So, it is said that there's three types of people in this world. Those who make things happen, those who watch things happen, and those who wonder what happened. Let me say this again, there's three types of people in this world, those who make things happen, those who watch things happen, and those who just plain wonder what happened. And I want to tell you that the difference between the people who make things happen and the people who watch things happen is very simple. Because the person who makes things happen simply has good habits. They have habits of a successful person. They have a winning attitude. They have really good habits. When they wake up every single morning, they established good habits. They established a way of life that leads them to their destiny. And tonight I want to talk to you about your destiny. I want to talk to you about something that each and every single one of us that we can relate here with because, I mean, I don't plan on dying tomorrow. I might, but I don't plan on that. I plan on living for a long time and I plan on doing something great in this life. And I know that you do too. Because as a Christian, like I said before, we have vision. We're going somewhere. We have something to look forward to. And if we're going to make it, if we're going to reach that destiny, we have to have good habits. Something that's going to hold us up when times get a little bit rough. Something that's going to hold us up when the wind and the waves come and we don't know what else to do. Because the devil will try to stop you from reaching your destiny. You know, I said we have a mega, mega vision. And you know what? That means we're going to have mega, mega opposition. Am I right? Do you agree? Have any of you guys experienced some mega, mega opposition in your life? I'm raising my hand. I'm going to raise my hand twice because that's me. When things in life don't go the way that you expected. You're on the track. You're on the right track. And boom, roadblock comes. And all of a sudden, everything in your life is shaken. Everything in your life is twisted around.  Because the decisions that you make today affect your future tomorrow. The choices that you make today will determine your tomorrow.    And if we're going to make it in life, if we're going to reach our destiny, we have to reach a point in our life where we're making good decisions daily so that we can focus on the prize, focus on what God has before us. So like I said, your daily decisions determine the outcome of your future. And the man of God, Prophet TB Joshua said that this year, 2014, is the year of crossing the bridge, the year of crossing the bridge to your destiny. So I'm going to say that again, this year you will cross the bridge to your destiny. You believe that? Amen. We believe it.  How on earth are we going to pack this place, pack it so much that there's not enough room that we have to get a bigger building? How are we going to do that this year? Well, I'm telling you the way that we're going to do it is this. We're going to have some really good habits. If you look at many of the characters in the Bible who made it in life, they simply had good habits. And I'm talking about making the decision to wake up and to read your Bible. The Word of God is so powerful. In fact, you cannot live without it as a Christian. You can't make it in life without the Word of God. I can remember a time in my life when I got saved and everything was going wonderfully.  But I reached this point in time a few years later where there was so much stagnation. I was so confused. I didn't know what to do. And I was just basically had no vision, no clue what I was doing. I went to college, dropped out of college, went back to college, was, you know, working part time, working full time and all these things, but I had no clue what was ahead of me. And I thought, what is wrong with me? And I realized that I was asking myself, I'm like, when's the last time I read my Bible? You can't remember the last time you read your Bible? That's a problem.  As a Christian, we need the power of God. We need a constant time in the Word of God. And so a couple years ago, something happened to me. I don't know exactly what it is or what changed in my life, but I think it probably had a little bit of something to do with going to Skowen, the synagogue church of all nations, because right after we came back, I got this Bible from my sister. And today, the Bibles, you know, it fell apart. So I'm thinking that that should be a good sign. It means that something in my life changed, and I noticed a really big change in my life after I made God's Word the standard for my life. Waking up every day and taking time in His Word, it became such a habit that literally I couldn't go without it. If I wouldn't be in the morning, I would crave it so much. I would get off of work. I would go find the nearest Starbucks and I would just read. It became so interesting to me. The more I ate, the hungrier I became. The more that I wanted it, the more that I desired it. The more that I desired more of God. And I saw that difference in my life. I saw that change, and I began to have dreams. I started dreaming of these wonderful things that God could do in my life. Whereas before, I had no clue. So I want to tell you tonight, if you don't know what your vision is, if you don't know what your destiny is, I encourage you, pick up God's Word and He will surely show you. He will surely guide you. And if you don't have a dream or a vision, get connected to this vision. Get connected to what God is doing here because you will find yourself on the road to your destiny here.  Because that is what God wants for you, that's what God has for you. And one thing is that there are two destinies that are planted in our lives. So every single person, you have two destinies. What? You do, you have two destinies. You have one that's planted by God and one that's planted by Satan. Because just as God has a plan for your life, so does the devil. Because the devil wants to use you for his plan and his purpose, which we know is to kill, steal, and destroy. But we know that God's plan for you is to bring life and more abundantly, not just for you, but for every person that is affected by you, to bring life and more abundantly. And the destiny that will guide your life depends on which one you water and which one you uproot. I'm going to say that again. The destiny that will guide your life depends on which one you will water, which one that you will care for, which one you will nurture, and which one you will uproot and command out of your life. That will determine which one will guide your life, either your destiny that's guided by God, or when we don't choose to nurture and take care of that destiny, we automatically choose the destiny planted by Satan. But we, as the people of God in this church, in this mega vision, we're going to water the seed planted by God in our lives. We're going to uproot the destiny that the devil has tried to use, to use as a part of his plan. And we're going to cast that out of our lives. We're going to follow the plan of God and do great and mighty things for him. I also want to tell you that there is no reality apart from God. I'm going to say that one more time. There is no reality apart from God. You can live this life, but it will be a lie, because without God and without the truth, reality is incomplete. Without God, without his truth, reality is incomplete, incomplete, because the truth is God. The truth is the Word of God. The Bible says in John chapter 1 verse 1 that in the beginning was God, and the Word was with God, and the Word was God. That's our Savior, Jesus Christ. He is the living Word of God. So I'm going to say it again that those people who make things happen in life simply have good habits. And I want to bring to you the story and the life of my favorite apostle, one that I find myself connecting to so greatly, and that's apostle Paul. I love apostle Paul because he was kind of a crazy guy, and I feel like me and him have so much in common because I'm just a little bit crazy too. And Paul, he was a Pharisee, and just like our friends here from Teen Challenge said, that Paul was a Pharisee, and he was well-versed in the book of the law. He was well-versed in all that stuff, and he persecuted Christians. He killed Christians. He was a part of that whole thing going on. And one day he's going all about his life, and he thinks that he is on track, and all of a sudden he meets with Jesus. He has this encounter on the road to Damascus. He meets with Jesus, and Jesus says, Paul, in fact his name was Saul at the time, he says, Saul, why are you persecuting me? And he's like, I don't know. And he has this encounter with the God of the universe. He has this encounter with Jesus, and his life completely changes. And Jesus gives him this vision because remember his whole life up until this point, he was a dedicated Pharisee. He was dedicated. He believed he was doing the work of God. He believed that he was in the right way. And then all of a sudden, boom, something life-changing happens to him, and he meets with God. He encounters God, and God gives him a vision for his life. God plans within him his destiny. He said, you will preach to the Gentiles. You will bring my message. You persecuted my people before, but now you will suffer very much for me, but you will do great and mighty things for me. You will preach to the Gentiles.   Something inside of you will change. How many believe that you will cross the bridge this year into your destiny? Amen. I want you to tell your neighbor, I will cross that bridge. So Paul, he has this encounter with Jesus, and then he goes and he does all this great and mighty things. But Paul, the interesting thing about his life is he received so much persecution. He finally has a dream. He finally has a destiny, and he feels like I'm going somewhere in life. I'm going to do some awesome things for the Holy Spirit, and this is going to be amazing. And the next thing he knows, he finds himself in chains. The next thing he knows, he finds himself in prison. And he could have easily just said, well, this is what I get for following God. This is what I get for following his destiny. He could have folded his arms and just said, this is not what I signed up for. You said that I was going to preach to the Gentiles, and it was going to be amazing. And that's what I believe. And here I am in jail with my friend Silas here. We're in jail. He could have done that. He could have easily done that, but he didn't because Paul had a really great habits. Because Paul was well-versed in the Word of God, and he encountered Jesus. And I believe that it's these two things that guided Paul's very life, his very future, because he knew the Word of God and he encountered the Holy Spirit. You and I, if we're going to make it in life, if we're going to reach our destiny, we have to develop these two habits in life. We need to know the Word of God, and we need to encounter the Holy Spirit on a daily basis. Everything that you do today will determine your tomorrow. It will determine the outcome of your future.  And it will determine which one you're going to uproot and throw out of your life. Paul, he had a vision from God. He had a vision given to him directly from Jesus. And he was going to stop at nothing to receive the promise that he was given, to fulfill the destiny that God has placed in his life. So when Paul found himself in chains, he didn't gripe, he didn't complain, he didn't murmur, but rather he worshiped God in heaven. When Paul and Silas found themselves in the prison, instead of complaining, they lifted their hands, they got to their knees, and they began to worship God. And you know what happened next? A great earthquake came, and it shook every single prison cell open. It shook the chains right off of their hands, and they were freed from that very prison. Paul had a habit of praising God, even in the worst of his trials. Even in the greatest of his circumstances, Paul had developed great habits. So that when troubled times came, that he did not lose his faith, he did not allow his circumstances to dictate the direction of his prayer. I mean the direction of his faith. Paul did not allow that to happen because he had amazing habits. He knew the word of God, and he encountered the Holy Spirit. And you and I, we need that today. If we're gonna see this mega vision come to pass, we need to know God's word. We need to encounter the Holy Spirit.  It's so important for us, as Christians, if we're going to make it in life. Because the vision we have, the plan that God has for us, it cannot be accomplished without the Holy Spirit, because it's so impossible. Humanly speaking, just like Jesus said, humanly speaking, what we're asking of God is impossible. But we know that with God, all things are possible. Amen? Do you believe that tonight, church? I can relate so much to Paul because maybe it's just in this season, in this time I don't know, but I feel like I can relate so much to Paul because every single thing he did contradicted his promise from God. He found himself in chains, he found himself in prison, he was mocked, he was ridiculed, he was falsely accused.  He was even stoned to death, they left him for dead. He was stoned by religious people for saying that I'm going to preach the Gentiles because that is what God has commissioned me. Everything went against his vision, everything went against what he believed that God had set in his life for himself. Paul quickly found out that the road to his destiny was not a bed of roses. It was not something that was just perfectly lined out by God, perfectly every single door open, he found that there was some troubles. He found that there was some trials along the road to his destiny. He found that the bridge to his destiny had a few bumps along the way and that if he was going to make it to the other side, the only way he could make it was that if he kept his eyes focused, Paul kept his eyes focused on the prize. He maintained his focus no matter what was going on around him, no matter if his hands were tied behind his back, no matter if they were throwing stones at him, no matter if he was locked up in prison and held there for many, many months, even years, Paul never allowed his circumstances to dictate the direction of his prayer, the direction of his faith. Paul stayed focused, he looked forward, he kept his eye on the prize because Paul chose to water and to nurture the destiny that God had planted in his life. He wasn't going to allow what the enemy was trying to do to stop him. He wasn't going to allow that to dictate his prayer, to change his confession, to change his faith. Rather, Paul kept his eyes focused on the word he knew the word of God. He knew that God's word says that I am more than a conqueror in Christ Jesus, that I have overwhelming victory through him, that if God is for me, who dare to stand against me? That if God has given me a vision, if he's given me a dream, if he's given me a purpose, if he's given me a mega-vision, then God will surely see me through. Amen. So Paul found himself in chains, and I want to... I want to read a scripture and take my proof text from Acts chapter 27 because during this time, as I explained, Paul has an encounter with God Almighty, everything changes in his life, God plants a vision inside of him, he finds himself in chains, he finds himself in prison, but he had really good habits, and he praised God along the way. And Paul finds himself in another dilemma, yet again, another dilemma. And in Acts chapter 27, I'm just going to explain a little bit because it is kind of long. I'm not going to read everything for you, but just to give you a little backtracking here. So Paul finds himself among some religious people, yet again, and he meets with these religious people, and he says that he explained that, I'm going to do these great things for God and blah, blah, and they were all fine and dandy with everything until he gets to the last part. And he says, I'm going to preach to the Gentiles. Let me tell you, these Jews were not happy with him. They said, no, no, no, no, no, no, no. We're not okay with that.  And so Paul has an encounter with these two different governors. The first one was Felix, the second one was Festus. And so he has these encounters with these governors, and they're listening to him, and they're like, we don't really see anything wrong with you wanting to preach to the Gentiles. We don't really know what to do. This is all religious, but for some reason, we just want to keep the rest of these Jews happy, so we're just going to keep you in prison because we don't know what else to do. So Felix goes away, and Festus comes, and he's kind of like, I don't even know why you're here. I really don't. This is weird, but okay. And then King Agrippa comes along, and he's this king, and he comes to pay his respects to Festus. And so Festus asks him, he's like, can you take a look at this guy and let me know what you think about him? And they have this trial with Paul. And as Paul is explaining his case to Festus at first, before King Agrippa comes along, Paul says, I appeal to Caesar, okay? King Agrippa comes along and listens to his story, and he's like, dude, we can let this guy go. I mean, he hasn't really done anything wrong. He just has this crazy big vision that he thinks he's gonna do these really awesome things, and that's really and truly why he's in this prison. And King Agrippa says, I'm ready to release him, except Paul appealed to Caesar, foolish.  Why'd you appeal to Caesar? Why'd you do that? Just giving you some backtracking here and some of my opinions and thoughts along the way, until I realized that why Paul appealed to Caesar? Because Paul had a dream and a vision to go to Rome. He needed to get to Rome because the vision that God had given him was to get to Rome. He's like, I'm gonna preach to these Gentiles and I have got to get to Rome.  We can preach to these people right here, these Jews, they need our help, and Paul's like, I gotta preach to the Gentiles. This is what God said, I've gotta do it. Years have passed by at this point and he has not made it to Rome yet. Paul finds himself in prison and he realizes, sneaky little guy, he realizes, I'm going to appeal to Caesar because the moment I appeal to Caesar, that'll take me straight to Rome. He had a great idea. And so right when they're about ready to release him, right when they're about ready to release him of all of his chains, they say, oh man. All right, we're gonna send this guy off to Rome then. Unfortunately, Paul gets what he wants, but the trip is not so awesome. To get there, it seems like, okay, he's on his way. Everything has now worked up. It's all been worth it.  Have you ever felt like, maybe it's just me. Maybe I'm speaking to myself and I'm gonna be a little bit honest with you here tonight that this message I'm telling you, I'm actually preaching this to myself right now. Okay, so I really hope that you guys can connect with this in some way and take a little piece from this. But Paul, he encountered a little problem because it felt like he was on his way. He was there. Here we go, smooth sailing. It's gonna be smooth sailing from here. I'm on my way to Rome, but on their way to Rome, Paul finds himself in a sticky situation. Life and death, as a matter of fact. So I'm gonna start reading here from Acts chapter 27 and verse 10. So are you guys still with me? Do you guys understand where I'm going? I know this is a lot of the word of God. I know it's a lot of back story, but I promise you I'm going somewhere. I really am, I'm taking you somewhere. So in verse 10, there on this boat now to Rome and the weather is terrible, everything's going wrong. It's the wrong season, but they just had to get there and he says, men, he said, I believe there is trouble ahead if we go on. Shipwreck, loss of cargo and danger to our lives as well. But the officer in charge of the prisoners listened more to the ship's captain and the owner than to Paul. And since Fairhaven's was an exposed harbor, a poor place to spend the winter, most of the crew wanted to go on to Phoenix, farther up the coast of Crete and spend the winter there. Phoenix was a good harbor with only a southwest and northwest exposure. When a light wind began blowing from the south, the sailors thought they could make it. So they pulled up anchor and sailed close to the shore of Crete, but the weather changed abruptly and a wind of typhoon strength called the northeaster burst across the land and blew us out to sea. The sailors couldn't turn the ship into the wind, so they gave up and let it run before they gale. So at this point, they're on this, they're in the boat and they're sailing to Rome and Paul says some bad stuff is about to happen to us right now. And the other guys were like, yeah, you're just a prisoner so we don't really need to listen to you. Paul's like something bad is about to happen to us right now. There is danger ahead of us.  It's no big deal. And boom, out of nowhere, a big typhoon comes and they find themselves in the midst of a storm. And in verse 18, it continues. It says, the next day as gale force winds continued to batter the ship, the crew began throwing the cargo overboard. The following day, they even took some of the ship's gear and threw it overboard. The terrible storm raged for many days, blotting out the sun and the stars until at last, all hope was gone. No one had eaten for a long time. Finally, Paul called the crew together and said, men, you should have listened to me in the first place and not left Crete. You have avoided all, you would have avoided all this damage and loss, but take courage.  For last night, an angel of the God to whom I belong and whom I serve stood beside me.  What's more, God in his goodness has granted safety to everyone sailing with you. So take courage, for I believe God. It will be just as he said, but we will be shipwrecked on an island. And this is exactly why I love Paul, because they were in this huge storm. It says that the sun and the stars were completely blotted out. It said that they had lost all hope. Paul was supposed to be on the journey to his destiny. Paul was supposed to be crossing that bridge to get exactly where God said that he was supposed to go. But Paul finds himself in a sticky situation. He finds himself in a dark situation. He finds himself in an unfavorable situation. But what I love is that Paul found that God was with him. That the people who said, we're not gonna listen to you about the storm that's coming, now all of a sudden they're listening to him because he says that the God in whom I belong to, the God who I serve says, it's gonna be okay. He said, you will surely stand trial before Caesar. So through Paul, they have a little teeny tiny bit of hope now. Paul did not allow his circumstances. Paul did not allow the bumps along his bridge to dictate the direction of his prayer because he said, I believe. Right here he says, for I believe God, it will be just as he said, we will make it. Some things are gonna happen. We're gonna lose our ship. We're gonna get wrecked, but we are gonna make it. Amen. Amen.  And we as a church will do the same because we have a mega vision, because we're going somewhere, because we have a bridge that we have to cross, because there is a destiny planted within us by God Almighty, and surely God will see us through. Amen. Do you believe that God will see us through? If you believe that I want you to raise your hands and shout unto God. Paul quickly found out that the road to his destiny was not a bed of roses. But actually, I don't know why I shut that. Let me read to you really quickly, just a little bit more, sorry guys, but it's gonna be okay. So in verse 39, it says, when morning dawned, they didn't recognize the coastline, but they saw a bay with a beach and wondered if they could get to shore by running the ship aground. So they cut off the anchors and left them in the sea. Then they lowered the rudders, raised the foresail and headed toward shore. But they hit a shoal and ran the ship aground too soon. The bow of the ship stuck fast while the stern was repeatedly smashed by the force of the waves and began to break apart. The soldiers wanted to kill the prisoners to make sure they didn't swim ashore and escape, but the commanding officer wanted to spare Paul so he didn't let them carry out their plan. Then he ordered all who could swim to jump overboard first and make for land. The others held on to planks and debris from the broken ship, so everyone escaped safely to shore. I'm so excited when I read this because Paul made it. He made it. Paul crossed that bridge in the midst of his worst time when he was supposed to die. There was absolutely no reason for this ship to make it across that bridge. Everything possible, all chaos that could have broken loose, it happened while they were on that ship. When it's so easy to think that that bridge that's supposed to cross us to that destiny, it should be easy. We spend our whole lives trying to find the bridge that we think that once we get there, it should be easy, should be smooth sailing from there. But if you will ask Paul, he will tell you, my bridge was not a bed of roses. My bridge to cross over to my destiny.  In fact, I bet you he was wishing that he was still chained up. I bet you he was wishing that he could only just go back to the time where he was in prison because at least he knew his life was safe because Paul found himself in a life and death situation. But Paul didn't fret. Paul didn't waver in his faith. Paul stood fast. He stood firm upon the foundation of the word of God. And I wanna tell you tonight that if you're gonna make it in life, you cannot make it unless you have this word. You cannot make it unless you know the word of God. This word of God must be on your lips. It must be what dictates your confession. Paul never confessed doubt. Paul never confessed lack of faith. Paul never confessed murmuring and complaining. Paul only confessed his victory. Paul only confessed that which God had said about his life. He said, I believe my God because an angel of the Lord came and he met me in the time of my need. And he said, Paul, you're gonna make it.   Your words matter. Your confession matters. Your habits, your experience with God, it matters because it will determine the destiny that will guide your life. What you will water and what you will uproot. We've been talking so much in our church and we've been seeing with our own eyes the power of God uprooting the plan of the devil out of people's lives. And we see even from these wonderful testimonies where God uproots addiction, uproots the attack and the plan of the enemy out of our lives so that we can nurture and we can water the plan of God so that we can see the fulfillment of God in our lives. And I wanna tell you I am so happy that Paul didn't give up. I am so, I am here today before you because Paul did not give up because he made it because I can read his testimony and it encourages my own testimony. But what's even more awesome is that that my life has been directly affected by Paul making it in life. About a year ago, I had the privilege to hear how my grandfather got saved.  His whole family was Mormons and there's nothing wrong with Mormons, they're nice people.  And as he got older, he completely just left the religion he left the church. He thought this is, I don't, I can't even do this. And he fell into a lot of things through drinking and he tried drugs and all this kind of stuff. And he just didn't even believe that there was God anymore. Why? Look at his life now. He found himself in alcohol, he found himself in drugs with a wife that he had a child with that was a marriage that was just up and down. They got divorced. All this kind of stuff was happening in his life.  And it was a really long pamphlet because this pamphlet happened to be the Book of Romans.  He had been to church, he had been to a Christian church before and he looked at those people and he saw they had their hands raised, speaking in tongues, someone getting the demons casted out of them. And he thought these people are nuts. Is this real? Can this be real? He went his whole life thinking there's no such thing as God. He goes into this church and thought, is that God? I don't know. I don't even know. And he kind of had this sour taste in his mouth. And somebody gives him the Book of Romans.  He was so fed up with the direction that he was going. He takes his Book of Romans. And he sits down, he starts reading it. And then he finds that he can't stop. He can't stop reading the Book of Romans. And he reads it from start to finish. And at the end of him finishing the Book of Romans, took him a few hours, he gets on his knees and he was so convicted. He said, there has to be a God. He lifted his hands in the air and he said, God, if you are real, you will show yourself to me. He says that in that moment, something like a wave just came over his body and shook him to his core and knocked him to the ground. And he thought it was only like 15 minutes or so. He gets up from the ground and discovers that it's eight hours later that he was underneath the presence of Almighty God. And it was from that moment that my grandpa became a Christian. It was from that moment that my grandfather got saved. He was so rocked by God. He had encountered God in such a strong way that every single person that he encountered after that got saved. My grandma got saved. All of my family members got saved. And today I am here before you because my grandfather encountered God after reading the Book of Romans. If Paul hadn't made it to Rome. See, Paul wrote the Book of Romans. He wrote it to them a couple of years before he went there, a few months or so before he went there, he said, I'm coming. God said that I'm coming and I'm gonna be there. He says it in the first chapter, I'm gonna be there. But if Paul never made it in life, then that book wouldn't be in there because then it would be a lie because Paul wouldn't have made it to Rome. But he wrote that letter. He said, I'm coming. And you know what? God saw him through. God saw him there. And it was because of that Book of Romans that my grandpa heard the word of God. The Book of Romans has so much foundation of our faith explaining the word of God. If you don't understand the word of God, read the Book of Romans. Read it and you will find out exactly what Jesus Christ did for you on the cross. You will find out exactly why you need God, why you should serve God and how you can serve him to the fullest in your life. And that's exactly what happened for my grandpa. I'm so glad that Paul did not give up on his journey.  You can't preach to the Gentiles. That's not right. That when he found himself in chains, he didn't give up, but he continued to praise God. He continued to lift his hands. He continued to confess the word of God. And Paul found himself going from danger into his destiny. And it was from that moment on that every single book that we read in the Bible, or excuse me, that was a lie, two thirds of the New Testament that we read is written by Paul because he didn't give up, not once. And I wanna encourage you tonight that what I see before me is I see a bunch of leaders in here. I see a bunch of people who have a dream and maybe, maybe you're tired. Maybe some things in life haven't quite gone the way that you have expected to. Maybe like Paul, that you have reached some storms you've encountered a few blips on the road to your destiny. And maybe like Paul, you've discovered that the road to your destiny is not a bed of roses, but you encountered some troubles, some things. But I wanna encourage you tonight not to give up because you will find yourself in your destiny if you keep your focus and your eyes on Christ. If you establish those good habits in your life to be able to make it, to have a winning attitude, a winning mindset, and that you will find yourself saying that humanly speaking, my dream is impossible. But with God, all things are possible. We will cross that bridge, we will make it to our destiny because we are the people of God and this is our promise. So I wanna encourage you tonight, do not give up. Keep on going. If you don't have a dream yet, if you don't have a vision, get connected to our vision and you will soon see the power of God working in your life and he surely will see you through, amen.


The choir state command of the Nigeria police has arrested 23 suspected criminals for various crimes bordering on kidnapping, ritual killing, armed robbery, internet fraud, among other criminal acts. The state commissioner of police, Paul O'Dammer, further noted that those involved in the kidnap of one magistrate Jumoke Bami Boye, wife of a former military administrator of Oggun, of Oshun and Bauchi states, Theophilus Bami Boye, early last year, were among the 23 suspects arrested. The case revealed that Abu Bakashifu, Alaa's doggo, and his gun were the kidnappers behind the kidnap of one Alhaji, Madaki Shaibu, at Aigun, Tuanikamp, sometimes in January 2023, where the son of Alhaji, of this very Alhaji, was killed. It was also revealed that doggo was part of the gun that kidnapped magistrate Bami Boye, also in that same month January 2023. The command said the suspects were arrested at Eokorin and Bannon Forest within the state in conjunction with local vigilante groups following intelligence reports. Other suspects were arrested for cultism, ritual killings, and internet fraud-related crimes. On 11th April 2023, their both mentioned suspects were arrested based on actionable intelligence to the effect that some suspected ritualists are seen gathered at an isolated hotel in Malete, Muroh, local government area of Quarra state. The anti-cultivism operatives were dispatched to the area by the Commissioner of Police, P. Paul Odama, S. B. S. Idagar, where the suspects were rounded up with all the above items recovered from them.


Really quickly I actually had this video done last week and I already plan to drop it today but I had to make one quick edit because two days ago Lil Nas X actually showed love to the channel. First and foremost man really appreciate that you definitely didn't have to do it and the fact that you did shows that you're a real one and not only is it big for the channel it makes you an inspiration for the artists producers and other business people that follow it. Wish you much success to you in your career bruh. Brain man community let's put some bowls in the comments for Lil Nas X. What's up everybody once again it's Brain Man Sean and we got to talk about why Lil Nas X is so great and even though things are going so well welcome to be a huge threat to his career and something all artists have to think about. Now first and foremost this video is not necessarily about Old Town Road but if you know who Lil Nas X is then you probably have heard Old Town Road viral hit the thing is super catchy created a little bit of controversy in terms of being pulled off the Billboard charts in the country section all that good stuff but what's so great about that track is it's another reminder that in this era all it takes is one track to bring attention to everything else you have going on and this is why Lil Nas X is so great and why he's in such a good position right now Lil Nas X didn't just start posting music he's been posting music for a decent amount of time and when the song that a lot of people would think and consider as a troll blew up Old Town Road ended up having the same effect as Doja Cat's Moo I'm a cow song when that blew up a lot of people saw her for the first time thinking yo who's this troll this girl's hilarious but then when they start to see the rest of the music they were like yo this girl's a real artist she's super dope the same thing is happening right now when it comes to Lil Nas X if you go listen to this dude's music this dude has a lot of really good music a lot of catchy music maybe it might not be your style but for the style what it is yo this dude is hitting man he got some slaps and the great part about it is this other music legitimizes him to a lot of people who thought of him as just this country rap guy who trolled with this song who has this type of music you can really get a sense of who he is for real for real through the rest of the music like in songs like carry on he actually goes pretty deep talking about some of his struggles some of the things that kind of put him in a depressed state and then in songs like Naserati and Sonic they're fun they have great flows and you can ride to him and he has a lot of those songs this means the fact that Old Town Road blew up created a lot of real fans for him a lot of people have gone back checked his music out and said yo this dude is like for real legit and I know OG fans like to hate on people who come in new but it should be that way everybody's not going to discover everybody at the beginning but let's talk about the threats that comes to Lil Nas X's career at the same time if you look at how he put things up yeah he hacked things together a lot of times right there's the visualizer which are basically just videos that are using clips from the things that he's talking about or relate to the subject of his song in some way just like Sonic shit he uses Sonic the Hedgehog clips in Old Town Road he used clips from Red Dead Redemption and so on and so on the only real music video I've seen for him is the carry on video where he's standing in the graveyard and in the same way he used a lot of other people's visuals he also from what I've heard use a lot of samples everything I've pretty much heard from him has been a sample so when you hear some of these songs and you're like yo this is super dope I want to listen to it all the time because they're on YouTube and then you try to go to Spotify and iTunes they're not on there and of course if you know anything about when it comes to Apple music and Spotify things like that those are avenues where you are making money on it for sure when it's on those platforms and if you don't own the music especially when it comes to samples samples can get tricky you got to get them clear then it creates a problem I guarantee he would have far more streams and listen to his music if it was able to be put on Spotify when I first looked at his Spotify he only had Old Town Road and the Old Town Road remix now on April 10th Sonic Shit was posted that got cleared up but Sonic Shit was actually be used by Lil Yachty and done by Digital Nas which is actually a funny coincidence because if first of all if you guys don't even know who Digital Nas is he's a really dope producer out of Atlanta but Nas is actually his real name when it comes to Lil Nas X Nas is not his real name but it's funny that the producer's Nas and the artist is also Nas maybe it was meant to be shout out to Digital Nas by the way he was actually one of the headliners at my music festival last year but back to Lil Nas this guy has a great set of music that he's able to rap over which makes him a little bit unique as well if you listen to all of his songs the production is so different but he knows how to fit in the pocket of each and this is what makes his career so promising in my opinion because at the end of the day like it feels like this guy can make another one he has banger after banger after banger it's been a while since I've retroactively looked at a new artist's music and just seen so much music that really hits that spot so right now to me he's at a standpoint where it's like yo you got this hit that actually brought attention to the rest of your music which is actually really dope as well so you have a lot of fans but you're not able to actually maximize on most of your music because it doesn't seem like it's clear that's the only reason I can imagine that so much of it isn't on Spotify so much outside of the fact that he might just be a kid who didn't think to do it but at this point I think there's enough people with a knowledge around him that they would have put it on there if they were able to but whatever is going on at this point that's holding up a lot of the songs from being maximized at this point I really do believe that he can make another hit and that's one of his biggest advantages he has the ability to make something catchy it's not the first song that combined country and rap or even doing a more rap version of country it's not the first in that space or category but he caught one now it's time to just see what he's gonna do with it can't wait to see what buddy does would love to know what you guys think about a little nice ex as well have y'all listened to his music and if you haven't check it out like for real if you're the type of person who likes that type of music trust me you're gonna be like yo he's that dude other than that if you like this video go ahead and like button if you like your mouse well share it and if you're not subscribed you know what to do hit that subscribe


Так что, я начну мою курсу, как профессор Куксин, я тоже даю 4 лекции на контроль серии. Это будет интердакторный курс и геометрический контроль серии. Это не очень формально, я не буду говорить про очень новые вещи. И я считаю, что этот курс... Дело в том, чтобы объяснить какие-то геометрические идеи с минимальной аналитической техникой, потому что эти идеи могут быть использованы. Они уже были использованы и я считаю, что часть этой идеи уже будет использована для миксирования, для эволюционации. ПДА будет использована по стакастике. И я считаю, что тоже что-то еще будет использовано в будущем. Итак, я начну просто с дефинитива. Что это контроль-систем? Контроль-систем — это простая форма. Если у вас есть эволюция, или дефинитивная эволюция, я буду работать с аудией, но как профессор Куксин, это был син. Курс, в принципе, вы можете думать об эволюции пидей, как аудией в более сложном месте. Геометрия — это значение. Если вы считаете, что все аудией в новом диаметре, то здесь может быть и та же геометрия, как пидей, но больше анализов не нужны. Мои форты могут регулярить. Мои форты могут регулярить. Это очень хорошая миксация. Но геометрия, в принципе, та же. Я уже показал, что это очень важная миксация пидей. Это работает. Можно быть оплотен. Но я делаю с аудией, поэтому я считаю, что систия. Я стараюсь с очень геометрией, чтобы я был немного меньше геометрией. Геометр-контроль-систем — это так. У вас есть только динамичный систем. Экс-биллун 무슨? У меня есть геометр-контроль-систем. Мой геометр-контроль — это очень �гיבие, но если вы не очень уверены. Некоторые из вас не очень уверены. Геометр-контроль — это просто domain in run. ФФ, давайте мы снижем. ФФс — это динамичные системы. Если вы хотите, и контрол-система, это формально, это фамилия динамичного системы, которая зависит от некоторых контрол-параметра. Для меня для вас будет открытый, но большая часть контрол-система, или просто вектор-спейс, потому что это используется для миксирования. Но в общем-то, это может быть тоже нон-линия, и вы можете быть в более компликатом специи, в ближайшем, даже более компликатом. Так, это просто фамилия динамичного системы, параметрирована с некоторыми параметрами. Мы надеялись, что это все с респектом. Но, в общем-то, в моем курсе я считаю, что это просто фамилия динамичного системы. Специальный случай, FU of X, это F0 of X. Мой случай для нашей курсы и аплодисменты. И FU — это просто FU of RK. Так, что у нас здесь? У нас есть какие-то динамичные системы, и это респект с другими динамичными. FU of X, это параметры респекта. Так, это почему мы делаем специальный серий, мы пишем много книг, если это просто... Это полностью включено в такой ситуации в теории динамичных системах, потому что у вас есть X, и у FU does not move, и это все, окей? Это параметры. Но это не...  Так что это параметры, которые мы можем выбрать, как мы хотим, и менять наш выбор в каждый момент времени. Это такой момент, окей? Для нас это параметры контроля, и функции контроля. Я уже думал, что я не буду дать много деталей аналитических деталей. Вы можете найти это в книге. Я не знаю, как это произойдет, в сайте или нет, в сайте, где все. Присоединяется. Провод в книге Агора Чев, Сачков. В контроле серии от геометрии. Геометрия. Это шпрингер 2004. И есть еще хорошая коллекция лекций. Здесь, в ICTP, если я понимаю, что это totally free, может быть, у них даже принятые копии. Я не знаю. В школе мы организовались здесь несколько лет назад. Это массематическая контрол-сери. Два вольера. Есть много курсов. Контрол-сери. ИСТП, лекция-сери. Это самое простое, чтобы найти здесь. Лекция-сери. Так, это ресурсы. Сейчас, окей. Контрол-фаншен. Это просто функция на сегментах НРПЛАС. Т. Ти. Ти. Титаль. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. Ти. если мы не depend linearly. На ухе мэп не очень хорошо оборудовывается и не очень хорошо на литературе, но в этом случае ухе-то это не очень хорошо оборудовывается и в инфинити это всегда возможно, без проблем ОЛ2, ОЛПС, ОТРАКУДБИ. Теперь, что мы делаем? Так что, это, действительно, невозможно, в случае стакастик-пертурбационных контроллсерий, в классике контроллсерий, УФТ — это то, что мы totally free to choose as we want. And the main object to study is actually the map. We can define the map, FT, family of maps that depend on parameter T, that we can, in order to... So now, what we do? If we select, we have our dynamics, dynamic is something that is done by physical law, or I don't know by say... We have a dynamics, we have a dynamical system that depends on parameters, and we can control some parameters. That's the idea. We have a family of dynamical systems, some parameters, like a car, or like a human body also. We have a body that actually, whose position depends on many, many parameters and some of them we can control and move and change these parameters whenever we want, in certain limits that are indicated here. And so we simply plug in this U of T, we get the map, control U of T, instead of parameter U, we are writing U of T now. And then we have under this setting, we have a well-posed evolution system. So Koshi problems in finite dimension is well-posed. At least for small T, but that details which I will not create. Of course, solutions may blow up in some time, but this I will not care about. It's easy to control anyway. Just do not to spend time for that. At least for any initial condition, X of zero, we have one defined solution. And let me in order to minimize number of variables to simplify formulas just to fix. So in order to get a solution, we need to choose U of T and control function and the initial condition. I fixed initial condition. I just fixed initial condition. This is going to be fixed from the very beginning.  If I have U of dot, I have unique solution starting from here F zero is just of U of dot is just X zero. So I assume that initial condition is fixed. We have a unique solution starting from X zero. And we take it and evaluate it moment. That's a map of T. It's actually the main object to study. There is a quite rich map, as I think you will see soon. What are properties we are interested first of all. Of course, we are interested where we can arrive. We start from position X zero. We can start without any position. But for the moment I fixed it. And we select control, we move somehow. And the question is our control capacities, where we can arrive. So what we are interested in, this is called controllability problem. To fix, to understand somehow the image of this map. Where we can arrive. Let me also denote by U. This is going to be space of controls. This will be script U. U is the space of this function U of dot. Admissible U of dot. As well as in your capital. And fine. So that's what we try to study. And the controllability, controllability problem. Is it true? System is controllable. That F of U script is the whole manifold. Can we arrive everywhere or not? That's the first question. For time T. Controllability for time T. Or for infinite time. Then just T is free. Let me explain immediately, before specification, that even in so general setting, relation of this problem, it's actually a problem that is relation with mixing. So here everything is deterministic. No stochastic thing. And as I thought, we simply study, select any control that we need. But assume that we don't know how to select our control. And we have some probability distribution. Some probability distribution on U. And just apply with certain probability, according to certain velocity distribution. Now I start to be close to the setting of Professor Kuxin. We have a time segment T. We divide it in small pieces. Or we may do more advanced things, consider kind of divided limiting case, kind of Brownian motion. A stochastic process with continuous time. But it's totally sufficient to divide it in pieces. And we use just piecewise constant control. Even piecewise constant control. Or some particular classes of controls. For piecewise constant control that I distributed with respect to probability measure on U. Some probability measure on U. We apply it here, arrive to some point. Then independently apply on the second segment, independently on third segment, independently on third segment. And we are interested. And then as a result, at time T, we will get not a point, but probability distribution. We have such a random work, if you want according to prescribed dynamics. We obtain a probability distribution at the end. And we are interested on the properties. And mostly we are interested. Does it has a limit for T equals to infinity? That limit that does not depend on X0. Unique limit for T equals to X. It usually does not depend on X. So I claim that it's a look. There could be, and I think in Professor Cookson lectures, at least in this papers that he mentioned, he used more sophisticated things. So they were not piecewise constants. So the probability distribution was defined on the space of U restricted to small segment, to the given segment. So it's richer things. It's not piecewise constant, but important that you take a certain distribution of control in the space of controls on given segment, and then you repeat it, but totally independently. Crucial words here independently. And what will happen at the end of the day or at the end of everything, for T infinity? I claim that the mixing property is extremely close to the just controllability properties. If you do not take naive, not actually mathematical problem, that question is not a mathematical question. So it's at the level of set. Normally if we use some real tool to check this, you have more. Because if you create, give a way to select control, which arrives at any point, it is not just you prove that it is. I explained this later in my course. You have really more. So what I mean? We have a kind of qualified. I say, I claim that a qualified controllability, controllability with some stability, some solid properties is essentially equivalent to mixing at least in finite dimension. In finite dimension yes. Because in infinite dimension we normally do not have We never have this. In infinite dimension we may expect only the closure of that. And it is a little bit other story. And you need much more analysis. In order to study the properties of my measure, you have to project it on finite dimensions. It's more delicate. And you cannot do it in the universal way. You need a certain class. It works for a certain class, but important class of PDEs. But in finite dimension it's more or less. What I mean is the qualified or solid controllability. Assume that we start from x0, and at time t we arrive. And there is a... And we have a... And as soon as we have ux... So this is x of t, of u t, of dot. We arrived at some point using specific controls. We start from x0. This is a trajectory. And at time moment t we arrived here. Maybe I drove it in another part of the box. Blackbot. We have a huge blackbot. So let us use it. x0, we arrive to x1, x of t, u t, of dot. And assume that it is not... We have a bigger property, greater property. We assume that the map is... Our map is open in the point u tilde. Ft of some neighborhood of u tilde in the space of control functions. Kavas, some other neighborhoods. Say like that of x1. Assume that it is open. And moreover, this size of this. And assume that it is like that. So essentially, normally not all neighborhoods is necessary. Since we have a finite dimensional manifold. Here I start to use a finite dimensional. We have a finite dimensional manifold of x. We can normally find a family. It's maybe not necessarily the complete neighborhood by some finite dimensional family. Family of controls near u tilde. Some perturbation of this control is efficient. But assume we have this and moreover somehow we may control the size. This guy may be much smaller than this one, but still with some minimal control. Absolutely minimal control. And how it can be controlled? Very often, and I explain it in the next lecture, maybe probably today afternoon, very often when I say qualified controllability, it means that if I perturb a little bit f, then we still have this property. Which maybe neighborhood becomes smaller, but we still have this property. So I do not only go to the, can go to the point. First of all, I go to the neighborhood. I have a sufficiently rich.  There are no other way. You use analysis to prove controllability. So using analysis, you automatically prove this property. But at least it's finite dimensional. We can have more. It is a stable. That property is stable. So if we perturb a little bit uf, uf is a finite dimensional family.  This is, you can take it as a neighborhood of ut. Not completed, it's too much normally.  So this is what is called solid controllability. Now look, now look. Take a time, say 1. Now look what happens. Assume that we have it. It means that now switch to the stochastic situation. In stochastic situation, this property means that we cover small neighborhood with a nonzero probability. If you have a distribution, such that all controls are presented somehow in this distribution, okay? Then we, we, we, we, it's maybe very small, extremely small. Exponentially small size, has a smaller size than this. But still with nonzero probability we can cover and enable it. It means exactly that. You can, you can understand it.  So, and if it is like that, switching is almost free in finite dimension. Look, the independence comes in the game. For time one we do it, okay? And I'm sorry because of course now I see that when we do stochastic view point it is not convenient to, to, to use a, use a fixed once forever initial condition, okay? So, so this effect actually depends also on X0, okay? Let us write like that. They play different rule. Like X0 and this play different rule, okay? And then what we do? Then what we do? Look. So, we have time one now, two. Yes, but I say about initial condition. Initial condition I cannot feel, because I have a dynamics. I have a semi-groups. When I go time one, then I start from the, then I continue going. I keep going, but start from another point. I start from the point where I arrived, okay? So, this property has to be somehow homogenous. Homogenous with respect to X0, okay? That property, this property of X0. But it is, it is, because indeed that what I say we have something bigger, because if we take little bit X0, then it means that F change just little bit, okay? And if we have a forgiven X0, we have a qualified controllability, then we have a for any, for any point, for any X0, okay? At least when we start from compact, we can cover by neighborhood and things like that, okay? We have qualified, solid or qualified controllability, which I mentioned implies that it works for any X0, okay? From a compact. So, look, we, now we understand that for any reasonable distribution of controls, we arrive to a point, if we really solve controllability problem, not just to claim something abstract non-checkable, set theoretic, that the map is surjective. If we really prove it, we got this, then, then, then what happens? So, we arrive to a point with some very small probability, starting from X0, starting from X0, we obtain X1, the small neighborhood of this, of X1 with very small probability, with probability mu distribution here is mu of that neighborhood, this one is epsilon, very small. So, very small probability, but still, it is separated from zero. Probability to arrive to such a neighborhood. But then we continue, we repeat our game, starting from here, and let us look what happens. So, if we arrive here with probability epsilon, it means that we do not arrive, mu of f2 arrive, arrive in O of X0. And probability, and probability mu of the whole guy minus O is one minus epsilon. It is a little bit smaller than epsilon. But then we repeat our game, but we do it independently. We do it independently, it means that for time two, we look the same neighborhood. For time one, do not come here, it is minus epsilon, it is probability minus epsilon. Then do not come here, for time one and for time two, it gives you, it is a time one. Time one, time two, time equals to one, time equals to two, that is a minus epsilon in square, just independence. We do not arrive for time one, and neither for time two, it is a product. Then we continue for time equal, and it is minus epsilon in power n. So, what we see, that eventually this probability, if we keep going long, long time, but our idea to do it up to infinity, probability not to come here is goes to zero. Absolutely, earlier, later, we come to this neighborhood, and if you have a controllability property, it means that we come to any neighborhood. Earlier, later, we come to any neighborhood, and with some positive probability. And this is essentially, almost all you need for mixing. Because look, we wait for the moment when we come here, but then still, if it is very long time, still it is, we have infinite time ahead. So may we repeat, repeat it, and at the end it is quite classical in the mark of processes, mark of chain, that everything is mixing. Due to that, first of all, we arrived everywhere, that I already showed, but since we arrived everywhere, still in finite time, we repeat this guy, which travels everywhere, infinite number of times, at the end everything is mixed, this is a basic property of mark of chain, at least in dimensional, in finite dimension, it's okay. And infinite dimension, as I mentioned, the main problem is that we still simply do not have this. We do not have complete controllability, we do not have enough resources. So that is, I would like probably exactly to start to explain why mixing is so close to control. And at the end of my course I will not use absolutely stochastic language and mixing, this remains to Professor Kuxin. And I will just study this controllability problem, controllability problem, but not only actually, in particular, in finite dimension this normal controllability is enough. In infinite dimension we have some intermediate step, that finite dimension of projections, because only, not solution itself, but only its finite dimension of projections may have this property. And then, thing starts to be more delicate, because when dimension grows, estimates become worse. And it starts to be very important not just to come here with some, but to come here in the best possible way. So here optimal control problem comes again and I will discuss also optimal control. In this language, how I can explain optimal control, optimal control questions. Two basic questions of control theory, controllability and optimal control. Contrary control used for applications, used in a lot of, for many things, but let me explain how it appears here, why it is getting to be essential here, here also in the, in the, in the, not without, without any technique actually, look. So, as I already explained, the main thing is to understand that, that we come with some controls, close. As soon as we arrived at some point, with some controls close to, to this point, we will cover a neighborhood, but still, but then, when it is only fine, if we actually need a family of that, this growing and growing dimension, that property simply, it's not enough, it does not work. It starts to be not applicable. And what we need? We need to cover it by, when I told, I did not, for me it was all the same, which kind of control I used to cover the neighborhood, okay. And for applications to PDE, for me it's important that it is controlled not big enough. It's well described family, and that is not so far from UT. Not so far from UT. It starts to be very important for estimator, okay. And for that optimal control, optimal control is useful. Essentially, what gives optimal control? Assume that we can get point x1 from x2. Point b from point a is in the school, in the high school. And then, and we have a cost to say if our control is good or not. And optimal control try to minimize simply the cost. Cost is maybe integral cost. In this situation, so we come, utility centers here, utility centers here, some utility say plus v, centers in the point nearby. Natural cost here in particular is integral of v square is just l2. You can build p on what we can really check. On a particular LP. And we try to minimize guy which sent us nearby. And there is a good, we can characterize for, as usually, it's a kind of generalization of calculus of variations. So you can characterize streamals, so we have one point, another point, and we try to find a corresponding trajectory such that that is as cheap as possible. Perturbation as cheap as possible. We can characterize it by some differential equations. So there is some calculus which extends classical calculus of variation. And this is actually optimal control series. I also discussed about it, what can be done. So this is what we plan to with. And now let me start. So as you see, as you see, the main here is the endpoint mapping. So which is quite rich. You see that it is not, it depends on the family of dynamics or even dynamical systems quite rich subject, but this one also. Let us consider, and I immediately, and at the beginning to explain some basic things and some maybe nice geometry, I restrict myself to the not even a fine, but linear case. So I consider the situation when f u of x, so we do not have dynamics with u control. When control is zero, we just stay. f u of x is just some of u i f i of x. And here the theory starts, and that so let's we we start at point x zero and we immediately would like to see where we can go, which direction we should go. Interesting things also in control theory it's what control theory is about when dimension of of m is case much smaller just smaller, much smaller than dimension of m. If dimension if k is a dimension of m and f i, f i let us assume linearly independent, locally at least just for simplicity, that may be dependent at some point.  Everything is fantastically good and interesting cases are when it is smaller and when applications to p d e interesting cases are when case finite but what I say dimension of m much bigger in p d e is infinite it's still we can manage at least finite dimension of projection let us look where we go we can go just write this equation we use analysis let us use small control f i of x put here epsilon and one of f i of epsilon u is x 0 plus with small control we can write a principle term we can write a principle term and it will be it's very clear if control is principle term here is just average of f u of x 0 d t plus of f so we can write like this so this is x of t without any any remain the term but if you would like to develop to extend it it's just a writing od what is here it's a written od but still we already have epsilon here and x is epsilon close since velocity velocity has size epsilon close to original point that we can write it put here 0 of epsilon square as it was obvious expected in the first approximation we just go in the direction of linear hull of this guys what I would like to mention here that there are another way to do things in particular maybe there are two parameters here time and size of controls we may have with a not small control but for small time and obtain essentially the same if we write u epsilon u epsilon of t equals u of t epsilon and this is maybe not small then we get changing variables in od e we get more or less the same the same just reshkailing time reshkailing time I omitted this calculations we have the same it could be epsilon u that could be u u epsilon of dot and for time epsilon since we start to use the effect that we can select our controls we take u then reshkaile the same u the same values of u of t one after other but go faster go faster not in the first approximation in general we have then f epsilon I am sorry just the same just the same to go time one with guy u or to go time epsilon with guy one just reshkaile fine approximation we do not have much we have something trivial but there is something here now I give first introduction for that part of this lecture then I start to be more precise I will explain how things appear but now I would like to have example of result simple result but to demonstrate theory works then I will develop it in more detail in more details so what we go is average velocity in direction of average velocity but if average velocity is zero let us consider u such that now assume that of t dt is zero so if average is not zero just we move in the direction of average velocity it's not so much but clearly we may expect much better as a direction if in first approximation simply don't move now change little bit notation starts to be more more geometric average of u this is linearly depend on u this is linearly depend on u it is yes so if average of u is zero then also average of f is zero because f is computed in one point we go in the direction of average and the initial point what we do in average of u the idea is to to see some laws where we go in terms of u so let me consider the curve gamma of t just primitive of u just primitive so that property means that gamma is a closed curve not closed curve in the space of controls moreover now I would like to specify more because my idea now to show not to drive lectures to show something geometrically interesting rather simple but geometrically interesting immediately so gamma is not closed so we go if f then we go in the direction f of gamma of one because integral can be taken here you can write this is gamma of one simply and if gamma of one is zero if the curve is closed gamma of zero and then where we go I show it's a simple exercise that you can do even by yourself then where we go then I claim that it follows that f epsilon of u epsilon is we have to compute second form that is quite easy here quite easy here and this is a epsilon square epsilon square this gamma let me now specify assume that k is 2 I would like to study just k is 2 but what I say at this level there is a nice generalization but I will not much more notation of what I say what I am going to say for any k assume that k is k equals 2 then what we have so this is a plane curve this is a plane curve and this is a domain curve it covers domain curve what I have here is a and it is a very simple exercise perhaps omit we get area of gamma multiplied by f1 f2 of 0 plus of epsilon curve so we go slow but we go another direction this is a I should explain perhaps so this is a free bracket so f1 f2 in coordinates f2 in coordinates just df2 df1 minus df1 over dx f2 of x, computed at point x0 computed at point x0 so this is what is called bracket commutator of vector fields so we have something new if field do not commute may recall it will be very useful for me also more formal definition of commutator why it is commutator and again I leave with you a sexy size we may think f is a vector field so at any point we attach some velocities to go we normally since in all text book and analysis it's immediately explained that we can think about it as first order differential operator when we apply linear differential operator this non-linear field is actually linear differential operator which are x like that if we have a smooth function say cinfinite of m then fx on a it's just definition fx of a fa the other function is directional derivative of a in the direction of f of x is a dxa f of x that we know then since it is linear operator we can we can we can we can iterate it we can write f1 f2a just a composition operator that is second order operator that is second order differential operator we can also write f2f1 this is another second order clear that when we apply f2 we get the first derivative of a then for the result we apply f1 for result we have second derivative here we have also second derivative but commutator that is everyone knows but it's not occasional this is a peos commutator and you see that nothing else could be appear here because since it is a we have some expansion of some we have epsilon of epsilon x a cure it's a cure in m its expansion of the cure starts from x0 second term is is a tangent vector must be tangent vector and it appears some combination of derivative of f1f2 it's only one of this you can expect it you can expect it so then f1f2 it is actually if we treat these guys as separators it is f1 it is indeed commutator f1f2-f2 f1 it is indeed commutator so now let me ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... И потом, может быть, я скажу сразу, что это не может быть саунд, потому что это может быть различные саунды, конечно. Это саунды. Если мы обмениваем ориентацию, то саунды меняют. Здесь и здесь, и здесь, и здесь. Не обмениваешься, а просто обмениваешься. В результате, это должно быть то же самое. Это саунд. Этот пацан воритый и воритый. Я не помню, что это, может быть, саундово. Но это не важно так же. Это саунд. Так что, в особенностях, если у тебя курица выглядит так, и ты идешь в эту сторону, начиная с 0, саундово. Это дает тебе плюс, и дает ориентацию в opposite way, и дает тебе минус. У тебя это важно, потому что мы не хотим остаться с саундами. Мы хотим идти вперед. Мы хотим идти вперед. Так что это саундово. У нас уже есть что-то делать. Если мы хотим идти, то всё. Мы берем абсолютно любую курицу, так как эта саундово есть позитив. И ты идешь здесь, если саундово идёт в opposite way. И ты идёшь в эту сторону, и эта курица может быть totally independent. Если вегтофилдсом умеет, то мы не берем любую курицу. И даже если ты хип, то вы всё равно не берёте курицу. И это важно для тебя, потому что это не очень тяжелый интерсайс. Если вегтофилдсом умеет, то это очевидно. Тогда это не важно, где ты идешь вперед, где ты идешь в следующий раз. Если вегтофилдсом умеет, потому что ты можешь его менять. Это означает, что результат... Многие Dinge могут быть объяснены перед calculацией. Результат зависит только, когда ты идешь в 1, в 1, и как долго ты идешь в 2. И не из-за сфистикации. Ты можешь выиграть любое, но вегтофилдсом умеет, и ничего не изменит. Результат зависит только от оборудования. Потому что всё это дает тебе. Если они умеют. И потом... Мы не можем это продолжить, потому что... Для контролации серии, это просто тривелый случай. Если они не умеют, то это невозможно. Если они не умеют, то это невозможно. И мы, конечно же, у них есть. Так что... Некоторые люди дают тебе... Некоторые, как это, дают тебе мгновение, но коэффициент это другое. Коэффициент зависит... зависит от оборудования, от оборудования, от оборудования. И... Окей, конечно. kasura, мы хотим максиминière система. Илиuned. Это оборудование. Я думаю, что мы хотим установить эту сторону. Мы хотим его adherence к тур Joan Erichon. Мы хотим Pierre Chamotект wisee. Так как кюфа-шота. Мы получаем много кюфов. Кюфы-шота. Кюфы-шота. Мы получаем, если мы считаем салюты изопериметрической проблемой. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Кюфа-шота. Для того, чтобы минимизировать интеграцию u of t, u of t minimizes its absolute value here. Для того, чтобы получить given area. Квивалентно, мы можем фиксировать ленту, мы можем использовать... У нас есть какие-то лимиды в качестве контроля, мы можем взять большой ленту и попробовать как можно и в направлении. Так что мы максимумим гамма с фиксированным лентом. Это та же проблема. Это периметрический проблема. И вы знаете очень хорошо эту soluцию. Солюция — это цикл. Если гамма с фиксированным лентом, это дает вам лучший коэффициент. И вы можете... У меня есть стандартная вещь, чтобы реализовать, что тратить сквей. Сначала один, а потом второй, а потом один, а потом тратить. Это лучше в любом смысле. Лучше, чем с фиксированным лентом. Во-первых, с фиксированным лентом. Возможно, один тратилет. Не именно один тратилет, но ворс коэффициент. И также, твой контроль — это нон-смой, но это не будет. Так что вы должны использовать цикл. И это очень просто. Больше интереснее, математически — в следующем случае. В следующем случае. Я надеюсь, что... Как это сделать? Итак, мы уже знаем, как идти в F1, F2, и даже иметь эффектный контроль. Если мы идем вперед, мы идем вперед, и мы можем повторять, повторить. И мы знаем, что делать. Приметив гамма, контроль, просто ротировать. Ротировать, ротировать, ротировать. Это контроль. Если F3 dimension, это F1, F2, F2. И если... Это F1, F2 — экстрадирекция. И когда мы... В контролье, мы просто идем вокруг цикл. Ротировать. Но в реальном случае, в контролье, в реальном случае. Но в реальном случае, в реальном случае, мы идем здесь, и идем так быстро, как можно. Мы получаем спираль, как это. Мы идем слой, надеваем спираль. Это очень простая пикция. Но уже на этом уровне, вы знаете, что действительно у меня есть часть этого курса. Так что, это важно, что эта law of efficient movement is universal. It does not depend on your vector fields. You find in the control space the best possible law. And then just plug in your system. So, somehow, good control theory is done without control system. It's not yet done, by the way. It's maybe just a dream for the moment. Without control system. We simply plug in any control system, but the laws of good behavior are always the same. If we do it with small controls, of course, we need some small parameter to do it. Or you do it for short time, and then repeating, repeating, repeating. But now I would like to discuss also next case, again with k equals 2. s k equals 2. Next case. So, assume that now that area that area of gamma is zero. So, gamma is something like that. Balanceria. Plus, and here it's not really balanced. The picture. Plus and minus. Balanceria. Then f. Then we can write some other expression of gamma. That is not area. It's a kind of momentum. I will not give details. Later, later. In fact, I can do it. In fact, I can do it. What we get here. What we obtain here. Without geometry so nice in geometric interpretation is here I do it. f epsilon of epsilon. Then now, of course, starting point. Starting point. And plus again, you know, epsilon cube. Again. Since now principle term is a cubic that principle term is just tangent to Yokeov. Yokeov, again, it starts from epsilon cube. But if you reshcale it changes parameters. Take epsilon cube as a new parameter, then it will have derivative. And derivative is a tangent vector. You can take epsilon cube as a new parameter. Derivative is a tangent. It must be tangent vector. It must be valley on some vector fields. And this vector field is cooked from f1 of 2. No other way. Again. Expansion is universal. f is just symbol. And here you can write it. Let me write. You want. Then you can interpret it also. Geometrics that I will do. But what I write now is a kind of expression which you can continue. You can write for any. It will be similar for any order. And here you have you have you have this is t1 this is t2 so you integrate over the simplex. And here we get control. So I can write it in terms of gamma. f of gamma 2 gamma u of 2 gamma dot of 2 say because the result depends only on gamma. Result depends only on the gamma. Let me even write. OK. But you see the result does not depend on the parametrization. That's what I would like to say. If different controls are just the parametrization of the same geometry is here also. The parametrization of the same curve that result will be the same. Depends only on gamma parametrization. Gamma of t2 f gamma dot of t2 gamma dot of t1 f gamma dot of t t2 d t1 dt So t2 is integrated until t2 t1 is integrated until t1 Essentially such a such an iterated integral that also first of all since we have a triple integral here and derivatives here then indeed it does not depend on parametrization of gamma and again we at the end what we obtain. At the end we obtain a point in the plane where we draw the plane so we started in the situation the span of f1 f2 f1 f2 and now let us draw the plane we have second order brackets and we have two second order brackets actually we have f1 f1 f2 only two because brackets are anti-symmetric we have only two f2 f2 f1 so here argument must be different because we are anti-symmetric and the first order bracket is just one but here we have two and we appear when we apply our control indicated by gamma we go in the direction of this plane we consider this plane we have arbitrary dimension manifold arbitrary dimension manifold and in this manifold we have a kind of plane I would like to show that it is not square on the plane but it is some plane which is not that one first order bracket we know how to go and we would like to go to next next direction that depends on the second derivative it is the iterated bracket so here say we have two guys f1 f1 f2 and another one f2 f2 f1 full orientation is controlled we will not give details because otherwise it will take too time and hard to follow I would like to explain just basic idea and result so we have a plane of controls commutative plane if you want u1 u2 and we have a linear map call it AFC that send u1 u2 into u1 v1 it is other plane because it is not v1 it is not control really v1 f1 f2 plus v2 f2 at this level we have a more direction to move in the first bracket v2 f2 f1 again just one direction here we have the whole plane and to go in these directions we apply gamma like that with balanced area the question is again the same try to find universe low which gives you better coefficient which with limited length of the curve give you best coefficient you have a nice variational problem universal problem it does not depend on f and it is not so classical it is not a parametric problem anymore it is more on linear more involved and it can be solved and you immediately try to continue and it often happens in mathematics if you go to the next it starts to be too complicated but at least at this level in this level you have a very nice solution so you understand that it should be something like that 8 shape because if you have a more complicated guide we cannot be best it 8 shape it indeed 8 shape because we can rigorously solve these problems in detail shape moreover you see 8 shapes kind of gauntel guys are always done with the fact that we have two dimensional results depends on the orientation you can rotate it if you rotate it it is parametric family but they are absolutely equivalent one getting from the rotate it is not like circle it is rotation and variant due to the fact that it is rotation and variant you can just one result and here and what is the best the best solution is 8 shape earlier elastic the unique best solution is 8 shape your earlier elastic earlier elastics are found by earlier equilibrium of elastic road it is in all text books on elastic theory one of the very few maybe unique one non trivial example which can be computed up to the end but they appear in other very often appears in optimal control problems essentially you see why as soon as you need second order bracket you need something like that maybe a little bit sorted but something like that and they have a nice geometry characterization actually in order to not describe equation for elastic they have very nice geolastic gamma is elastic curve gamma in the plane elastic curve that result does not depend on parameterization this property of the curve if and only if if and only if curvature curvature is a plane curve of gamma at point x is a fine function of coordinates curvature is a fine function of coordinates gamma is gamma is say V1 V2 and the curvature of gamma is alpha plus a1 gamma 1 or better I cannot need to write this one curvature is alpha plus a gamma curvature of gamma at any point at any point of gamma where a is a fixed vector constant vector and this is constant so you see you see what happens for first order bracket just if there are no bracket if we would like to go to the direction of linear halve 1f2 of course we go the best way to go along straight line shortest way straight line and the solution is curve with zero curvature if you go to the second first order bracket the best way then we need close curve and the best way to take curve with constant curvature of course they are all special in such formulation they are all special cases of elastic but degenerate most degenerate if you go to third order bracket then you already you use only gamma with a balanced area and among them the universal independently of f the best one is 8 shape elastic elastic there are a lot of them but only two periodic circle of course and this one then and with inflection point looks like that and among them there is exactly elastic here you find a circle when you do not move it always repeats as one of possibilities and here you have 8 indeed if it does not move there are two types of elastic they are related also to pendulum equation and these are two they are related to pendulum so another characterization of elastic is that if you parameterize your curve by the lens so your velocity is always in the circle has absolute value 1 then the curve is elastic if and only if this angle is satisfied pendulum equation standard pendulum equation another characterization classical characterization this is with particular parameterization and non-linear this is total mathematical pendulum theta dot this equation where theta this is a gamma dot and this is angle theta and we have for pendulum equation we have two kinds of behavior it may oscillate when velocity is small or it will rotate when it oscillates according to the definition this is the velocity change direction so this is second derivative change sign and this is second derivative change sign and this family and this family corresponds to rotation like that with big wheel that is what concerns elastic my time is almost over maybe maybe I have 5 minutes maybe I start it was preliminary как я уже говорил но конечно нужно продолжить взять высокие брыки и рассматривать керфы так как керфы это полинома керфы но потом и это полинома и это и это и это это это это это это это это это это это это это это были Это уже для рецепта ж Wouldn Если вы считаете, что кей больше, то это не кей, но я только интересен в первом рейке. Вы получите вырезанную soluцию, очень приятно. Это аналитическая и интригонометрическая функция. Это тоже комплектаризация. Также спешевые кейфы, которые очень-очень вырезаны. Они изменили чебушев. Они тоже имеют другие extreme properties. Как линия? Один один. Один один, но в любом дайменте. В любом количестве контролов. Нет-нет-нет. В следующем дайменте, в первом дайменте, даже в двух дайменте, вы можете найти ваше время для очень специальных рейтей, чтобы получать хорошие кейфы. Потому что потом вы должны быть более балансовыми. В частности, что хорошо сделано, это рейтей, который вы получите, используя хайпер-элиптические кейфы. Так что я не хочу вырезать их. У них есть хайпер-элиптические кейфы, которые имеют более что-то подобное. Так что вы получите много балансов, и с хайпер-элиптическими кейфами, вы получите высокий рейтей. Но очень специальный. У них есть кейфы, у них есть плюс, минус, плюс, минус. Так что вы можете убить 3-3-4-3-4-3-4-3-4-4-4-4-4-4-4-4-4-4. Но у них будет только очень-очень специальный рейтей. Так что для потеки и лосистема нон-комьютатив, это называется чейн-система, когда очень-очень специальные рейтей. Есть много симметрии, а нон-зиру, это работает тоже. Но универсальная пикча начинается быть очень-очень специальным рейтей. Может быть, я перестану здесь, потому что это естественно. И в следующем лекции я буду старт регулировать ревеллобменты этого конкурса, и Introduce some other tools в стадии контроля медипров.


Thanks everybody for starting off CF Summit with us in the experiments and extensions track. I'm Angela. Yeah I'm Florian, we are really happy to have you all here. We had a lot of submissions so we had to unfortunately throw out a lot of talks that were suggested. Now we are down to I think 12 or 13 something like that. Yeah there's not really much to say, we will quickly go through the agenda for today and tomorrow and then we probably can already start with the first session. Okay that's today so we try to pick sessions from different areas. So we have some open service broker related things, we have Kubernetes stuff, we have Bosch things, we have UI things, we have K-native somewhere in there and today we are starting with service brokers. We have another session about Bosch deployments, then there will be a session about, I think it's about Irini and Cloud Foundry and Kubernetes and Diego and things like that. Another session about testing open service brokers which seems to be a pain point right now. Another session about upgrade of Cloud Foundry applications especially in context of database migrations and the last one today I'm working forward to is KALS engineering. We hope to learn something in this session and talk about tomorrow. Yeah and then so tomorrow we can see that it's a little bit more Kubernetes heavy. We start off with sort of an introduction and primer to K-native. We're going to look at sort of one marketplace spanning across like maybe Kubernetes and Cloud Foundry accessing Cloud Foundry marketplace. You can see it's a theme from your Kubernetes cluster and again in addition looking at managing your applications on both CF and Kubernetes so really looking at the two of them together and then we'll sort of shift gears towards the end of the day and we have an interesting talk on using Vault with Bosch and then finally customizing your Cloud Foundry UI. So we're really excited. Hopefully this sort of gives you an idea, helps you plan your schedule for the next couple of days and we'll see you back in this room and with that we really don't have much else to say other than we're really excited and we'll let Georgie give the first talk of the day from SAP on well we can look at the schedule here on the subtle art of keeping your broker multi-platform compatible which I think I'll start in five minutes. Yeah thanks everyone.


You being the type of guy you are and you and him being together, I can only imagine.  No, no, no, that's real crazy. Yeah, we on boss talk one-on-one, one-on-one. Yeah, we gonna talk.      I was talking crazy because I said, they say that they trickin' if you got it. And I said, it is trickin' if you got it. And I said, y'all got a number one song Pimpin' all over the world. Ludacris, you got Pimp Squad, click TI and you got a PIMP 50 cent. So I went off, which I was out of order. And I apologized to each and every one on many times. I said, I meant 50 cent actually called me, remember Pimp Curly? Yeah, I know. But that Pimp Curly, that was the result of that. That was the joke that me and 50 did to kinda clean it up, you know, that I went back and forth. What did TI, did you ever get to talk to him about? I never talked to TI, but I talked to his manager. I talked to his people.  Booney was like, I said, Booney, man, I was just trippin', man, you know what I'm sayin'? I was eatin' off the Pimpin', you know what I mean? Everybody was payin' me for intros and outro, so these niggas was talkin' about a trick or they ain't got it. And I was like, no, man, please don't do that. I didn't want them to do that, so instead of being a gentleman and comin' to them directly and breakin' it down to him, could nearly have Pimp Juice, you know, I was winnin'. Niggas givin' me $8,000, $9,000 just to talk on CDs. So you know what I'm sayin'? I was tryin' to really defend myself, but I didn't know I was bein' offensive. So along the short, you know what I'm sayin'?  It's crazy, man, because, you know, being with Pimp C and hangin' out with him, you know what I'm sayin', you bein' the type of guy you are and you and him bein' together, I can only imagine.  No, no, no, that's real crazy. I don't even, I don't even see the profile. You don't even put that kind of energy out there. That's what I was sayin', that's what was so crazy to me.  But I like you did anything to me. That's the way they are though. It's just, what you say.     I made a mistake, you know what I'm sayin'? Me, you know, they said they goons. I took the goon pistol. I hope they got a refund from that nigga. You know what I'm sayin'? And you know what I'm sayin'? I pistol whipped the nigga. You dig what I'm sayin'? I call him, I vent, and I left it at that. You know what I mean? And nigga's like, man, you better watch them niggas.  You know what I'm sayin'? I didn't see them niggas plenty of time. You know what I'm sayin'? I ain't scared of them. They ain't scared of me. You know what I'm sayin'? Ain't no hoe, they ain't no hoe. We understand that. But at the same time, you know what I'm sayin'?  That's why, that's the problem.  You know what I'm sayin'? Over some words, at the same time, there was a bunch of niggas said worse than me. Yeah, but then you... I'm sayin' but no, but I'm sayin' During that time, you got these cups, y'all running around here and y'all really, really controlling that. People don't talk about that era. But that was a time when that whole movement, the pimp, ology and all that stuff, before even, I think Pimp C did pimp ology. When y'all was running around, when you did the stuff with 50 and all that, that was a whole movement. Dumb one, I remember that man, but you know what though? Dumb niggas was doin' the same thing. They was all talkin' about each other and goin' at it. 50 and Ross was goin' at it at the time. Fat Joe and 50, you know what I'm sayin'? So I didn't do nothin' that nobody else did. Yeah, they out doin' it. You know what I'm sayin'?   So I said, yeah, that might've made a little sense.   You know what I'm sayin'? And like I said, I didn't have times to talk to the niggas, you know what I'm sayin'? They know who they is, we know who they is. They know what happened, we know what happened. I didn't talk to them, they know man, I ain't know nothin'. What about you?  Yeah.  Yeah, yeah.