Melinda hated driving at night. She did her best to avoid it. Short trips to the store if she just realized she ran out of tampons or had nothing for dinner after getting home, that sort of thing happened now and then. But she did her best not to go out after dark unless someone was coming to pick her up. So naturally, she found herself on the longest drive of her life tonight, with no moon, few stars, swirling clouds above her, and acres of forest on either side. As so many unpleasant things in her life, this was her father's fault.  No, that was wrong, it would be yesterday by this time. Out of the blue, her phone rang, and his voice was on the other end. I need you, Millie. Please come. No. He'd said just that, and then the line went dead.  It felt like she had been dreaming, waking up to hear his voice again after all these years. It sounded like he was crying. His voice sounded just the same as the last time she'd heard it. As though in a dream, she had risen, dressed, and gotten in the car. She was well out of town and halfway to the odd place before realizing that she had no way of knowing if he even still lived there. She received updates from her mother from time to time over the years about where he was. The last time she heard from her mother about him was seven years ago. Had he ever stayed in one place that long? Not to her recollection.  Prior to that, a move had come every few months. The house that they had been living in was their longest stay in one place, a full 16 months. It turned into two years after that, and then the next house had been the one she left when she moved out on her own. In all that time, she heard from him sporadically at best and had finally decided it was best to simply forget about him. Until tonight. She had found out after a two hour drive that she had been right to wonder if he was still in the same place. His last known address was a sketchy apartment in a low income area of the town she had grown up in. Had he been number 24 or number 42? Maybe he was 14. It definitely had a 4. It didn't matter. His name wasn't on any of the buzzers. Bastard. Her drunk of a father had called her at night, all but demanding she come to him for reasons he didn't even feel were important enough to tell her over the phone and then just expected that she would know where he lived now. In a flurry of rage, she turned and marched back to her car, slamming the door and starting off in the direction she came. She was so angry she didn't even look where she was going and missed her turn off. The next thing she knew, she was on this lonely stretch of road. Cars were sparse, but she took some comfort in the fact that she would pass one every half hour or so. Her dashboard clock now read 227 a.m. She had been driving for more than four hours since leaving her house at night. Every five minutes or so, she checked her cell phone. Ever since realizing she was lost, she had checked her phone and found no bars at all. She even stopped at a gas station, closed of course. Just sure there should be some service around here somewhere. But nothing.  You're over 30.   You haven't seen or spoken to your father in just under half your life. You have no time for your friends or relationship thanks to the aforementioned job you hate. And now here you are trapped on a road you've never been on before at night. And you can't even so much as call for help, let alone check Google Maps. Smart lady, you are. She briefly considered stopping and flagging down the next car that passed. She quickly realized the futility of that plan. Any car on this road would also have no service. So there was nothing for it. She'd have to drive until she saw a house. She'd feel bad for waking someone up, but there was no choice. She needed to find her way back to the main highway. But so far, all that she could see on either side was trees, mile after mile of trees, no lights shining through the boughs, no sign that anyone had ever been here before, except that there was a road and people were obviously still driving on it. There weren't even any road signs other than the mile markers. Had she really found the middle of nowhere? She was in the middle of this thought when her headlights illuminated something just up the road. A square wooden sign obviously made by someone other than the government. This wasn't a gas food lodging sign or a mile marker or a distance to sign. This looked like the kind of signs advertising a private business was nearby. She slowed down to read it. Granny Royce's Roadhouse. Come stay the night at Granny's. She'll take good care of you. Room. Board. Low prices. Next exit. Her heart sped up. She certainly wasn't interested in spending a night in Granny Royce's, but every business had a phone. At the very least, she didn't have a map or know the way back to the highway. She decided she would stop there. She almost missed the turn. Granny Royce's Roadhouse was buried at the back of a long dirt driveway secluded amid the trees. She was almost past the little dirt road that led to it before realizing it was there. She skidded to a stop and turned in. The little house lay ahead. It was two stories and looked to have about eight to ten rooms. Big for a home but small for anything announcing room and board. She got closer and looked for a vacancy sign. Nothing. It wasn't that the sign wasn't lit. There was no sign. The porch light was on and the front of the building was illuminated by that light and by her headlights. No signs of any kind. She almost wondered if she'd gotten the wrong place, but she was certain that she had seen no other exits between this house and the sign announcing it. She paused in the driveway and took out her cell again. Still no service. She did a quick search for any available wireless signals. To her complete lack of surprise, there were none. Not even any secured. There's no one here but me. She thought. At this point, she wouldn't be surprised to find the house empty as well. But the light was on and this was supposed to be a roadhouse. Someone would be manning the front desk. She got out of the car and headed for the front porch. As she turned around to make sure the lights flashed when she hit the lock button on her fob, she thought she could see a flash of movement in the trees. Something human shape. She stopped and looked again. Nothing. She decided she imagined it. At the front door, she hesitated. If it really was a roadhouse then she should be able to just go in. But what if she got the wrong house? If she tried the door and just walked in, she could find herself arrested out here, wherever she was. Cautiously, she tried the knob. It turned. She pressed gently on the door. It opened. Relief flooded through her when she saw that she was in a small, but tastefully decorated foyer that had obviously been repurposed as an admissions area. A quaint desk with an honest-to-god guestbook had been placed in the far right corner and some chairs had been set out, along with magazines on a table. She read the titles briefly. Mademoiselle, Blue Book, The New Country Life, Arts and Architecture, before turning her attention to the little desk. There wasn't a computer. That was a cute touch. It was like the house was from a past era. Perhaps old Granny Royce really didn't like modern technology. There was, however, a little bell, just like there would have been in 1929. It wasn't even the round silver kind you slapped to ring. It was a little porcelain handbell. This place was starting to out-cute her. Please let there have a phone and please let it use the number plan, not 50s exchanges. She picked up the phone and gave it a shake. For a while, nothing happened. Then she saw light come in on the back room and the shadow of an old woman sprang up on the wall. The shadow moved toward her and within a few seconds she saw its owner, Granny Royce, who perhaps looked like every grandmother in every storybook ever. Well, goodness me, she said. My lads, good morning, dearie. Pardon my tardiness, but it's been a while since we got guests at this hour. Can I take your name, honey? Granny Royce was smallish. Her gray hair tied in a neat bun behind her head, a dress that would have looked like it belonged to a senior citizen in the 20s, and a faded pink sweater. Melinda thought that she looked just like she would have wanted her own grandmother to look like, but her mother's mother had died when she was young and she'd never met her father's mother. It almost hurt to deny this sweet little woman her business, but nevertheless she had to get home. Actually, I'm sorry, she began, but the fact is I'm lost. I'm not even sure where I'm in the direction of. Oh, you poor thing, said Granny Royce.  You must be cold. Really, thank you, but I'm okay, Melinda said gently. I just need to use the phone, if I could, or if you've got a map, even that would be lovely. I really only live a couple of hours from here. She trailed off, not knowing if she was even right about that. She easily could have driven those five plus hours in the wrong direction entirely. Oh dear, said the little woman sadly. I'm sorry, honey, but the phone lines are down. As for a map, well, I used to have one. And if I look, I still might, but it's probably quite out of date by now. The highway moved since then. I know that much. Melinda's heart sank. How could her look get any worse? No phone, cell or landline, and no map. What could she do? She had to get back home. She was expected to work at 8am tomorrow, and why were the phone lines down? The weather was coldish, but clear. Were they fixing a line nearby? She told Granny Royce the name of her town, but Granny only said, Believe it or not, I've never heard of that town. What did you say the name was? She told her again. No, doesn't ring a bell. I'm sorry, but I could not say which direction it's in. Why don't you stay the night, sweetie? I'll give you a discount for your trouble. Thank you, that's very kind of you, but I have to work tomorrow and I need to get back home. I'm not even sure why I'm out tonight. The only reason I had doesn't seem to matter anymore. Honey, I wouldn't advise trying to drive back that far tonight, Granny Royce said. Why? It's almost three in the morning, and you've not had any sleep. Maybe the lines will be up in the morning, and you can call your work and let them know you'll be late. That won't work either, she replied. I'm the opener. No one will be there. No, no, I'm sorry. I've really got to leave. I'll head in the other direction until I find the road I was on. At that, Granny Royce's expression, already one of kind concern, seemed to shift somewhat, to one of fear. She paused, looking at Melinda as though she wanted to say something else to keep her inside. Finally, she said reluctantly. All right, honey, if you're sure, just you be careful now. Don't speak to nobody until you're back on the road. That last warning seemed a little silly. After all, what was Melinda, a little girl? She thanked Granny Royce for her kindness and headed back to the car. About halfway to the car, she remembered thinking she saw something moving in the trees. Her eyes scanned both sides of the secluded little cleared area she was in, looking for anything that appeared to be moving on its own, rather than being blown by the slight wind. She saw nothing. Satisfied, she headed for her car. All four tires were flat.  She leaned down and saw long slash marks on each tire. Someone in this little splice of green acres had slashed her tires in the time it took her to find out that she had no way of contacting anyone tonight. Kids from a local farmhouse, gotta be, she thought grimly. Nothing else to do, so you might as well go out at night and slash tires. She stopped and let the reality sink in. She wasn't going anywhere tonight. She had no choice now. She had to stay the night here until morning, when hopefully the phone lines would be up and she could call someone from work to ask them to go in for her, and then AMA to get her tires dealt with. She sighed and walked back in the house. She could hear Granny Royce as she was walking back to her room. She had already turned off the lights. Resigned to her fate, Melinda rang the little bell again. That you miss? She heard Granny Royce call. Yes, it's me. She answered. Sorry to be a bother. My name is Melinda Orton. Sorry I never mentioned it before. I guess I will take a room for the night, if the offer is still good. Oh, of course it is, Deary, said Granny Royce, re-entering the room and turning the lights back on. Melinda. Oh, that's such a pretty name, honey. Well, let's get you situated. You put your name and arrival time in the book there and I'll get you a key. All the boarding rooms are on the second floor, and there's only a couple left. There are others here? This was surprising. Not a single car had been in the front lawn when she pulled in. Oh, yes, Miss Melinda. Granny was puttering around in the adjacent room. Mr. Norris, young Calvin, there's a few of us here. She came back with a key in her hand. Just out of curiosity, what made you change your mind? She seemed to brighten as she asked the question, as though relieved that Melinda would stay after all. Oh, it's probably just local kids getting kicks, she said, but I found my tires slashed. Granny stopped suddenly. Her face twisted with concern and worry. Then she resumed, as though nothing was wrong. Nothing to be done for, I suppose, she said, with an air of sadness. Well, not until morning in any raid, said Melinda. Then hopefully the lines will be up. Oh, said Granny Royce, distractedly. Yes, hopefully. She led Melinda up the darkened staircase into an empty, quiet hall, or perhaps not so quiet. From one end of the hall came the muffled sound of someone crying. Whoever it was was crying softly, not with anger or petulance or fear, but with deep sadness. It sounded as if crying was something this person was used to, but they were still unable to stop. Who is that? She asked, pointing in the direction the crying was coming from. Oh, pay that no mind, honey, said Granny. That's just Mr. Norris. He's been like that a while.  Not all there? She tapped her temple. I understand. Melinda replied, but wondered privately how an old, out-of-touch man would wind up at a roadhouse. Has he been here long? A while, I'd say, answered Granny. Don't really recall how long, exactly. I guess he doesn't drive, she said to the old woman. Actually, it doesn't look like anyone else here has a car. Granny started at this, looking up with an almost guilty expression. Oh, well, that kind of thing is the business of a guest. I don't ask about such things. She turned the key in the lock of the room she had led Melinda to, and opened the door. Turning on the light, she showed Melinda the quaint little room. Melinda thought it looked like stepping into the past. She could swear this room would have looked modern in the early fifties, at the earliest. Come to think of it, so could the rest of this place, she thought. No wireless service, no computer, that old bell, and those magazines. They looked new, but that thought was cut off as Granny put the key on the nightstand and started in with instructions. Now, the bathroom is down the hallway there. You'll be sharing with the whole floor, so please bear that in mind if you have to go. There's a shower schedule on the door as well. First come, first serve. Just add your name to the first available line and that's the order the showers are in. I wouldn't worry about that if I were you, though. I'm sure you'll be first in line. I get up at 6am sharp every morning and start breakfast, but you come on down whenever you're ready and I'll whip something up for you. Oh, and one last thing, my dear. I would strongly advise you not to leave the house until sun up. You just never know what could happen out there in the dark. Of course, she replied, I'd never go out there in the dark even if I didn't have to. She stopped that train of thought right out of the gate. After a few moments, she was alone. Alone, without anything to wear to bed and nothing to shower, brush her teeth or hair with in the morning, she sat on the bed and looked out the window, which faced front. Her car still sat where she had left it, the only thing for miles that seemed like part of her world and an expensive over large paperweight until I can get ahold of someone, she thought bitterly. Despite the hominess of the room, she felt an unwillingness to rise and shut off the light. Somehow the thought of going to sleep in this backward little room seemed unthinkable. So instead, she continued to sit and stare out the window. A figure in black detached itself from the shadows of the trees and made its way to her car.  She jumped and ran at the window. The figure was tall and seemed to be wearing a cloak made of night. She saw as its arm extended. In its hand was a long, jagged dagger. It dragged the dagger across the side of her car, leaving a long gash mark in the paint and metal. Hey! She shouted. The figure kept dragging the dagger. She reached for the window to open it. It wouldn't budge. She looked for a lock, but couldn't see one. Hey! She yelled again. This time, the figure raised its head. She could see the glint of two eyes under the hood. The figure raised the dagger slowly, determinately. It pointed it straight at her face. She leapt away from the window and ran for the door. A noise on the other side stopped her. Footsteps dragging, shambling footsteps and crying. The sound of a person for whom deep longing sadness is a way of life. Mr. Norris. She waited. Somehow she just felt that she should let the old man pass before she opened the door. Before he got very far, however, she heard other footsteps. These much quicker and lighter run up the stairs and stop near the door of her room. Stop it! hissed Granny Royce. Go back in your room right now. You know better. She can't see you yet. Hopefully she won't have to at all. Now you go back in there. You've got no business being out here at this hour anyway. What on earth? How could that sweet old woman talk to another human that way, let alone an old man with a foggy mind? She almost opened the door right then, but somehow her hand stopped and waited until the shuffling, crying man had made his way back down the hallway. She heard the door open. She opened her own door just in time to see his foot, shod in a well worn house shoe, slide into his room. The door closed softly after him. That poor man, she thought. But now she was determined to find out what was going on. The punk outside in the Halloween costume slashing up her car, followed by Granny yelling in an old man made her begin to understand that not all was well here. She went back down to the front desk area, which was completely unlit except for the moonlight and porch light coming through the window. There was, however, a light on near the back room that Granny Royce had emerged from before. Melinda paused to take a look outside the front window. The maniac with the dagger was nowhere to be seen for the moment. But she was now determined that it was he that she had seen moving through the trees. He could have killed me. She strode in the direction of the light, seeing that it was the light to the kitchen. She kept going, expecting to find Granny Royce still puttering about with whatever an old innkeeper did with herself during the early hours of the morning. Instead, she found Granny sitting with a young man of about 20. He had dark hair and a scruff of stubble and was wearing a dark brown quarter eye shirt and khakis, along with a pork pie hat. He looked like he was ready to go sell newspapers on a street corner in the thirties. He was quietly sipping tea while Granny was admonishing him from the other end of the table. Now that was a horrible thing to say. She said, When I was your age, young men minded their manners. That's a laugh. Talking about my age, muttered the young man with a sneer. And just how old are you? Do you even remember? Calvin Davidson, you are trouble, young man. She hissed back. Neither had noticed Melinda yet. One of these days, you're going to say something you'll regret. Oh, come on, Granny, what could I possibly say that will make things worse than they already are? Demanded Calvin. I mean, look at old Mr. Norris up there. Both of us are... Oh, uh, hello, Miss. I didn't know we had anyone else here. He had just seen Melinda. Uh, hi, she said. She had the feeling she'd walked in on an old argument the two of them had had many times and that did not concern her. Her fear and anger were forgotten for the moment. Calvin had been talking to Granny like a sullen kid, but something about what they were saying seemed wrong. Can I help you, Melinda? asked Granny Royce. Is there something wrong with your room? That brought her back. No, she said. The room is fine, but nothing else is.  Why are most of the rooms full, even though mine is the only car out there? Why did I hear you talking to Mr. Norris like he was a dog? And why would you want to make sure I didn't see him?  Could, Lord, she's not even been here at night and she can see it. Why did you even let her in, Granny? Why don't you just bolt the door? Hell, if I could go take down that sign, don't you think I would have? By now. Lord, love, and duck. There's something you don't hear many young men say, thought Melinda. She decided to ignore Calvin for the moment, otherwise. And besides that, there's someone out there.  And you can't even call the police.  There was a long pause in the room. Neither Granny nor Calvin seemed willing to break it. Calvin scratched at his neck. For the first time, Melinda noticed a red slash at his throat, half hidden by his collar. It looked like either a very fresh scar or a slightly healed wound. Listen, Miss. I don't know your name. He finally said. Melinda, she told him. Melinda, you repeat it. Melinda, I think you should sit down. I have to tell you something that you may find troubling. Melinda did not like how he said that. She also didn't like the way his tone had switched from solemn child to serious adult. He looked several years her junior, but he was talking to her like he was her uncle or her boss. He swallowed a sip of tea and sighed. Then he looked her straight in the face and said, the reason I don't have a car out there is that when I got here, no one my age, no one in my line of work would have owned a car. It would have seemed like an impossible dream. What are you talking about? She asked hesitantly. I worked in a textile mill. He said the mill was shut down by the time I got here. Most businesses were. So I struck out on my own, a drifter looking for what work I could find. And I stopped here. Forever. Businesses were shut down. I don't understand, said Melinda. We're having a rough time of it now, but businesses are mostly staying open. Not then they weren't, said Calvin. Sadly, I arrived here in 1929. Melinda blinked, something had exploded behind her eyes. This place was new then, said Granny. My man and I had just opened it, and young Mr. Calvin was a sweet young lad of 16. I offered to take him on as a hired help over my husband's objections. Well, my husband was a well-meaning man, but he knew how to pinch a penny. It was a year after I took Calvin on that Mr. Royce died. Calvin and I have been here ever since. And every few years or so, someone joins us. Yep. Calvin broke in. Miss Tilly was first. She was a woman of ill repute who ran here, pregnant and scared that the man who'd run her trade up in New York was going to find her, kill her. She and that baby. He broke off, now seeming on the point of tears. And then, said Granny, there was Mr. Standish. He was a traveling minister. He doesn't travel anymore. Mr. Norris got here in 69, said Calvin. His story is probably the worst. He was a, well, he was a bank robber, you see, carried a pistol. And he didn't like learning how long we'd all been here. He paused, stood and walked to the kitchen window. He tried to leave on his own, you see. He ain't the first to try it. That was me, actually. I warned him not to try, but he wouldn't listen. But when he got outside, and he met him, Calvin, hissed Granny. We don't talk about this. She's got to know, said Calvin. There's no point in her finding out slowly. There's still a chance for her, said Granny, in a stage whisper. All she has to do is wait until morning. She's not going to wait until morning. No one ever waits until morning. The fact that she came down here is proof enough of that. Besides, what good would that have really done her? Her car is useless. We have no phones here. There was no phone when this place went up, and there won't never be a phone here. You know that. Okay, everyone, stop, shouted Melinda. That's enough. Now you can't keep me prisoner here, and I have no intention of staying any longer. Only that knife-wielding maniac out there is keeping me from running up the road this minute. Now, I need to know what's really going on here, and I need to know it now. We've been telling you, Calvin said. Granny may not want you to know everything, but you need to, because you won't be leaving. Oh, we're not going to try to keep you prisoner.   Listen, child, said Granny, rising from her spot at the table. Listen, please. None of us mean you harm, my dear, not even Mr. Norris. There's scant he can do anymore, and he knows it. That's why he's up there crying all the time. But we're stuck here, all of us. I hope there was a chance for you to run for it in the morning. But Calvin's right. There's no guarantee you'd be safe in the morning anyhow.  Choked out Melinda. She was beginning to break down. She could feel the tears willing in her eyes. It was about a month after Mr. Royce died, said Calvin. When he came, he was wearing that long black robe carrying that ridiculous dagger. I saw him when I was trimming the hedges in the back. I told him he needed to get out of here, because I didn't like his look. He moved so fast I never saw it coming. And he got me. From here, Calvin touched his neck. To here, he touched his lower abdomen on the opposite side from the neck slash. He began to undo his shirt. Melinda almost vomited.  She could see bone, muscle, and intestines wriggling within that mangled rune. I died that night, said Calvin. But then, I didn't. The next thing I knew, I was being dragged into the house by Granny. And when I woke up, I nearly scared her to death. She was sure that I was gone. The thing is, I was. But I was awake. I could talk, walk, do anything I could while alive. Well, except take any enjoyment or nourishment from food or drink again. I still drink that tea because it keeps my skin from turning ash gray. I learned that about 50 years ago. He didn't go away, though. Granny broke in. I went out to deal with him, carry in my axe. He took my axe and buried it in my back. I won't show you the wound, honey. Calvin shouldn't have shown you his either. No one should have to see it. But that's how he works, Melinda, continued Calvin. He's got that knife. But if you try to use a weapon on him, he just moves like he does and takes it from you. You never stand a chance. He'll use whatever weapon you try to take him down with to end you. Mr. Norris learned that the hard way. This, this is not happening. Melinda was ready to break down. She had to hold it together. She had to get out of here somehow. Nothing about this was right. Nothing about it could be real. It was all a dream. Too much didn't make sense. Her father calling her out of the blue, her leaving to go to him without a second thought, getting lost so quickly and so irreversibly. No cell phone service anywhere on the road. This place, everything about it. She was dreaming. That had to be it. But if so, she was going to survive this dream. She turned and ran for the stairs. Her purse was still in her room, but she was going to grab it and go. She'd had enough. Protesting voices began babbling behind her, and she didn't care when she saw Mr. Norris waiting at the top of the stairs. Contrary to Granny Royce's description of him, he wasn't old at all. No more than about 40. But she saw instantly what she meant by not all there. The top half of Mr. Norris' head looked normal, like a reasonably attractive man with dark hair peppered with gray here and there. His eyes, a clear green, were moist with fresh tears. The lower half of his face was a ruin of bone fragments, shredded muscle, and blood. So much blood. His arm hung on a few hanging strings of muscle. His hip was just as much a mess of bone and blood as his face was. He kept his one good hand on the banister as he shuffled toward her. Behind him stood a young woman in a bra and a pair of panties. Her stomach was cut open, and looking out of the wound with bright intelligent eyes was the mangled remains of a baby. Melinda turned and bolted for the front door. Her hand had just closed around the knob when Calvin rushed up to her, placing his freezing cold hand over hers.   After a while, you learn to function with the pain, but it never goes away. Sobbing, she asked the question she'd been afraid to since coming here. Who is he? We don't know, said Granny, from behind Calvin. He just came here, and he won't go away. He likes to watch us and do things to incite us to come out again. As soon as someone does, he hurts them more, but no matter how many times he kills us, we don't die. Believe me when I say, we all wish we could. Melinda had had enough of this. She pushed Calvin away and threw open the door. He was standing on the porch.  Melinda ran into him at a rush, the knife puncturing her right eye and its tip sliding on through out the other side.  A few hours later, the house erupted with screams from upstairs, as Melinda awoke to a world of pain, the like of which she'd never known.


Welcome back to this NPTEL course on game theory. In the previous session we introduced the core and discussed some examples. So now we continue the study of this core. The most important thing we would like to say that the core if the allocation is not in core that means there is some correlation which can be improved. So this is a very important fact and if an allocation belongs to the core that means for each player unilateral deviation will not make player strictly better off. If once something is in core no player would unilaterally deviate because he cannot change it without decreasing someone else's payoff. So thus the core is a very interesting concept. Now we would like to say when the core is non-empty. So core need not be non-empty all the time. So there is some characterization of the core non-empty. So let us we will start describing this characterization of games with non-empty core. So this basically it is due to Shapley and Bondareva independently. So we consider the following linear programming. So let us say we are given this transferable utility game nv and look at this min x1 plus x2 plus so on so xn subject to summation xi inc this is bigger than or equals to vc this is true for every subset c in n and then of course x1, x2, xn is in rn. So basically we are trying to minimize x1 plus x2 plus xn such that summation xi is bigger than vc where the summation is taken over all inc and c is a subset of n. So now this is basically set of linear inequalities and then you are minimizing a linear function. This is a linear. Once you take this thing this is basically a kind of an allocation once you take this one. So what is really happening is that which is the this LP determines the minimum amount of transferable utility which is necessary for an allocation so that no correlation can improve upon. So this LP definitely has a solution if it is feasible if this linear program is feasible then there will be a solution and this is because all the inequalities are greater than type and also there is a structure which makes it feasible. For example if you take this one summation xi has to be vc all of them are this thing and you are minimizing it in fact you can say that this is a x1 plus x2 plus xn each x1 is bigger than or equals to this thing. So therefore you can easily say that there is a lower bound certainly and then even mathematically one can see that there is a solution to this problem. So in fact one can verify that this is feasible also from the linear programming argument. So let us take let x1 star x2 star xn star let us say this is optimal solution of let me call this as LP here this is the linear program of this so what would like to say is that x1 star plus x2 star plus xn star this is certainly bigger than or equals to vn. So this is the main thing that is why the difference is what you can change. Now there are two possibilities one is this x1 star plus x2 star plus xn star is strictly greater than vn and in this case the core is empty.  So in fact as I said let us go back to this one why does this linear program have a solution. So even if we simply look at it you are looking at the linear equations which are above something and then you are looking at the sum of entire thing to be minimum. So all of them for example v1 plus v2 plus vn is a lower bound to that one and then you are looking at infimum among them so they are certainly lower there is a lower bound for that and then you are looking at the infimum so this x1 plus x2 plus xn having that one. So therefore one can easily see that this program even just purely looking at from an optimization point of view you can say that there is a solution.  Now if there is some solution where this x1 star plus x2 star plus xn star is equals to vn and satisfying this then that should be the solution because you are looking at the minimum. If every solution of this one if the sum is bigger than vn that means the core has to be empty so that is basically the what these two points are saying. So if x1 star plus x2 star plus xn star is strictly bigger than vn the core is going to be empty if that is equals to vn then core will be missing and in fact not that this can never be less than vn because by the very definition of the linear program this has to be greater than equals to vn. Now in fact in the previous examples whatever we have discussed we can actually try to write down the linear program and see what is really happening so I will not go into those details. Now we would like to ask when the core is non-empty. So let us look at the linear program so our linear program the primal problem let me write it is minimum summation xi i in n subject to summation xi i in c is greater than equals to v of c, c is contained in n and then x is in of course Rn. Now if we write down the dual of this problem it actually becomes the maximum of for each coalescence c we have a number alpha c vc and then this summation is over n for each of this inequality you have a number and then you write down that and then this is subject to summation alpha c is equals to 1 of course c is c contains i and this should be true for every i in n and alpha c greater than or equals to 0 for all c. So here I am using the LP duality results so if you write down the dual for this problem so this for each inequality you have a number alpha c so that is what I am saying here alpha c for each c each inequality that is indexed by c alpha c into vc is basically the total worth vc and n into the summation of alpha c for each i all those c contained in i that should be 1 and alpha c I will not go into this LP results but let us look at this. So now we have this strong duality theory the linear programming we have a strong duality theorem so if primal has an optimal solution then the dual has an optimal solution and the optimal values are same of course I am not going to give the details of this duality theorem so if we apply the duality theorem the primal has a solution then the dual has a solution in fact you can also say that if the dual has a solution then primal also has a solution and in such a case the optimal values are going to be same. So now in this present case we know that the primal problem has a solution so therefore the dual problem will also have a solution and then the two values are going to be equal. So we apply this strong duality theorem that means there exists an x star in Rn and alpha star c for each subset c in n so that we have the following thing let me write down summation xi star i in c is greater than equals to v of c this is there and alpha star c is greater than equals to 0 this is again true for every c contained in n and not only that alpha star c summation of alpha star c is 1 for all c containing i this is true for every i in n so this is going to happen so we are basically writing then these conditions if we write down those conditions these are the things the solutions x star and alpha star they should satisfy this one. Now let us now look at the following thing so summation alpha c is equals to 1 with c contains i for every i contained in n this is the condition that we have this implies c c contains i alpha c vc is less than equals to vn. So this is what we are saying this is the feasibility of the dual problem the feasibility of the dual implies the objective function of the dual is less than equals to vn. So this is exactly the what we are looking at it this particular thing so the this alpha c vc is less than equals to vn. So now of course sorry I think there is a small error here this is see this is subset of n so if this feasibility implies this if I take this as a condition then what we can easily say here now is that the optimal value is going to be vn because we know that the optimal value has to be bigger than or equals to vn and here we are saying this is less than equals to vn therefore both should be same vn is there so under this condition this automatically implies in fact this is going to be a necessary and sufficient condition so whatever this condition is basically characterizes just the non-emptiness of the core. So this is basically known as a necessary and sufficient this is known as a balanced this condition is known as a balanced condition. So let us now define the games so a tu game nv is called balance if and only if c contains i alpha ci is equals to 1 implies summation c contained in n alpha c vc is less than or equals to vn this condition is balanced condition that we introduced if a game satisfies this condition then you call that as a balanced game. So what we have proved is that every balanced game has a non-empty core. So when this condition is satisfied we call this game as a balanced game and what we have proved says that a balanced game has non-empty core. So now we switch to another important solution concept for cooperative games which is called Shapley value so now we will switch our attention to Shapley's. So now let us get we are interested in now Shapley value. So before I start about this Shapley value let me just recall that in this cooperative games the core can be empty or non-empty even if it is non-empty the core can be infinite set. So therefore exactly choosing a correct solution is a non-trivial fact. So the Shapley value is another solution concept which is we can define irrespective of what kind of cooperative whether the game is balanced or not so it always defines a unique value. So we will now spend time on discussing this Shapley value. So let us look at it. So let us start with the cooperative game and let us take we are interested in developing a solution concept PV which is basically the allocation for each player the Shapley develops a solution concept which basically satisfies certain axioms. The whole idea here is that these the solution concept satisfying these axioms is uniquely given by the Shapley's value. So we will now discuss these axioms. So Shapley's axioms we will start discussing. Let us take a permutation we start with the game NY let us say pi is a permutation on N then consider N pi V is a game such that the following thing pi V of pi i i in C is nothing but VC. Basically what we are doing is that we are permutating the permuting the players instead of giving 1 to N let us say we give them index pi i pi 2 pi N then their worth of that correlation is basically given by the original ranking C. So pi i i belongs to C is the let us say permuted names of those players then the original names is given by C itself therefore the for them the worth of this particular permuted correlation is exactly VC. So now this is so that means the role of the player i is essentially same as the role of the player pi i. So this is a new game so what Shapley before I go further let us introduce a simple example so that this concept will be illustrated better let us take N is equals to 1 2 3 3 player game and then let us define pi 1 to be 3 pi 2 to be let us say 1 pi 3 to be 2 now N pi V is going to be the following thing pi V of 1 is nothing but 1 is a new index for the original player 2 so therefore pi V 1 is simply V 2. Similarly pi V 2 the 2 is the new index so that is given to the original player 3 so therefore this is going to be V 3 and then similarly pi V 3 the 3 is the new index that is given to the player 1 so therefore this is V 1 so like that we can look at the other situations for example pi V of 1 2 so 1 is the index of the player 2 2 is the index of player 2 3 therefore this is nothing but V 2 3 so like that we can do this is basically the idea of this this thing so the axioms are basically the following thing symmetry linearity then carrier so these are the axiom let us start explaining these axioms symmetry for any V in R 2 power N minus 1 so take any characteristic form V then any permutation pi on N and any player i in N so what I am saying the pi i of pi V is same as phi i V so what it says is that it does not matter the player what name you are giving it is whatever he gets he will get he will get the same thing in any permutated situation whatever name you give it to him he will always get the same thing this is the symmetry assumption so the second assumption second axiom is linearity so let us consider two games N V and N W and define P let us say P is a number between 0 and 1 now consider N P V plus 1 minus P W new game where P V plus 1 minus P W of C is nothing but P V C plus 1 minus P W C let us say this is defined for every C in N so we are if we are adding two games and the worth is just some of the individual word so what the linearity says is that if a player i in this sum of these two games P V plus 1 minus P W whatever he gets is nothing but the sum of what he gets individually that is P phi i V plus 1 minus P phi i W so note that once again here like in Nash bargaining thing we are defining the solution concepts through certain axioms so we are defining this solution procedure for all classes of games for any game you take it and what then you assign some value and that should satisfy certain axioms so that solution rule should be linear here so this is the of course here we are only taking the convex combinations but we can always look at directly also without convex combination here so let us look at the other assumption the carrier so a correlation D is said to be carrier of this correlation game and V if V C intersection D is same as V C for all C intended N okay so what it is saying is that if V of C intersection D D is a correlation which we want to call it as a carrier if then V of C is same as V of C intersection D so whenever D you intersect with D the worth of that is not going to change V of C intersection D is same as V of C this is true for every C okay so now let us look at it look at the following thing what exactly does it say let us say D is a carrier let us take I not in D then what is V I V I is nothing but V I intersection D because D is carrier and I D is not in I therefore the intersection I is empty so this is nothing but V of empty that means this is 0 that means if a player is not there in this carrier that means he is going to get a 0 value okay his worth is 0 therefore so if D is a carrier all players J in outside D are dummy players okay because their entry into the correlation does not add anything when they join any correlation they are not improving the worth of the correlation so in fact you can say that V of C union I is same as V of C for all I not in D this again follows from the same this thing so we if I is not in D then by adding I to a correlation C then you are not improving the worth of it okay D is the basically the only players who can influence some worth so that is less thing so the carrier axiom is the following thing okay V I V is 0 value for all I not in D if a player is dummy then he should get 0 value so this these are the axioms that sharply introduced then using these axioms he characterizes that his value sharply value as a unique solution concept satisfying all these three axioms will continue the proof of this shapely result in the next lecture and today we will stop with this thank you


you take a look at some of the top free agents Charlie Morton will be one great season with the Astros this year Patrick Corman with the Diamondbacks and the Machado and Harper and they're always connected with the Yankees and I just think and you mentioned and do hard he's close he needs work on his defense are you willing to trade off 30 million dollars a year or more for Machado for what you're gonna pay and do hard the production you got in his rookie year I'm not ready you know this guy offensively is a machine he had more home runs than I thought he would and somebody's got to take him this offseason give him some time away rest regroup a little bit get a little bit stronger get in the weight room and then get down to Tampa Florida and work on your defensive game and I think more of the throwing it right the throwing got to be a little bit more consistent Fran do hard but he did so much this year and was such a pleasant surprise in the running for the rookie of the year but there's room for improvement I think he will I'm in agreement with you and although I know the Yankees will be attached to a lot of these big-name free agents I look at Manny Machado and the potential for a 35 million dollar a year payday and then you look at and do hard will make less than a million next year and it's incumbent upon the Yankees to help make him a better defensive player the defensive run save statistic worked against him this year he was a below average third baseman we saw what happened tonight he did not play principally because of his defense they thought CC base hip shot ground balls be headed towards the left side but I still think that he's their future third baseman and as far as Harper goes another very sexy name you go back to last year Stanton kind of cancels out Harper they've got Hicks they've got judge they've got Stan we don't know the future of Gardner and McCutcheon it'd be hard to squeeze Harper in there unless you're making Stanton a full-time DH and even though they got under the luxury tax I'm not sure that means that they want to surge over the luxury tax by X amount of million again we'll see how the offseason unfolds we know the Yankees will be attached to some of those players yeah it's almost a conversation with Harper and he's a great player there's no doubt about it but at that price tag 35 million a year let's say does he make you that much better than what you already have because you also by the way if he's healthy you have Clint Frazier in the minor leagues as well Clint Frazier at a tough year with the concussions there were so many opportunities that he missed he's still somebody that they're very high on in the organization and I'm with Jack I just don't think the Yankees are ready just to say we're gonna open up the vault and hand all this money out and that's gonna get us over the hump there's such a good nucleus of young players right here they they're ready to kind of take that next step I don't know if Harper and Machado fit in from a makeup of this club standpoint and Brian Cashman and the members of this front office are so proud of the young players who have come up and as I said there are more of those players that are coming how Steinbrenner is on the record is saying multiple times that he doesn't think that a team has to have a 200 million dollar payroll to win a championship and less he suddenly changes his tune on that that's why I think the Yankees are going to continue to be smart and continue to say as we're saying right here do you want to end do hard for less than a million or you want manning Machado for 35 manning Machado is a wonderful player he is a marquee franchise type player but and do our showed you this year what type of player he could be and I'm glad you referenced the injuries because Yankees won 100 games this year I wrote down some of the guys who have judged Sanchez Gregorias Hicks Glaber Tadaka Sisi they weathered a lot of injuries still 100 games still won the wild card game and still gave the Red Sox a 108 win team a tough series the Red Sox proved to be the better team I think Brian Cashman Aaron Boone would say the same thing


Ni mefuga mi fereji, hanku na kukota kwa sofa aminu na handa. Nwuhu Actionasha maiaunufu na handa, nulawu kwa na kwa vanu nCova. Ni mefuga mi, nwo hiwa na handa. Ni mefuga mi, nulawu kwa samipu... ...a lafututa en deleku tokk��po. Nwa mi ma kofyo agon kuwenia kwa kusaba abu. ...pigei na ma kofi bha na. any time mukiskiya sofaya ko in town afadali muvunji ke mugu mukimbiya ya potu juzi mejiya hea potu kibao kumbe sofaya wa tuna kupenda awa diwa na kulana ugali awa si kwao kwanzo weo beni ui ui atueni kwa sofaya atueni kwa sofaya kwa na subui wa kona wei ui kwa so ni muwaju wei nini muna penda sofaya mintakum choy wa radi kwa sababu tukona wa tu ambaoni kiki kundikubo sana na onaduwa of course sofaya ki tembe na tembe yangana jeshi ya mi watu miya si yule wa kwa api 100 people but tukona brand tofoti tofoti apa wanyu amekuja na lazima tuwape na pizzi wazime yambo senamla evyo kwanza ni ni wutem na yua mi na gombe ya kitichi wu gavana na irobi 20 27 na niko na deputy governor officially running me to a couple neyema sheikh akuja seime kitu alaf 20 le karibusa na neyema ladies and gentlemen members of the 4th estate as our brothers have said that you play a very vital role in peace making in this country and to today or precisely let's say this month is a month of International Women's Day and as a lady as a female running mate of Kasipul and then coming deputy governor it would not have been right for me to sit down and see my sister here and my governor you know doing the pull and push thing online and the blogs and all you know wana jo kucho chosana blogs are very important lakini sometimes they play fitina kido ga apa na pali so we want to say that these are very peaceful people and today as you have seen we are all in one in one kikundi and in the coming few days you will see so much happening and I just want to say that let us preach peace as you write those blogs to anzeku letawatu pamoja amana muna gani asante ni sana na mubarikiwe maisha tamta uskadi deputy governor nga kikera zokusinda governor uskwongo na niosha kuhizi panema ngependa sana pia kukaribisha dadeitu waridi waridi ni mwaja wawatu amatume kwa tukifanya naema endorsement kibao juzi mmeneona mombasa tukifanya kampuniya logistika endorsement we work together with waridi and is also part and parcel of team yakasipul ngependa kujaseme kitu alafupi ono jo mimi tulao for the first time na sofa mi mi marafikizanga ono wanga marafikiza sofa na lazima ni kikuwa pahalipenye niko lazima ni kujena kwa sababu awesi kukuwa tukwamba sofa yakotawu na mimi msi kunae so lazima ni mwau introduce mpema doki kujapia mwau kotoa na kotoa na mi karibu sana waridi asante sana kwa na kaspul the incoming governor Shukurin sana di upomani na naitwa waridi na i'm so glad that today it's a special day where we are we're here to make sure that peace it's fair between those people who are friends once and when you are friends you become friends again so we're so happy I'm here to celebrate sofa leo na hi mwezi ni mwezi wa wanawa ke duniani na ikiwa ni sikuwa wanawa ke wikiwa wanawa ke duniani it means that women, you know the future is female so I celebrate this sofa and I'm so happy you are in the industry with the bank and definitely with Kaspul here when we come as a team na juwa ita kuwa warazairi kama katikuna peace ni warazairi na kia ni kukarimise in the green period movement nini atunafanya because we are trying to promote the green period the reusable sanitary tower which is a program that I've been working on in Tanzania I just came yesterday in Pemba, Zanzibang and Darisa Lab so Pia, the fourth state you guys are my fellows and I know to tazidiku angaliyama zengirayetu visuri as you are greening the country and we are making the music and the ad are bigger thank you makofiyake jameine onajiwa sofa atikuwa mombasa kuwa the Lecran Role Festival kuna kijano limwana meva blue kukamtewa kakua naibu wa chawa anamdo muskwizum kato ametambasa na Tanzania na onajiwa ni productiako when do limwana e kudya onajiwa karibishu for the first time wangembela sofa na takana ni yensi siku ni onapata mshara kwanzuna mele teya lasu e ibu tunakfungiha tunakfungiha medium wanangu ongiha apakiru weni na maokot miyambu za mi na shikuru sana ka ku miyambu metokeya alafu leo mimi kwa ni skiafra kama bini debi tia lika chinia kasema inakua jeskiawa na ongiha alafu gawa naivi naivi alafu madamsofa yamonye wa apam kubwa to kasema iki tulazima tuki malizendu guzang so mi mi mi fraikiya sana na onga madamsofa yu kuapa ni na fraikiya londa okotapa alakubia ni nain international artist na mwaan alafigia bongo na mwaan umtusu na mwaan ni wana kumia na kumia ususundia na shinda bongo zuchiwa mwoni oyu kasumbua zuchiwa na mwaan wana kwen tukwa na msania pa international felana ampige ni mbukali sana na kalgra na inazidi kwenda so mi na fraikiya sana na leo apa leo na tokaba na mihambili sheikh mihambili kwa zopa na okotapa kumbawu tokaba asanda sana mashpuli ningependa tu kutambu webo ya balo actor asante balo kwa kukudya alafu kuna kenong kenong ukiwa na sofanya usipwana kenong onini mwo ujuhe nimugonjuwa Koseb Tali ano e kewa e ano e kewa king ano e kewa magic Koseb Tali kumwana sofa e ayu kumwana muntopta kenya atakaribu asan tisana alo guys ah thank you so much for coming sinamengili au yaksema lakin ni mefraikiya sana to see my brother Kasipul na mbependa sana sheikh ha ha ha ha na boss uni boss wanguyu sofa e ya ni mi nambependa sofa e manaki Sofaya kuna rosafisa na Sofaya is always ready to support Upcoming, talent is inyawatu wa fikrii wan eza supporti wa Sofaya is always ready to support talent And that's a very beautiful thing me as the artist manager na Friya Gasana Nikiwa na iyo raw My God bless you so much And then not forgetting international superstar Felana Uyuwa pa Ya Ha, wana ni kumusiwa wana Ha, ru diwa Long boy, long boy, long boy Kuna kijana mrefumu niyebalancing niye na Mshindanga Sana Super Stambo Sana Ama piyano, tundu, tundu Ama piyano kengu ama piyano apa Nemi wana juzina Tajiriya, wana wana muna kuna na Sofaya Wana wana muna kuna wana muna kuna, wan tu tumba Wana kumbiwe ni fungiya pa Wana wana njo, karibukat Wana jami miya tajiri Hausio Eje miy sa kwa kaspulu kupua Hao niya jemi gofiri Muliniona hile sikul kwa miye pandeza Anasuki anasuki owevo Anasuki owevinabado Nisha rogwa? Nisha rogwa, lakini nisha rogeka kitamwa. Sema baraka nyingi. Anam kubali sana kaspun. Ame kwa mchuwa kwa na kuni support pia, nikiwa meru muliona. Sinlifuni kwa sana yuwa kweni. Nikiwa kweni. Nikiwa nisha umbewa mahaji. Nisha umbewa. Seza kwa na ni yonge, weyendelea kwanza ni kuskize. Ah, karibu sana. Karibu sana katunu. Weyendelea kwanza ni kuskize. Nikiwa naka kweni. Nikiwa naka kwanza ni kuskize. Naka kweni kwa sana yonge. Naka kwanza ni kuskize. Naka kwanza ni kuskize. Naka kwanza ni kuskize. Naka kwanza ni kuskize. Karibu sana. Karibu sana kwa sana. Naka kwanza ni kuskize. Good evening. First of all, I'd like to thank God Lord Almighty for giving us the chance. And I'm so far very grateful to meet you today. Belan. I'm so happy. Governor. Yes, thank you very much. With the debit. I'm so happy guys. So let me just go straight. This is one of the most mature friendships I have seen. Regardless of what transpires we are human beings but today what is happening today I'm so happy because it shows the level of maturity, the level of brotherhood, sisterhood, family. Na jua kuna watuengi walikua nantaka kukuliia hii. Lakidi mungu wa mengiliya kachikati. So us as Lua Royalty we are very happy. Na na jua, Kasipul. Mambo ine na na jua. So thank you so much guys. Thank you so much. Asante sana. Una jua kuna watu to sofa yali adapt. Una natu to sofa na kwa mbi Niki ni sofa yali uta iwanisha na ita ni uta uta iwanisha Mani niki ita una dada. Demurifes. Demurifes wa kujia pata, awana una natu. Ka bisa. Ongi mani nomawidi matisa pumuasuki. Yes, sina kwa jih? Governor. Nikua pa na Soango, Wadamsu Fire, thank you so much. Thank you, Farana. Farana, thank you. Me, I'm very happy. By the way, mimi mizoya kameramodya. Namikwajatu kameramodya, nisimem bili tansumis kia. Mamu inaisha hapa. Laki ni sasa hapa na shubu ani adresu kia. Ni anzi hapa ni malizia wukulekin ni I'm very happy. By the way, nashkuru sana. Niki wakwae grup manzimi niko save. Thank you very much. Mi uto murife. Soango, thank you. Mungu wa bariki. Hamu jambo ni njotu. Komajina ni kalcha. Mindi wa last pono wa sofae. Mindi wa kadogo. De mushtu kwa man. Yes, Komajina ni kalcha. I want to give thanks to sofae. Erlana. Depit. Depit. And Mr. Gavan. And Wazi. That's great. Chunu wa pelfu shitu komoje. Haa haa haa! Thank you very much. Thank you very much. Nta komchua aradi kamani mwachum ti uta eji onge. Roi, of course, roi na na fungatia. Durabadao na pudya. Ni kama kulizapadu ni katolek. Haa. Karanja mi dibidia bagamu tutumoli. Haa, karanja. Bigap Karanja, bigap Karanja na naku Shambu asana wepohako.  Sasa ni wakati na takani karebishi felana aseme jambo, wasabopu felana siwa wakuongia, kusili na fosingi kwaongia kwa media, we always push her to talk. Ia na sema nga na tzima ya kwaongia, ia na tzima ya kwaimba, ana tzima ya kufanya ni, ya kwaongia. Ah, adjusa 001, chinia ya, aba nabu oi monewe, maa maa maa. Ah, ya, sana. Kabula jambuneta felanda. Ia jwa mili na taza mwa sana na wa tu hocha, wa tu onyumba ni. Suku na wa tu karbi wa tana nuliza, who's so fire. Na jwa umjazo hea, awana ni onaga kwa masimi, so mativi, so wei ni puto mativi kwa kuba. Sasa, ataji eleza monewe, monewe ni kabula, ataji eleza, ataji niguzia kidogo. Maa na minta wa tumia yu video. Na tumia nga mamangu dana onyosa hoti. Sasa, so fire, ni maa na monewa, amba na mimi niya kwa bipaj.  Amba ni wana fanyanga before music. Nakini, nili po ingiwa kwa mziki, niguzia kukutana na watambola ni shawishiku, maka nambia tafta so fire. Inama na kuna tumia na kwa mini apart from sisi. Soma kiangalia faces zote, ni maiutu tupu, so ni maa na mombayana mi niya talents, kuna ula lini uliza kujoini team, atiana fanyaji. Siya tu wende kwa mbuganga unta kujoini team niya so fire. Tiga kazi, tia bidi kwa neshima, eshima wa atu alafu wa saksha wana, when ni hardworking, kutaza kujoini afu. Mili salimimimu kono, ni kapata shuki tengela, tarekumina tatu epreid, ni kupala ma piyanotu wa. Baria kusalimia, tiana nima salimia, utaniwa Skotafrika na niki pandandegu. Amen. Gavana, Santissana piya kwa barakazaku, asu siyo nimeshutu. Katoon 47. Sema wunyama. Wunyama mingo kipanandegu, tutu e katoon kumpe jinalani. Ah, kito aya jina, ratu aya jina barash. Katooni bipi manango. Nyeshisha angu di alini pa. Ah, longboy. Aya. Okay, ladies and gentlemen. Wa chani karibisha fe lana, ase me jambu, alafu kimi kimi tumalizi imaneni. Karibu. Thank you. Well, as Uncle Cassie said, I don't like talking too much. I'm just going to say I'm really happy that my friends have school and so far I have decided to make peace. It's really good to see them. Good times. Dopa tajiri angi mingi. Dopa tajiri huyu. Angi ni mingi. Angi na se mani ni. Kwa ukuna chakula, friji me jya. Magari ni ku. Wewa ni wunga. Takbaka matumbu jihia. Wa yung bogeja karango fry ni. Taha huji. Mungu se idea rotoangu ase kuwa maskini. Ladies and gentlemen, nantaka ni karibisha. Kimi de kimi. Karibu sana. Mca. Govon. Mca. Mca. Uyu di tujuaku kuna. Mbero asalami watu na mkuni ga. One week, we'll be some men. Kwanzaa, asantini sana wa komedia. Asantini sana sofaya. Asantini sana muzongo. Asantini sana ni mekudu e lewa asantini. Ewaridi. Kibiya kwanzaa. Mimi si pendagi kudanganya mutu. Nasi pendiki kujipende keza. Me na sumama on my work. Me kudia apaleo kukue kwajili ya kule. Uyu ya kuape. Na kujili ya bossi. Miskia kila kipu eni ituliyongia juzi. Lakin ni amekubali kukua kijana mzuru. Ui ni gavana. Ui ni gavana. Mwenyata kusini na ni timoanyu. Alafu weo kasi na tu mwenyama na fanyanga. Nia itu sumui kichuana. Lakin ni kitu ya kwanza. Tu anybody mwenya kuchini ya bossi pulani kiri ya kwanza trust ni kitu muimu sana. Trust ni kitu muimu ya pili ya siwa. Ongerakini ongerakini. Trust ni kitu muimu sana. Ya siwa pia ni kitu muimu sana. Muna jwa kwa nyumba kwa society kwa family. This is a big family. Na vita i na kwanga. Mama aki piga mu totu na baka na muiko I was illetwa kwa social media. But wakambo, wakambo, wakambo, wakambo. Aki tuna mu totu, yutu na hana kwa media. Sinu kweli. Kasipul. Nadada wakwen go terms. Duma na tikwapa. Ya pili. Akuna aja mutu eiotia blame media eiotia ti bloga sijiwa na weka chumbi ama wana kahuza chumbi. Mutua media na dikaka chen yume mpa. Ukeli wama. Ukisema uyuni nugu. Mutua media atani katukimikili bia illetwa nugu. Sababu hili semu waivo. Nona. Siya kitu ya maana. Sababu hili gavana mutaraji ya mjiwa. Kuma nisha tu koneko ofisimoja loa na pali mimi na sumama kama mca. Infakt na shinda sambiliya subui. Are you getting that right? I get it. Are you getting it? I get it. Ukuena ishima. Uli kwa weni prodigal san, tumeku mis mayanku. Tumeku mis. Sababu wakatu uli kwa pali. Uli kwa una kwa kama nguweitu. Ya ni uli kwa una to protect. Siya siidume baki na dahada na catri. Catri ishima ya. Ya nafanya mambu kwa ofisi. Baki wana murini mumu. Nasi mimi saza mutu moja sinina piti watu. So rudi kwa tim. Nona na unge una furafura. Ebu smelki dogo. Wata kula zimeu, smelia. Ya muishu. Mimi ni me malizayo. Ya muishu. Mimi na unge tu mambu ya siya saka dogo. Sababu mi ni ma nasiasi. Ya. Siya mimi na miwa wakenya wote. Tu ome Baba ingia au. Baba ki siya ingia au. Ate ui gaba natapata kazi. Uli sa kuombia kazi. Surataka feza kampeni. Ida tokawa pika mufon ni kazi. Siya siya siya baba ingia au. Wakenya tu ome ni Baba sababu. Mimi ni mesapa nguwe ofisi. Ane isi jumi na isi chiniaki. Ni tafanya kazi ya kuwanya. Kila ki kuwa na kula, ni naonja kadogo. Baba ki ona ni mekufa iwa kuli tena. Hasemi sana gaba ni. Thank you very much. Iksmai ki naza kuwe kwa pali kwa sababu. Ni ki concentrate na imoja. Ita fectizi zingine. Ikwa sana. Imezi ma unapata saun. Unapata saun. Muko fiti. Muko fiti beni. Nata kani. Imizi na iimone ni kudia pa. Ni isi kumzuri. Ni isi peningene. Kwa sababu, kwa katikuna tatizo aama kuna misunderstanding. Nanda fuku kwa na amani. Nanda kwa ni isi kwa mabawu. Bingu pii na fraya. Siku zote. Panapuku na shida. Panapuku na msukosuko. Panapuku na vita. Aku patikani kuna amani. Ni ngependa sana kwa anza. Tukoku sema kwa sababu ni takaribeisha. Nga inisikuwe tu mimi na eh? Kwanza kulikuwa na misunderstanding wato kufikiru ya mimi na sofaya tunavita. Sofaya hatweziku pigana tunapigana adi. Tunavita gani. Of course kuna misunderstanding zinaza kukua. Kwa kila paali kila ofisi penyekuna riziki, lazima watu pakosane mdi owa elewane. Kitu amaone mdi funza katii yangu mimi na sofaya na ningipenda kufunza watu paali inje panapukuwa na misunderstanding please mu reach out to each other na mu iyonge. Siyo muna skekutua kwa 3rd party na 4th party. Watu wengi wali tikuwa advantage, sikunya tikuwa natu konaishu mimi na usofaya. Wengi sana wali tikuwa advantage. Wengi wali balisha kama kitoza uchumi. Kwa sababu wakachi wanaongi jeena kasi pul kwa sofaya wakipele kama neno wana juwa hapundio tutafanya ni ni tutapata kupata chetu ya kuwa kakumfuku. Which is okay? Which is right? Thank you very much. Na hindi oki tote nendelea uki angalia sterikali, uki angalia wana siyasa, watu wengi wana zunguka wana siyasa wote, bila kukuwa na kisirani, watu watashiba. Ni ni wato media mu le tengeneza kitum kaka kumfuku. Kwa sababu gani muna pata views kasi pul anagibu sofaya muna pata views. Sani sofaya naongi kasi pul muna pata views tulilisha watu watu. Utupege ni makufu wa tuwa media. Kwa kwa yapea views kuwa wengi. Yote tanu tisha ni ya kuwamba. It is okay. Ni kituwa kawaida. Ni muezim tukufu wa ramadani. Ni muezim bau ni holy. Ni muezim wana wake ya kuwa shimu wana wake. Mimi akuna siku agenest kwa kuwongi yam tuwa kikiya vibaya. Kwa sababu uyu sofaya kuwa media wajelu ni didangu. Nada yadakuna siku na unulizana ni na didaka. Una fight ni na didaka. Nugia kota fight ni na kwa sababu muna unulizana ni na yama shamba. Mituwa didaka wakitu kaaende. Waja wajelu nasima mi gogo. Aksenda waleke penyanu waleke. Shamba na kuwachia. Mimi na takaku eka clear. Sofaya and I atuna issue. It was just a small misunderstanding that people took advantage of it. People waka ibadlici eka kwa kitu kubwa eka kwa ni mani nomazito have never disrespected sofaya and she knows. Ni ilefiti na nyi ni mulem pelikeya. Kasipula mi semeivi kasiipula mi semeivi. Muna jaza sofaya. Sofaya na onakuna mada rau katiangu mimi na ehe. Sofaya know of me in persona. Sofaya na ni juya kwa wu kasipul ni mutuangu na ni muanda ni wangu akaribu. Onakuna putiwa point. Nase mukuli na mase mukuli. I am close to sofaya. Sofaya na takani kwa mpeki tumoja. We have no beef. Iitu meida tuatua. Media kwa ambia kwa mba sisi ni mandugu. Hakuna siku ni utakusana na ehe. Hakuna siku ni utapigena na ehe. Dada hangu watami ni kiputusi. Yo maisista. Na hukini tusi wani dada hangu. Uta ni dimulia na ni sawa. Dada Siku zoda. Konbo. Dada Nukuega mania. Nukuega, rolling. yotatano tisa I want ishuhi angu nasofaya watu wa jwe akwamba We need to tolerate one another Lastima tu pendani tunazakuwa na tofotize tu zakimawazo Zakisiasa Xaman nubingi Lakin at the end of the day We need to tolerate one another Lewii Mweshimewa Williams Samuel Ruto Hai Misalimiana Na Rayla molo odinga Umuona mani me patikana kwa inchi, ni kwa sababu gani, kwa sababu kuna watu sanye vite na tokezea, watu anasahidika, na wengi no ana umia. So, as we move forward, lazima tu pendane, tu jengane, tu natskumuwa jatom ta ki kwa mbia kitu kusu sofa ya tafa dhali muti oto a midi wu sindete, daku piga mabo pa kada muita toka. I'm being honest with you.  I want to put it clear, because at the end of the day, I love my sister and we are working together, sofa ya as a team, kwa sababu kisha nasimama gavana. If I don't have sofa ya next to me, it's a kuaji. What's your point? Na sofa tu dakawe pia, wu toka austria, wu kuji, kwa sababu, slocha ya women, dha punataka kupe. Ha, women repikido wu wadu. Tu dakawe wu timo? Na, su mama duku tu president, saye ni was chan. Duku tu president. Bas kimi kimi kimi amesimama yo kimi kimi akwa kuwa dunia jakarana. Kishiwa ke kuwa jakarana, but saye mmao na rona ziki pripa kwa machu hake. So, we have to say maivi, nan tarudia. Na, ni takuwa very honest nae. Ni akwa mba sofa ya, we have launched a campaign. We have buy. Tuna anza, pamao ya nanema sheikh. Ema sheikh atakwa ngaraniwech. Kimi nasimama gavana na Nairobi. Nana kuomba pia, with time think about it. Tungi penda pia we wu kuika mawimende. Tufu ni campaign kwa pamao ya. Kwa sababu tunama li zahi mziki. Natu tatatengeneza. Wakana katuna wana kuji nyuma. Roi yuko apa kama manager na tengeneza yo maneno.  All in all, ngependa kusema, mimi na sofa ya hatuna ubaya. Ya le amao sofa ya li yungia, mimi li ritchikuli ya kama dada hangu. Vilana yunga lisha ndugi ya ke. Kama ho li ritchikuli ya sirias, enda umese weme. Ukae, ukufei kuwe. Nakini mimi na sofa ya wewa, one thing. And for the corporates, when ya wali kuwa. Sofa ya wambia, yenda li nipakopret. Sayi mimi ni brand ambasada wa credit. Kata ni brand ambasada wa play to net. Katasi hof, sofa ya. Mimi ni brand ambasada, when ya wa ridi. Nemis. Nemis, logistik. Nye wa li nita mombasa kani peya. Katasi hof, sofa ya. Leo yungia na enda ma dunia na pana ege. Kwa sababu sofa ya alia nziki shima ya kusema kwa mbaka spul as a brand lazima apana ege na mumutuena konvo. You started it. Iyo shima bada na kwa shimuna ege.  I will never in my entire life. The fact remain na inabaki akwamba tuna ishima since in a sofa ya. Na wali wote ni ma brand endorsement ni mezifanya. Ni katasi hof sofa ya. Sofa ya kisema hivyo. Ana maanisha kwa nambia wali wa tu lakini sasa. Ani mawa piyesi mawa mawambia ni meto yo kawuli. So when you wanna kudya wa kudya tu kusaba wali yungia na tari meti yungia na zewa. All in all, zakari karimisha sofa ya. Semi kitu alafu tumali zewa, karibu sofa. Hi guys. Once again. So I want to first appreciate all online media. I really appreciate your guys. I appreciate your support because you guys are always supporting me whenever I need you or whenever we need each other. So thank you so much. I'm glad to see you here. So I will also recognize Deputy Governor. I met her today and this was amazing. She welcomed me from there. Thank you so much. I really appreciate. I want also to appreciate my brother. We are actually here. I want to make this clear. We are here to spread peace and love. I'm always saying, guys, the energy you have as in Kenyans or Kenyans we have so much energy and I wish this energy you could use it on something productive. Okay. Miwi na upenda sana and yes, there were some misunderstandings that I want to make it clear that kuna mutua kusangi sindio. You can also have a fight with your mom and you can talk about it. Kaspul is not only that we are working together or something like that. He is more of a family. Everyone was missing him in the team. Am I right? No. Like everyone was attacking me like no. So that bond is there. So I want to appreciate all of you once again. I don't have much. I also want to thank my Felana. My Felana as we do so many things together. But she is doing well. I think you will see the work she is doing. Her music, doing collab with so many different kind of people. Keep supporting her because she is just amazing. And it was also nice to meet my sister. We are ready. We are ready the director name is and we have a lot of trust in Kaspul as a brand ambassador of the company. I know. So I'm so happy with you guys. No, no, no. My ambassador is out there being.  Everything is fine. We are good. Kaspul is still the same that you knew before. Pray, hey bring those jobs. And in fact we are going international. So maybe probably, I don't know. I don't know. Probably in next two weeks or wherever we have something big outside the country. Again to represent Kenya, Makaspul and the whole team. So guys keep on loving each other and spread love. Now Apenda Sana, take care of yourself. Thank you very much. Next month because of the trust that he has put in you again. Yes. We extending our branch name is in Tanzania. So next month we are going to Tanzania. Yes. We are going as well to raise our new office. Yes. We are going to make a deal. So. We are going to make a deal. Thank you. We are going to make a deal. Because of the trust. Yes. We are going to make a deal again. And the peace that we have put in you again. We are going to entrust you again with our office in Tanzania. Of Nemi's Logistics. Of Nemi's Logistics. Where we do clearing and forwarding from Mombasa. We are going to have an office here in Nairobi. And already there is an operational office in Tanzania. Like a school seal is going to be our brand ambassador. So. Thank you. Na amani kuwa pamoja. Yes. And I just also to want to say to congratulate you on your bid of governor. And let the other opponents know that you guys don't take him. You guys are taking him like it's a joke. Like he don't want to buy amana. And I just amani kipindi. These guys are so serious. And it's time for the youth. Yes. Now as you can see the women out here. Including in the art industry. We are bringing the revolution. We are bringing revolution. And much appreciation Kasipul. Because we are bringing the revolution of art industry. And music in general. And we have a lot of hope in the female artists of this country. And I just want to applaud Felana. Because juzi nili kuwa. Ani mewami ani mefi kajana kutoka Darisa Lam. Na mzikiwa Felana. Na kali graf. The latest one in Achezo Sana Darisa Lam. Na also was in Pemba. In Achezo Sana. So keep on doing good music. And of course Kenya we are doing good music. Na easy bifu ndogondogo to watch it. To watch it. It's not important. As you can see women are loving each other. In the art industry. Na kwa naume. To benan. Ano ma benan. To upenda sana. Especially in the art industry. We are doing a lot. And we are going to do. Thank you so very much already. Just one more thing. Like for my brother of course is a future governor. Of course I have your back. Thank you. And I will always have your back. Despite what and what. Thank you. So don't worry. Thank you. As team Sofaya. Can be also MTA. Yes. But I have your back. Thank you ma. Thank you. So much. So bro come do your thing. So thank you guys. Thank you Sofaya. Thank you Kasipu. Yes. We want to make it clear. Because aiku kuakiki. It was something that Ilikwom is understanding. Kidoga will be mixed here. And on that note. Because they are here. Ngataka handshake. Kwa ahahana. Ngataka handshake. Ngataka handshake. Ngataka handshake. Ngataka handshake. Ngataka handshake. Nimefuga mi feregi. Aiku na kuokata kwa Sofa mi na handshake. Alright. Thank you so much. On that note. I think we have a brother here. As a gift for you. A. wakameja. OK. Say thank you because on behalf of women tu me rejesh a man. Thank you so much, for putting your problems aside and all the things that you guys went through on behalf of women in this country and in the entire world in general. We want to say thank you for showing an example. Indid, kidole moja, haki fanyi ni? Haki hu yu ja Takibisa, kwaevo tu, shikani na tu kuwe pamaoja. Asante ni sana. Dariki... Hahahaha Alright We just need you ni Bahasha. Mianakata wilewa ma niyana. Niyana niya kata... Sofaya, sofaya. Oya sofaya. Haia ba si Fungo. Si Fungo isi wali. Mamu maine ya kwa Thank you so much Kwao Meriza sa I use crystal stones I got a julo makesh kikada Yes please So I use crystal stones and resin ya wow wao does amaze so to apeshen na kiawan ya Thank you so much What's your name? Amskaya Kretia okay you live here in Nairobi yes thank you so much guys look at this job this is a very nice surprise support his work I will follow up where exactly and how he's doing it but I really appreciate you and guys you've seen that I mean support this young guy and I really appreciate you, thank you so much. So we want also to thank... You can't tell people where he's doing this. Okay, come bro, come. We want to know where he's doing this. You know I'm shy on camera but... Okay. I go by the name Skyart Creative. I do skyart resin art. If you want anything portrait in the house, baby. You can find me on Skyart Creative Tiktok. Skyart Creative on Instagram. Even on Facebook. Ya. So my number, if you want my number you can... If you want my number you can get<PHONE_NUMBER>. Thank you. Thank you very much. And you can keep out your number. Adyusa. Adyusa. Bana boy. Thank you. Bami. Big up Adyusa. Mutuanguku sana. Apendi camera. Adyusa. Ana chakekina mutusha. Adyusa kashuku. Also we want to big up Carlos. With suku. Carlos, piyamagina una tu pehanga jamini. Suku suku suku. Suku suku suku. Carlos big up very much. Thank you very much bro. Nakumbukulini peyapaka keja maze nikaji nice. Maze big up bro. Ani kwa hi hensu na ni peyapaka keja budha. Aho eni mutuanguku sana. Thank you very much. Thank you very much. Nini watya ni ano? Ha? Ako api. Okay big up watya ni watya ni yazosa na ni. Nani nugi hangu ama nizie. Thank you so much guys. We appreciate. And there is peace now. Asa teni sana mongo abari. Thank you.


Thankfully, it's November, and Appalachian Wireless is offering the Samsung GS8 or the GS8 Plus for $100 off the regular price with two-year agreement. Better service, bigger savings, that's today's Appalachian Wireless, an East Kentucky network company. The Floyd County Emergency and Rescue Squad was in the water at Dewey Lake Saturday testing a new tool. The agency is now the only emergency response organization in the world with a Chimera electric bodyboard. When Tim Cooley says he discovered the device while watching an episode of ABC's show The Shark Tank, and while the board was marketed for recreation, he could see an immediate application for water rescue. What I needed was to be able to try to obtain some type of transport from one side of the river to the other, without putting a swimmer in the water, basically, a couple of reasons. Tag a line across the river or whatever, which is the hardest thing to do, to get an intentional line across. Or to get medical equipment or a PFD or something to someone that's stuck in the tree. We've done this before. The company failed to obtain funding on the show, but that didn't stop Cooley from contacting the creators to share his ideas on making the Chimera a better fit for first responders. So my two ideas were, I need a burst of power, I don't care if it runs two and a half hours. I don't need that, because we're not going to play on it. I need quick bursts. I don't care if it runs an hour. I just need speed, fast, and I need my power when I call for it. The other thing was much like a four wheel or a gasoline engine. If worse came to worst and power was used all up, I wanted a reserve of some kind. It's kind of like a four wheeler does with gasoline. The company went on to implement Cooley's ideas. And after Saturday's test, Cooley says he has sold on the Chimera's potential. After my test today and seeing some things in steel water, I can see that my members need, they've got to get used to it. It's a new toy so to speak. It's another tool in our toolbox that we can utilize. If I had a call for it today, I'd use one of my members that I've watched already today. I wouldn't hesitate to put it in. Next up is more training and a test in moving water. Reporting in Pressensburg, I'm Ralph Davis for EKB News.


Hello, everybody. Welcome back to another Photoshop tutorial. This one is going to show you how to get rid of the bounding box. When you notice, I've clicked on my little text here, and no bounding box is around it. Why? Very simple. What you got to do is you just want to click on this Show Transform Controls button. This is the one that affects that bounding box. If you want to change the size of this, and you don't have the bounding box, you can just simply go over here, for example, and go to your text tool or your type tool, and you can just go up here to the font and increase, decrease the size. And again, the bounding box does not show up. If you want the bounding box, go to your move tool or just click V. Make sure Show Transform Controls is selected. Thanks for watching.


So as you may know, a tract is a bundle of axons. In this video we'll be talking about three tracts that are involved in the transmission of subconscious motor signals. This being our brain, this our brainstem and the spinal cord. We're going to remove the midbrain, pons and medulla so we can see the vestibular nuclei here. A nucleus is a discrete chunk of gray matter and gray matter is the cell bodies of neurons. These cell bodies receive information from neurons that are coming from the inner ear. They're transmitting info about the head's position in space from the semicircular canals through the vestibular nerve. Having dropped that info here, this neuron's axon heads down in a tract known as the vestibulospinal tract. Descending just posterior to the pyramids of the medulla, the axon then fires on the cell body of a lower motor neuron in the anterior horn of the spinal cord's gray matter. So that's the vestibulospinal tract. It receives info about the head's position and conveys it to muscles of the head and upper limbs which can adjust our positioning if required. The reticulospinal tract is up next for which we will bring this in, the reticular formation. Reticular formation is composed of many nuclei and spans the medulla to the midbrain. So with their cell bodies in here, our axons then descend in a collection known as the reticulospinal tract. They drop their information on cell bodies again in the anterior horn of neurons which head out to muscles in the torso and upper limb. The purpose of these messages are to maintain our posture, especially while we're in motion. The tectospinal tract begins in the tectum which is this part of the midbrain. So within the tectum we have these little mounds of gray matter called colliculi, Latin for mount, and we have superior colliculi and inferior colliculi. The superior colliculi receives visual info, the inferior auditory. If we see bright sudden movement or hear loud sudden noises, this information is passed down the tectospinal tract to activate muscles of the head, neck, and upper limbs. So any sudden movement in response to something you weren't expecting to see or hear, that's the work of the tectospinal tract. So the tracks that we've talked about have a few things in common. They all transmit subconscious motor information and they all move down through the medulla behind or posterior to the medullary pyramids and that is of course why they're known as the extra pyramidal tracks. All right so I hope you've enjoyed that. If you have hit subscribe and we will see you next time.