I was a communist for the FBI. Starring Dana Andrews in an exciting tale of danger and espionage. I was a communist for the FBI. From the actual records and authentic experiences of Matt Severick, come many of the incidents in this unusual story. Here is our star, Dana Andrews as Matt Severick, who for nine fantastic years lived as a communist for the FBI. For nine years, I managed to live on a communist diet, a diet of indigestible ideals and poisonous philosophies. But even I was shocked to learn that red poison came in canned. This story may save you from a violent case of political tomein. In a moment, listen to Dana Andrews as Matt Severick, under cover man. Dana Andrews as Matt Severick, under cover man. This story from the confidential file is marked, Prison Comes in Canned. I should have been used to darkness by now. My life had become a series of grotesque shadow dancers for the FBI, with the commies playing the music. But you never get used to darkness when the shadows are alive with treachery. When the mist is like the breath of disaster. The fog hung like a soggy veil over this tiny waterfront town. The buildings, the blurry street lights, everything seems without shape or form, swimming in a limbo of mist and darkness. And what was I doing here, walking the wet pavements of this waterfront street? I was looking for one particular building, the home of the Oceanic Import Company, a food importing concern that no one ever heard of. That is no one but me and the commies who sent me here. Then, almost too suddenly, the fog swirled with movement. A light appeared over a doorway just ahead, and the darkness spoke to me. Static. Who's that? Wagner. Oh, I've been looking for you, Conrad. No, mind that. This way, in here. I stepped out of the darkness into the lighted doorway, a door closed behind me. And it stopped blinking. I found myself facing the distinguished director of the Oceanic Import Company, Conrad Eric Wagner. He welcomed me with typical commie friends. You're late, Static. I know, but that fog has caused the fog. Of course, the fog. Nevertheless, you're late, aren't you? Well, I suppose I am. Aren't you? All right, I'm late. Do you want a note from my mother? Hmm. I suppose your record for competence makes up for your lack of discipline. Yeah. Come along. Here, sit down. Thank you. You've been briefed on this project, I imagine? No. I was told to report to the Oceanic Import Company. I was to find you there. It looks like you found me. Yes. This is the Oceanic Import Company. This? Well, it's practically a barren room. All we need. Now, about your reason for being sent here. You know nothing about it? Well, nothing. Hmm. Tomorrow morning at 8 o'clock, a fallen freighter will dock at Pier 2. A freighter? I didn't think this port had any overseas traffic. Very little. It's primarily a fishing town. But as I say, tomorrow at 8 a.m. Pier 2, okay. In that freighter's cargo is a small crate of canned tuna. It's listed for delivery to the Oceanic Import Company. Canned tuna. That's right. But in the world of the party, weren't we... Everything in time, Static. Everything in time. You're right. You're right. You will meet that freighter in the morning, Comrade. As a representative of Oceanic Imports. You will check for the cargo inspectors to see that our crate is properly dispersed. That's all? That crate of canned goods must not go astray. Why not? Because, Static, in those cans are microfilm of top-secret documents from the Communist International. Oh, I see. Oh, what sort of documents? The new revised plan for red action within the United States. The new timetable for the proletariat advance. I see. Can goods seem to be going up in value. Yes. But if you should permit these canned goods to reach the open market, the price will be frightening. The Oceanic Import Company. Is that it? Yeah, that's it. Has the crate been checked through yet? It's not going to be checked through at all. Huh? The crate's gone. Gone? Yeah. What are you talking about? Here. Here's a manifest straight from the ship. It says the canned tuna was damaged in shipment. It started to spoil, went bad. Just a minute. Let me see that. It is black and white. The crate of canned stuff went bad. Last night, the crew dumped the crate overboard. It was there in black and white on the cargo report, all right? The crate of canned tuna had been tossed to the bottom of the murky harbor. Now the official red timetable had been put to sleep in the deep out of reach of the eager commies. But I was still very much within reach of Comet Wagner. This report from the cargo inspector, Svettik. Your shore is complete. I'm afraid so, Comet. Get your coat. What? Your coat. Put on your coat. Where are we going? I'm taking you for a boat ride. Look, Wagner, it's not my fault that the crate was broken. You didn't try explaining anything, Svettik. Just get your coat. You come along. Just one minute. Are you afraid of the water, Svettik? All right. Let's go. Looks like the American voice was C, eh, Svettik? Our own middle yacht and everything. Yeah, everything. Why so glum, comrade? Don't you enjoy the sea air?  My stake in this project is as great as yours, Wagner, and I don't know... Relax, Svettik. I think I'm entitled. Relax. I'm about to show you exactly where our crate was thrown. Our crate? Is at the bottom of the harbour? There's point prugas over there, the entrance to the harbour. Just beyond it, our diligent comrades tossed the crate off the freighter into the water. Comrades, you mean we had party workers on the ship? Svettik, you really didn't think the party would let so valuable an item out of a pan for even a moment. Well, I... The crate was tossed overboard at a specified point by specially instructed comrades on the crew of the freighter. In this way, we avoided the risk of a possible cargo inspection on the dock. Understand now? Well, I guess so. They like the hard way to do things, though. Difficult, perhaps, but safe. Now, note this location carefully, Svettik. It will be up to you to get the crate with the microfilm out of the water. Oh, I see. I see. You'll hire a diving crew to dredge the bottom. Oceanic imports will secure the permit. Hey! Hey, senority! Are you with your mother? Who's that doing that hollering?  Forced by mother, senority! And it's away! You've got to be... One of those fool fishermen. Better change your course, Wagner. You're heading toward his net. Take it easy. What are you doing? Let him change his course. He's out to snare some measly fish. We're out to haul in the world. Well, thank you, operator. There you are. Bigger this is red. Still sloshing around the waterfront. Listen, Bigger. My little chums have tucked away a crate of hot microfilm. The FBI can use it. Yeah? Where is it? At the bottom of the harbor. At the bottom? I'll give you the location. I've been ordered to dredge it out for the commies. But I'll stall it off... We'll let the coast guard ride. What's the matter? Well, if you get the job done tonight...  I'll keep Wagner away from the shore. Now, look. Here's the location. Got a pencil? Right. The fog that night was thicker than ever. A rotten blanket that smothered all activity in the harbor. I kept Wagner away from the shore all right, but the fog kept the coast guard away too. Then Wagner met me the next morning. The commie timetables were still asleep in the deep. Wagner, however, was very much awake. The diver to get the crate, Spettich. All arranged? Well, you know the crews around here are pretty expensive. I've been shopping around for a decent price. Price? Spettich, do you realize what the price will be if we lose those microfilms? No time for false economy now, Edith. Just get that job done. But, Beaker, I can't stall Wagner any longer. You've got to get that job done tonight. Fog on no fog. Well... I'll postpone the diving job. I know. That fog's been awful soupy, aren't it? At night, yes. But the days have been clear enough. If you can't handle a simple task like this, comrade... I can handle it, Wagner. Don't worry about that. I'm not worrying, Spettich. But I suggest you start worrying a little more. If the crate isn't out of the water and in our hands tomorrow... Well, this is red, Beaker. What's the matter? We checked it twice, didn't we? Well, the Coast Guard had divers walking all over the harbor bottom. They combed every inch of it. No crate, no... Nothing. Beaker, it's got to be there. I know it's there. Maybe the tide or the currents or something. The Coast Guard knows enough to allow for that. The crate just isn't there, Matt. Great. Well, keep your boys around, Beaker. They may be picking me out of the harbor next. I was a communist for the FBI and the second act of our story. The United States Coast Guard had spent the night scouring the bottom of that murky harbor, searching in vain for the creative communist microfilm. Now, it was my turn. By early afternoon, I was on the bars with a diving crew and comrade Eric Wagner, who had come along evidently to expose his nerve ending. We inched toward the area beyond Point Frugus, with Wagner becoming increasingly jumpy every bit of the way. I was wondering how he was going to react when he learned the bitter truth when... Hey! When one of the crew hopped from the deck of the tug to the barge. Hey, which one of you is Mr. Svennik? I am. What's up? I was up there checking these instructions for the pilot of the tug and I... They're all right, aren't they? Your crew can understand them, can't they? I mean, nothing is wrong. No, everything's fine. You're sure you want the divers to go ahead with this job? Well, yeah. I thought we hired them for. Okay. You're the boss. Now just a moment. What's on your mind? Well, this crate we're looking for. It's a crater cantuna fish, ain't it? Yes, of course it is. Is there any doubt about that? No, just that one of them Portuguese fisherman pulled in a whole crater cantuna the other day. What? What's this? Where? Where was he fishing? He'd spread his nets right out there and we're going. At least twice. That's what I understand. Can you say he pulled in a case of cantuna? Yep. I saw him tie up at the dock. You want a happy fisherman, that guy? No, I ain't sure. It was your crady haul then, but... Turn back. Tell the pilot to turn back. Don't be foolish, Wagner. We've gone this far. We might as well... Turn back, I said. We can't let that fisherman... You, you. Who's the fisherman? What's his name? I don't know his name. I just see him once in a while in the docks. Who is the man for the love of heaven? Who is he?  Mike, we'd like to find that fisherman. What did he look like? Well, like a fisherman. They all look alike to me. Well, isn't there anything that... Well, you saw his boat. Did it have a name or anything? You know, I come to think of a Spanish name, or maybe Portuguese. Uh, a pal, pal.  Paloma, that's it. La Paloma. Turn back. We have to find it. Turn back, I said. Listen, won't you quit clawing at me? No, not pilot. To turn back immediately. It'll be a pleasure. More ruckus about some crummy can to spoiled fish. For the sake of that unsuspecting fisherman, I had to find him before Wagner did. If he'd opened those cans and found the secret crummy microfilms, the reds were licked. But if Wagner got to the fisherman first, he was in for trouble, bad trouble. Searching the harbor area, we found that most of the fishing boat were out at work on the water and wouldn't return until about sundown. As for the inevitable fog, it didn't help a bit. The only thing I could find with no trouble was Wagner. He stuck to my side like a barnacle with a complex. Static, I hold you fully responsible for this mess. Me? Why me? If you hadn't postponed the diving for two days... Oh, cut it out. I intend to file a complete report of your laxity with the control commission as soon as... Look, Wagner, we're wasting time this way. We ought to split up. Go in different directions. Mmm. Might be wise. Look, you search the south end of the harbor and I'll cover this bay area. We'll cut the time in half. Good idea. And static, don't stop looking till you find that boat to La Paloma. Don't worry, comrade. I'm as anxious to find that fisherman as you are. The murky waterfront was well covered that afternoon. I roamed the bustling piers and creaking docks. I studied the flocks of fishing boats, huddled at anchor in the crescent of the shoreline. But La Paloma seemed to have flown from her nest. I walked along the edge of the seawall, trying to read the names on the boats that swayed at anchor below me. One boat swayed more than the others, as if to keep time with the loud singing that floats on my deck. That boat bore the name La Paloma. Hey! Hey, mister! You call me, senor? Yeah, is that your boat? See, it's mine. I won't eat it. You mind if I come aboard? Come, come down, amigo. You can jump from the wall, all right? Well, I can try. Okay, amigo, take a chance. Leave! To mendiness? No, I'm sorry. I came to talk business. Fishing is my business, senor. So we talk about mending this, eh? Well, uh, I'm with the oceanic import company. Huh? Yeah, we import food, canned goods, tuna fish, that sort of thing. Tuna fish? I import too. I catch a whole tray of canned tuna in my nest. Big import, that's me. I give you competition, eh? Oh, that, uh, that tuna you found, that's why I want to talk to you. You want them? I tell you, I'm pretty cheap. No, no, I don't think you'll want any either. The fish in those cans is bad. It's spoiled. Bad fish in cans? Yeah, I hope you haven't eaten any.  See? See, I know. You sure my tuna's bad, senor? Look, I spent all day looking for you so I could warn you. I didn't do it because I needed to walk. See, see. Maybe I'd better tell my wife, eh? Well, look, I'll do it for you if you like. After all, my company's responsible. See, you do it. You tell my wife, I'm in the nest. Okay? Uh, where do you live? Right down the bay shore. Dos, dos uno. Two, two one, bay shore. Over that way. Okay. Oh, uh, my name's Severic. What's yours? Tamorina. Pietro Tamorina. My wife, she's Marie. You see her. Make her give you up the canfish. I hope she won't mind my butting in like this. Go on. You tell her. But, amigo, hey. You be quiet about it. Do not wake the baby. Well, I was in the lead now. I'd found a fisherman and I knew now where the creek was located. I was all set for the home stretch. I looked up to judge the distance for my little lead back to the seawall. And suddenly I knew my lead was gone. There on the seawall, looking down at Tamorina and me, was Comrade Wagner. Come up here, Stetich. Sure. Give me a hand. You found the boat in the man I see, Stetich. Uh-huh. Does he have the crate? Uh, no. He hasn't? Then where? Who has it? I'm not sure. Come on, let's walk. What is it, Tamorina? You had put the wrong way on me, God. I told you my house is that way. Losing your sense of direction, Stetich. Come on. Mrs. Tamorina. What do you want? I'm Matt Stetich. This is Mr. Wagner from the Oceanic Import Company. No, not at nothing today. It's imperative that we talk to you, madam. My baby. We must talk to you now, right now. Of course, of course. And you're not so loud, eh? We just talked to your husband. It's about that crate of canned food he hauled in the other day. So? It is his, no? It belongs to our company, madam. We've come to claim it. Oh, nobody claim it. He had to haul it from the water in his snare. What's not yours? Well, let me explain, Mrs. Tamorina. That canned fish is bad. It's rotten, spoiled. Bad? Why so bad? Bad. No good. Can't you understand that? If you wake my baby, I call a colic-hop. You'll do nothing of the sort. You?  That's there. There you see you wake my baby. Adios, sonoros. Go away. Adios. Mrs. Tamorina, please. This is important. Adios, adios, adios.   Huh? Kill, huh? That tuna fish is no good. It's poison. That's why we threw it to the bottom of the harbor. Food like that is dangerous. Oh. What's wrong? Oh, my sister. I gave some of them to my sister. Well, we never see the end of this chase. What did your sister live? Come, come in. I, I must keep the baby. Yes. My sister, she lives on the street. Right close to the bait shop. For favor, send your sister the baby. Static, stay here. I'll get the system. No. No, you stay with Mrs. Tamorina. I can make it faster. You get along better with this woman. If they put, I'll be back. That is just a minute. There was no time to argue now. I had to get away from Wagner in a hurry. I ran toward Mrs. Tamorina's sister's house, passed it, and kept right on running until I reached the bait shop. There was a payphone on the rear wall. I started dialing the local FBI office. But I realized that by the time they'd cover the distance, Wagner and the microfilms would be gone. Police headquarters? Oh, a senior, a policeman to my house, hurry. I live at 221 Bay Shore, senior. A man is trying to steal from my house. Hurry, please. Eh? Or name? Or me? My name is Tamorina. You got that Pietro Tamorina. I knew the local police would find Wagner there all right. But to make sure the evidence was found too, I called the FBI and told them to follow through on Wagner's arrest. Once those microfilms were linked to Wagner, one more red would be erased from the commie spectrum. In a matter of minutes, the police cars zoomed by the bait shop and stopped at the Tamorina phone. I walked away from the phone and turned inland, away from the shoreline. The fog was beginning to roll in from over the water. A foggy veil to hide the face of the waterfront. At this time, the fog was like a welcome friend that gave me cover, obscurity, the security of darkness. But when you must wallow in treachery to defeat treachery, you learn to greet the gloom more readily. You walk more securely in darkness, as long as you walk alone. Dana Andrews will return in just a moment. This is Dana Andrews, ladies and gentlemen. It was Ralph Waldo Emerson who said, we want a state of things which allows every man the largest liberty compatible with the liberty of every other man. We have at State of Things in America today 150 million definitions of the word liberty, one for every citizen of the United States and room for every one of them to flourish. That in itself is the essence of liberty. In the story you just heard, names, dates and places are fictitious to protect innocent persons. Many of these stories are based on incidents in the life of Matt Staviric, who worked undercover for the FBI. Next week, another fantastic adventure. Join us then, won't you?


Okay, folks, welcome to Best Oktrarch for the coming week and I'm really happy to make this video because something that we've wanted to do for a while now is to transition over to a more engaging platform for a forum and we're beta testing it right now. We have a bunch of members that have already signed up for what will replace our existing forum, which is really bare bones at current and we're beta testing slack, which I've never used until yesterday and so far the feedback has been good. I've been playing with this thing all day long and the functionality seems really great. I've been able to post the week ahead commentary in the forum area. It's also posted in the blog area. I sent it out by email last night. I've been able to post charts. I can't do this with my current forum, meaning I could post a link to a chart, but I can't post an image that I can look at and say that's interesting and blow it up. It's like Twitter, so it's really cool and I could post links from Twitter, etc. on here. Members seem to be enjoying it. I'm getting feedback. We have a link here. This is the main channel, stock market observations, slack feedback and we're just building it out and getting feedback from other members who use this constantly for their own businesses. More to come here. Changes are being made. We are raising prices in Q1 of 2021. Please lock in now. Prices do not go up on existing members who joined in 2020. You're in. That never changes. Prices are going up in 2021 and this is a piece of the new functionality that is going to be available now. Join up. Look forward to having you and I would love your feedback on the new channel. What are we going to talk about today? We're going to talk about how our week was. I'll give you a higher level of view of my thoughts on the market and then we're going to talk about stocks we're watching into the new trading week and in particular the cybersecurity plays are looking very good. Crowdsource is our primary. Cyberark is another name you could look at. If you want to diversify a bit, you can simply buy the ETF HACK hack, appropriately named hack. Another symbol that we're looking at is CNST, Constellation Pharmaceuticals, VNM. That's the Vietnamese ETF rocking. I've been talking about that for months. I've been waiting for a major pullback. It just won't come. It just keeps going higher. We're going to talk about that a strategy for entering. And in fact, there's a thread going on in the new members area now about VNM, my price targets. I have a chart where I'll show it in a moment where my alert is set on TrendSpider. Speaking of TrendSpider, I think they're still 55% off effective today. So use the link below. They're having that Black Friday sale, early Black Friday sale. The next startup is going to be TCP Pipeline Partners. And we'll go over all these charts. First, let's talk about, we already covered the new members area, the forum. And now we'll talk about last week. So last week was another week where they kicked off the trading week with another spike, right? Two weeks in a row of coronavirus vaccines, they're coming. 90% pure rate, 94% effective rate. Now fires, it comes back. They're 95. They wore 90. Now they're 90. I mean, there's probably going to be another attempt to spike the market on Monday. I have little doubt about that. The problem is, is that the laws of diminishing returns are occurring here. I mean, you saw a fade, the week prior to last, that's the Pfizer week, last week, this past week was Moderna week. And you saw a fade last week on the markets. And the close was not wonderful on Friday afternoon. So, in looking at the spike higher last week and knowing how the prior week went with that fade, I said, you know what, we're long of ExxonMobil. Energy stocks are doing very well. We've come a long, long way. We sat through the X dividend date. We're going to get paid our Divi 87 cents per share. Let's make some profits real here. We bought all the way down here. And we booked half profits at a very large position that's been halved now, but we're going to get a big fat premium in the mail in the next couple of weeks. So love that. I still like ExxonMobil. I did not like the news of inventory builds last week. That's a concern. I do not like the fact that yields are dropping yet again. That is not good for the cyclicals. Remember why cyclicals rally when yields go up? It's because it's a sign of domestic growth, organic growth. We don't have that. While oil did well last week, I don't know why. For the life of me, I can't tell you why. You saw natural gas prices just get absolutely annihilated. So while oil prices still look as though they're going to head up higher, I'm concerned. So fast forward. We booked profits, half profits, I should say. In the beginning of the week on ExxonMobil, by the end of the week, we had reversed most of those gains, all those gains, and first out, best out. You need to know when the market is getting manipulated, move to the sidelines when necessary, because when you see yields drop, you've got to look to technology. And I'll be honest with you, even technology faded last week. This is the XLK. They should have done well in a declining interest rate environment. They didn't. Take a look at your semis. They close up on the week, but man, they're just barely holding onto support. If they drop down next week, it's all over. So it's going to be a very important week. Seasonality favors stocks this time of year through to December 31st. After that, I don't know, man, we need to be very, very careful going into the new year. We added to short positions last week. We've been hedged. We added more. We got a little bit more aggressive last week. So I'm not ready yet to go all into the short side at current, but I'll tell you, we're keeping a cash horde ready just in case, but we don't want to fight seasonality trends at current. I went over this a bit with members yesterday on the weekend commentary. I'm going to post the podcast tomorrow on YouTube and on Google Play. And was it the other one? iTunes. So if you want to check that out, check it out tomorrow. If you want the full video experience, become a member, 14 days for trial offer. You can't go wrong. Cancel at any time. Fire me. Okay. So those are my thoughts on the market. I'll leave you off with this. Don't forget Sunday Night Futures live tomorrow night, folks. 6pm Eastern Standard Time. Click the notification bell to get notified of when we go live. But if you want to not miss a moment of the show, because it's a pretty good show, use the link below. Enter your email address on any one of the email links. There's one link. If you don't want to get anything in the mail other than an alert, 15 minutes prior it was going live, click that link.  You're going to get mad at me. I don't want to spam you. All right. So enter your email address on it. Bob's 5 Most Powerful Candlesticks. If you're already on that list, don't enter it. You're going to get alerted prior to it was going live. Okay.   All right. So, trip queues. This is a weekly chart. Let's go to the daily chart. This is what I really do not like here.  We've been in a somewhat of a declining downtrend channel, a consolidation. I don't even want to say downtrend. That's not being fair. And we are short of the triple queues. We have a hedge on our long portfolio using the triple queues as short. We have broken out in the past only to fail to hold support. We did it once. We did it twice, Friday, third time breakout point failure, aka bull trap. So there are warning flags out there in this market that should cause us some concern. So we're going to go into the week believing that in all probability, given seasonality trends, the Santa Claus effect, the Santa Claus rally that all is right with the world. However, we're ready to pull the trigger short at any given moment. So more to come members with alerts. Let's go through our charts that we're watching for the new trading week. First one up is going to be crowd source. I'm just going to go over the weekly charts. I did a deeper dive with members on the weekend commentary. Again, posted in the members area. Okay. So on a weekly timeframe, we broke out last week above resistance. Very, very nice. A W formation higher low on RSI and it appears as though we're going to break out and validate this breakout on price. So crowd source looking very good. If you want to take a look at hack, I haven't taken a look at it yet, but it did pop up on my screener. This would be my first time in a while looking at this chart. All right. So we don't have a breakout here yet per se, but it had a good week last week. You know, if you use the automated trend lines, it's time saver again, link below. What's trying to spider at now? 50% off a 12 month plan today, folks, and it drops off even lower. It ends on the 31st. I think the bottom of their percentage discount has been hit and it looks like it ends in the next couple of days. Then they have a seven day free trial offer. It's also included free with our silver and gold level memberships trend spider free or you don't want my membership. That's fine. That hurts, but just use the link below and get 50% off of trend spider. Great product. All right.  This is how we know. Don't touch it quite yet. Click of a button. Bam. There are your resistance levels above in red. Here's your support level in blue. And you can see above we have a couple of other significant resistance levels that we need to respect. Right now we're kind of in no man's land. We are consolidating nicely here. If you wanted to scratch the edge, I think I'd be fine with opening up a position on hack. It looks good. Crowd source is already broken out. So obviously it's behaving as best of breed. Cyber arc is another one that has been looking good, but crowds strike is looking better. I mean, we're very close to a breakout point, but let's face it, crowd strike already did that. So we want to tip our hat to that stock is being in all probability, the best of breed. And I haven't taken a look at investors.com yet to do my due diligence. That's just an assumption, but I do know that cyber arc is a very good company. I have traded in the past and treated this very well. So CRWD at current appears to be our favorite play. So I spoke about a entry plan for crowd source on the weekend commentary. Go check it out. Next chart up CNST. Now you can see that RSI broke out last week. Again, this is a weekly chart. And if you use the automated trend lines, pop, click up a button, we broke out. So we're looking good here from a long perspective. I think that we are going to head up higher. So constellation pharmaceuticals, very nice members more to come on this trade. And again, for a deeper dive, go over to the members area, check out the daily analysis as well. Vietnam. Okay, I've been pounding the table on Vietnam as long ever since COVID hit. I've been saying that there's going to be a supply chain shift. Not only have I been right. I've been very, very right. So right. In fact, that China is now building a wall between them and Vietnam. So the talent from China can't go into Vietnam and work. So Vietnam I've been waiting for a pullback on. I should have taken advantage of it back here in October. I didn't. I was hoping for a bigger pullback. Unfortunately, it didn't happen. We broke out above significant resistance last week. So now I may have to pay up a little bit here. I do have two alerts set one, you can clearly see here. And two is down here. So when those fire off or if, if the 1551 fires off, we'll look to open up or add to positions at those levels. The US dollar appears poised to break and break hard. I'll be talking about that chart tomorrow night on Sunday Night Futures Live. So join us. I'm going to be talking about gold, the dollar and what we should expect going into 2021. I'm already looking at 2021. The books are closing on 2020. So now it's all about positioning for the January effect. What does well in January? Gold, miners, silver. We'll talk about that tomorrow. 6 p.m. Eastern Standard Time. So Vietnam looking very good. We have a breakout on RSI, higher lows, higher highs. Everything's good here. All is right with the world. For the daily chart analysis, go to the members area. And in the, there's a threat going in the forum, the Slack forum regarding VNM and how we're planning on trading that. So go check that out. TCP and that's the value of the forum. That's what I've always wanted. And I think that with Slack, we're going to get to that level. All right. So TCP pipeline partners. I'm, I like the setup here. I'm concerned about oil prices and the influence that they have on TC pipeline. I don't know the correlation yet. I haven't done my due diligence going from off the top of my head. I'm willing to bet that it's a pretty tight correlation between oil prices and the TCP pipelines of the world. So it's a yielder yields about 8%. This is a master limited partnership. So you may not be able to buy it in a retirement account. So just be forewarned. I guess there's a little bit more risk with these. But last week, speaking of the technicals, we broke out. But very nice breakout. I have a manually driven line drawn line here. You don't even need that really automated trend lines did just fine as well. They picked it up and you take a look at your RSI higher lows. We've broken out on price on RSI looking very good here. So again, I do more of a deep dive on the weekend commentary posted in the members area and in closing folks, please sign up for the 14 day free trial offer. Get Trendspider for free or if you don't want to join up fine, take advantage of a 50% discount, which is better than my normal discount. I do a lot of business with them. Use the link below and join us tomorrow night, 6pm Eastern Standard Time here on YouTube. Enter your email address in any one of the links below and you get notified 15 minutes to a half hour prior to going live. Everybody enjoy the remainder of your weekend and I will hopefully talk to you tomorrow night. Be well


Welcome to modulating. I have boldly named it as the metric trinity. What we are going to do today to discuss three most important theorems according to me in matrix space theory. So one of them is Cantor's intersection theorem. The second one is Banach's contraction mapping principle. The third one is Baer's category theorem. You can call all of them as principles. They have from theorems to they have become principles anyway. High status of a theorem is to become principle. The CIT, CIT I mean contraction mapping, okay. Sorry the Cantor's intersection theorem. This is so fundamental that even in the proof of Baer's category theorem we will be using it. Banach's contraction mapping theorem is slightly of different flavor. It doesn't use CIT directly, okay. The method of the proofs of all these three, they are themselves quite agitative. So often you may have to employ that in your own research work if you want to do, you know, deep analysis or topology. So I would like you to pay attention to not only the statement here, how things have been arrived. The proofs also should be learned properly. So let us begin with freezing this symbol X, D or just X for a metric space once for all in this section. The first theorem Cantor's intersection theorem to start with a complete metric space. Take a nested sequence of non-empty closed subsets of X. Nested means one contained in the other, but the other way around. Fn contained in containing Fn plus 1 and so on. So here they are decreasing here. Okay nested could be the other way around also. So here they are decreasing but that comes automatically after the second condition here. So delta Fn denotes the diameter of each of them. So this sequence of real number converges to 0. So this is also condition. So each Fn is closed, which contains the next one and the diameter goes to 0. Then the statement is that intersection of all these Fn's consists precisely one element. This is stronger than saying that it is non-empty. This is precisely one element. The proof is surprisingly very simple. Surprisingly very simple. You will see that. All that I do is Fn's are non-empty. So pick up Xn belong to Fn for each n. Then look at this sequence Xn plus m. Okay it is less than delta Fn because both of them are inside Fn. The delta is what? Delta is the diameter is supremum of all such numbers where X and Y range over Fn. Therefore the distance between Xn and Xn plus 1 becomes less than delta Fn. But delta Fn itself tends to 0. Therefore this can be made less than epsilon etc. So as soon as this is a Cauchy sequence, this will be also Cauchy sequence. That is the condition. So we have got a Cauchy sequence. But now I use that X is complete. Therefore Xn is convergent. So let us take X to be the limit. Okay now we also know that if you have sequence Xn, you see the entire sequence Xn is not in any one of the sets. But suppose you choose some Fk here, then k onward that sequence is there. The limit of that portion of the sequence is also X. Right? The first k terms does not matter here. Therefore each of these sequences can be thought of as a sequence inside Fn. Okay? And the limit therefore must be inside this closed set because Fn's are closed. So it follows that this limit point is inside all the Fn's. So here we have used that Fn's are closed and they are monotonically, you know, decreasing one content in the other. That is also understood. That just means that intersection is non-empty. The second part that it must be a singleton comes very easily because of its delta Fn goes to zero. You see that this, the diameter of this one will also become zero. So diameter is zero, the set can be only singleton. Anyway, if Y is not equal to X, you know, then DXY will be positive. Therefore it will be bigger than delta Fn because delta Fn is converging to zero. Once it is bigger than delta Fn, both X and Y cannot be inside Fn. Right? If it is not in one Fn, it cannot be in the intersection. So any point which is not equal to X is not inside the intersection. So there is only one point. So that is the proof. Now I have to make a definition because there is some term in the Benach contraction mapping that in the name itself. So it will come in the statement of the theorem also. So take a function from one metric space to itself or to some other metric space also. This will work. But right now I need only this definition. We say F is a contraction mapping or just a contraction. If there exists a positive constant strictly less than one. This strictly less than one is important such that the distance between FX and FY is less than or equal to C times the distance between X and Y. For example, if C is half, each time you apply F, okay, so two points at distance one will go to distance less than half. Next time they will go next 10, 1 4 and so on. Okay, that is the meaning of contraction mapping. Okay? If you take the layman's language, a map of a say your campus or a country or just a state, if the map is up to scale, definitely it will be a contraction mapping. Okay? From the actual object of which it is a map to the map, you can think of holding the map in your hand sitting, you know, you are standing in the country. So the map is inside, so the function F is from the country into the country, but it is a contraction mapping. Now what does this theorem say? Let us say, okay. So for example, contraction mapping is always continuous because if I can, I can control, I want to control distance between epsilon, this one less than epsilon. I can make this one less than epsilon by C, that is all. So it is always less than epsilon. So continuity is obvious. By the way, this condition constant C on both sides, we are familiar with that is equivalence of matrix, right? Similarity of matrix. So this is not a strange condition at all. This is quite a nice condition. It implies continuity. Contraction mapping can also be defined from one matrix space to another matrix space, which I already told you. So the theorem says that if X is a complete matrix space and you have a contraction mapping F from X to X, then F exists a point. Fixed is a point means there is some X such that F X equal to X. Moreover, such an X is unique. So then there exists a unique X belong to X such that F X equal to X. That is the statement. Once again, proof is this time slightly, little longer than the proof for Cantor's Intersection Theorem, alright? So let us first take care of uniqueness. Suppose there are two points X and Y such that F X equal to X and F Y equal to Y.  D of F X, F Y. F X is X, okay? F Y is Y. So it is DXY. DXY equal to D of F X, F Y. But because it is a contraction mapping, it is less than would C times DXY. But C is less than 1. So this is observed unless DXY is 0, which is same thing as unless X is equal to Y. So the proof of that uniqueness theorem, uniqueness part is as easy as in the first part. Now for the existence. So one may say that, you know, this Benach's contraction mapping, where he got the idea? Maybe he got the idea from Newton. People who are familiar with some miracle analysis and so on, they will know this kind of iteration method, you know, which was again used by Picard and so on. Start with any point, okay? Apply F. If it is different, apply F again. If it different, apply F until you get, you know, whatever you have F X equal to X, that is the whole idea. But it may not happen at all. So that is where the ingenuity comes. So don't give up the method yet. So look into deeper into it. That is the point. So given, if you start with X1 belong to X, inductively define Xn to be the image of F of Xn minus 1. So apply F to that previous one and take that as Xn. So X1 is any point, I do not know. X2 will be F of X1. X3 will be F of X2 and so on. The claim is that this Xn is a Cauchy sequence. So this time, it is not all that obvious. You have to do little more work, that is all. Otherwise, you know, in the case of CIT, it was easy to see that Xn is a Cauchy sequence. Once it is a Cauchy sequence, completeness comes into picture. There will be a limit point, the limit point of this sequence. The beauty is that that limit point cannot go anywhere. It has to be that F X is equal to X. So that is the point we are seeking. So let us see how the proofs of these claims are coming. So put r equal to distance between X1 and X2. We are assuming that X2 is not equal to X1. If X1 is r equal to X2, then there is nothing to bother about going further at all because then what is X2? X2 is F of X1. If it is equal to X1, we are home already. So we are not going to do that. Put r equal to D of X1, X2. Then look at distance between X2 and X3. That is by definition, distance between Fx1, Fx2 because X2 is Fx1, X3 is Fx2. But then this is by contraction mapping part the C times distance between X1 and X2. This we have denoted by r. So it is a C times r. So distance between X2 and X3 will be less than or equal to C times r. What happens to distance between X3 and X4? One more C will come. One more C will come and so on. So what happens is inductively distance between Xn and Xn plus 1 will be less than or equal to C power n times r. So X2 and X3 is the r. Xn and Xn plus 1 will be just the index will be 1 and less here. So maybe I should write it Xn minus 1 times r which I had written earlier. Anyway, it does not matter. Then it follows that distance between Xn plus 1 and Xn plus 2 is less than or equal to C power n plus 1 times r. Once you have proved this one. Therefore, if you look at distance between Xn and Xn plus m, see we are trying to prove that this is a Cauchy sequence. So distance between Xn and Xn plus 1 is less than or equal to I range from 0 to m minus 1. Distance between I start with Xn go to Xn plus 1, Xn plus 1, go to Xn plus 2, Xn plus 2, go to Xn plus 3. I use triangle inequality and then I get this summation. The distance between Xn plus I to Xn plus I plus 1. So this is a summation. But each of them is r times C raise to n plus I, 0 to m minus 1. So you can rewrite it as r will come out. I range from n to n plus m. Do not worry about n plus I. Now it is C I. It starts with I equal to instead of 0, I equal to n. This is just a rewriting this. What you know is C is less than 1. Therefore, this is a geometric series. Mother of all series. So this is a convergent series. We know how to conclude the limit also anyway. So geometric series because C is less than or equal to 1. C is less than 1. And hence the partial sums say 1 to n C I, they are cos sequences. So this is just difference between n plus 1 partial term to nth term. Only n to n plus 1 I have taken. So if this partial sum is a cosy sequence, this number can be made less than epsilon, any epsilon bar r. So r times epsilon will be less than epsilon for sufficiently large n. That means this is a cosy sequence. So we have got starting with a point x and repeatedly applying f, f, f and so on, we have got a cosy sequence. That sequence converges, take the limit. Now we apply, if we say continuous function, we apply f 1 x, f of x, what is x? x is the limit of all these x n's. But x n I can write to the f of x n minus 1. So I can take this x n plus 1 and write to the f of x n because f is continuous. Applying f of x n, the same thing as limit of x n plus 1. But limit of x n plus 1 or x n plus 2 or whatever it is, add tends to infinity is same limit which is x. So x is a fixed point of f, uniqueness you have already proved. So the third theorem takes a little more time. Therefore let us first consolidate these two theorems today and we will do the third theorem next time. So let us look at some easy comments here on this. Look at the Cantor's Intersection theorem. There are, what are conditions? Delta f n goes to 0, f n or a n whatever. a n's are closed, x a is complete. And a n's are one contains the other. The point is, if you violate any of those conditions, something will go wrong. So conclusion will not be as strong as you like. Conclusion may not be there at all. For example, delta a n does not tend to 0 but because they are smaller and smaller it may tend to something fine but positive. Then you will not get the uniqueness. You may be able to prove the existence that it is namely intersection is non-empty. There is some point but you will not be able to prove that it is a unique point. Similarly existence itself is violated if you do not put the hypothesis nested. If you take arbitrary subsets f1, f2, fn without any relation between them maybe half of it is contained in there or they are disjoint and so on. There is no intersections can be easily empty. That is not very surprising. The third comment I make is here. It is easy to construct a nested sequence a n of close of sets of 0 to infinity. By the way, 0 to infinity is complete metric space such that all the diameters are infinity yet the intersection is empty. So it is not going, not only it is going to, it is not going to converge into 0, they are all infinity. Intersection is empty. Can you think of a set here? What should be a n for each n? Remember it must be close of sets and a n should be containing a n plus 1, containing a n plus 2 and so on, smaller and smaller. Can you think of that as a sequence? Yes sir, if I take n to infinity close to infinity. Put a n equal to n to infinity very good. So intersection is empty. It satisfies all other things but now delta n is not going to converge into 0. All the time it is infinity. Yet the intersection can be empty. So here another question is there. Can you construct a nested sequence of subspaces of a n with finite diameter such that intersection of a n is empty? You can do it in R itself actually but this time I am not putting you see nested sequence I am putting diameters also finite. I am not saying diameters are converging to 0 but what I am not saying is that they are closed. Right? There is no word closed here. So is it possible now think of some subsets of open interval 0, 1. Open interval 0 to 1 by n. n or instead of going up n to infinity 0 to 1 by n. Right? Intersection will be empty. Now can you do the same thing as you did a but this time a n's must be all closed. Closed subsets nested that's all. Diameters I am not putting. Diameters can into 0. Is it possible? This is this is a little more harder right. Think about this. The next one is a little more harder also. Can you do the same thing as B but in the usual metric space in the R with the usual metric? So this is a hint for this one. Maybe you can change the metric okay and then try to do that not in the usual metric. So C is much harder to think about them we will answer them in the due time. Maybe as an assignment you can work it out then we will explain if after checking your answers we will explain you the result okay. So that is all for today. So let us meet next time. Thank you.


Senior night for Bemidji Boy soccer as they hosted East Grand Forks. First minute of the game, the Green Wave passing it back to their goalie, a little bit off-target. Paul Messague takes advantage, first varsity goal of the year. You take him any way that you can. In the 18th minute, Bemidji on the attack, Blaine Sauer with the cross. Ethan Mach, the left-footed kick, nothing but net. They go up 2-0, Mach gets another, and Bemidji wins 3-0. Lakeland PBS


Thank you very much. First of all, I'd like to thank the organizers for giving me a chance to talk in this wonderful workshop. In this talk, I'd like to talk about our works on so-called buy-on southern points, which are expected to play an important role in understanding nonpartisan physics and research instruction in a CPM signal model. So this talk is based on the series of papers in collaboration with these people. So one of our motivation to study resurgence is to understand how to evaluate the path integral in physical system like field theory. Quantities like partition function is usually given in the form of path integral like this and formally it is said that this kind of path integral is a kind of integral over all field configurations. But of course, it is almost impossible to expressly evaluate this kind of integral over all field configuration. So we have to use some approximation method. One of the approximation methods, which we can use almost all cases, is the part of the expansion with respect to some coupling constant in the model. Such part of the expansion gives good approximation if the coupling constant is small. But it has to be known that such part of the partition series is a kind of factorially divergent asymptotic series and in many cases such part of the partition series is a model. So we have a kind of imaginary ambiguity, which is corresponding to the singularity on the plane. So we expect that we have to take into account nonproductive subtle points, the contribution of nonproductive subtle points, which usually takes this form. Here S-sigma is the value of action at the subtle point sigma and this power series is the kind of perturbation series around subtle point sigma. And then we construct trans-series by appropriately summing these subtle point configurations. So then we expect that this kind of trans-series gives a correct physical quantity and we expect that there is no ambiguity here. So what you'd like to do is to check if this really gives the correct physical quantity or not. So the first step to construct this kind of trans-series is to find the subtle point or critical points of the action. In terminology of physics, these subtle points correspond to the solutions of the equation of motion of the action S. But as in the case of ordinary finite dimensional integral, when we construct trans-series, we have to take into account not only real solutions, but also complex subtle point solutions. So we have to consider another analytic continuation of action by regarding the action as a function of the homomorphic variable, phi, by complexifying that model, and then we can find the subtle point by solving the Euler-Lanche equation, which can be obtained by taking the variation of action with respect to this homomorphic variable. Then we can find the subtle point configurations corresponding to, for example, part of the vacuum and instant configuration and so on. Then next step we have to take is to find, to determine how to sum this trivial subtle point contribution. So we have to determine which subtle points are and which integration contours are relevant in this trans-series. So this can be done by using the left-shift-temple method. So in this left-shift-temple method, we first determine the symbol j sigma and dr-temple k sigma associated to each subtle point sigma. Then we can use this symbol j sigma to calculate the subtle point contribution to the partition function, z sigma, and we can determine the coefficient in this trans-series by looking up the intersection number between this dr-temple and original integration contour. So this is the procedure of this left-shift-temple method, but in general it's very difficult to perform this kind of procedure in infinite dimensional configuration space. So this is a kind of challenging problem. In this, in our work, we kind of indirectly solve this kind of problem by using a kind of reduction from infinite dimensional configuration space to finite dimensional subspace of this infinite dimensional configuration space. And then by applying the left-shift-temple method in the finite dimensional subspace, we calculate, somehow calculate this kind of partition function and the physical quantities. So this is one of the main points I'd like to talk in this talk. I'd like to tell you in this talk. Okay, so the model we are interested in is the cpn-1 sigma model, which is described by fields, which can be interpreted as a map from to the base space M to target cpn-1 and action of this model is given like this. In this talk, we identify this field as the inhomogeneous coordinate of cpn-1 target space and this GAB is the Houdini study metric of the target manifold, target cpn. So because of this SN isometry, this model has SN symmetry. And this G is a constant, a bare coupling constant, and we are, we would So we consider expansion and nonpart of the effects with respect to this bare coupling constant or renormalized coupling constant which will be which will appear after renormalization procedure. Okay, so this is the basic model we are interested in. The reason why we are interested in this kind of cpn-1 model is that this is, the model can be understood, interpreted as a kind of 2D analog of 4D gauge theory which, like QCD, which describes our world. So it has been known that 2D, two-dimensional cpn-1 model can be interpreted as a kind of toy model of 4D gauge theory in the sense that they have many common properties like a sympathetic freedom and instanton and large end and mass gap and so on. So our, we expect that this 2D cpn-1 model has a similar research instruction as the 4D gauge theories. So we expect that we can we can accept that we can obtain some hint for so called IR renormal problem from relatively simple 2D models. So our motivation is to use nonlinear 2D cpn-2 model to get the hint for this IR renormal problem. So let me explain what IR renormal problem is. So a IR renormal problem, okay, so in generic physical theory, physical models, it is said that factorial growth of the perturbation theories is related to the factorial growth of the number of Feynman diagram contributing to the N's order in the perturbation theory. But in the theories like 4D gauge theories, it has been known that there is another source of factorial growth of the perturbation theories. For example, this kind of diagram which has N fermion groups in the larger loop gives a kind of factorial large contribution like in factorial. So by, so this is, this gives the factorial growth of the perturbation theories, and if we take the, what a resumination of this kind of diagrams, then we get singularity in the model plane at 1 over g square N. So, so there must be some non-trivial subtle point corresponding to this singularity, but this can cannot be the Yang-Mills instanton because the action, the value of action for this Yang-Mills instanton is like 1 over g squared. So this is this is much larger than the value of the this thing, the position of this singularity. So, and particularly this action of this instanton vanishes in the two-fifth limit, in the large end limit, and on the other hand, this singularity does not this, it does not go away in the large end limit. So this Yang-Mills instanton can never be the singularity, subtle point corresponding to this singularity. Do you understand, in the U.S. U.P.N. although you don't go, you can say, please stand or go to a large end limit, yeah? No, no. You cannot perform fields, it depends on the metric on the surface. Yeah. So, okay, anyway, so from this argument, we expect that there is another other subtle point that is called renormalon, and this has been a long-standing problem, because this we could not, the subtle point corresponding to this renormalon has never been found for a long time. So this is the IR renormalon program. But several years ago, there was Algiers and Instalt gave a proposal for this candidate for this IR renormalon. That is called Bayon. This Bayon is a field configuration, which consists of a pair of fractional instanton and anti-fractional instanton. So these two objects are so prior and important around in this talk. So let me explain what... Is it a zero-typical church? Okay, yes, right. They don't have that. Bayon doesn't have a typological church. Okay, let me explain what they are. So Oh, we heard that. Let me... So let us look at some figure just for fun. Okay, this is a figure of an instanton on cylinder. Instanton in CP1 signal model on cylinder. So here this red region correspond to the location of instanton. And if the size of instanton is much smaller than the radius of this compact direction x, this instanton looks like an ordinary one single instanton. But if we shrink the size of S1, then this instanton splits into two objects. And this is in the case of CP1 signal model. If you consider CPn-C1 signal model, single instanton splits into n-fractional instanton. So, okay, each of them are identified with a fractional instanton. So, okay, so this plays an important role. So let me explain this object more in detail. So, okay, so the model we consider is the CPn-1 signal model on cylinder. And in this talk, I will always call the non-compact direction as Euclidean time. And I will denote it by symbol tau. And spatial direction is denoted by x, and it is compactified with period 2 by r. Then action we consider is like this. So this is actually a little bit different from the previous one, because the derivative is now replaced with the covariant derivative. So this means that there is a, so we introduce the background gauge field for SCN global symmetry, MA, which takes value in the Coulton subarrangement of SCN global symmetry of this model. So we introduce this kind of background gauge field. So basically these parameters can be arbitrary, but if you consider this specific value of the background gauge field, and this action has enhanced SCN discrete symmetry. So this value of background gauge field is called a GN symmetric background. And the important point is that if we choose this background, then it is expected that this model has so-called adiabatic continuity. By using this, we can continuously connect the, we're coupling the description of this model to the strong coupling description on R2. So anyway, we are mainly interested in this, in this GN symmetric case. Okay, anyways, let us solve the equation of motion of this model to find the subtle point of action. We can easily find a solution of the equation of motion by rewriting the action into the sum of positive semi-definite term and topological charges. In this model, there are two relevant topological charges. One is ordinary instanton number, which is given by the integral of the k-reform, a proof of the k-reform. And another topological charge k is given by this quantity. So this is, so sigma is kind of obtained by the fairing of the moment map of SCN and the background gauge field. But anyway, this quantity gives a difference of values of this sigma in the future infinity and the infinite past. So this means that this quantity depends only on the boundary conditions. In this, in this sense, this is topological. So these two topological charges are invariant under continuous deformation of the field phi. So we can easily get the solution of the equation of motion by minimizing the positive semi-definite part, which takes this one. So this is positive semi-definite. So we can easily minimize this quantity just by a requiring that this equality holds. Then we get these PPS equations. I'm sorry, this m adjusts constants? M, M. Yeah, right. Yes. So you just deformed the standard of the ACPR model and zero set of M-rays. Okay. Just the question, because in series, there's a counterterm here, because there's an organization. What is the counterterm of this? Actually, at this moment, we don't consider, we just consider only bare action. We are, yeah, we'll introduce the counterterm later. Should we jump with this correction direction by something? Yes. Okay. So yeah, now we are considering only bare action. So this is a VPS equation. This can be easily solved by, this is just a very simple equation. So we can get the general solution like this. Here, F, A are arbitrary low-down polynomial of the coordinate on the cylinder defined in this way. Okay. So this is a general solution. So we, by choosing various F, A, then we can get various VPS solution, like solution of equation of motion. The most basic solution is the single instanton solution, which can be obtained by setting one of F, A to be degree one polynomial and others to be zero. Then this configuration is a kind of single instanton solution because the instanton number is one. And then we can calculate the action, the value of action for this configuration. It's given by 2 pi over g square. But this value is much larger than the value of action expected to be a sub-point for the iar phenomenon. So this... What is the definition of instanton number? It's all the characteristics of the bundle, vector bundle over r-class, but it's trivial bundle, so it's zero. No, no, no. But it's kind of normalized because it's not complex cases, integral curvature. Okay. So instanton cannot be the iar phenomenon. So we have to find another solution that can be responsible for this iar phenomenon. That is a fractional instanton, which can be obtained by setting one of F, A to be constant and others to be zero. So this is the solution of a fractional instanton. And this solution has two degrees of freedom corresponding to position-modulated parameter and internal phase-modulated parameter, phi. Anyway, if we plot the function, sigma, as a function of tau, then we can see this kind of kink profile. So basically this solution, fractional instanton solution, is a kink solution corresponding to a kind of tunneling process between different minimum of action. So, and we can calculate the value of action for this kink solution. Then we get this value. And if you set the value of this background gauge field to the gn symmetric point, then we get this value of action to pi over g square n. So this is one over n times single instanton solution action. So this can be, this is... Sorry, this is sort of a functional evaluation, right? Sorry. This is sort of a functional evaluation. Okay, so that you get solution plug-in back to the... Yes, yeah, yeah. So this is one over n times single instanton. And this is the same order of the expected value of the action for the IR renormalon. So this can be IR renormalon. But actually the fractional instanton does not contribute to the partition function because partition function contribution function receives contribution only from periodic configuration on this Euclidean time direction. It's compactified with period beta. So fractional instanton is a kind of kink tunneling process. So this cannot be periodic. But if we consider bion configuration, which consists of kink and anti-kink, then this kind of configuration can be periodic. So this kind of bion can have a non-trivial contribution to partition function. So the question is if bion, this kind of configuration, can be identified with the renormalon or not. This is the question we want to consider. Okay, so in our work, we explicitly calculate this bion contribution by using the lifted-temper method. So I would like to talk about this explicit variation of this bion contribution. Can I ask a question? How do we know that it exists in the m-acool zero limit? In the m-acool zero limit, this solution doesn't exist. But... So the point is that... So this is defined on the cylinder with this periodic boundary condition. And we expect that if we choose this value, then there is an adiabatic continuity. Then if we take the r-infinity limit, this vanishes. But because of this continuity, the theory on r2 without this m is related to this theory. How does one prove this assumption or just define it? Yeah, actually, in the large-end limit, there is a proof that there is no... Actually, in the large-end limit, there is a kind of, let's say, volume independence. So we can show about... For general end, it's a kind of conjecture, I think. So what do you mean? Can I... I will never obtain bion solutions? Or is it unstable? Sorry. In large-end limit, you don't have bion solutions? No, no, actually. I think we expect that there are bion solutions, also in the large-end limit. But then these will be different ones now. Different? Yeah. Why do you think so? I mean, because it will be equivalent to the equivalent of this formula, because this deformation parameter from the equation is gone. Actually... Oh, yeah, yeah. If we take the symbol of large-end limit, this will appear, but if we fix this r, then we can get some configuration. Okay. So this is the intercombination. Yeah, yes. So you're reading that if you don't time, it's just even, so it's... Well, there is no temperature, right? Okay. And then you introduced the temperature and reading the solution, which depends on your flow, but not on x, right? Right. Something lost. Okay. At this moment, I just considered zero-temperature limit. But when we calculate the partition function, we introduce the temperature. So we consider... The solutions which we will reach and they don't depend on x, right? Don't depend on... The solution, okay. The solution, right? There was only tau dependence, but not x dependence. No, no, next. And they still satisfy the equations of motion, right? Yes. So, okay. So let me explain our model. So the model I want to consider is the 2Dn equals 2 to supersymmetric cpn-miron-sponsible model. Because, actually, this supersymmetry is not necessary to calculate this biome contribution, but it's very convenient to consider supersymmetric model because we can use exactly that to check our biome solution is really correct or not. So this is the model. We added some fermion fermionic terms. And, okay. As I said, to calculate the partition function, we need to compactify the tau direction. So, okay. We introduced a compactified period of this compactified time direction beta. And x is also compactified. So we consider theory on torus. And as I said, we considered a background gauge field along this compactified space direction. And we introduced the same background gauge field for both terms and fermions because in this way, we can keep the supersymmetry in this model. So from now on, you'll be having toric partition functions, right? Actually, okay. Yeah. Actually, we want to consider a kind of generating function of this observable by adding a source term to this Lagrangian. So we want to consider this observable by evaluating the path integral for this action. And we consider endpoint correlation function of this operator by differentiating the generating function. What is M there? Sorry, M. M is the moment map of this. M is the background gauge field. This takes value in the SEM sub-algebra, the algebra of the SEM. So we consider this point correlation function. Actually, we can calculate, in our paper, we calculated the bionic contribution in general CPN model. But just for simplicity, let us focus on the case of Cp1 signal model. Then the explicit form of action looks like this. And we consider generating function for this height of this Cp1. And we consider the kind of correlation function of this operator. So the reason why we consider this kind of correlation function is that by taking the small radius limit of the space direction, then we get quantum mechanics in the 1D limit. In this 1D limit, we can exactly calculate this correlation function by using the Schwerding equation. So the zero-point function is just a grand state energy. And it's, of course, there, because of supersymmetry. And one-point function is given like this. So this contains infinitely many non-part-of-d terms. So this is completely fully non-part-of-d. And more interesting quantity is the two-point function, which takes this form. And actually this has a non-trivial research structure. So let us closely look at this quantity. So by expanding with respect to the coupling constant G, we get this part of the variation series for this two-point function. So the coefficient of this series is gamma n plus 1. So this is factorial divergent. But if we look at the non-part-of-d part, we have here, there's a, so imaginary part of this non-part-of-d contribution jumps at when coupling constant pathodility real axis. So this quantity has this kind of non-trivial research structure. So another question we want to check is that if this kind of structure can be reproduced from the analysis of biome. So that's another problem we want to discuss. Okay, so the first... What is E2? How do you compute this? Okay, E2 is the kind of this kind of two-point function integrated over this Euclidean time. And we can use... So in the 1D limit, this model deduces supersymmetric quantum mechanics. And we can solve the Schrodinger equation in the supersymmetric quantum mechanics. By using the solution of the Schrodinger equation, we can calculate this two-point function. Exactly. This is something that's trickling at zero radius or something. Zero radius remains, yes. So we can get this kind of non-trivial research structure and we want to check if this non-trivial structure can be reproduced from the biome analysis. Okay, so let us solve the... Let's first determine the biome solution by solving the equation of motion. So we consider the complex equation of the target space by the complex space. Then we use the coordinates of this space, phi and phi tilde, which... So this... The original CP1 target space corresponds to phi tilde equal to the complex conjugate of phi. And then we consider the analytic continuation of action by regarding the action as the holomorphic function of phi and phi tilde. And then we solve this equation of motion for this by taking the variation with phi and phi tilde. Because now we are considering the two-dimensional field theory. So the equation of motions are two partial differential equations. So it's very difficult to solve in general. So we consider these x-independent standards like this. So this x-dependent... If we use these x-dependent standards, we cannot consider several points which contains ordinary instanton, because instanton depends on x-direction. But if we are interested in the leading order non-tripartial contribution, which is expected to be given by Bion, then we can ignore x-direction because Bion's configurations are independent of x. So we use these x-independent answers. Then the equations of motion reduce to two ordinary differential equations. And actually this model has two symmetries. One is time shift symmetry and phase rotation symmetry. So we have two conservative charges in this model. And the degrees of freedom of this model is two. So we can use the two conservation laws to determine and to completely fix the form of the solution in this way. So the solution is essentially given by the Jacobi-Eleptik function. And there are several parameters A omega k. They are just complex constants depending on the parameter in the model and a pair of integers pq. So pq is our integers of the solutions, which takes in this range. So this means that this solution we have infinitely many subtle point solutions. And the important point is that these are complex subtle points because for generic p and q, phi tilde is not equal to phi bar because these are complex constants. So they are complex subtle points. So let us look at the simplest example of a solution. So this is a real biome solution corresponding to p1. This is a single biome solution which looks like this takes a form of sine hyperbolic in a very infinity limit. So this is the orbit in the target Cp1. So this corresponds to the tunneling from north pole to south pole and if we plot this height function as a function of tau, then we can see that there are kink and anti-kink. So this is a biome configuration. So this is called real biome solution because in this case phi tilde is equal to the complex conjugate of phi. So this is a solution in the original Cp1. But if we consider only this kind of solution, we can show that suji grand state energy becomes non-zero because of this non-part of the contribution. So we can index zero in this case. What is written index? Sorry, this is... From zero, then we can index past the zero, right? This is... Yeah, okay, so this is... Okay, written index is n. n. But then energy cannot be different from zero. If written index is non-zero, energy of the vacuum is zero. Vacuum is zero. Vacuum is... So this contradicts with the suji grand state. So there must be another contribution to cancel this contribution. So that is a complex biome contribution. This is also a p equal one solution with p equal to one which looks like a cosine hyperbolic in a better infinity limit. So this is called a complex biome because in this case phi tilde is not equal to phi bar. So if you brought the height function as a function tab, then we can see that this is also like a tunneling solution. But in the tunneling process this value of height becomes complex. So this is very peculiar solution. But we need this solution to guarantee that the suji grand state energy is zero. So this kind of complex solution is important to obtain the result consistent with suji. OK. So these are single biome solutions. And for general p and q, for example, this is a figure for p, q equal three one. So there are multi-bion in the configuration. So essentially p, integer p is a number of biomes. And q is a kind of a label of subtle points in p-bion sector, which basically controls the combination of complex and real biomes in the configuration. So OK. So this is biome solutions. So now we have subtle point solutions. Now let's consider the semi-classical biome contribution by calculating the d-ding order term in biome contribution this part. So naively, we can calculate this kind of quantity just by evaluating the determinant of this infinite dimensional version of matrix of the second derivative. But actually we cannot do this because in a weak coupling limit we are interested in, there are some nearly flat direction of action. More precisely we can show that this matrix in the weak coupling limit has some zero eigenvalues. So this means that in the weak coupling limit there are quasi-zero modes for which we cannot perform the Gaussian integration. So we have to be more careful carefully treat the integration along this direction. So to do so let us define a so-called body of action so roughly speaking this body of action is a kind of finite dimensional subspace on which the real part of action is nearly flat. To define this precisely let us define this set of configuration called value solution by this parameterized by a quasi-mosaic parameter corresponding to the direction of this zero eigenvalue of this operator. Then by this value solution can be obtained by solving this value equation which is obtained by projecting the equation of motion until the normal direction to this direction. Anyway so we can define this kind of set of configuration. So let me briefly before showing the solution of value equation let me briefly mention about the relation between value and the symbols. So symbols are defined by solving these flow equations in the value, this finite dimensional subspace, the flow equation is given like this. Here S effective is the effective action on the value and this GAV is indistimetric on this finite space finite dimensional space and we can show that if we have the solution of the flow equation in this body we can embed that solution into the solution of this flow equation of original space. So this means that symbols in value is contained in the symbols in the original configuration space. So this factor can be used, this is very useful when we consider intersection numbers and so on. Anyway so we can actually explicitly write down the solution of value solution in the case of single biome and weak coupling limit and better infinity limit. So this is the solution, this is actually a kind of kink anti-kink configuration because this is some of kink anti-kink and this value solution is parameterized by one quasi-modular parameter eta whose real part corresponds to the relative position of kink and imaginary part corresponds to the relative phase degrees of freedom. This is the solution and then actually this set of solution contains real biome start point and complex biome start point corresponding to these specific values of quasi-modular parameter. Okay, by using this value solution we can compose the degrees of freedom into the direction along the value and normal direction in this way. Then we can reduce the action in the weak coupling limit as in this way. So here this is effective action biome effective action which is defined in this way and this is basically the function on the value, action of the value of action on the value and start all points of this function correspond to the biome solution real biome and complex biome solution. And for normal direction and fermion direction we get Gaussian form. So by evaluating the integrating out the normal direction and fermion direction we basically get schematically we can write the single biome contribution in this way. So here this is the one loop determinant corresponding to the functional determinant which can be obtained by integrating out the normal direction and fermion direction. And we can evaluate this one loop determinant by using the counter-climbing mode expansion which is basically the Fourier expansion and then for each counter-climbing mode we get this operator, differential operator delta B and delta F becomes a kind of 1D shredding operator. So we can use a kind of technique to calculate the 1D calculator functional determinant for this kind of 1D shredding operator. Are you still considering 2,2 supersymmetric model? Sorry. Are you still considering 2,2 supersymmetric model? Yes. Yes. But the background is non-BPS so there is no such structure. That seems with the fermions. Yeah, right. So by using this kind of technique to calculate the 1D functional determinant of the 1D determinant then we get this x is given like this so this summation over the counter-climbing mode is divergent. So this is a kind of ordinary UV diverges in field theory so we can use some regularization in standard regularization to regularize this divergent sum. Then we get this expression for the 1D determinant. Here now there is a cut-off scale introduced to regularize this quantity. Then by using this 1D determinant we can combine this bare effective action to get the renormalized effective action which takes this one. This renormalized effective action takes depends on the renormalized parameter, epsilon tilde. This is shifted by the quantum effect and constant Y which depends on the renormalized coupling constant which is defined in this way. So we get renormalized effective action. R is here. R is equation. R is radius. R is compactification radius. Compactification radius, yes. Then finally we get this form for the single-bion contribution. So this is finite-dimensional integration over these quasi-modular parameters. But we are now considering the complexized theory. So quasi-modular parameters are also complex files, so we have to determine which subtle and which contours are relevant for this quantity. So that can be done by using the restive number method. Actually for this renormalized action we can explicitly determine, solve the flow equation to determine the symbol and dr-thimble. So this is a picture of the dr-thimble. Actually this is a 3D projection from a four-dimensional space. But anyway we can explicitly determine symbol and dr-thimble. Then we can find intersection number and integration path explicitly. Then we can leverage the quasi-modular integral. Then we get this result for the generating function. Single-bion contribution to the generating function. So this is very complicated. But the important point is that this contains a jump at this imaginary g equal to zero. So this is so yeah if the sergeant works in this model then this should be related to a variety of singularity at the value of this exponential. So furthermore we can see from this jump of this nonpartavity part we can how to say So this implies that the partavity part of this quantity should have this large order behavior. So this is kind of how to say prediction from the bion analysis. But it's very difficult to check this because high order, large order behavior is very difficult to calculate in the field theory. But if we take the 1D limit we can use the shredding equation and we can calculate this kind of high order behavior by using the partavity analysis by using the tools like Vendor package and then we can compare the Vendor analysis and bion analysis by taking the ratio of this coefficient then taking the large looking at the large behavior we can see that this ratio approaches one for any value of the source parameter epsilon. So this means that bion analysis is resurgent. So bion result is completely consistent with resurgence argument. Okay So this is the result in the CP1 model. We can easily generalize the result to the CPn-1 model and see that there are n-1 types of bion but for each bion we can repeat the same type of calculation then we can calculate the single bion contributions. So this is a result for the single bion contribution. This is a jump of the single bion contribution. So this is there is a jump very part of the generating function but this is a little bit so difficult complicated. So let us focus on the the geometric point by setting MA to this value. Then we get this expression for the generating function. So important point is that this is proportional to quantity. So this is mean that there is we have a jump in the imaginary part of this generating function. So this means that for the part of the perturbation series perturbation series should have variable singularity corresponding to this value of action. This point 4pi over gr2n so this is nothing but the expected value of the action for the IR normal. So this means that this result is completely consistent with the proposal that bion is responsible for IR normal. Okay, so this is okay. So yeah another thing I want to mention is that because in the 1d limit our bion solution is actually the general solution because there is no x dependence. So you can try to sum all other multi-bion contribution and p-bion contribution can be calculated in this way. So this is very complicated but also in this case there is a jump here and by summing over a bion number we can get the trans series for this. This is the result. We can see that the grand state energy is zero and this is completely consistent with the exact result and we get this expression for the two-point function and here we have a jump in the imaginary part of the two-point function. Actually this is completely consistent with the resultant structure and from the exact result. So this means that our bion calculation is completely consistent at all order in the bion number. Okay, so let me summarize the talk. We explicitly calculated bion contribution in cpn-1c model and we got completely consistent result. We expected the structure and we got consistent result with the proposal that bion is related to IR renormalon but to show that if this bion is really identified with IR renormalon we have to check that the higher order behavior of the perturbation series is really agree with our bion result. So we have to check explicitly the higher order perturbation series in cpn-1c model. This is an important future work. So as of here, thank you very much. Thank you very much. So any questions? Well I actually have two questions. One is did you try 0,2, and 0,1 supersymmetric signal models which kind of interpolate these two extremes where you have all control and no control? Because in four dimensions we expect that confinement is governed by QCD strings. So in what sense this is analog of QCD string solution? String solution. Okay. That's the right mechanism for confinement in this two-dimensional model. Yeah, actually that's okay, for the first question, we tried n-course 1,0 but in that case yeah, actually we couldn't calculate the So what was wrong? In a quantum mechanics limit we can calculate anything and the result is actually almost the same. But in the case of field theory because renormalization is much more complicated. So yeah we cannot do this kind of thing. So yeah we cannot we couldn't calculate anything in the case of field two-dimensional n-course 1,0 and so for the second question okay, so so it's about confinement Yes, actually yeah but I have to say that 2D CPU and second model is very similar to Gaetz theory but not exactly the same. There are several differences. For example 2D there's no, for example symmetry breaking phase transition in the 2D model but in 4D theory there can be such phase transition. So yeah, they are similar but there are differences. So I think we cannot use this completely this cannot be the complete analog of the 4D theory. Yeah, perfectly. This renormal also kind of improvisation on this. Yes, yes, but the renormalizations would provide that direction. And in general it kind of got confusing when we do this. But in a more complicated situation that several running conflict constants means that actual actions some of the very big numbers are actually seen since how one can justify this people's speech because you have sort of equations more than running conflict constants as well. In your situations just to scale a conflict constant is the same equation Yes, okay. So yeah, I think that the point so because we are now considering weak coupling regime which means that coupling constant is small but to access strong coupling regime we have to use something like this kind of adiabatic continuity. So we cannot perform this kind of analysis with small coupling regime but we can use some this kind of property by using to access that regime. Any other questions? Maybe I have just a small question which you talked about the Foubini-Strudy metric on CPN, last one. But did you ever use the singularities? That has some polls because there's a denominator. Do you use the singularities of that somewhere? Similarity. Foubini-Strudy metric. Yes. Do those appear in the calculations? The singularities of the Foubini-Strudy metric. Singularity. Complex file. Complex file. Okay, okay. Actually, yes. Actually, yes. It's chart similarity. It's not a physical similarity, right? Yeah, actually this complex It's singular in the complex Yeah, right. In a complex case. In this complex file solution hit that singularity if coupling constant is the real. But if we introduce complex file coupling constant, we can avoid that point. Actually, this is an important point. Thank you.


Okay, let me get started here. I am Really proud to be here, and I want to especially welcome Mark and Shelly Heath's parents And I'm proud to assign this bill into law It's going to strengthen Pennsylvania's child Endangerment laws and protect our children from abuse and mistreatment House bill 217 was passed unanimously by both the House and the Senate And there's really I think it was a recognition that there's no more important job But that we can do here than to make sure that we're protecting our children We're protecting them from abuse from mistreatment and to ensure that that everybody Who endangers our children gets the full punishment to the fullest extent of the law And this bill allows courts when punishing a perpetrator of this heinous crime to take into account The age of the child who is put into danger as well as the degree of harm That change helps us more accurately reflect the reality of the situation when deciding how we're going to bring justice to those Who harm Pennsylvania's children and it's going to strengthen our child endangerment laws The greatest resource we have here in Pennsylvania is our children and we need to make sure that as they grow up They have the ability to do all the things children do to strive to learn to socialize and become Ultimately productive members of our society and our economy. We all need them to get to that point Harm neglect mistreatment inflicted at a young age has a ripple effect through life The child who's mistreated is lucky enough if that child is lucky enough to escape to adulthood They they still face all kinds of problems throughout their lives Those effects can impact their ability to get a job to succeed at it What's they get a job to build meaningful relationships throughout lives become contributing members of our communities and our economy? Not to mention the child endangerment as we know and the riders know to their great sadness can often have fatal results We all know the tragic story that has led us to this point today and to take a hard look at the laws and make this change Mark and Shelley have lived through something that no parent should ever have to endure Though this can never fix and what we're doing today can never fix what happened to them This bill will make it so that anyone who endangers a child in the state of Pennsylvania Faces a punishment that fits the horrible crime. They have committed This bill once it is law will make sure that no longer can guardians We trust to safeguard our children get away with or get off easy for harming or neglecting them So I'm proud to sign this bill today and I want to thank representative Ron Kauffman for his hard work I'm going to ask him to say a few words and I want to just also say A word for Mark Fogel the district attorney for Franklin County for for being here for all the work that he did to help Us get to this point. So let me turn this over to representative Kauffman Good morning Thank you governor Wolf. We appreciate This event today and the swiftness was with which you're Signing this legislation. I have to recognize The Ryder family Mark and Shelley and grandma Deb and brother Aidan and We are glad you're here today and Matt Fogel If it weren't for him, this would not have come to fruition Matt as he was prosecuting this case and ran against serious Roadblocks, he came in with with mark one day and we sat down and we chatted about how we Make sure that that no family in the future experiences injustice in the face of tragedy and So with working with with district attorney Fogel and the Pennsylvania district attorneys association We came up with legislation and it's hard in Harrisburg to come up with legislation that everyone agrees with Those of you in the press recognize and the governor recognizes how difficult that is and But we came to that At that point where we we found legislation that that could go swiftly and it took a couple of sessions to get there, but In in my career this this will be Really one of the greatest accomplishments that I've been able to work on To make sure that Heath is remembered That's what this legislation here today is to make sure that he's memory lives on in What I believe is going to be act 12 of 2017 and that in Heath's memory Boys and girls across Pennsylvania Will not Hopefully not see this kind of treatment, but we'll always see Justice and so thank you very much governor wolf. I can't thank you enough for For this this event today and bringing this to to a conclusion With the the signing of this act The representative and anybody will take questions on topic if you have any questions right now, I'll do a gaggle off To the side afterwards any questions on this bill Okay, then let me sign it. I'm gonna have representative on one side and Heath's brother Aiden on the other side


There was a sage in northern part of Karnataka who is today revered and celebrated as one of the pillars of the Veerah Sahiba community. His name was Allama Prabhu. A yogi came seeking Allama because he heard great things about Allama. He wanted to compete with him. This yogi who came to meet him, he was a little over two hundred and odd years. With very rigorous yoga, mastering the elements within the system, he hardened his body in such a way, he defied age. So this is his pride. Everybody that he knew has fallen dead, but the man lives and strong as a youth. Rock like his body. So he came to Allama. They met on a bank of a river and he told Allama, I am the real yogi. If you want to test me, you take your sword, hit me on my head, see what happens. Allama said okay and took his sword and smashed it on his head. It just bounced back like you hit a rock. So the yogi said, this is my strength. No sword can slice me. I am practically immortal. He asked, what can you do? Allama laughed and said, well, you can also use your sword. So he hesitated but Allama did not look so strong, rock like. He looked normal. Allama said, go ahead, don't worry. So he took the sword and really went for his head. The sword went straight through as if it's through air and hit the ground and he lost his balance and fell down. So he asked, what is this? He said, this is not this or that. This is Shiva. This is not this or that. If it is this or that, then it has qualities. This is neither this nor that. This is Shiva. This is that which is not.


What's up everybody, JZ here for Jatsby'sKageRays.com. This is a little team random filler That helps fill a prism World Cup soccer pt number one Where you guarantee the team and a chance at a big team like Portugal guys. So again guys We're gonna give away two free spots for early birds So if you bought one of the first 10 spots get entered to win two free spots top two names get two extra free spots And then we'll match you up 16 names 16 teams We're only gonna randomize the names and then whatever team you match up with there is what you get from Portugal Was like a 350 dollar team all the way down to these teams here So again these teams here actually after Australia so Cameroon Costa Rica Ecuador all those teams are not actually sold per team They're usually in an 11 team combo For like $220. So basically just to kind of help this team random be a little cheaper instead of making only like a six-spot break We made it a six-team spot break and everybody's guaranteed one of these teams here So we're gonna add these extra teams to the list and like I said, you're guaranteed a team no matter what and you're in So that's the good thing But of course you kind of want to be in the top five just because of course those teams were a lot more pricier But doesn't mean you can't hit nothing ice though Still get hit some good stuff there Just wanted to let you guys know that though. So in case I was like, oh, I want to buy Serbia next time It's like well unless we do another team item like that. You can't really buy them that way only the 11 team team random all right, so Here we go guys. So basically here's a dice roll. Here's a customer name So these are the first ten that bought only the first ten get randomized to win two free spots So top two names get a free spot each then we'll paste in the two names here with everybody else and Timothy got last Bob Mojo that'll make it 16 names total. We're randomized only the 16 names and we'll match up here with this list here So here we go. Good luck guys roll Got ourselves a one and a three four times. Good luck top two names get free spots one two three and four and Boom splitting it Chris and Grant. Congratulations Three and one four times Let's paste in your names here.  Very nice Chris with Croatia Chris with Japan Grant with Australia Timothy with Cameroon Grant with Costa Rica Chris with Ecuador Ghana Iran Keva Morocco Chris with Qatar Saudi Arabia or Chris Bennett Senegal Nicholas with Serbia and Chris you got the last one there as well Tunisia I Don't know all the countries. Oh guys. So apologies. So now I'm just gonna add these names to the sheet here guys And then we'll start the wrecks break guys. Thank you