These speakers made a heroic effort to track their thoughts complex as they are for hoping we can follow and I'm sure there are people here who did follow those thoughts and perhaps they sparked questions on your behalf. So we have Alan Lincoln and Adam with Scott backing up here ready to ask questions you might have. Russ. You probably better come up here to be heard. We can't really give a good answer to your question because we're going through the scriptures and interpretation and that's really all we have in the matter. In the case of Alma he was talking about salvation and the necessity that mercy as provided by the Savior's Atonement include repentance. He said that if it did not include repentance then God would fail to be God and all I can say is that I think my own opinion is that you would not have asked that as a rhetorical question but as an actual question that if God tried to have a plan of mercy that did not require on our part repentance which is the changing of our behavior then he would cease to be God because the purpose of mercy is to bring us back to God but we can't come back to God if we have unclean behavior. We have to change our behavior which is by definition repentance. So my opinion is I take the question literally that it would be possible for God to fail. Other people I'm sure would have different interpretations and in the case of Lehi talking about opposition again in order for us to grow and mature and to learn from mortality we have to have opposition as Lehi explained and if we had a plan of life or a plan of salvation that did not include opposition then the purpose of God would be destroyed because we really couldn't achieve the result of becoming like God without having opposition to give us choices to make. The choices began in the Garden of Eden with the choice of the fruit and we have choices in our lives and without the choices being available that we can't really learn and grow because we just become mere robots. So my feeling is that I take it literally I'm sure other people might have a different view. If we address to any of the three or all of the three there's a heavy reliance on natural law that informs each of the presentations but that was not flushed out. Are they making a reference to natural law allostoicism, natural law alloscolasticism or some construct of their own and then I will follow up question based on that. You would like to try what kind of law I think they're probably thinking of physical law rather than briefly in regards to my presentation I'm making no assumptions about a particular definition of natural line open to considering how any of those that you mentioned or others that we could talk about would fit into the paradigm not particular. Give a further response to that. Well I present your mention that God follows natural laws and exalted beings must be obedient to natural law. If that's the case does that not entail implicit neoplatonic ontology and all the problems that that brings with it? I don't think that necessarily follows unless you believe that there is a first law. There may be an infinite regression of laws in which laws are embedded. Some people think infinite regressions aren't rational. I disagree but does that answer your question? You want to follow up on anything? If you say that God must be obedient to natural law is that a coherent argument or is that a way? In my presentation where that was mentioned what I'm doing there is I'm portraying an interpretation of stuff coming from Mormon scripture. Where it talks about as DNC88 talks about there's no space in which there is no law. There's law in all space and it talks about and if you look in the paper which will be available on the internet there's a whole bunch of references to passages of scripture where it talks about God working according to law. So I'm making no necessary assumptions about what the authors intended by law. I'm perfectly willing to adopt all kinds of interpretations about what that law might be. Do you want to add something about that? Well I actually thought given talk yesterday addressed a lot of those ideas. The idea of Latter-day Saint concept of God is not necessarily the same as traditional Christianism. That God necessarily must pre-exist or pre-suppose the universe. But that is he is a participant and exists in it. And so when I talk about law I'm really talking about physics. It's presumed to know everything about physics or presumed that anybody on earth knows everything that we know. But it's not necessary. I mean there has to be some governance of interaction. And if he exists in the universe just as we do he has to be subject to those same governance of interactions. Whatever they may be. Assume that there is this larger substrat of interactions in this metaphysics. Where does it exist? And how is it that it controls God? And you can still say that God is God through the standard definition where he's perfect, powerful, blah, blah, blah, blah. It exists because it has always existed and there could not be existence. I would not necessarily say that laws in a materialist sense there is no other where there is just the universe. And so it has to exist in the universe. I don't speak of laws being something that has to have a where. It just is. How does it form physical beings? How does it form physical beings? Because it is there. And in other words you can't have law or you can't have interactions if there isn't some way of governing those interactions. And so the contrary of your question would be how could it be otherwise? This sounds like a conversation we'll have to go on over lunch. Lloyd. There seems to be a bit of confusion when we talk about natural laws as governing material or God being obedient to natural laws. Because natural laws, if I said okay I'm going to go outside and violate the law of gravity. We're kind of confusing. What do you mean by violating the law of gravity? The big question that makes your point is when we talk about natural laws we're not saying that natural laws govern the world.  Exactly. And so it seems to be kind of nonsensical to talk about God violating natural laws. What would it look like to violate natural laws? This doesn't seem to make any sense to talk about that notion. I'm not a physicist but I am a computer programmer. And in computer programming you can create physics engines like in the virtual world second life. And those physics engines may allow humans to fly which doesn't work very well in our world. And you can have those physics engines embedded in our world where the objects behave differently. So the physics engine in the embedded world doesn't violate any physics laws of our world. And if you want to talk about natural laws as being the way we describe the world then there would be natural laws that are different in those two worlds. The denizens of a virtual world would describe their natural laws differently than we describe our natural laws. But also going back to this question here just momentarily, the God that I worship personally, I'm not going to speak for anyone else, doesn't necessarily even know the answer to your question. And I'm okay with that. I'm okay with finite gods. Yes. This question is for Alan. Alan, I think you said, and it sort of follows up that, you know, the God has to abide by, the God has to abide by natural law. And you also said that some, I think you said that somewhere someone had printed a conclusion that the other end of the universe, the laws of physics and gravity and all that are the same as they are here. Yes. Two questions. How do we know? I mean, how can you measure that all the rules of interaction that we have here really are the same, 80 billion light years from here? And number two, I guess I, and it's really a fault, but I don't understand why we couldn't, why God can't create virtual world and why this itself isn't a virtual rule and that God has set the rules just as Lincoln would set the rule when he set it up in virtual, in a second life or something like that. Why, you know, why God couldn't change the rules and create another universe, create this universe differently? The same that I gave concerning natural laws in this world being also those in the galaxy, six billion miles light years away, was the recent development or advancement in science in which they were able to study the, I don't know the details, I'm not an astronomer or a physicist, but they were able to study the laws that seem to be in effect within this distant galaxy and they were obeying the same type of physical laws that we have in this world. Joseph Smith said that truth is, truth is things as they are, things that they have been and things as they will be. Yes, God could create a virtual world in which he could have whatever conditions he wanted, just as with second life, for example, that we can have virtual worlds that allow us to do things that are not physically possible in this world. But virtual worlds of that type are not reality. They're a creation of some intelligent being, but they're not reality because reality is things as they are, things as they have been and things as they will be. All we can do is take the scriptures that we have and then again try and interpret them in terms of consistency among the context within the different scriptures. But doesn't that just, I mean could you say that God did set up the laws? I mean why is it impossible for God to set up the laws for the universe? And they are the real laws that we have, saying no creation, let's develop them. I use the term law to refer to the relationships and the conditions that govern matter. We're all aware of the physical laws that are studied by science. I have extrapolated from that into the supposed laws that would govern material matter. Joseph Smith said that spirit is matter. So to me reality is the existence of matter where the physical matter or spiritual matter and we know through science, we're learning through science the physical laws that control physical matter and then we extrapolate a similar or parallel situation for spiritual laws. The scriptures don't really say that there are spiritual laws. This is sort of an extrapolation from our world to the spirit world. So this is reality is the existence of these elements and the relationships between them. In Abraham we do read that God said let us go down and take matter and organize our world which indicates that the matter, I can't really say that it would be pre-existent to God but it would be at least pre-existent to the creation of our world. And that the laws would be the laws that govern that matter. If God wanted to create a virtual world with different laws, he could do that. But the virtual world would not be reality in the terms of actual elements that exist. It would be just a fabrication through software or whatever the medium might be that would be used. But to me reality is the existence of real elements and real laws that control the relationships between those elements. Anything else is not reality. Sure, this is for Adam about agency. In the Doctrine and Covenants it talks about agency being a matter of accepting or rejecting light. And then coupling that with the LDS concept of the light of Christ that fills the immensity of space. I'm wondering if you could just, or if you have played around with the idea of light or light of Christ being information that's embedded. I mean as you're talking about quantum you're saying that it allows information to be imposed onto wave forms. There's some corolla that you've played with in that respect. I've read section 93 many times and I still don't understand everything about it. The light of Christ in my mind can't be just the photons, the electromagnetic radiation that we typically associate with. And so it has to be something more and it's not physically tenable to be just that. And it may well be something that helps assemble the information so that we get the simultaneous interaction with the information that we need. I think that's a really good idea. How to make it into an observable would be a real intriguing problem in question. I don't know if that answers what you're thinking about. But ultimately I don't know a whole lot about what section 93 is talking about. You were talking about detecting intelligent matter and I want to know what you or anyone else does with the dawning realization that some huge fraction of the matter in our universe is dark or essentially opaque to us. And that most of the real numbers we know about are uncomputable. How do you sustain sort of technological optimism in the face of the awareness of those limits? Why not give up and write novels? So what she's talking about is that 95% of the universe that we observe is some kind of stuff that we have no idea what it is. Some 30% of it is dark matter, which is a matter that we don't know what it is. And then the other stuff is dark energy, which is we don't even know what it isn't. And it doesn't behave anything like matter that we know of. Now, I don't know an LDS physicist who hasn't thought, oh, maybe dark matter, spirit matter. And so that is an intriguing idea and it has a lot of appeal. But it's something that has to be looked at very, very carefully. For example, we don't know if spirit matter has the possibility of interacting gravitationally, which is the defining characteristic of dark matter. So it's an open-ended question yet for me. And dark energy, well, we just don't know what it is. But it also presupposes that our cosmological model is on the right track. It works well with the model that we're working with and it works extremely well. But we also have to face the fact that the idea of something being untreated, having always existed, doesn't really work, doesn't really mesh very well, at least to me, with a finite past. We can't have all the intelligent matter in the universe suddenly appear some 13.7 billion years ago. What about Christine's question, will we ever be able to see this, or are we doomed to blindness to 95% of the universe? Well, I think the answer is yes, eventually. That's indeed one of the insurances of the Doctrine and Covenants, is that in the fullness of times, which means pre-millennium, all the orders of all the planets and stuff will be made known. And so, I have great optimism that we'll figure out some stuff. In the back on the wall. Yeah, there are some points that are being made about artificial intelligence and a problem with intelligence arising out of anything that we can do. But it seems that, more in doctrine, there should be a conflict between this thing that is temporarily becoming and yet eternally being. We have a Christ who is always the Christ, who was always the Christ, who will always be the Christ, but yet had to perform the atonement to be Christ. We have us who can become gods, and yet, once we become gods, we are eternal. Could it not be that to create artificial intelligence or make artificial intelligence in a computer sense, you're simply organizing matter according to the laws by which intelligence is organized, by which intelligence becomes what it is, and yet, once that intelligence is, it will be eternal, just as Christ is eternal, just as we will eternally be gods? I'll grant you that our use of the word eternal and stuff like that is a little loosened and so on. But if we want to create what we call a true intelligence, it has to come from something that is the cause of itself. And anything that we create will necessarily violate that condition. Now, if we can somehow incorporate intelligent matter into, I say, a robot of our own construction, then we could get a true intelligence. But without the, I don't see any way around the philosophical argument that... Organizing, if we can organize it according to the laws of intelligence, what makes it intelligence is intelligence. It's not so much creating it from scratch, but it's organizing it into this. Yeah, one of the ideas that I hold is that intelligent matter in and of itself isn't necessarily intelligent. It isn't necessarily what we'd call an intelligence, but that we didn't really become an entity in the way that we think of an entity that had a spirit body assembled around it. And then we became the intelligences that Abraham talks about. And if we could somehow tap into intelligent matter and manipulate it and assemble with it a body to go with it, then yes, we could make true intelligence. But in our present condition, none of our technology allows us to do that. One more question, Richard. This is for LinkedIn. Should the LBS church embrace an officially broken piece of technical artificial intelligence? Not a specific one, no. But we should be officially, in my opinion, endorsing the value of science and technology. And I think we do to some extent, but we can do it a lot more strongly. We've come to the point where we're going to split for just an hour for lunch. We're going to split in the sense that there are various paths we can take. We have a meeting with us today, the LDS Council, which is the sponsor of this entire program. And they are going to go down the walk over to the Johnson boardroom. We want to go out down the stairs and into the parking lot and down. And if you'll hasten over, there's lots of work that Joe Bentley has for you. For others, Claudia tells me there are lunches outside. We're not exactly sure we have enough lunches for everybody because we have no idea how we're coming. So we have preserved 15 lunches for the participants because we don't want the rest of you greedy people eating up their lunch when they're the ones who did all the work. So you can go and if you're delayed here, there will be a lunch reserve for you in room 110. And for the others, you're welcome to take a box lunch and enjoy yourselves. If you want to get away from all this for a while, if you go south, we're on the equivalent of 9th Street. If you get down to 3rd Street on Harvard or Yale, you'll find a multitude of very attractive restaurants that I think you will enjoy. So go south and to the right and you'll be there. So then we'll come back convene once again shortly after 1 o'clock. So thank you for all who took us this morning.


So, the next talk is about good randomness tests, and by Zhuang Ji Zhu, Yuan Ma, Jiang Lin, Jia Zhuang, and Zhu Wu Yin, and Zhu will give the talk, please. Hello, everyone. As we all know, RMB, they are doing many cryptographic applications, and these people have a lot of thoughts on such a quality of the data, and under the non-heritage, and finally, we've got a conclusion to this text, and for these tests, and there are 15 test animals to verify the hypothesis from different aspects of the everyday pollution. And then I will give an introduction to the whole test procedure. First, the whole sequence is divided into 10 sequence blocks, here and once on, and then we will do the test at her, and come to the left side of the vitals, and do the first level test, and the second level test. And the first level test has the capacity of having a new quantity of the left side of the vitals, and I come to the new vitals called RMB. The 15 test animals are divided into two blocks. Here I will talk about our contribution. We found out that the p-value of the phenomenal vitals are anchored by the second level test, although it is proper to do since the stated p-value p of phenomenal vitals is a standard of terminal value of v, and the problem comes from the absolute value of p-value of this animal from the terminal value of v of this abnormal vitals. We can see that there is one and two anchored, and for stated p-value test, we can see that there are three and four anchored, but since two and three are not anchored, this is the problem. Here I will give an example to show how this problem adapts to testing. To construct, for example, we do the testing if for each block it is more than that of the block, otherwise it keeps us locked and changed. The process sequence is significantly faster, and the number of one is larger than that of zero in all blocks. However, the process sequence still has a very high probability to pass the country. If the zero and one have equal rules for each block, all the p-p are greater than what is thought of. For both of the new match p-values, p-value is very nature, since the problem comes from the abandonment after the value, and we check the corresponding p-value instead of p-value. As the other cataclyses your p-value and change, p-value also includes the test parameters. Sometimes the observe is inconsistent with the zero, sometimes there is a difference. As the p-value has p-value and p-value test, it is more powerful with sensitivity. Here is the definition. So actually, that p-value is also different to the p-value we have to read in theory. Here I just gave the details. Another improvement is about accurate distribution. As we all know, with any infinite p-values available, and our Taylor physics, all the figures only have problem with the p-value, and the dashed-land with no symbol is... p-value also has p-value and p-value, and the dashed-land represents the... You can see the p-value line is closer to the unit, and the cumulative function between p-value and p-value is the parameter in theory, that p-value is the p-value we have on the following yarn days of p-value. So are there any questions? I have one question myself. So as I understand you, in the beginning you had this artificial distribution that tricks the NIST suite, and now you have a better test that is not tricked by it. But could it be that there is some other artificial distribution with different ideas that would actually then... that would be biased and pass the q-value-based test? So you have a distribution that passes the p-value test, but it's biased. Can it be that there's another distribution, a different one, that is biased, and passes your new test, the q-value-based test? Okay, thank you. Any other questions? Then let's thank the speaker again. And that was the end of this session, everyone have a nice evening.


I'm again in Austin, Texas.   Slime I'm gonna be running down your face when you're done. Eww. Eww. What's up players? What's going on ladies and gentlemen? This is Dan Wimmer from ZenDude Fitness and Today we've been getting a lot of questions in the YouTube community about How do I run and jump rope at the same time? And I'm like, y'all I'm gonna teach you. I'm gonna teach you that running in place Jump rope style. You feel me? Brandon and I are here to make these videos to help you guys become better at jumping rope So you can ultimately just feel better look better and have more fun in your fitness regimen So whatever videos we can make to speed up that process or to make it easier for you to get the results Just let us know. That's what we're here for and this is a shout out to my man Diego Wild West in the YouTube community Diego representing Mexico. That's awesome. My dude. Love that country today We're not jumping rope and no we ain't skipping rope. We're doing saltar la cuerda Saltar la cuerda. So for me it would be salto la cuerda. Did I get that right dude? Let me know. Let me know It's cool. I won't be offended if you guys want the rope used in this tutorial Go ahead and click the link below it's the cross rope again best most durable rope that we have out there if you guys want more of these free Workouts and a more structured manner and you want daily access to burn into myself and hop in our free four-week challenge So we can coach you up and give you some advice as you start your journey becoming a lean jump rope ninja The first thing I want to talk about is the regular bounce fundamentals Now I know I say this in every single video that I shoot But I cannot tell you enough how you need to if you watch me in the footage here All you need to be doing is making sure that your elbows are in the arms are bent at 90 degree angles The rope is mostly controlled by the forearms and the wrists Don't think so much about jumping over the rope, but keep the knees bent stay up on the toes You should not be coming more than an inch or two off the ground and check out these videos too If you have trouble just doing the regular bounce I linked them up right here next what I want you to do is put the rope down And we are just going to practice running in place and just like the last video I shot for jump rope for beginners I want you to imagine the rope coming under one time for every time that you put your foot down Not twice for every time you swing the rope just once so as you see in the footage here when I'm running in place I'm envisioning I'm kind of fake jump roping and envisioning myself swinging that through under my feet under each foot one time instead of two I cannot stress enough how important this is alright guys next what I want you to do is grab the rope Start doing regular bounce and then let's just work in some running in place if you can Every five to ten skips or so so I just want you going as you can see me here I'm just doing regular bounce and then I'm just throwing in a running in place and then stopping So regular bounce throwing in a running in place and then stopping I'll let you guys follow me here as I take it a slow motion and finish The next thing I want to talk about is the click of your wrists now I like to think this it's very important that you find your rhythm when jumping rope And so the next thing that goes into this is every time my foot is about to lift up off the ground So in this case right foot left foot right foot left foot every time that's about to lift one of those is about to lift up I click my wrist a little bit forward just to give that rope the momentum it needs to get around if you see in the footage here My wrist is basically controlling Everything and just skipping so what I'm doing is as my foot comes up slightly That's when my wrist clicks pushes the rope forward and gives it the momentum to go under as my other foot is coming down Less is always more with jumping rope. There's a big tendency for people in the running in place to basically do high knees That's great. I'm glad that you like to overachieve, but it's not necessary Keep your feet nice and low to the ground and everything from the waist up should look the same as if you're doing just regular bounce One thing you can do to make this a little bit easier is add in music I like to do a lot of 90s hip-hop or just hip-hop in general electronic music Something that has a good beat and that you can find your ribbon too. So one two three four one two three four You should be counting that out in your head as you alternate your running stance So that's it today guys for the run-and-place tutorial if you have questions leave them in the comments below And we'll see you on the next Zendu fitness tutorial or workout ladies and gentlemen It is hot as hell out here, and I'm leaving


The study examines the relationship between redlining and present-day summertime intra-urban land surface temperature anomalies in 108 urban areas in the United States. The results reveal that 94 percent of studied areas display consistent city scale patterns of elevated land surface temperatures in formerly redlined areas relative to their non-redline neighbors by as much as seven-seat, regionally, southeast and western cities display the differences while Midwest cities display the least. Nationally, land surface temperatures in redlined areas are approximately 2.6 C warmer than in non-redlined areas. The study suggests that historical housing policies may be directly responsible for disproportionate exposure to current heat events. This article was authored by Jeremy S. Hoffman, Vivek Shandas, and Nicholas Pendleton.


We will with the definition of a set the question is that what is a set although it is easy to ask this question it is not so easy to answer what has been realized that this simple question leads to several more difficult questions in this lecture we are not going to discuss the difficulties which leads to eventually introduction of axiomatic set theory instead of that we will discuss a somewhat working or operational understanding of a set what we note that in mathematics or in several other applications when we talk about things we somehow understand a collection of things which we are interested in for example when we are talking about integers that is 0 plus or minus 1 plus minus 2 plus minus 3 and all that we rarely think of the set of elephants or set of cows or set of students on the other hand when we consider set of students we usually do not consider the set of complex numbers at the same time or we do not consider set of all possible subsets of the set of integers thus there is an idea of universe which we will denote by script u so when we are talking about set of integers then we will simply say that our universe u is the set of integers the z which is the set of integers we may be talking about real numbers then you will be are the set of real numbers or we may be talking of the set of all students in IIT the set of all students registered in the IITs so these are not numbers these are human beings of course we can label them by numbers we can label them by names but there is a trouble that names of two students may be same so possibly we will label them by their enrollment number and the name of the IIT and like that but of course they are not set of integers nor they are set of all subsets of integers so like that there are different scenarios where we have different universes the elements of an elements of a universe is called objects that is the things that make up the universe in case of integers the objects will be integers in case of real numbers the objects will be real numbers in case of the set of students the objects will be individual students here we will use elements and objects synonymously now once we fix a universe then any collection of well-defined objects inside that universe will be called a set provided that the universe is not too large we are not going to discuss the issues that when will the universe be too large and all the other complicated questions we will simply take the examples that I have discussed already and many such examples where this description of a set works nicely so we can even say that if we fix a universe fixing universe the any collection of any collection of well-defined distinct objects is said to be a set now of course this is not a definition it is just giving an idea of what we will mean by a set it is not a definition because the question that what is a collection will will be raised if you call this a definition and then we have to define somehow the collection the main idea over here is that we fix a universe so we fix the type of objects that we are dealing with and within that type of objects we specify certain objects carefully so that when we encounter an object in that universe we are able to say whether the object that we have encountered has that specified property and this collection or ensemble of these objects which within a universe which specifies properties is called a set for example if we consider the set of integers z which is given by 0 plus 1 minus 1 plus 2 minus 2 and so on if we consider the set of integers which are multiples of 2 that is set of even integers we can now we can easily determine given an element in z whether it is even or not so let us call e as the collection of even integers this collection e is a set the reason is that we have fixed the universe and once we have fixed the universe if I say that I am interested in the set of even integers then given an integer I can determine whether it is even or not and then I can conceive of the collection of even integers in case of objects which are not numbers if I consider the set of all students registered in IITs then we can consider the students registered in IIT Roorkee so the students registered in IIT Roorkee forms a set in the universe of all the students in registered in IITs so we have more or less understood what we mean by a set now we move on to subsets if CD are sets a universe you say that C is a subset of D and write C C every element of C is an element of D in addition D contains an element which is not in C then C is called a proper subset of D and this is denoted by C properly contained in D this symbolically will mean that for all sets CD from a universe you if C is a subset of D then for all x in C implies x in D we introduce some more symbols here that is the symbol this and the symbol inverted a this symbol which looks like epsilon means belongs to belonging to or simply in this means for all thus the sentence that I have written here can be rewritten as for all x x belonging to C here we have another symbol for implies which is this one so I write over here this means implies x belonging to D we will be using this symbols very often so it is good to get used to use to these symbols now there is another symbol that is used frequently which is known as this means there exists we will see say that C is a proper subset of D that is C a proper subset of D implies there exists x belonging to D such that x does not belong to the set C the converse is also true that is if there exists x belonging to D such that does not belong to C and of course here C must be a subset or equal of D then C is said to be a proper subset of D now we question that what is the idea of equality of sets that is when do we say that two sets are equal for a given universe you the sets C and D taken from you are said to be equal we write C equal to D if C is a subset of D and D is a subset of C so here we note the chain of arguments first we give an idea of a set and we give the idea of a universe and then once we give the idea of a set then we give the definition of the subset relation that is we take two sets from the universe and then we say that the set the first set is a subset of the second set if all the elements of the first set are elements of the second set so that is subset equal and if it so happens that the second set has some elements or at least one element which is not in the first set then we will say that the first set is a proper subset of the second set and then we say that if we have got two sets C and D of course consisting of the elements of the universe which we have fixed before starting all these discussions then if it so happens that C is a subset of D and D is a subset of C that is all the elements of C are elements of D and all the elements of D are elements of C then we say that the two sets are equal this leads to some results related to subsets which are somewhat easy therefore I will just write the results and leave the proof to the audience so the first theorem states that let A, B, C are subsets of U that is I have fixed U and A, B, C are sets then if A is a subset of B and B is a subset of C then A is a subset of C B if A is a proper subset of B and B is a subset of C then A is a proper subset of C C if A is a subset of B and B is a proper subset of C then A is a proper subset of C B if A is a subset of B and B is a subset of C then A is a subset of C these are extremely straight forward results and as I have said that I leave it for exercise now let us look at some examples suppose we fix our U to something very small that is 1, 2, 3, 4, 5 and consider two sets A 1, 2, 3 and B 3, 4 now we see that A well another set C 1, 2, 3, 4 so we see that A is a subset of C because A consists of 1, 2, 3 and C consists of 1, 2, 3, 4 further we see that 4 is in C but 4 is not in A therefore A is a proper subset of C similarly we see that B is a proper subset of C but if we consider A and B A is 1, 2, 3 and B is 3, 4 then A is not a subset of B and B is not a subset of A next we introduce another very special set that is called the null set so the null set or the empty set is a unique set containing no element as I have told before that when we are when we have fixed the universe then a set in that universe contains some specific elements of the universe or it may as well contain all the elements the only thing that we expect that when we say that A is a set in the universe U then given an element or an object in U I should be able to decide whether that object is inside A or not now if A is whole of U then the decision is easy because if you give me any object then I know by default that it is in A because A contains all the objects of U if A has some objects in U and some not and some objects in U are not in A then also hypothetically we can have some kind of rule or listing by which we should be able to say that whether an object in U is in A or not but this thing when extended to the other extreme where A does not have any object in U then also A is a well defined collection of objects of U because when we take any object in U we know that it is not in A so A contains no object and this is a very special set called the null set or the empty set and it is denoted by ? or just two braces without any anything inside one result related to the empty set which again is very obvious for any universe U let A is a subset of U then ? that is the empty set is a subset of A if A is not equal to ? then ? is a proper subset of A so this basically says that the empty set ? is a subset of any set A and if A itself is not ? then ? is a proper subset of A the reason behind this is that we say that a set C is a subset of another set D subset of D if x belonging to C implies x belonging to belongs to D now as long as this statement is true that is any x belonging to C belongs to D then C is a subset of D now given any pair C and D if we want to show that C is not a subset of D then we have to find out an element x in C which is not in D so that this statement is false now the trouble here is that when C is equal to ? then C has no element therefore we cannot find an element for which x belongs to C and x not belonging to D holds therefore we cannot prove that this is false and therefore we have to take that ? is a subset of D or in the case of the theorem this is a so therefore what we see is that the empty set ? is a subset of any set we will do this theorem one once more when we formally study logic in after some lectures now we will briefly look at the problem of representing a set so one form of representation we have been doing so far rather intuitively is to put the braces around certain objects for example if we have certain names of students like let us say Sudhir, Aman, Umesh, Dinesh then the set containing these students possibly may be denoted by S and written within braces Sudhir, Aman, Umesh, Dinesh of course we understand that these students are coming from some universe that we have fixed before with numbers we have already seen and we have been doing that suppose we want numbers from 1 to 5 that is integers from 1 to 5 we have just written something like this suppose I denoted by n and I write 1, 2, 3, 4, 5 so in this way we can collect the objects and put braces around them and represent a set but as is evident to all of us that if we have an infinite set or a very large set it will be very difficult to write all the elements or more often impossible to write all the elements within braces then we take some other alternatives for example what we can do is that first we fix the universe you suppose I want all integers from 1 to 10000 then fixing the universe you I can write the set let us say I as x belonging to you such that 1 less than or equal to x less than or equal to 10000 thus we can avoid listing down 10000 integers by writing this inequality and understanding that you is a set of integers but we have to be careful here because it depends on how we choose the integer how we choose the universe because suppose we choose the universe to be set of real numbers then instead of a set of integers this same looking set will be an interval which I am writing as int between 1 to 10000 of course it is possible to write other sets in the same way for example suppose we would write we would like to write all the matrices all the 2 by 2 matrices with real entries whose determinant values is non 0 then we may write it like this that g is equal to a b c d such that a, b, c, d belongs to R and ad-bc is not equal to 0 of course this is an infinite set so I cannot write all the 2 by 2 matrices with real entries with non 0 determinant I cannot list them but with this notation I can specify them quite precisely next we move on to the idea of the power set of a set now suppose a is a set of objects from a universe u the power set of a is a set of all subsets of a now let us look at an example suppose a is a finite set containing only three elements now we start writing the set of all subsets of a the first and the most obvious which is a subset of any set is Phi that is a set containing no element and then we have the sets containing just one element that is 1, 2, 3 and then we have the sets containing two elements 1, 2, 1, 3 and 2, 3 and finally we have the set containing three elements that is 1, 2, 3 and if we put braces around all these sets then we have the power set of a which we denote by Pa now if we count the number of elements in Pa we see that this is 1, 2, 3, 4, 5, 6, 7 and 8 we write that as simply writing Pa within two horizontal lines and this is 8 by very easy counting argument we can prove that if we have a set containing n elements then its power set will contain 2 to the power n elements suppose a is a finite set containing n elements then Pa will contain 2 to the power n elements and the notation that we have used here is quite general so if we have a finite set then by writing that set symbol within two vertical lines we denote the number of elements in that set suppose S is a finite set then is the number of elements in S in today's lecture we have started with the definition or not really the definition but a description of the idea of a set we have talked about how to conceive of a universe and then conceive of some the some collections of specific objects within the universe and after that basic description we have defined the terms such as subsets proper subsets null sets null set or empty set and lastly we have talked about power sets and number of elements in a set in the next lectures we will discuss more on sets such as operations on sets and laws of set operations but this is all for today thank you.


Hey guys welcome back to this new video now today I'm going to talk about how to take your football academy to the next level So if you haven't already check out the the first three episodes of this four-part series Now if you watch those three then this last one is going to make a lot more sense Okay, if you just watch this one, then you won't have a Scooby-Doo about what I'm talking about All right, so how do you take your football academy to the next level? now I Get questions every single day from from coaches who are based here in the UK. They reach out and they say Leo I'm having trouble doing this or I'm having trouble doing that Or I don't know how to recruit new players or I'm looking to to get my business to the next level now business owners of Football academies might be at different everyone's going to be at a different stage with their business some might be satisfied with Having a certain amount of of players that they work with each each week others might want to expand and Start working with hundreds of players each week Now obviously if you want to work with hundreds that requires Staff it requires systems it requires organization and It requires marketing and promotion and all of that fun stuff So how do you take your business to the next level now the average football academy here in the UK? has between I want to say 30 to a hundred clients in their program, right? There's other ones that are Bigger or that have been around for long, but on average the the average coach and the average business owner who has a football a football academy here in the UK has between either 30 and a hundred clients active Throughout the year Now when I talk about football academy, I'm not talking about a club program, right? I'm talking about more specifically performance-based training so a program where your clients are coming to you each week for Performance training so to get better either that it that might be technical training that might be mental training That might be strengthen conditioning tactical and positioning training Whatever it is, but it's more performance base Okay, so I know a lot coaches watch our channel and they Reach out and they say right here. How do I build a football club? Right. This isn't about building a football club This is about building a performance training academy where your training players Who are might be actively playing for a club, but want that extra supplemental training? that They want to get better. Okay now Some coaches what they tend to do is now that they have a an academy in place They have a training program Now the next step might be okay. Now. I want to have a club system set up Okay. Now having a club system set up is a monster. All right. It's it's a very big and it's a very complex process Because you have to register that club with your local FA and you have to have specific People within your club that that run specific roles, etc And I'm not going to get into that because that's not what make money coaches sport specializes in we work more with trainers or coaches who have performance academies so If you have between 30 to 100 clients, what would now be the next step? To your business right so for some coaches that might be okay. Well, I want to recruit I want to get from 30 to 60. I want to get from 60 to 90. I want to get from a hundred to a hundred and fifty Players and clients training training with us on a yearly basis So how do we get to that next level now? I want to share with you a couple of things that It coaches that are in our program are currently doing That can help you to scale and to grow your business even more right now The first one is a referral system now I touched on it in previous in the previous video about how to recruit new new clients and you plays into into your program into your academy, but if you have a Really good and consistent referral system in place You will be able to get your your business to the next level in 90 days Okay, and I would even say less than 90 days I've seen some coaches who go who've taken their business to the next level in 30 days but it requires a really good referral system in place where every single month you're reaching out to your current clients about Promotion promotions or referral and promos that you're running within your academy that can help to To get other client like mining clients into your program Because as I touched on in the previous video if you have like-minded clients all in one program Who are then referring other like-minded parents into you? Imagine where that will that will take your business your business will explode and also your customer retention Which is something that I'm huge on Will be really high. Okay, so you're gonna go from having cut clients with you for for maybe one year To three or four years. Okay, and if you have clients with you for three or four years Imagine the cash flow in your business every single month All right, and it becomes predictable because you know, right these clients are committed these clients are gonna stay with me And these clients want to keep growing and keep being in my program For the long term. Okay, so number one if you want to take your business to the next level You have to have a really good referral system in place With your business right if this is something you want help with getting contact with me My email is make money coaching sports at gmail.com Send me an email there. I can schedule a call of you to show you steps on how to set up a really good referral system in your business Now the second thing and this is something we help coaches and trainers with is Email marketing all right or promotional campaigns But I want to start on more specifically email marketing So I know the average Football Academy business owner Doesn't run many email marketing campaigns. Okay What most coaches do is when they have an upcoming clinic or when they have an upcoming camp or When they want to recruit or or if they have trials coming up That's when they're gonna run an email camp marketing campaign But what we do at our company is we teach coaches how to run these campaigns on a regular Basis right where you're sending maybe two to three emails out every single week To keep your clients engaged to keep to stay consistent and to keep clients Thinking of your brand Okay in this market where it's very competitive where there's so many new trainers every single week Coming up with new academies You have to be number one in your your clients Mind your clients thoughts and when other clients talk to other parents. They're talking about your academy They're talking about your coaching. They're talking about your program Okay, so email marketing is something that will if you do it on a regular basis Will help your business to get to the next level and then the set the third the third one is obviously social media marketing Very similar to email marketing, but social media marketing and how to create really good Content how to create really good promotional campaigns on social media and also how to use social media on a consistent basis where your Creating engagement and you're turning a viewer or a follower Into a client right so those are the three things that Our company really specializing and we help coaches every single week in right So the first one is if you want to take your business to the next level is having a really good referral system in place The second one is an email marketing campaign where you're running on a weekly basis, right? This isn't Something you're running every half term. Okay, when you have an upcoming camp or when you have upcoming trials No, a good email marketing campaign where you're sending out Engagement and emails that engage your reader two to three times per week We're they're getting on a they're applying to these emails and getting on a phone call with you or You're constantly sending out promotional Campaigns or promos to your email list So you can sell them on an upcoming camp and I'm coming clinic or Or even promote your referral system through your email marketing Okay, so that's the second one if you're consistent with that that's going to take your business To the next level third one is social media, right all parents today Especially here in the UK and I know all around the world I'm talking about more specifically in the UK most parents are going to be on social media Right, so you've got to figure out where what platform most your parents are are they on Facebook? Are they on Instagram? Are they are they on tiktok? I know a lot of parents now. We're starting to engage more tiktok Okay, so where are your clients? Where are your parents and if you want to take your business to the next level You have to learn how to use Social media okay, how to market how to promote on social media to create engagement and turn a viewer or a follower Into a paying customer. Okay, so if you need any help with this And like I mentioned at the start of this this video If you haven't already go back and watch the first three Episodes they're going to make a lot more sense to you, especially when you get to this fourth one So if you need any more help or more personalized help, okay reach out to me Okay, you can either Schedule a phone call with me in the link is in the description of this video Or you can send me a direct email at make money coaching sports at gmail.com Right, I respond to every single coach or trainer that reaches out with any questions or Or concerns you might have with your business and taking your business to the next level, right? So I hope these these these four part series really helped you and I look forward to to see you on the next one


the speed of light, the cloud of dust, and a hearty, high of silver, the lone ranger. With his faithful Indian companion, Toto, the darling and resourceful mask rider of the planes led the fight for law and order in the early western United States. Nowhere in the pages of history can one find a greater champion of justice. Return with us now to those thrilling days of yesteryear. From out of the past come the thundering hoofbeats of the great horse Silver. The lone ranger rides again. Oh, Silver, let's go because I am Silver. Thunder Martin's mules have been pastoring for some time on the rafter H. Claire Bell Hornblow, who owned the ranch, tolerated the mules. In her rough way, she rather liked the big mule skinner, and Thunder thought that Claire Bell was all that a woman should be. Ah, I wonder if she had a face like a horse. Well, I've seen some downright handsome horses. When she sits on the meal, Gents, I want to tell you that woman can sure do things with her up. Look, here, Thunder, if Claire Bell Hornblow does such awe-firing fancy cooking, Brian Blazers, don't you stay at the ranch instead of coming here to the cafe to eat? Well, you see, Gents, Claire Bell was a little put out today. Yes, when Claire Bell Hornblow is a little put out, it seems when someone else is mad enough to eat horseshoe nails. Oh, you should see her when she's really around. I want to tell you it's like a double-twisted tornado mixed up with a thousand of patches on the warpath in a thunder-enlightened storm at noon on 4th of July. Or even my mules duck for cover when Claire Bell gets real mad. She out of sorts today, Thunder? Well, she ain't throwing and shooting mad, but it ain't a day to take a chance on her cooking. Is it Lem Sherman again? Yeah. That ornry two-bit sidewider don't know when he's late. You still got notions of getting a rafferate, huh? Why, the poison-hearted lame-brained jughead don't know when he's late. He ought to realize he's got no chance to get Claire Bell's lamb when I'm on hand. Well, he blamed your guy that a short time ago. Seems to me, Thunder, it was that masked man that thought up the way to beat Sherman. Well, me and the lone ranger worked together the last day. You see, he thought up a way to beat Sherman, but the way he thought it up called for using my mules. Well, then it ain't you that works with the lone ranger. It's your mules, eh? Same thing. I'd sure like to see Lem Sherman put where he belongs. That land-grabbing coyote ought to be in jail. He'll never get put in jail. He's too slick. He works schemes that keep you inside the law. I'm sure I've been watching him close ever since the talk started. What talk? Sherman bragging that he'd own the rafferate is the last thing he ever did. That's nothing but drooling. You know, I tried to tell Clairebell not to take that talk to heart, but she got mad anyway.  He's gonna try something, Thunder. He's sure as you're born. Let him try. That's all I ask. Just let him try it. I'll unhitch his arm and knock his ears off with his own elbow. Well, if you know a way to find that masked friend of yours, you'd better find him. Why? That's what I wanna know. Why do you say that?  No. Oh. I wonder where the Lord Ranger's at. Pardon me, gents. Hi there, stranger. My name is Higgins. Well, welcome to town, Mr. Higgins. This is Lefty, and that there's Thunder Martin. My name's Elle. Sit yourself down and relax. I'm only stopping by, hoping to get a smidge of information. Well? I, uh, got a herd of sheep outside of town. Sheep? You a sheep herd? I knew walk right in here like it was a man. Well, all the out-nought nerds. I don't know. I'm ordinary sheep herd. They're coming in here. My herd is every... Paul it. Just don't speak up too brash, Mr. Higgins, because I'm not lead to trouble. You're in company that's none too healthy for a sheep man. Yeah. Recognize, Ellie. State your business, and then I'd advise you to shove on. I'm looking for the Rafter H. You're looking for what? Land-sakes, Mr. Did I hear you say the Rafter H? Well, yes. Well, you act like you found it and found you wasn't welcome. I wanted to see Clarabel Hornblow. Reckon she owns it, don't you? She owns it, but I'm top-hand. If you tell me how to get there, I'd be downright appreciative. I got no time for sheepmen. Neither has Clarabel Hornblow and neither has a Rafter H. I've got a message for her. That's all. I'll take that message. I don't know about that. But I do. It's not that easy, Thunder. It's a letter. I got it here. What's that you dropped? Oh, it's just a cartridge. I was told to hand the Clarabel Hornblow along with a letter. Here you are, Mr. Higgins. Well, what's your matter, Lefty? Have a look at this cartridge, Al. Silver! That's what I thought. Say, who gave you this letter? What's that? Silver, you say? If you will tell me how to get to the Rafter H, I'll deliver this letter. If you won't, you'll have to find it for myself. Well, that letter must be from my partner. Pardon me? You are the silver bullet, the low ranger. Come on, Higgins, I'll take you to the Rafter H. Higgins had little to say during the ride to the Rafter H. Thunder's countless questions brought little information, and Thunder was out of patience when he dismounted at Clarabel's house. I never in all my born days seen a man as contactless as you are, Higgins. I got to deliver this letter. All I heard for the last half hour. Who have you got there, Thunder? There she is. Boy, you must be Clarabel Hornblown. I am. I've got a letter for you, and a silver bullet that showed that it comes from a friend of yours. Silver bullet? Lance Sate. From my friend Clarabel from the low ranger. Did he give this to your personal? Yes, him. And he gave me particular instructions to go with it. Boy says... Hmm. Don't go on curious. It's hard to believe he read it. That's why he sent the silver bullet. He figured you might have doubts about it. Yeah. So you got to sell a flock of sheep, huh? Oh, every sheep heard it. For special reasons, Miss Hornblown, I got to have cash now. I got to send it east to my folks. Where's the sheep now? On open range on the other side of town. I got a couple of dogs and two men watching. One of the men who watched the sheep was masked. The other was an Indian. It was the lone ranger and Tonto who waited with the flock while Higgins called on Clarabel. A cattleman. Not like sheep on range. They'll have to make the best of the situation, Tonto. Maybe drive women out of country. The sheep won't be around here long, but nearly long enough to kill the grazing. You do plenty of big favor for sheep, man. Who, Higgins? He needs money very badly, Tonto. Clarabel Hornblown has a cash. She can spare it for a few days. Oh, that's right. And in return for the favor, Higgins will help us. You sure him help? I'm counting on my judgment of the man. I think you'll do what we asked him. It'd make plenty trouble if Higgins make double cross. Tonto, I don't like to think of the trouble it'd be if Higgins double cost us. How soon him come back here? He won't be back for quite a while. He's just about reached the point of negotiating with Clarabel Hornblown. I'll buy your woolly critters. Clarabel, you can't do it.  You can't put sheep on the range.  It's treason. It's treachery. Downright revolution and dunderheaded carelessness. You can't herd sheep. This is my ranch, and I can herd with a darn please. You don't like it? You can clear out. Oh, sugar. I sure appreciate this, Miss Hornblown. You must need money bad to sell at that price. I do. I'll buy him as the masked man asked me in the letter. If there's a range war, he'll have to help me out. Bleeding good for nothing, garage-killing sheep that smelled the high heavens, a fine thing. Leaping rattlers, I'll never live this down. I'll buy the sheep, but the cattleman sure won't like it. She beats the close to the ground to get the roots and kill all of them. Yeah. Clarabel can't get away with it. You won't stand for it. She can't do it. She won't stand for it. The cattleman were out of loss to understand Clarabel's mood. They felt that she'd violated an unwritten code that she'd betrayed them. They finally went to her house, fuming, raging, storming, threatening. You can't get away with it, Clarabel. Have you lost your mind? You can't bring sheep to the range. Get rid of them. Yeah, get rid of them. We'll do it for you. Clarabel! Hold it! Listen to me, you pack-a-drewin' daughter in maverick. Listen to me. I'll let the other barrel of this shotgun paint among the Latia. As long as I own the Raptor H, I'll do what a doggone will please. Lam Sherman has made a special study of the laws around here, and he does what he pleases, being careful not to break a law and land in jail. Well, blast your hides. I'll do that same. You think I can't herd sheep? Go read your laws. While public sentiment ran high against Clarabel Hornblow, the man from whom she bought the sheep appeared at Lem Sherman's ranch.  I sold my sheep for almost nothing. Here's a bill of sale, you can see for yourself. You did sell sheep. Miss Hornblow got a good buy. That's why she was willing to buy them, count of the low price. Higgins, why'd you come to see me? Miss Hornblow bought the sheep, figuring to sell them to a man that's coming through here in a few days. She knows the cattleman won't stand for her keepin' sheep, so she'll get rid of them quick. She'd better, if you so. She has to sell them soon. I'd hang around here myself and wait for this Eastern gent, but I can't. I had to have cash quick, then get. Well, now, if the buyer don't like the looks of the sheep and don't buy them, she'll be stuck with them. Then every man around here will help to run her out. Even the lawman will be on her side. I still can't see why you're telling me this. You want that woven out of here, don't you? Well, I can fix it so that those sheep will look so miserable that the buyer won't touch them at any price. You can? I got some stuff that I can put in the rafter-h waterholes. It'll make the sheep powerful sick. What about the cattle? Miss Hornblow will water the cattle at the creek if the sheep use the waterholes. What, uh, what'll you pay me to fix things, like I said? Higgins? You get out of here.  The idea of you thinking I'd pay you to poison waterholes. But, sure. Go on. Get going, or I'll help you along with gun lead. Travel or I'll shoot your heels. I'm going. I'm going. Hey, boss! Boss, what's the shooting for? Oh, butch, I'm glad you're here. Come inside. Who was that, I'll bet it just could battle so fast. That's Higgins. He saw Clare Bell Hornblow the sheep she bought. Oh, butch, he's given me a slick idea. Yeah? Now listen, butch, what's the stuff that can be put into water to make sheep look like they're sick without hurting them permanent? Oh, I don't know. But I can find out. And you know sheep pretty well. You'll find out. I got the slickest idea I ever had. The curtain falls on the first act of our Lone Ranger story. Before the next exciting scenes, please permit us to pause for just a few moments. Now to continue our story. Clare Bell Hornblow stirred everyone in town and on the nearby ranches to a high pitch of anger when she bought a flock of sheep. No one was more furious than her friend the mule skinner, Thundermarkin. Clare Bell, are you sure the mask man said you was to buy those moon-eyed bucktooth quitters? I'm sure, and even if I weren't, it'd be none of your business. Any time you don't like the way I run my ranch, you're free to take your mules and get it.  Yeah, I got them up. Worked all afternoon on them. Wore myself out stretching fence wire for sheep to find things. You're sure you fenced them so they can't get to drink from the creek? You're darn right. I made it pretty sure they'll have to stick to the water holes. You don't catch me letting those sheep spoil the creek water for the cattle mules.  A thunder. Huh? You're poor, simple-minded, homely-looking galoot.  It ain't just me, Clare Bell. Every rancher around here is more than mad about you buying the critters. I know that. Now calm down and listen to me. I'll tell you just why the Lone Ranger sent Higgins here to sell that flock to me. That there is something I crave like blazes to know. It was a little later the same evening when Lem Sherman rode into town and dismounted in front of the sheriff's office.  The sheriff stood in the doorway. What's you doing here, Sherman? I want a few words with you. That's all, Sheriff. A few were the better. Come on inside. After you. Thanks. Well, what's on your mind? You made a lot of charges about me, Sheriff. Don't like it, huh? I don't mind what people say. I just want you to get a few things straight. Go ahead. You've been trying a long time to find reason to throw me into jail. And you know why, you want to repoll cat? You've tried some mighty shady tricks to drive Clare Bell harm blow out of here so as you could get her land. Ever broken the law? If you had, you'd be in jail. It looks to me as if Clare Bell is going to be driven out of here without my help. You've heard the talk that's going around since she bought that flock of sheep, haven't you? I've heard it. Don't know what possessed the woman.  No. I know you didn't. That's what I wanted to get straight. I know how you feel about me. And I don't want you to get the idea that I had a hand in stirring up the cattlemen to drive Clare Bell and her sheep away from here. You know, I thought for one minute you did have a hand in it, Sherman. I'd have you in jail fast and one of them sheep could take... As long as you don't figure on trying to frame me for what happens, I'll get on my way. I don't figure on framing you for anything, Sherman. But there's one fact you'd better get through your head. Yeah? If I ever do catch you in an underhanded deal to get that ranch, my gobs I'll throw you in jail so hard you'll bounce. Don't count on that, Sheriff. The way things are going, I'll get the chance to buy Clare Bell's land within the next few days. Goodbye. Skunk, unreason-deacon skunk. Like to jail him, huh, Sheriff? What the? I came in the back way. Masked? Why gobs your mask? Take it easy, Sheriff. I'm the one who told Clare Bell to buy that flock from Higgins. You? And maybe you're in cahoots with Sherman? By places if I could... Don't try to get on, Sheriff. Where? Why'd you come here? To help you jail him, Sherman. What? You're literally jumping at the chance. Speak up! How can I jail him? What's he done? How can I put that scheming polecat in the calibus? Did he have a hand in getting them sheep on the rafter age? No. He had no hand in getting them there. But I think you'll try to keep them there. Will you come with me? Where to? Without asking questions. Without asking? Yes, my gobs. I'll go with you without asking questions. Come on. It was some time after dark when Lem Sherman reached his ranch house after the rides in town. He lighted the lamps, then sat down near the front door to wait. In half an hour, he heard steps on the porch. He opened the door. That you, Bush? Yeah, it's me, Mr. Sherman. Can I come inside for a minute? I've got something to tell you. Come in. What is it? Got to the water holes on the rafter age. All of them? Yeah. Put some of that stuff that Andy got in each one. The sheep haven't been moved yet, have they? Ooh. I reckon they're going to be moved from the open range first thing in the morning. There's only one thing that bothers me, boss. What's that? Well, if Clair bell keeps the critters fenced on her own land, none of the cattlemen will have cause for complaint, will they? She can't keep them fence long. They'll have to be turned open range if she doesn't sell them in a few days. It'll be all right then. This stuff you put into the water, it better do the trick. Andy says it'll make the sheep mighty sick critters. Somebody's coming. There might be Andy or one of the boys. If things work out as I expect, butch, I'll see that you get a handsome bonus. I'm counting on it. Hey, mess, you! Don't reach for gun, will you? What's this for? Sherman, I want you. I'll see you here. Hit him, butch. No! My hand! Don't try another gun. Get him! Get him, butch! I'll show him! Butch! Want some more? Sherman, you're coming with me.  Let me go.  Butch! Andy, Jake, help! Help me! I'll get you for this. You keep stuggling. I'll have to give you some of the medicine to put your friend to sleep. You can't drag me out of my own home, will you? All right, Sherman. No! Pleasant dreams. Wake up. Get up, Thunder. Wake up. That's the shortest night I've ever seen. Hey, what's up, Thunder? Hey, it's dark out. Donald, you here in the bunker? What the Sam here? Hey, what's the matter? You get boots on. Come to Ranch House. Plenty quick. Ranch House? What's happened? Are they coming on the rampage? He's clear they're all right. Come quick. Them Sherman there. Sherman! That triple distilled double twisted coyote. Give me them boots. I'll fix that. I'll fix that. Sneakin' poor cat. I'll teach him to leave my girl alone. Where is the Jadir in Salamander? Where is that cat about? Clare Belivis. There's the Sakes, Thunder. Calm down.  Hado said Lem Sherman was here. Right over there in the corner. All right. Right here. Great day in the morning. Now, Clare Belger, you should not have hit him that hard. You might hurt your fist. Why didn't you call me? You. If you'd have hit him, you'd kill him and that'd be murder. Murder my eye and be downright good legislation. Anyhow, it was the lone ranger that brought him here. Where's he at? Right here, Thunder. Sakes a lot. Why it's downright good to see you? If I'd known you was here, I would... He brought Sherman here so I could talk to him. I'll have the law on all of you. Well, you'll feel better when you hear why I wanted you, Sherman. Why? You still want to buy him a ranch. Why'd he ask? Looks like I might have to sell out someday. Oh. So you got word of how the cowmen feel, eh? Sakes alive. You sure did get rough handling. Thunder, get Sherman a pitcher of water. Get him! Waiting on a pulled cat like Sherman. I don't know as I'm interested in buying right now. I thought you figured on selling the sheep. What gave you that idea, Sherman? Well, I... Ain't but one man know that and that's Mr. Higgins. You talk to him? Well, no. Why should I talk to him? Here's the water. I reckon you'll feel better for a drink of cool water. I just figured... Here you are. I just figured I'd see how high you'd go for the ranch and if the price was high enough... I don't know as I'm interested. Thunder, you better go fill the pail again. You gotta go way out to that water hole, you know. What's that? What water hole? Oh, I'm having trouble with the well. Thunder got a pail from one of the holes a while ago but slot most of it out totin' it back. What? What's the matter with you? I thought the water tasted salty. It's poisoned. That water's poisoned. Are you crazy, Sherman? We've been using it right along.  Here you get me a doctor.  How'd you know it was poisoned? Makes you think so. Butch done it. I tell you, I know. Hurry, help me. Butch poisoned the water hole? Is that what you say? Yes, yes, you gotta help me. Why did you do that? Don't ask questions now. In the name of mercy, help me. Listen to me, Sherman. And let go of me. You'll not get help until you tell more about this poison. Later. Later on. Doctor, something has stopped the poison. I feel faint already. Oh, Sakes Alive, help me. Why did Butch poison that water? Did you tell him to? Oh, help. Help. Did you? Yes, yes, I told him that.  It wouldn't kill him. Only make him sick. The sheep. But it might kill a man. You wanted to make the sheep sick so that Clarabel couldn't sell them. Isn't that it? Yes, yes, that's it. I admit it. You knew she was going to sell them. You wanted to kill the sales so she'd have to keep them here. Is that it? Yes, yes. You wanted the cattleman to turn on her? Yes, yes.  It's all right then, Sherman. There's nothing wrong with that water. What? Thanks for that confession, Sherman. Sheriff, looks like I got you this time. Trick me. You mean no poison? You hadn't been a crook at heart. You'd never have taken the suggestion Higgins made. And you did take that suggestion. Higgins. We all have been waiting in the next room for this, Sherman. You crook. All you needed was the suggestion I gave you and you acted on it. Even double crossed me. But you mean I ain't going to die? No, but you're going to jail. Sheriff, as evidence, you can draw a sample of the water. I won't need none. We got witnesses to Sherman's confession. I reckon Butch will admit his part too. I'll buy the flock back now, Miss Hornville. Anytime, Higgins. You mean to say you ain't going to keep the woolly critters at all? Nope. The whole thing was just a plan to put Temptation in front of Lam Sherman. It was the masked man's idea to put him where he couldn't pester me no more. You mean to say I strung all that fencing for nothing? You didn't tell me that part of the scheme. The fencing will be needed to keep the cattle from the waterholes until the poisons worked out. This ain't right. That woman schemed the whole thing. She framed me. You better be careful what you say about Claire Bell. He'll roll, troublemaker. You confounded old Seabass. Sherman, one more word out of you. Come on, Sherman. We'll head for the jail. Give me. Jaded because of that old troublemaker. You're going to tie war, Jeff. I bet I hit him just as hard as you did. I heard that mask man go. The story you have just heard is a copyrighted feature of the Lone Ranger Incorporated.


Hey guys Brian Bailey here with System Dynamics. We're in Denver, Colorado. I'm here with my new friend Connor Visser with Ever Jones. We're having a great time. You having a good time, Connor? It's a good crowd, guys. We've got a lot of realtors, a lot of mortgage professionals piling in here. We're in a great town. Great time here. Come see us when we're in your neighborhood. We'll see you guys at the System Dynamics event.


So, I hope that we all know that fMRI is a relatively poor temporal property, so as most people know, fMRI has a poor temporal resolution and has poor temporal accuracy in the detected signal. So, in part, for sure this has to do with the vascular nature of the fMRI signal, so the bold signal is measured as a vascular signal and part of this temporal nexity is due to this vascular nature. However, what I'm going to try to convince you of here is that part of the temporal in accuracy is also due to particular methodological decisions that we take in the fMRI data analysis pathway. And so, improving the temporal accuracy is important for event-related fMRI for studies of functional connectivity and for studies that look at the coupling between neuronal activity and vascular responses. All these three techniques are interested in the precise dynamics of this fMRI signal and so, improving the temporal accuracy by which we can extract this signal from the data would be relevant to all these types of different studies. So, here I'm trying to convince you that there's a new method for doing this. So, basically, this talk has two parts. First, I'll just talk a little bit about the standard way of creating these whole-brain volumes and the standard way and the new way to do that. And then in the second part, I'll do a little bit of a try to evaluate this new method in the context of simulated data and some real-world data. So, a key part of fMRI data acquisition is that the fMRI data is collected in terms of slices. So, at each point in time, when an fMRI experiment is going on, the machine is sampling just a little bit, a little tiny part of the brain. And so, when you're in the machine, it is sampling sequentially or in some other form, but it's sampling at each point in time just a little part of the brain. And so, for example, if you have just a brain with just three slices, you would first sample this part, then this part, then this part, and then the bottom part again, that's basically how fMRI data is acquired. This is just a different way to represent that. Here you have time, you have the three slices, and you can see that at each point in time, you just have a little portion of the brain as your data. So, in this raw format of your data, it's actually impossible to do whole-brain analysis, because at no point in time, you have a whole brain available. So you need to do something. The standard solution to do this, to be able to do whole-brain analysis, is to basically shift these slices in time. So the idea here is to just relabel the time point at which these samples were taken. So you would say that actually, slice number one is not acquired at time point zero, but it's actually acquired at time point one. And so what happens when you do that is that you create whole-brain volumes. So you create brains in which all the slices are assumed to be acquired at some point in time. So you can see that you have a whole-brain volume. So you can see that you have a whole-brain volume. In which all the slices are assumed to be acquired at some point in time. And so I should say that this step is often confusing, but this is a step that happens basically when you convert your diagrams to your NIFTs. And this is the step D, this panel D, is when you actually start your fMRI analysis. It has nothing to do with preprocessing. This is really the first thing that you do before you start your analysis. And so there are two major problems with this solution. And that is that these volumes that we have in this way, they contain temporal distortions. So it is not true that this slice here was acquired at time point one. And that this slice here was acquired at time point one. Because you have just relabeled them. And so it's temporally not accurate this data. The second problem is that you lose temporal resolution. And that you actually sample data at time point zero and at time point two and at time point three. But unfortunately in this representation of the data, that temporal resolution is lost. And this leads to a typical resolution in fMRI that is only order of seconds. So typical fMRI experiments that have a TR that is around between two and three seconds. And that have a number of 30 slices or more. You have a temporal resolution that is around on the order of seconds. So what we have come up with is to create whole brain volumes that are composed out of slices that are all acquired at the same point in time but relative to a stimulus. So this method requires that in your fMRI experiment you should present stimuli. And then you compose your volumes based on slices that were acquired at the same point in time relative to a stimulus. So to explain that a little bit. Imagine here you have again this fMRI data but now you have three stimuli. So S1, S2 and S3 are three stimuli. And they're presented exactly in phase with the acquisition of these three slices. So this means that stimulus one is presented exactly when you are sampling the data from slice number one. So this means that slice number one, that data is sampled exactly zero milliseconds after the presentation of the stimulus. So simultaneously with the presentation of the stimulus. For stimulus number two the second slice is sampled exactly zero milliseconds after the presentation of a stimulus. And likewise here slice number three is sampled exactly zero milliseconds after the presentation of a stimulus. So what you then can do is combine these three stimuli these three slices that were acquired for these three stimuli and Create a whole brain volume that is composed out of slices that were all acquired at exactly the same point in time relative to stimulus and actually if you fill out the data More because you were presenting these stimuli in face with the slices You actually get a whole brain volume at each time point where you sample data So you get a much you get more accurate data and at a higher temporal resolution So this method solves these two aforementioned problems that you With this method you don't no longer have these within volume temporal distortions Volumes are composed out of slices that are all acquired at the same point in time And you have a much higher temporal resolution. So with normal fMRI data when you have about 30 slices and the TR of two seconds you can get Up to a maximum temporal resolution about 70 milliseconds Okay, so I hope that is clear That's basically the the the theory part So this method really fundamentally differs from standard fMRI methods It differs in how volumes are created. It also differs in the way the statistical extraction of the signal works. So I Don't have really time to go into this But I Just want to say that when you do normal fMRI analysis, you have a time series you model an entire imaging run In your model in this case, we have Epochs so we have a data that looks much more like EEG data Where you have a certain a certain epoch that is fixated all the stimulus and you You model each time point in this epoch separately You can ask me about this more in detail if you want so here I just wanted to Evaluate this method so and we did this in the context of Simulated data, so of course the advantage of simulated data is that you know what the signal is that you want to detect and you can use Your method this slice base method that we have Developed and compare it to how well it does against the standard method. So the standard method of extracting fMRI signal Is this method called fur or fear? and Yeah, this is just the way that The standard ways of extracting bold signals So we are using that as our Stand as our comparison The idea behind the simulation is to Create a large patch of fictitious neural tissue and we assume that across this entire fictitious neural tissue There is the same hemodynamic response so We would expect that if fMRI were to sample this This this fake this neural tissue you would exact we would expect to see the exact same signal coming from each part of this neural tissue because The hemodynamic response in the signal is exactly the same everywhere Okay, but so we are sampling this In this particular simulation we just use three slices We have a TR three seconds and we just do sequential sampling So slice number one slice number two slice number three To keep things simple So we using this idea we generate basically an fMRI experiment We use 60 stimuli as a slow event related type experiment where you have long pauses between each Simulus presentation to let the hemodynamic response go back to baseline Each stimulus generates exactly the same hemodynamic response using this double gamma HRF and so again each Sample each slice samples exactly the same hemodynamic response function So the questions we had here was how well does each method the slice-based method or this fear method? We cover the ground truth signal And we can look at that by a simple correlation between our ground truth signal and our observed bolt signal We also looked at how well is the signal similar across the three slices? So each slice Samples exactly the same hemodynamic response And so you would expect to see the exact same signal across these three slices So this is results from this fear method So you see the in color you see the results from the three slices. So this is the bolt signal is extracted from this Fictitious neural tissue with this fMRI parameters that we that we that we chose So the red is the first slice green the second blue is the third slice and a dash line is the ground truth signal And so you can see that actually there's this temporal shift Of the of the of the signal across these three slices and this actually makes sense because as I said before The standard method of volume creation relies on creating volumes in which you in which you not exactly Which the slices are not acquired at the same point in time So you so you get here these temporal distortions within each volume and that's what you recover here That's what you see By contrast in the slice-bath method here you see that actually the signal is captured extremely accurate So there's a 99% accuracy And by which the signal is extracted and that is because each volume here is composed out of exact exactly Slice that were slices that were acquired at exactly the same point in time relative to the stimulus So you have no temporal distortions also the The similarity of the signal across the three slices here is low and it's much higher in the slice-based method You can increase the temporal resolution of the data by increasing the number of slices. This is a common method And by jittering the stimulus So you don't present the stimulus exactly at the TR, but you jitter this a little bit This is a common method to increase temporal resolution Again, even with 250 milliseconds you can see that the slice-based method retains about 99% accuracy compared to the standard method where really the performance goes down and this is about 77% Correct So in this particular simulation the slice-based method really more accurately extracts this bold signal with Near perfect accuracy. It's also the accuracy across the slices is much higher If you look at all the simulations that I did so I did much more simulations than the one I just presented here You see about a 25% improvement In addition the variability that the signal is detected is much smaller So it's also a more precise method In terms of real-world data We did We took data from a picture naming task So this is a very simple task with subjects are in the scanner They see a picture and they just have to say what it is So for example in this case you see a picture of a horse and you see a horse So this is also a slow event related design with long pauses in between To really let the bold signal come back The Logic here was that previous research has shown that in this task in the picture naming tasks There's a large portion of motor cortex that is active You're speaking your mouth is moving so motor cortex is supposed to be highly involved in this and we looked at We looked at three slices that were Centered on motor cortex assuming that each slice would see a similar hemodynamic response Okay, so that was the key assumption that we had three slices and that this whole patch of new motor cortex here would Show a similar a hemodynamic response FMI parameters the only thing that is important here is that this is a really standard EPI protocol So this is not this method is applicable to very standard Run-of-the-mill EPI sequences. You don't require multiband or anything like that. We didn't do a Much pre-processing we didn't use any smoothing We just extracted the signal from three slices in one single voxel voxel with the highest signal intensity basically So what you can see here? This is from a single subject This is the standard method and you can see I hope that you can see that the single actually is a is more Diverse across the three slices and here you have a more coherent version of that signal so Assuming that the same hemodynamic response underlies these three slices that are very close together here in motor cortex You would expect a more similar bold signal across these three extracted slices If you do that across the entire group of subjects, so 30 participants There is a significant improvement and enter slice correlation for the slice-based method compared to the standard method also the Slice-based method detects less peaks So there's a different peak in one slice versus another peak You would expect all slices to show the same peak if the same signal was underlying each slice Okay, so this method allows to extract the whole brain bold signal at With high accuracy and with high tempo resolution, so I think this is important for these three methods so event-related fMRI functional connectivity and your vascular coupling I think this has applications in both in also in clinical neuroscience where Accurate action of these bold signals could be used as early biomarkers However, I should make a big Beware here This is to say that we can now extract high tempo resolution bold signals, but we should not equate The bold signal with the time course of neuroactivity these things are not the same and there's a lot of studies that have looked at how well Bold signals may map on to a neural activity and if you're going to use this method You should really be aware of the limitations of using that So to conclude this is a method that is really fundamentally different from a normal Method of analyzing fMRI data the slices and by which you can you can create whole brain volumes That is really different the way that statistical method for extracting the signal works is really different And I think it improves the accuracy and the temporal precision of fMRI Thank you Thanks I Because you need to have one slice one of each of the slice of the volume to be exactly the same time after The experimental design so first let's say you have 40 slice It means that you have to have a jittering of 40 the jittering And that means that the sampling of those slices doesn't I mean that that many something That's one that's one remark. The second remark is that it's in the same the sampling thing It's not like a you know only something in time as soon as the subject moves You have a 40 sampling problem Right, and that's that I haven't seen at all any of the I mean, that's a major problem That's what that's massive problem. So that may be completely so I mean the constraint on the experimental design and the Movement seem to be two major aspects that you're not discussing very much I think a general comment on that is that there's no free lunch I mean if you want to improve the temporal resolution you have to do something I mean is the same machine the same data. So something has to change Yes, you have to present more stimuli to do this. There's no way around that With respect to motion. Yeah, that's I mean, this is a problem in fMRI And and this Yeah, this is something we should look we are but I don't need to look at I mean it's it's I I mean I have looked at many issues such as motion correction and and Other types of preprocessing Ideally, I would like to do that with a simulated data set. So I know what's going on But it influences the analysis for sure. Yes Do you do the slice repositioning or how you call it before or after motion correction? I Did both I And it matters. That's a similar point that was made there And with these picture naming data if you if you look at the signal that is extracted Before motion correction after most in motion correction. There's a difference in the in the similarity of the signals. So Yes, there's it matters for sure and how do you know which one is better or you don't know You don't know. No, yeah, that's why I think we should do Simulated data sets where we control The ground through signal and we can see exactly see what is the influence of this. Yes Thank you very much. Thank you


And welcome to the video lecture on Oscillators Using Operational Amplifier Part 1. At the end of this session, students will be able to describe the working principle of oscillator and they will be able to describe the working of RC phase shift oscillator. So, before moving towards the concept, you have to know about basics of OPAM that is IC741. So, let us see first what is mean by oscillators. Oscillator is a circuit which generates the repetitive waveforms of fixed amplitude and frequency without providing any external input. There are number of uses of these oscillators like different applications for example, the electronic devices like laptop and mobiles use this oscillator to generate the clock signal. It can be used in many receivers that mobile or TV receiver to generate the local carrier frequencies and it is also used in signal generators to generate the different kinds of sinusoidal and non sinusoidal waveforms. So, let us see about this oscillator working principle. So, oscillator is a type of feedback amplifier in which the positive feedback signal is given at the input from the output. Block diagram of oscillator is consist of the amplifier, let us say its gain is A v and the second block is of feedback circuit with the feedback factor beta.  So, according to this diagram, we can write the equation for differential voltage as v d is equal to v in plus v f that is input voltage plus feedback voltage. Then we can write the equation for output as v o v out is equal to A v into v d, then the next equation for feedback we can write v f is equal to beta into v out and we will take the ratio of output and input that is v o upon v in is equal to A v upon 1 minus A v beta. But it is a oscillator, so we cannot give any external input here, there is no requirement of any external input. So, the v in is equal to 0, still it is giving some output voltage there. So, we will consider v in is equal to 0 and v out is some non-zero quantity. Now, putting these values in the above equation, we will get A v beta is equal to 1, it can be expressed in polar form as A v beta is equal to 1 and the phase angle or phase shift is 0 degree or 360 degree. So, in any kind of oscillator to obtain the sustained waveform oscillations, we have to satisfy two points which are called as the Barkhausen's criteria. So, the criteria is the magnitude of the loop gain that is A v beta must be at least 1 means the loop gain should be unity and the second is total phase shift in the loop must be equal to 0 degree or 360 degree. The oscillators can be categorized into two types, the first type is sinusoidal and second is non-sinusoidal. Basically, if the amplifier provides 180 degree phase shift, then the feedback circuit should provide the another 180 degree phase shift to make the condition satisfied that the total phase shift should be 0 degree and 360 degree or 360 degree. So in sinusoidal oscillators, it will generally produce the sine or cosine waves and non-sinusoidal oscillator generally produce the waves like square, triangular, south tooth etc. Output of the oscillator depends on the components used in that circuit as well as the oscillation at the output depends on the components used in the feedback circuit. So, there is no any input voltage externally provided. So what will be the input voltage basically is the circuit's noise itself means initially the input is taken from the circuit noise as we provide the input supply. So, let us see about one of the sinusoidal oscillator which is nothing but the R C phase shift oscillator. So, we will draw the circuit for R C phase shift oscillator yes. So, first according to the oscillator block diagram, it is the amplifier circuit and it is the feedback circuit. So, for this amplifier circuit we will use operational amplifier that is IC 741. So let us draw first the opamp circuit pin number 2 that is inverting terminal, pin number 3 is non-inverting terminal. So, we will provide the supply voltages plus 12 volt minus 12 volt it is at pin number 7 and it is at pin number 4. Now pin number 6 is the output voltage we will consider it as a V o this is R in and this is R f that is feedback resistor. So, I will use this opamp in inverting amplifier mode. We have satisfied the amplifier circuit in the oscillator now we have to design the feedback circuit in the oscillator design. We have to connect some circuit as a feedback from output and from output to input I will extend this. So, this is the feedback circuit consist of R and C components so it is called as the R C phase shift oscillator. So, here it is feedback circuit and it is the amplifier circuit which is inverting amplifier. Circuit should work on the principle of Barkhausen's criteria. So, it should satisfy the two conditions. First is it should take the overall phase shift as 0 degree or 360 degree and the loop gain must be equal to what these two conditions should be satisfied here. So, we will see the first condition of phase angle now as it is inverting amplifier it will give us 180 degree phase shift. So, the remaining 180 degree phase shift should be obtained from this feedback circuit. So, how it is obtained we will see one consider this is single R C stage. So, theoretically we can consider it will give the phase shift of 0 degree to 90 degree. So, theoretically we will consider the maximum phase shift which is given by the single R C stage. To get the 180 degree we can just use the two R C stages in the circuit instead of three R C stages. But the practical problem is that if we have to use these two R C stages then it is considered that it is giving 90 degree phase shift. So, the value of R is nearly equal to 0 and due to this typically gain will be 0 for this feedback circuit and it is not satisfying the criteria. So, we will use the three R C stages in the feedback circuit. So, single R C stage will give the output with nearly 60 degree phase shift. The output is leading 60 degree because R C circuit is nothing but the phase lead circuit. Now we have to use the three R C stages in the feedback circuit. So, here we can consider each stage will give 60 degree phase shift. So, after this 180 degree phase shift 60, 60 and 60 will provide us the total 180 degree phase shift and this total will produce the 0 degree or 360 degree phase shift. Practical circuit will not provide 60 degree at each stage, but the overall circuit will give us 180 degree phase shift. So, it will fulfill the first condition of Barkhausen's criteria that is the total phase shift is of 0 degree or 360 degree. Now, we have to see about the second condition. According to the calculation we will get the attenuation of 29 means here beta can be written as 1 by 29 and here we have to choose the value of R f and R in such that the gain must be equal to 29 because A v into beta is equal to 1. So, here the gain is considered to be 29 and accordingly we can design R f upon R 1. So, we will consider the mod value of R f, R f upon R 1 is equal to 29. So, accordingly we can design the values of R f and R in sorry is equal to 29. Now, these two conditions are satisfied at the particular frequencies it is called as f0. So, f0 is nothing but the frequency of oscillation and the frequency of oscillation can be given as 1 by 2 pi root 6 into R c. It is for 3 stage R c network. So, it is the frequency of oscillation which will give us the sustained oscillation output. This R c phase shift oscillator can be used in low frequency ranges nearly 5 hertz to 1 megahertz and it is mostly used in audio frequency range applications. These are the references. Thank you.