going over all of this and also be discussing exactly what are funnels I'll be going over the features of ClickFunnels. I'll be talking about the integrations that make it really cool I'll be talking about analytics and CRO or conversion rate optimization and how ClickFunnels does this. I'm talking about the training within ClickFunnels and also the affiliate program, which is one of the reasons why ClickFunnels is very popular. I'll also be discussing the pros as well as the cons of ClickFunnels, why it's great and why it might not be the perfect solution for you depending on your circumstance. So we're gonna be going over all of this in this video and I'll be walking you through some of the specifics of the functionality of it right here on my computer. I've made millions of dollars with ClickFunnels. I actually have an award somewhere that says, you know, I've made millions of dollars with ClickFunnels and I'll be discussing how you can exactly use it right here on my laptop computer. So let's get into this. Hey, John Crestani here, internet marketer and two comma club award winner with ClickFunnels, which means I've made millions of dollars setting up funnels with ClickFunnels. I'm gonna be going over what it is, how it works, who it's useful for, how much it costs. So first off, what is ClickFunnels? ClickFunnels is a program for building website funnels. Now, most people out there are using websites. They don't just visit one single page. You might go visit the home page. You might want some pictures of the product or the people using it. Then you might go on to collect their email and then you might go on to actually have them, you know, purchase the product after you've collected their email and sent them some information about your product or services.  Whether you are trying to learn how to lose weight or whether you're trying to learn how to make your skin look more beautiful or maybe you're looking to figure out which gun to purchase for home defects or maybe you're interested in how to correctly do the interior design for your home. Whatever you're doing, you're generally doing research in the beginning and then later on, once you've done a little bit of research, you want to know what are products for services or maybe you have more specific information of what to figure out. Maybe once you've decided, okay, for home defense, I want a shotgun. Now, what shotgun do I purchase, right?  You have a little better understanding of what you want. You're saying, okay, home defense, I don't want a baseball bat. I don't want a pistol. I want a shotgun. Then you're saying, which are the types of shotguns? There's 10 types. And then finally, at the end of the funnel, people are looking for a product to purchase or a phone number to call or a form to fill out or a software to sign up for a free trial for. And typically, this is where people are making a product decision and spending money. And to get people from the research phase of looking for products or services all the way down to the purchase phase, it takes a couple different steps. And usually those couple different steps, you can create a website funnel, take people who get the basic point of doing research or you know, whatever it is to getting the actual money, which is where you as an internet marketer make money. That's what funnels are. So we kind of spoke about that. Now, the features of ClickFunnels, I'm going to discuss, but ClickFunnels has a lot of features specifically for what we call direct response marketers. For people like me who are designing websites that are going to make us money. I'm not designing websites so I can have a pretty place to you know, to blog and just to show off some information or show off some cool things to friends or family. I'm building a website to make money.  And if you're building a website to make money, ClickFunnels is there to help you out every step of the way. I'll go over those in my computer in just a bit. ClickFunnels also has a lot of integrations so that you can actually run your business kind of all in one place. And that's really cool. Whether you want to actually collect money, you can integrate ClickFunnels with PayPal. You know, you can integrate PayPal with your website so that people actually paying money on your website. You can collect email addresses. You can post YouTube videos or put up other videos on your website. You can create photo galleries from other sites. You can integrate Facebook comments. There's all sorts of things you can do with integrations. And I'll talk about that in a little bit. You can also use ClickFunnels to do split testing and test different styles of web pages to make money from and look at numbers and be able to really run your internet business so you understand what people like and what people don't like. Now, the famous management consultant Peter Drucker has a very famous quote which is you can only manage what you measure. Let's say somebody like me doing YouTube videos. I'm looking to see what do you like the most? What is the most engaging topics that I can talk about? And if I talk about a topic that really nobody's interested in. I used to try to talk about data analysis and how to determine statistical significance in online advertising networks. Nobody's interested. Nobody wants to watch that. But if I talk about how to make money on YouTube, that works out a lot. And if I want to become rich and successful, I need to be doing more of what's working and less of what's not working. This is just plain Jane fact of adding value. Now, it may seem like a boring thing but the fact that ClickFunnels allows you for a very cheap price to actually do all of that and look at what's working and what's not working and all of the numbers behind it. It means that you can run your entire business through ClickFunnels and make a multi-million dollar business just with the data within ClickFunnels. Very exciting stuff. Now, the other great thing about ClickFunnels is they include a lot of training in it. They have mini documentaries, they have training, they have training series, they have webinars. They have so much training in there for anybody looking to create websites or learn how to do this. I mean that alone is worth the price of admission which we're going to go over in a second. And lastly, they have a great affiliate program with lots of different offers and ebooks and webinars and software services that you can offer to people and make money from. So ClickFunnels actually pays me more than $10,000 more than what I spend with ClickFunnels every month simply because they have a great affiliate program and I recommend them out to others. And so can you once you remember ClickFunnels. So first off, ClickFunnels, the cost is not cheap and the cost is actually $97 a month. But if you're running an internet business, it's almost invaluable and I'll go over the pros and cons in just a second here. So $97 a month gives you access to all of this stuff, the training and everything. Now I'm going to go into the pros and cons and then I'm going to start showing you some of the stuff of how it works here on my computer. The biggest, biggest plus of ClickFunnels from my perspective is that it requires no code whatsoever. It's totally built for non-technical people. Most people who got started on the internet and made a lot of money like Elon Musk and Bill Gates and Steve Jobs, Mark Zuckerberg, they know how to program. They're very smart, smarter than the average pair. They can do all sorts of things with code. Now if you want to build a website, my guess is if you're watching my channel, you don't really know much about technical aspects or how to code or whatever and that's fine. Neither did I when I got started and being able to have a website build a bit requires no code that allows you to advance marketing things is a very powerful thing. So that's one of the other things. Next thing is easy UI and UI stands for user interface. So having an easy user interface means that you can very easily just navigate around. You don't need to be an expert to actually set up websites. It just helps you out again. Just being simple is one thing, but being able to figure out the platform is a whole other thing entirely. ClickFunnels really focuses on these two things in a massive fashion. Next is they have what's called DFY done for you templates and websites. Let's say you just want to change some text around. A lot of the websites ClickFunnels has are built for you. So all you have to do is go in and change the text, change the images. You just click and substitute image, etc. And I'll show you all that stuff in a second.  Now, the negatives, the cons of ClickFunnels are a few things. One is $97. Anybody who's living in America or United Kingdom or Australia can afford $97 a month if it's going to add some sort of benefit to them. Everybody's paid more than $97 a month. And if you're running a website and you're selling a product or a service, you should be able to make that work. But people in foreign countries can't really make that work. The second con is that it can be slow at very high traffic volumes. Now, because it's built with the beginner in mind, because it's built to help people go from zero to 10 million, it's great for that. But as your websites get more and more traffic, my websites get almost 2 million people visiting them every single month. ClickFunnels gets bogged down by how much traffic I get to my web businesses. It just can be very slow. And you'll want to eventually transition to Amazon AWS for your landing pages. But that's even more expensive for the average person. And you need to have a full-time developer to really make use of Amazon to AWS. Okay, now here we are inside of ClickFunnels. And as you can see, there's a lot of options, a lot of things you can do. But let's start with the actual funnels themselves, which are actually located right up here where it says ClickFunnels. And we can select our funnels here. But you'll also see there's a lot of other options such as you can have contacts stored within ClickFunnels. So you don't need to use a separate program. You can see the revenue. You can track revenue and actually charge people money for products or services within ClickFunnels. You can actually buy other people's funnels or you can sell funnels in the funnel marketplace. So there's a lot of stuff there. But for now, we're going to concern ourselves with the actual funnels themselves. So as you see over the course of the years, I've built lots of funnels. I've built lots of websites through ClickFunnels and they make it really easy to copy and paste and build new funnels. It's so easy to build websites. There's no reason not to be doing it. So here we are in one of the funnels that I built to be an affiliate because what I do for a living is I sell other people's products for a living. I help other companies get customers and they pay me to generate new customers for them. So full disclosure, I'm an affiliate for ClickFunnels and every time somebody works with ClickFunnels, I get 40% commission. But that being said, I use ClickFunnels every day. So I'm not just recommending it because I'm an affiliate. I'm recommending it because it's an amazing program and I use it and this has been able to really just change my life, my career because I don't need to know websites and the UI is so easy. I wouldn't use anything else even if it was offered to. So and all of the other software programs have affiliate programs too. So here's a page that is built in ClickFunnels, which is a quiz page. It's a battery reconditioning program. Instantly bring any old battery back to life again as the headline. Now here we'll start seeing some of the features that makes ClickFunnels so great is you'll see I actually have a quiz here. This is not a standard website feature right here. We can say this. Do you know anyone who works for a battery manufacturing company or a company that manufactures? So I'll say no. Do you believe the old way, the only way to deal with the batteries by a new overpriced one from a big battery company? Yes. Have you struggled with an old battery company? Yes. We'll just click a couple things. They'll say analyzing your results. Then it will say it gives people some rules in order to see the product that I am selling. So you'll see it says, okay, accept these rules. This is pretty complex. This is five different steps. You have to read a lot of different stuff but it makes a lot of sense for people who are in this market. You click that and then you're brought over to the product which I am an affiliate for. This is no longer my website but what you did is you went through five different web pages that explain basically talking about reconditioning an old battery and seeing if somebody's a good fit. So I got them through five different websites using a quiz funnel which is something you can't do very easily on WordPress and I got them over to an affiliate site. Pretty cool, pretty slick and what's even better is I can share this page. If you also want to use this page, I can share this with you and I'm going to show you how you can get the copy of this exact funnel at the end of this video so that if you want to start using ClickFunnels and you want to start marketing other people's products specifically, you can use this funnel which is already working and making me money every single month. You can use it as well. I'll give you the link closer to the end of this video. Now, another really neat thing about ClickFunnels is the statistics. So you'll see on every page they have your steps which are your funnel steps and then you have a tab which says statistics. It's allowing you to figure out what's working, what's not working, how many people are visiting your sites, etc. Or even how much money you're collecting. Now, I don't use ClickFunnels to actually collect money. I'm working with ClickBank and DigiStore. But you'll see right here, I can see at a glance how many people visited my website in the last week. And for this particular page, we can see 5,000 people visited this website and 14,000 people visited this website. So very easily, I can actually get an idea of how many people are visiting my websites. And if you are using ClickFunnels integrations with different payment providers, you can see how many people are opting into your website. You can also see how much money you're made from the people that are coming to your website. So you can see a lot more information if you become a power user of ClickFunnels and you can see it all in ClickFunnels. You can learn your entire business through ClickFunnels and I know a lot of people who do. Now, I can't leave this out which is email lists. Now, you can set up email lists through ClickFunnels through what are called follow-up funnels and you can set up broadcasts and auto responders. You can do everything you want through ClickFunnels. Anything that's made to market a business essentially, if you're running a business where you're selling products or you're selling your service or generating leads, whatever you're doing, you can do it all through ClickFunnels. And they're actually built, they're specifically built to support those types of businesses which are trying to make money from their website or companies that are trying to get people contacting them from their website. This will take your business the whole other level and working with a company that specializes in that is very profitable. Now, all of us need training to figure out how to use the internet to make money. This is the mastermind of the part. If I spent a hundred thousand dollars to join a mastermind for a year to learn from people that are more successful than me to learn how to just make more money and be more successful in business. So I invest a lot of money in my education each year. I invest way more than this in my education because I'm always trying to learn from people who are more successful than me. And if you want to be successful in business, I suggest you learn from people who are more successful than you and learn about the programs you're working with. And ClickFunnels has all sorts of materials as you'll see to help you become more successful. They have their success path. They have documentaries. They have videos about building funnels. They have videos about how to actually write web pages that make a lot of sense to people and make people want to buy. They have videos to help you get more people to your website. They have so much stuff to really help you make money here. And you'll see right here they have just a ton of content. They have their 30-day challenge which is pretty exciting. They have 30 videos which will help you over the course of 30 days get started in business. Get your first dollars coming in. They have everything you need to get started. I've been through the challenge before and it's awesome and it really helps you even as a business owner and somebody who's making a lot of money. The challenge is a really good thing to help you just really start your business and get your websites up and really use that form of leverage which we call the internet to just start making money and selling stuff. So, I suggest you go through the 30-day challenge. If you're interested in going through the boot camp there should be a link down below in the description which goes over the 30-day boot camp to help you get started. Now, last but not least is ClickFunnels affiliate program. ClickFunnels is a great company to work with to actually earn money and have them pay you. And when you work with ClickFunnels, you're essentially helping people get information on how to start businesses online or you're helping them by recommending their software to people to use to start their own online business and you get monthly recurring commissions. So, that means you get a customer and you earn money from life which is pretty exciting and that's the real trick of how to build a stable income in the kind of very unstable internet marketplace. So, what you'll see right here is you earn about 40 percent recurring commission which means you earn about 40 dollars per month. Now, the other great thing about ClickFunnels is they'll pay for your car. Now, once you get 100 members in which means you're earning about $4,000 a month which means basically on a full-time income off of ClickFunnels, they're actually going to also buy you a car and they'll put as much as $1,000 down towards your car. So, now you're working with a company, they're paying you, they're paying for your car. There's a lot of perks to working with ClickFunnels and they have a lot of materials to help you be successful. So, here's an example of some of my earnings. As you see, I've earned over $177,000. With ClickFunnels, I earn $1 to $200 every day like clockwork with ClickFunnels. It's just a program that works very well and you see they have a ton of different programs that you can advertise. They have the One Funnel Way Challenge and the ClickFunnels program and the book and they have a book bundle and more books and all this sort of stuff that different ways that you can advertise and they have a lot of help, they have a lot of support to help you advertise that, a lot of trainings to help you become successful. And there's a lot of people that are earning full-time incomes as a ClickFunnels affiliate. A lot of people getting cars, a lot of people making a lot of money with ClickFunnels. I know people who've made millions of dollars just by recommending the ClickFunnels. I know people who have had no audience to speak of but they've been able to get people signing up for ClickFunnels and earning a consistent income. So, the opportunity here is really exciting. Woo! So, I hope you learned a little bit about ClickFunnels, how it works, the ins and outs of the interface and whether or not, figured out whether or not it's a good decision for you. Now, if you feel like this is something that you want to use to build your websites, really get started using the power of the internet, check out below. There should be a link below that says, John Crestani, whoa, free website. And you will get that funnel that I just showed you in this video. You will get that funnel shared with you so that you can actually start doing affiliate marketing. You can promote that product on ClickBang. You can start earning money, whatever you want. But that's already set up for you, that quiz. And if you want to change that quiz around, you can do a lot of things with that. So, you have your very first funnel that's proven to make money right today. Now, if you wanted to just learn how to be an affiliate for ClickFunnels or go through the 30-day bootcamp, I'm also going to put a link down below, which is johncrestani.comback.comback.com. So, you can go through the bootcamp, you can learn how to start your business and start earning commissions as a ClickBang affiliate. So, both those links will be in the description. So, I hope you liked the video. Please make sure you just murder that like button, subscribe to my channel if you want to learn more tips and tricks and software and how to make money and how to get traffic online. I've been making money online for the last eight years and I've made millions of dollars, tens of millions of dollars actually. And I try to help others make money online. So, hit the subscribe button, hit the notification bell to be aware of live streams or Q&A sessions I do from time to time. Also, if you have any questions, ask them below. If you have any answers, please help other people and answer their questions. We have a huge community going on and I'm really excited for all the people within our community here. We have different community outlets. We have a subreddit if you want to chat on Reddit, it's kind of like forum. We have a discord channel if you'd like to chat with other people in real time. We also have a Facebook group where we post many announcements on and there's some chatter on there. And we also have our own forum which I think it's released by the time this video is up. So, make sure to join any of the community outlets that engage you and interact with others. And please for everybody that's a part of this community and learning how to make money online, I recommend answer other people's questions too. I only answer about five questions out of like 2,000 questions a day frankly. So, I encourage others to help each other out and answer questions that you know. Thanks for tuning in, looking forward to seeing you soon and looking forward to helping you make some money in your online journey. Thanks.