All right so today we're going to be talking about how to get a mining internship in Canada and this is the question that I've been getting from a lot of people. So if you're new to this YouTube channel, thank you for joining us. We answer questions on careers in mining engineering, how to get a job in there, what the field is like. If you're a returning subscriber, thank you so much for the continued support. I know I haven't been posting for the past couple of months because I was very busy but now if the new year coming in I'm looking to put up more videos and hopefully answer more of your questions. So back to the focus today, how to get a mining internship in Canada. The focus will be today is assuming that you're already enrolled in a mining related program within Canada's university. This doesn't matter if you're in a bachelor's or your master's program. The important thing to know is you do want to be in an MNG program versus a MASC, Master of Applied Science. The reason is because you're in MNG, it's a core space master so signal to the employers that you're focused on working in the industry rather than a Master of Applied Science where you're signaling to the employers that you want to go into academia. So with that out of the way, let's talk about the four main steps. The four main steps are one, decide whether you want to go and enroll into a co-op program in your university. Number two is the job search process. Number three is the interview process and number four is the offer.


step with progress, our Navy still observes the old and glorious traditions of the sea handed down by the brave and hearty seafaring men who fought to obtain and maintain our democracy. In memory of the cause for which these men lived and died, a modern manor war pauses for a brief time and in a traditional manner the ship is dressed from stem to stern with flags as a salute to the symbol of liberty which all true Americans love and cherish. And having paused she once again puts to sea to take her place as a unit of the United States fleet headed southward to equatorial waters. After a journey of days the fleet approaches the boundaries of the domain of Neptune's wrecks. Though the weather is tropical polywogs in heavy winter clothing and using boxing gloves for mittens are detailed to keep a sharp look out for Davy Jones the Royal Emissary. Shellback searched the ship rounding up all rebellious polywogs for these rebels must be thoroughly subdued and taught to show due respect to his Majesty King Neptune when he arrives on the morrow. It looks as though the shellbacks have a tough job on their hands but the methods are effective. Before the long day ends the polywogs will be too weary and worn to offer further trouble. At dusk the lookout to report that Davy Jones is approaching the ship and the welcoming committee of shellbacks assembles. Davy Jones with his royal retinue of deputies boards the ship and the subdued polywogs and landlubbers are held in readiness by the shellbacks for his royal pleasure. A few of the polywogs are still unruly and must be handcuffed. The captain of the ship greets and welcomes Davy Jones with his retainers deputies of his Majesty King Neptune. Davy Jones reads a proclamation from his Majesty stating that all polywogs and landlubbers must be initiated into the mysteries of the deep before the end of another day. His deputies take their stations and from well-filled bags produce royal subpoenas to issue to all polywogs and landlubbers. These subpoenas carry royal orders to appear before his Majesty King Neptune for initiation when he boards the ship in the morning. Dawn breaks. The great day is at hand. Shellbacks are exuberant with expectation. The polywogs apprehensive with misgivings. His Majesty King Neptune, ruler of the deep, who recognizes no rank among polywogs, arrives on board to receive a salute from polywog junior officers. His royal retinue of strange denizens of the deep leave their seaweed homes and threaten the polywogs with leers of sadistic glee. Through Guards of Honor King Neptune with his retinue proceeds to a specially constructed platform where the captain as senior representative of the Shellbacks bids them a hearty welcome. King Neptune receives command of the ship and immediately orders that his flag, the Jolly Roger, be hoisted as a warning to all seafaring men. The ancient ruler of the deep goes modern. With the microphone he welcomes all Shellbacks to his domain, warning each and every polywog that he intends to be as severe as he can for their offense of entering his domain. But if during their ordeal they prove themselves to be true men of the sea, he will be glad to welcome and acknowledge them as tried and trusty Shellbacks. Accompanied by the ship's band, his Majesty inspects the ship while his royal retainers prepare the infernal machines and search all nooks and corners to ascertain that no polywogs are trying to escape the pleasure of his royal wrath. While other Shellbacks look on, King Neptune complains that the presence of so many landlubbers is disagreeable and orders all polywogs, lounge lizards, freshwater sailors, and amateur mermaid chasers to be brought before him. He mounts the throne and his royal retainers assemble. Queen Amphitrite, mistress of the sea, fairest of the sea flappers and ruler of the mermaids. The royal navigator, charter of ocean breezes, controller of sea currents and keeper of the keys to Davy Jones Locker. Royal police who search the seven seas for polywogs. Royal doctors, originators of seasickness. The royal undertaker who views the polywogs with malevolent satisfaction. Royal guards who have the difficult task of protecting the queen's mermaids. The spectacle of King Neptune on his throne with his grim retainers assembled close about him is a sight polywogs never forget. All is in red and for the first time in history, a president of the United States while in office presents his credentials to King Neptune. The royal retainers engage in heated debate as to the manner in which so illustrious a visitor should be accepted and initiated into the mysteries of the deep. While his royal majesty King Neptune looks on and becomes impatient and wrathful with his royal retainers and finally in deference to his noted visitor, his majesty with royal dignity and pride steps down from the throne and in words that all may hear speaks to the president of the good old days when the rumble of ships propellers did not disturb the peace of the sea nor submarines invade his kingdom of the deep. With venerable reminiscence he speaks of the great figures in history whom he's met and bids a hearty welcome to the commander in chief of the United States Army and Navy and the first citizen of a mighty nation. Other members of the president's party and the polywogs of the ship's crew present their credentials and these unfortunate polywogs of lesser rank get the works. Many of the polywogs lose their heads but never in this manner for this wicked looking blade is only wood. The hot seat where polywogs come in contact with the electric eel and the indicator registers their manliness. Under the 10 demonstrations of the royal doctors the polywogs on the operating table feel the caress of the electric knife suffer the prods of probing thumbs and receive pungent and bitter pills of cayenne pepper to warm their innards. After having been warmed up by the electric chair the electric knife and the hot pepper pills the polywogs need cooling. Plenty of cooling and do they get it? Just watch. Slap day shaves of the order of the day the royal barbers waste no time. In Queen Amphitrati's bath freshwater polywogs are baptized in brine. Looks rough but it's all in fun and no one gets hurt. After the cooling brine a bit of warmth is at it. The ordeal is almost over. Royal fragilators with well-placed wallops to tender stern sheets harass the luckily polywogs who run the gauntlet to emerge at the end as full-fledged shellbacks. Who have earned the right to receive from King Neptune one of his royal certificates to be treasured for a lifetime and shown to envious polywogs and landlubbers. Each new shellback eagerly awaits the day when he too will have the opportunity to initiate polywogs into the mysteries of the deep. Long and memorable day over ships of the fleet steam majestically onward into the dawn of another day when the serious work of maintaining a mighty arm of the nation's first line of defense will be resumed.


Hello! Within this part we'll focus on Event Flux. We'll start from stm32-cubemix and our cubic IDE. This is my case. I'll create a new project with an existing workspace, so File New and the stm32 project. I'm using Nucleo L476RG board and this is why I'm selecting the micro L476RG and the name of the project would be 7 underscore event underscore flux. I press finished. You can reuse any of previous exercises because in these exercises we would need only three tasks with equal priority and one interrupt. In our cases we are using the Nucleo board. It will be blue button connected to PIN PC-13. There is no configuration of N3RG as a part of the tasks, so all components related to Event Flux we need to specify manually within the coding part. So starting our exercise I would first declare PC-13 as external interrupt. Okay we can we can specify its label as well. So this blue button. Please remember that the labels are defined within main.h file later on after we generate the project. What is important is to select the debug interface so within the system and core and this group I'm selecting as a debug trace asynchronous SW to have this serial single-wire viewer or serial wire output PIN and I'm changing the time-based source from default SysTick to Timer 6. This time-based source is used by the library to define all the timeouts and delays and it should not be the same like let's say the timer used by the operating system which is the SysTick in this case. Okay so from hardware point of view at this moment that's all. Let's continue with 3R2S so I go to middle-wares. 3R2S I select interface CMC's V2 and then from the configuration I go directly to tasks and queues and I will change the default task into the task 1. So I double-click on its name and within this window I just rename it to task 1 priority normal I would keep it. I would change the stack size for this to 256 words and then the entry function to be start task 1 and that's it. Then I would add two more tasks. Task 2 would be used within the first part of the exercise task 3 would be used a bit later on. Okay so task 2 the same priority level so normal 256 start task 2 as an entry function that's it and task 3 the same priority so normal 256 words and start task 3 as an entry function and what would be the role of those of those three components you can see it on the slides but let me repeat so task 1 we'll wait for an external interrupt in our case this is our blue button connected to PC 13 and it will wake up for task 2 action in order to let's say perform further actions so in order to perform an action within task 1 we need to do something within task 2 and press a button. It will in fact give to let's say event event flux which would unblock our task 1. Task 2 will set 1 within event group which we will use here or let's say event flux and the next part of this event group or event flux would be given by our interrupt which is used within blue button. Task 3 we will use later on just to demonstrate that some combination of the flux can be reused by more than one tasks at the moment. Okay so we've got three tasks let's continue with the configuration of the 3-year task because as we can see hip size is let's say too small the declared one so within config parameters I need to change it to 4,000 bytes and the second point just to verify library max syscall interrupt priority set to 5. I will come back to NVic configuration so interrupt configuration and I would first enable the interrupt from our blue button and then I need to specify its priority to the level which is in the range from this max syscall to the lowest possible priority level so from 5 to 15. This is due to the fact that this interrupt will be used to execute operating system functions and to protect the complete system it is strongly recommended that all of the interrupts which are using operating system functions should be they should have the priority within those boundaries so from max syscall to a minimum possible priority so between 5 and 15 in our case. Okay this is all for this part so I will generate the code clicking for example this icon and we should have our main.cfile opened if not we can open it from core and SRC this is this one I would like to mention one thing which is quite important even if we have not put any configuration concerning event flags those are automatically added to our middleware library and all of the functions were right now use are stored within this file event underscore group dot c and it's header file event underscore groups dot hfile of course we'll use cmcs OS version too so the porting functions are within this folder and are stored within cmcs underscore OS 2 dot cfile. Okay let's continue with code processing then so I just opened main.cfile it is located within core SRC and main.c so as I told you there is no configuration of event flags or event groups event cube ID or cube mix so we need to declare everything manually so we'll start with private variables of this object and as usual we will start with some handler so this component is called event flags so the beginning of the type def would be the same then there is ID underscore t and I would name the variable of this type event groups event group 1. Okay so this is declaration of the handler then we need to create it and the good place for this is for example this one so event group 1 is equal to OS event flags as it is let's say name within cmcs OS and I would not use any arguments so I just put null and that's it so our event flags object is created its name is event group 1. Okay before we continue I would just add one function which is our interface between our OS and the console it is using ITM interface to let's say to send the data from the tasks and interrupts into the console so this function is task action accepting one argument and it can be of course implemented in a different way using for example uward I would locate it when this part to be sure that it will be it will be not removed and during create generation of the project as I'm using ITM interface I would start from ITM then send control space there's no proposal so send char there is a functions like function like this then I need to pass one argument and then in the second line I would just send a sign of new line okay so this is our task action then we need to say fill our task tasks functions body so as I as I told you at the beginning task 1 would be the task which would wait for some specific combination of the event flux it will be 51 hexadecimal and part of those flux would be set by task 2 and part of those would be set within the external interrupt callback so we'll start from this function waiting for the flux so OS event flag control space weight this group is event group and the flux flux is 51 hexadecimal and the options concerning options I would come back to the declaration of the function and I need a definition so I would go to middleware's third party's freer task source and CMC so as V2 and this file CMC so as 2.c file and within this function I need this field this flux this flux means that we will wait for all of the flux specified within this white function so this is something which we are interested in we don't we don't want to have either 1 or 50 for example but 51 hexadecimal time out would specify as OS wait forever and then after this will give sign of life and that's it as we are waiting for the flux there is no need to put this task additional in the blocked state please remember that this OS flux weight function is sending this task to the blocked state till all of the let's say flux specified here would be set within this object event group one okay so now let's continue with task 2 within task 2 will set part of the flux so OS event flux control space set and again it will be event group one and the flux in this case it will be on the one the rest one would be set from the interrupt routine then we are giving sign of life so task action 2 and we are sending this task for three seconds for example to the block state we are not modifying task 3 at the moment we will do it in next step of our exercise so at the moment we are setting part of the flux within task 2 and we need to add the remaining part so 50 hexadecimal because those flux would be odd with an interrupt routine so we will switch to STM32L4XX underscore IT.c file which contains the interrupt routines active ones and I would need to find this external interrupt handler for external interrupts from line 10 to 15 I will go to this declaration I can see that my flux are cleared so I don't need to take care of them and then after this there is a callback call this callback is defined a bit below as a week so I can just copy paste it and reuse it in a my code so it will be called within this external interrupt routine so I will use again this user code for section for this and within this I would set just copy paste will just set the remaining part of the event crew event flux so it will be 50 hexadecimal and my sign of life would be exclamation mark okay let's build it and let's check whether everything is working I can see no errors no warnings so now it is a time to start the back session my port is already connected so I'm clicking on this back icon then on the debugger tab I need to enable this serial wire viewer which is used to send the data over ITM interface I need to change the core clock to 4 megahertz which is the case in let's say our exercises because this swv is clocked with the system clock then apply and okay okay next we need to configure and start let's say the ITM data console I've got already this tab but in case you do not have it please go to the quick access over here press swv and select this line with the monitor icon after this we need to configure it so we've got this icon we need to set this zero channel which is this swo line pb3 and we need to start tracing after this I can start the complete application I can see that once per three seconds I would see some activity on task 2 now I would try to enter task 2 is sending one within the event flux so task 1 cannot be unblocked because it is waiting for 51 hexadecimal so I will try to add this missing 50 because the event group or event flux is orring together the things which are setting something to the selected event group or event flag so if I press the button I can see that there is a sign of life from the interrupt this is this exclamation mark and I can see immediately task 1 which is woken up if I would press again the button I can see the same action if I would press more frequently I can see a lot of interrupts but still only one let's say execution of this task 1 this is due to the fact that there is no accumulation of the flux so even I tried to set this event flux many times if it will be not taken so absorbed by let's say the task 1 which is waiting for it it cannot be accumulated anywhere so it is not like for example counting semaphores so as you can see it is quite nicely working in the next step I will check whether it is possible to wake up or activate more than one tasks on the same event flux object so thank you for watching this video and let's continue with more extended exercise okay let's continue with our let's say experiment on event flux so I stop debug session and within our main.c file I would add some code within task 3 entry function so what I would just do I will copy paste the code from task 1 but I would change these to 3 so we will have at the moment two tasks task 1 and task 3 waiting for the combination of let's say two different let's say event event flux so in total is 51 and those event flux are set from task 1 and from interrupt so let's now compile the code and start a debug session okay there is no additional configuration because we already did it I would just show this data console configuration should be already done I start tracing and start an application so again once per three seconds I can see let's say the activity of task 2 if I press the button I can see that there is exclamation mark coming from the interrupt routine and then I can see the activation of both tasks task 1 and task 3 and the second interrupt and again activation of both tasks so as you can see using the let's say the combination of task flux we can unblock more than one event which is not the case when we are using for example semaphores so it can be better mechanism to synchronize to unblock multiple tasks on multiple events so this is very very effective communication channel which can be used in more extended operating system based applications okay that's all for this part thank you for watching this video


It's sports park. We're here Santa's we're showering because we're gross. Let's go in there and we're about to have a day These giraffes came from New Mexico where they were created by Frederick Prescott He used visual and emotional impact a brilliant color on moving steel Everything surrounding him in the world serves as a constant inspiration for Frederick Prescott And the vibrant colors that find their way into his sculptures are drawn from none of this tells me why there's giraffes here You know like I need that connection Just when you thought I couldn't get any better they roll out fake giraffes from New Mexico None of it adds up Not a bit of this adds up you think the guy's happy No, I think he tried to sell these to a lot of places like zoos Zeus would be a Over your left shoulder I did it even up cooking all morning Very angst Who the rays? go the rays Just go the angst better go the angst better Go the yanks I got to open this up. What a nice present He gets it. You can wear that every day. Yeah, you could wear that Balan. Hey, $11 beer. I think you just look fine They go booters rays of a hooters in their outfield Raise up a hooters in their outfield pose I'm Carl Hubble His name was wood paper straw just in paper what a day Young Prince Jake's guy mom blue Both way the dimensions Testing the limits Come on This dude's dirt jeeter shirt The show coming on the show coming on the show Boardwalk Boardwalk is an area where they put down planks of wood Boris and you walk it down interesting Maybe they change it for the mind usually boardwalks have some games Try and find some food on Real cool feature here at Charlotte. What's Charlotte Sports Park is the first of everything The first spring training here memories. So a lot of good memories a lot of highlights Stole second February 27th coming up on the Come up on the 11-year anniversary. He took off Not enough goes not stated no a game was happening.  We're having some Cheese steaks Before we get going the bread to meet ratio seems poor And that's just me being honest.  Oh helicopter officially back like Now they're calling a Homer. Oh my god.  Yeah Miguel and you are show some power going to the opposite field if he can bring that to the short porch He could have a pretty special year so it is a lot of bread like they could have cut the bread off here And just packed it and I think we'd be happy right? You know what I'm saying? Let's try it. That's a better sandwich a better sandwich. He said that is right. Yeah, I should do what I do I'm sharing this so that would have been gross what you did. You're sharing that too by the way. I Will buy another one I don't know man. This is just a cheese steak Yeah, all right It's not bad little fly on there. It's not bad enough to not buy. Oh Tough like if someone's like, hey, is that worth it? I'd be like, yeah, yeah, you know if you're in the mood for cheese steak I guess technically and bread It's cool. It's a cheese taking that comes with a side of bread Which is really nice of them I mean, it's honestly a bread that comes with a side of cheese steak.  Yeah, this is a hard three out of ten hard. Yeah one Too much bread to a little cheese steak. I Don't want to be use the bread. I don't want to be harsh here. Just reduce the bread Too much bread and we're bread enthusiasts being harsh sometimes you have to be yeah, that's life And Andy hard hit a home run during this so that's good. Absolutely fantastic I'm gonna finish this and I'm gonna hand my regular old bread to bill for his half That's like just the funk right when did that happen like Like was that little league and it just kept going in the coat? I don't know if you asked me. I thought that was normal like and then everyone kind of comes out to you It's like, dude, like Realistically, yeah No, I'm serious, okay Healthy arm. Yeah, that's okay. You mix another stop thing. What's your pitch? Change up?  We got feeling there you go Jack oh Roodle so what is that?   What time is it? 1201 Technically day six. We're counting it as day five Ploof is somewhere in there You can see them waiting for their bags There's a fake Trevor close Kind of just bigger beer bigger beer. Let's just pick that guy up You know I'm waiting on it still what's that? Catch a ball today Airline might have lost plus bag Blame and bill it's tough Brutal could be tough Luckily, Roosevelt's gave us a ton of shirts. We have so some in the shorts or something Playtrip can fit into some of my shm mediums Yeah I Made it Coach, you know no big deal company man really taking it for the team. Yeah, and we lost my bag But other than that I don't even I'm not even tired. I'm ready to go


The 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 Sevettik, come many of the incidents in this unusual story. Here is our star Dana Andrews as Matt Sevettik, who for nine fantastic years lived as a Communist for the FBI. I always thought I'd like to travel until I took that long nine-year ride on the red wagon of the Communist Party. The road was bumpy, the accommodation's terrible, and worth of all, there's no return trip. This story is part of that fateful journey. In a moment, listen to Dana Andrews as Matt Sevettik, under coverman. This story from the confidential file is marked, One Way Ticket. Those mystery missions for the commies. You know the time, no questions answered, no reasons given. They just hand you a slip of paper with a name and a dress on it. You're told to go there, that's all. Just go there, tonight. The name on the paper, Victor Rocco Photographer. The address, a sleazy penny arcade on the street near the waterfront. A great place to find a photographer, alright? Shooting gallery on one side, and ski ball on the other. In the middle, two rows of diamond quarter slot machines showing real-life movies, the kind men like. Against the rear wall, a counter clotted with stale popcorn, dribbled glasses, giant-sized plastic ears, ice tubes containing insects, trick dice, or other esoteric items. Next to this counter, a booth festooned with faded Bantam snapshots under a sign reading. Any size, any price, any pose, snapshots for all occasions, fastball show for license identification, novelty follow for the folks back home. Any size, any price, any pose, no waiting. Excuse me. What size for you want, mister? We got all sizes. I'm looking for Victor Rocco. That's me, photographer. That's my job. Does it keep you out of the red? Sure, sure. Come in, Svetik. Come in. Back here. All right, comrade.  Wait a minute. I didn't come down here to get my picture taken. Yes, you did, my boy. What? Please?  Listen, I'll tell you all right now. Turn your head this way. Just a little more this way. That's it. Hold it that way. Hey, watch your left a little, huh? All right, hold still now. Done. Would you mind telling me what this is all about? You come to see a photographer, a photographer takes your picture. Why else do you come here? Because I was sent here to see you. You don't have to wait for your copy of the picture. I'll take care of it for you. Why do I need my picture taken at all? Oh, and if I don't see you again before you leave, comrade Svetik. Bon voyage. Bon voyage? What are you talking about? First, I find a commie photographer in a pinning arcade. That's strange enough. Then he insists on taking my picture, whether I like it or not. That's even stranger. Then he tells me to enjoy a voyage I know nothing about. That's when things stop being strange and become sinister. For two days, I sat around my room trying to figure it out and couldn't. Then, I had a surprise visitor who didn't help at all. Mr. Svetik? Yes? My name's Moore. Here are my cards. You know his immigration office? That's right. Yeah, come in. Yeah, sure. Come in. Here, sit down. Thanks. What's the immigration office want with me? Just some questions, Mr. Svetik, if you don't mind. Depends on the questions. We're doing a routine check on an acquaintance of yours, Victor Rocco. He is a friend of yours, isn't he? Acquaintance, yes. Friend, no. Say, why are you asking me about Rocco? I only met him once. Please understand, Mr. Svetik. You aren't required to answer any of these questions if you don't want to. So? Oh, that's all right. I just think you drew a dud when you picked me. Can you tell me anything about Mr. Rocco's background? Not much. I know he's a photographer at one of those penny arcades downtown. That's about all. He snapped your picture on Monday night, didn't he, about 9.45? Yeah. Why? You mind telling me why you chose Mr. Rocco to do the job? Well, he was recommended. By whom? By some people I know. Mutual friends, friends of yours and Rocco's? Acquaintances. I'd like to ask you one more question, Mr. Svetik, if you don't mind. Go ahead. Why did you have your picture taken? By Rocco? By anyone. I don't know. You don't know why you had your picture taken? That's right. Mr. Svetik, if you don't want to answer that question, okay. I'd prefer not to have you head you around. And I'm not hedging, Mr. Moore. I'm telling the truth. I don't know why I had my picture taken. Do you? No. No, I don't know either. But somehow I think I should know. Well, that's all, Mr. Svetik. Thanks a lot. Because this is red. Matt, where are you? In a booth near my house. Anything wrong? No, I'm not sure. What's all this hocus-pocus about the immigration office and Victor Rocco and everything? Oh, there's more call on you? Yeah. Well, there's no need for all that sort of thing. If I knew anything about Rocco, you guys would know it too. Moore doesn't know about your job, Matt. He knows you simply as a busy little red. What's he want with Rocco? Mr. and Mrs. Rocco have applied for passports. They've been in and out of this country a lot lately, but they've never bothered to file for citizenship. Oh. The State Department isn't sure what to do about Rocco. They may detain him, Moore, let him go, and then close the gates behind him, him and his wife, that is. Is she a commie, too? Yes, but we need to know more than that. We don't know what Rocco does to earn his keep in the party. We don't know why he and his wife roll up all that ocean mileage. We have to get something definite on the mat, and soon. I wish I could help, Baker, but I'm more confused than you are. You've got to help, Matt, somehow. Yeah, somehow, but I... Look, Chum, we have a long chain of facts and figures on the communist operations in this area. The Rocco's may be an important link. If you can help us pin something on them. Okay, Baker, I'll try, but I may end up with a chain around my neck. I left the phone booth more confused than ever. The FBI and the State Department's immigration office had plans for Comrade Rocco, all right. But beneath all the unexplained circumstances, it was obvious that Rocco and the party had plans for me. Until I knew what they were, I couldn't help the FBI or myself. I headed back to my room and determined to get some sleep, to forget Rocco and the Reds just for a little while. I fixed out my keys, intending to unlock the door to my room. And then, suddenly, I was playing host to a skinful of goosebumps. The door was unlocked. Someone had opened it while I was gone, and that someone was undoubtedly sitting there in the dark now, waiting for me. I gathered up all my goosebumps and some of my courage and headed for the light switch. Ah, Comrade Sosetti. Who at last? What are you? Oh, I know, I know. It's impolite to break in this way. That's right. Well, a little impoliteness for the party won't hurt, will it? One advantage to being a woman, you can use bobby pins to pick locks. All right. You're here now. What do you want? Just keeping an eye on you, Comrade. You don't mind my being here, do you? That depends. On what? Oh, it's perfectly all right with my husband. Oh, I forgot. I'm Teresa Rocco, Victor's wife. Oh, I see. And your husband sent you here? Mm-hmm. To keep an eye on you. He'd like to see you tonight, too. Not tonight. Tell him I intend to get some sleep. After you see Victor. Hello, Mrs. Rocco.  Foolishness? Yes, all this hush-hush stuff. All the mystery, the unexplained actions. I don't like being watched by fellow comrades, and I don't like being surprised by strangers in the dark, even when they're beautiful women. What's more... Oh, where have you been the last five or ten minutes, Comrade? And I don't like the way your husband... Comrade, where have you been the last few minutes? Making a phone call. Why? Does this phone work? Well, doesn't it? It isn't good policy to talk party business on this phone. What party business? All right. I was trying to phone your husband. Oh, really? What for? I wanted to warn him that an immigration officer was here asking questions about him. And you, too. No, more. Harold Moore. Yeah, more. From all indications, Mrs. Rocco, you and your husband are about to be deported. No, no, not yet. What do you mean, not yet? How can you stop them? Oh, they'll kick us out all right. Sooner or later. But not now. Right now, the party doesn't want Victor to be kicked out. So I may go, but he'll stay.  Even the Communist Party can't keep the American government from it. Come on, let's go, Comrade. Go where? My husband wants to see you. Why? Come on, come on.   I have news for you. I'm not interested in your vanity Are you interested in the welfare of the party? Of course I am. And are you interested in your own personal welfare? The party comes first, of course. Then for your own sake and the party, stop talking so much. Are you coming with me? Ah, okay, let's go. Ah, your father's okay, Arthur. He didn't object too much. Ain't I got a terrific wife, Sveta? Yeah, charming. Oh, thank you, Comrade. Okay, Rocco. What do we do now? Place a key ball or take another snapshot? Oh, I got the picture we need, Sveta. We've got it here someplace. Now, I had... Oh, no, here it is. What's that? Passport. You mean the State Department approved your passport after all? My husband approves his own passport. Well, this is a good one, all right. Like they say, I made it myself. Oh, I think it's Sveta. That's yours. Mine? I don't need a passport. Here, you see? Your picture's right in it, and it's good, huh? But...  All right, Teresa, all right. No, Sveta, you take another look. That name under your picture in the passport. Victor Rocco. Wait a minute. My picture, your name. What's the gag, Rocco? No, I thought maybe Teresa told you. The party don't want me to be deported yet. So you go in my place. What? Teresa, call it out. I can't help it. He looks so funny. Why so worried, Comrade Sveta?  There's nothing to it, Sveta. When America kicks out Mr. or Mrs. Victor Rocco, you'll be Victor Rocco. After all, you're doing it for me and the party. Just a minute. You can't kick me out of my own country. Oh, no. You'll watch and see, Comrade. Starring as Matt Sveta, in I was a Communist for the FBI and the second act of our story. Who wants to live in America anyway?  I couldn't answer that to where I wanted to. I still had to play the part of the loyal Red, even though I was being deported by the Communist. You know, Victor, I think Comrade Sveta doesn't want me for a while. Rocco, this can't possibly work. The immigration office is bound to find out about those phony passport... Oh, sure, sure. They'll find out, but not right away. You see, I've got work to do here. I've got to finish it. While the immigration people are finding out about this, I'll have time to finish my job and you'll have time to get to Europe and do your job. Just what job is that? Deliveries. My work is passport, citizenship papers, all sorts of legal documents. I make them up for party members who need them. You mean you forge passports, legal papers? Oh, sure. Me and Therese. We have a lot of comrades overseas you know who can be very valuable to the party here in America. I see. And I'm to deliver the phony passports to them. That is? That, that's it. Well, I don't know my way around Europe, you know. I do, Comrade. Oh, Therese, this is a big help. She'll take care of you.  Oh, listen, Sveta, do you good to get out of America? You're getting those sentimental bourgeois ideas. What about her passport? Oh, my passport's all in order. Sure. I put it in order. Now, listen, if you've got any loose ends to clear up, Sveta, you better go do it. You sail for Europe in two days. Loose ends. I was at loose ends, all right. Soon I'd be leaving this country with the name, identity, and reputation of a man I despised. The man despised by the American government. And Rocco, he'd stay here, brewing new poisons for the commies to use until the hoax was discovered. I left the Rocco's at the penny arcade and headed for the street. I had to get word to the FBI or to the immigration office or to anyone. I had to do it now. But it was late. Too late to find a cruising taxi. I crossed the street, turned the corner, where the traffic was heavier. Hey, taxi! Taxi! Hey!  Stepping off the curb like that, I might... I'm sorry. I've got to get across town fast. Sorry, but I got a fare. But this is an emergency. There aren't any cabs around here at this hour. My flag's down, but sorry. Move back, will you? It's important, I tell you. Maybe if you ask your passenger... Or yourself. Pardon me. I hate to be so melodramatic, but would you mind if I... No, I don't mind at all. Oh, hello, Mrs. Rocco. In fact, I was going to ask you In fact, I was going to stop by your place. Why? To see if I could help you pack or anything. Or, uh... Did you have other plans? No. No other plans. Well, thanks. Thanks for the lift. Are you sure you don't need help? I imagine you have lots to do. Yeah, but I'll manage somehow. Thanks anyway. There are lots of tricks to packing for an ocean voyage, you know. Well, if I need help, I'll call on you, Mrs. Rocco. Good. I'll be around. Yeah, I know that. I didn't sleep that night for the next night. Everywhere I turned, I seemed to see eyes. Cold, red eyes. Downstairs, on the street, right below my window, a car was parked all night. And its driver was very much awake. During the day, I kept noticing faces that were vaguely familiar. Always behind me and just out of reach. The man across the aisle from me on the streetcar was the same man I'd seen eating at a nearby table in a restaurant in another part of town. Maybe it was my imagination, nerves, jitters. Whatever it was, it kept me from getting in touch with the FBI. Hello? Mr. Svedi? Yes. Who's this? Sorry to bother you again, Mr. Svedi. Who is this? This is Moore, Harold Moore of the immigration office. Moore? Oh, man, am I glad to hear your voice. What? Listen, listen harder. Hello? Hello, you still there? Yes. I thought we were disconnected. Yeah, I heard it too. What were you saying about being glad to hear my voice? Oh, well, I... I've been having trouble with this phone. Couldn't get incoming calls. It's good to know it's working again. Oh, I thought perhaps you'd have more information for me about Victor Rocker. No, not a thing. That's the only reason I called. No, I... I can't tell you anything more. Nothing. All right. Thanks anyway. Bye. Bye.  Just testing my bobby pin on your lock. Mine. Were you... Were you here while I was... While you were on the phone? Yes. You handled that fool very well. All right, Mrs. Rocker. What do you want this time? Nothing. Just stop by to see how you are getting along with your packing. Haven't done much, have you? I want to see your husband first. Now? Now. Let's go. Rocker, what about those phony passports I'm to deliver overseas? Oh, they'll be ready. Don't worry. I haven't packed yet, Rocco. Because I want to hide that stuff the right way. Is it much of a package? No, no, no. Just a large envelope. Sit behind the lining of a suitcase easy. Okay, let's have it. Not till you get to the pier. I'll supply the suitcase. My luggage is a matched set. An odd suitcase would attract attention. Give me the envelope now. Now listen, comrade. Too many things can happen between now and sailing time. What's wrong with you, Rocco? Come on, let's have them. Are you sure you'll be... Be careful. Give them to me. You can check on the way I hide them if you want. All right, all right. I'll get them. My plan wasn't very clever, but it was the only chance I had. I intended to sew a dummy envelope into the lining of the suitcase and mail the real thing to the FBI. But I must have undersold myself on Rocco's diligence. All right, Svenic. Let's go. Is that the envelope? Yeah. Come on. Wait a minute. There's no need for you to... I think there is. I sew this in the lining of the suitcase on my own mind. I don't want you to be questioned at the peer. Who's your luggage, Svenic? You've been keeping track of your luggage? Stop worrying, Rocco. I had it taken aboard. Was mine with yours meant? Yes. What? Stop calling me Rocco.  He's Victor Rocco. I wish you'd stop being so mean. I have to be nervous now. Pardon me a moment, sir. Are you Victor Rocco? Uh, yes, I am. Oh, I see a passport a moment. Oh, wait a minute, what's the meaning of this officer? There's no reason. Just make sure it's up with the luggage, sir. What sort of mixer? It isn't lost no no no ma'am would you mind stepping into the customs office, please? This is your luggage isn't it mr. Rockle? Oh, yes, yes, that's it those bags over there mine if you like to look through those I think this is an outrage customs Suspects the man must have some reason for it. That's right Nothing to be alarmed about as long as you haven't got anything to hide How do people usually hide things depends usually they find a spot in the lining of a suitcase. Well, we'll see You open the suitcases. I found myself praying that he'd find the hidden envelope Praying like I'd never prayed before This was the last chance I had the last chance to stay in my own country and keep my own name and identity Well, that does it Sorry for all the inconvenience folks if you like I'll see that your luggage you didn't find what you were looking for Well, you needn't sound so disappointed. Come on. Let's get on the boat. Oh, please. Sorry folks have a pleasant trip The state room should be right or here it is State rooms B7 and B9 That's us. Aren't you coming in Rocco? No You look grimmer than I feel. What's the matter? Why should you feel grimmer?  This isn't the time for a speech Victor Aren't you gonna say goodbye to me? There's still a few minutes. I've come in for a second. Okay. Come on in Where are we? Hello everybody? Who was? But you'd never get here My name is beaker federal Bureau of Investigation. What there must be some mistake. We have nothing to worry about I just came aboard to bring you something Rocco something from me. No, Sveta. It's not new Rocco What here two passports one for Victor Rocco and one for Mrs. Rocco Oh, there is a mistake. We have our past don't know how you manage that these passports were just approved by the State Department Approved. Yeah, that's why I'm here now The government wants to be sure the Rocco family leaves America for good this time You two won't be coming back under any name Come on, Sveta. All is sure Your luggage is still in the customs office. You're not going anywhere. I Left the ship with beaker the Rocco's left America on the ship Caught in a trap that was sprung when they wouldn't wait for legitimate passport approval They would you to pay the price of failure that I read come until we see For the all-important envelope went from the lining of my suitcase to the files of the FBI. I Learned from beaker that the commies weren't the only one who had been keeping close check on me He designed some friends to the job too Sure, I tried to thank him, but how how do you thank a man for your freedom? This time as I walked away from the harbor back to the people I despised and the work I hated Things seem to make more sense Behind it all there were friends and there was freedom Knowing this it was easier much easier to walk the crooked red road to walk that road alone Dana Andrews will return in just a moment This is Dana Andrews friends As one of our greatest philosophers has pointed out our government was founded on three basic ideas one The love of liberty to believe in progress and three Faith in the dignity of man if we were to sacrifice any one of these three concepts We'd lose them all if we let that happen then we just don't deserve democracy 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 Savettick who worked on the cover for the FBI Next week and other fantastic adventure join us then won't you?


Thank you. Can you hear me? Thank you, Sebastián, for the introduction and I would like to thank the organizers also for the opportunity to speak in such a nice conference, in such a nice institute and city. Okay? So as Sebastián said, I'm going to talk a little bit about geodesic flows on surfaces of non-positive curvature that are burnally. So let us put the setup of the talk. Well, it's actually here, but let me write it properly. So you have, sorry, M2. It is a sinfinity compact boundary less surface. We assume that M is not the torus. We also assume that the sectional curvature, or here the Gaussian curvature because it's dimension 2 is non-positive. Okay? Well, given this and given this, I have a Riemannian manifold. So I can consider the geodesic flow. It was already actually defined in Keith Bernstock. So let me consider phi. Where does the geodesic flow live? It lives in the tangent bundle. We can restrict it to the unit tangent bundle. So we have a flow on the unit tangent bundle. It flows along the geodesics at unit speed and it sends one vector to the respective vector. Okay? And for the purpose of this talk, I'm also going to consider a measure, which is going to be an invariant measure for the flow. And let us restrict ourselves to two cases of the measure. So either phi is Liouville, or phi is a measure of maximal entropy, just like in the case of Jerron-Busy's talk yesterday. So measure of maximal entropy. Okay? So we have a system and we can ask many questions about the system, whether it is ergodic, whether it has stronger mixing properties. So it was actually mentioned also yesterday, a conjecture that people still don't know whether the measure mu be equal to Liouville, whether this thing is ergodic. So this is an open question, whether mu is ergodic. But it is known that the measure of maximal entropy is unique, has ergodic. This was proved by Knipper. He actually proved in the setting of rank one manifolds, which covers this case. So we know that this guy is ergodic. And the goal of my talk is to go beyond these things. So we know that this guy is ergodic, okay? And provided also that this guy is ergodic, I'm going to convince you, I'll try to convince you, that in both cases you can go beyond ergodicity and prove that actually the measure is Bernoulli. Or the system given by this triple is Bernoulli. So this is the goal of, it's to go from ergodicity to Bernoulli's for these two cases, okay? So I have to tell you first what is a Bernoulli flow. So let us stop for a little bit and remember a few definitions of ergodic theory for flows. And I'm going from the easiest property to the most complicated one, which is Bernoulli. So I think we are all comfortable with the definition of an ergodic system. So actually let me fix here x, the space a sigma algebra, phi t is the flow and mu is an invariant measure for the flow. So I want to remind you what it means to be ergodic, what it means to be weak mixing, what it means to be mixing and going further, what it means to be a k-flow. And finally what it means to be a Bernoulli flow, okay? So ergodicity is the same thing. If you have an invariant measure, then this measure is constant. I'm not going to write the almost everywhere statements, okay? So the idea is that if you have something invariant, this something has to be trivial. It is indecomposable in the measure theoretical sense. Weak mixing is something that is stronger. So I'm going to put this inclusion here. And it says that if you have an eigenfunction, and in this case, because it is a flow, it has to be written, an eigenfunction has to be written like this, okay? The application of the function after the iteration of the flow, it's the function times this thing here, this corrective number here. Lambda is going to be the eigenvalue. So again this, the system is going to be weak mixing if a function that satisfies this is constant. Mixing is the same thing also. So if you get two sets, measurable sets, then the measure of this intersection is going to converge as the time goes to infinity to the product of the measures, all right? So now let us go to the k-flow into the Bernoulli flow. So what is a k-flow? I can give you three definitions of the k-flow which were proved to be equivalent. The first definition is something in terms of mixing. So I won't write properly what it is, but it is a sort of uniform mixing. So because it's uniform, everything that's k is also mixing. And well, we can check also that everything that's mixing is weak mixing, okay? So this is a much stronger condition that we impose on the flow. I can define in these terms or I can define in two other terms. The other one is actually why the number, the letter k comes from, is that the flow satisfies Komogorov's zero one law. And what does this mean? This means that if this letter here that I don't remember the name is a finite partition, then the tail of this partition is trivial, okay? It is to say that tail measurable events are trivial and this is exactly what Komogorov's law, zero one law is about. And finally, and it would be the one that would be more useful for us, it's the definition of a k-flow in terms of completely positive entropy. And what does that mean? Well, every system has a bigger subsystem which has zero entropy and this is called the Pinsker factor or the Pinsker algebra. In the case of a flow, the Pinsker factor of the flow is defined as the Pinsker factor of an automorphism. And the automorphism can be taken to be any time of the flow as long as it's not zero. So you can fix the time one and define the Pinsker factor of the flow as the Pinsker factor of the time one map, okay? And saying that this flow is Komogorov is saying that this thing here is trivial. And if I told you that this is the largest factor of the flow of the automorphism that has zero entropy, well, this thing here is equivalent to saying that every non-trivial factor of my flow has positive entropy. And this is the notion of completely positive entropy. All right, so finally we'll get to the definition of a Bernoulli flow. And I guess that we all know what a Bernoulli automorphism is. A Bernoulli automorphism is just the IID iterations of random variables, right? You have a finite alphabet and you consider the measure on the sequence given by this finite alphabet and this measure, you consider it to be a Bernoulli measure. So it's the product of the same probability vector. And this is what is called a Bernoulli automorphism. And what is a Bernoulli flow? It is a flow such that for every non-trivial time, this automorphism is a Bernoulli automorphism. So that flow is going to be Bernoulli if phi t is a Bernoulli automorphism for every non-trivial t, okay? And it is a theorem that to check this, it is only necessary to check this property for one time. So usually people state this that a flow is a Bernoulli if the time one map of the flow is a Bernoulli automorphism. Okay, so now you know what a Bernoulli automorphism is. But the question is whether they exist or not. So I will give you an example of a Bernoulli automorphism now to tell you that they really exist. So an example, not of a Bernoulli automorphism, an example of a Bernoulli automorphism we all know of a Bernoulli flow. This is called the Totoki flow. And what is the Totoki flow? It is a suspension flow. If you remember Federico's talk last week, yeah, he defined what a suspension flow is. And what is a suspension flow? Well, suspension flow, you need two data to construct a suspension flow. You need an automorphism, so you need a space and a map, and you need a roof function. In this case of the Totoki flow, what is the automorphism? The automorphism is the two-sided shift. And the roof function is a function that is constant on the trivial cylinders here, on the cylinder that has the zero position and zero in the zero position one. So let me write the sigma, although it's totally disconnected, but I'll write it in just like an interval. And I'm going to consider the partition. The left one is the cylinder that on the zero position has zero. And the right one on the zero position has one. So I'm going to tell you what is the roof function now? Well, the roof function is constant here and it's constant here. Here I can make it be equal to one. And here I make it be equal to alpha, where alpha is an irrational number. So constant one on zero, zero, oh, not zero, alpha on one. And the main property is that this alpha is different from zero. Oh, it's not rational. So I have my basis and I have my roof function. And what is the flow that I consider? Well, I just flow at unit speed on this space. When I hit the top, when I hit the graph of the function, I come back to the section according to my map on the basis. So I, for example, if my sequence starts with zero one and I'm going to start here, I'm going to flow time one here until I come here and I keep doing this. Okay? So this is the Totoki flow. Totoki showed that this flow has the K property. So Totoki is a K flow. And Onstein showed that it actually is Bernoulli flow. So yes, they do exist. But the construction is totally probabilistic. So in the basis, you have a Markov chain and you consider the suspension. So now I'm going to try to convince you that actually these Bernoulli flows, they are more, they appear in many other places and some of them were actually not expected during the 70s. So let me mention a little bit of the literature. A few cases in which people proved that the flow is a Bernoulli flow. And what is nice is that in all these cases, the flow is a deterministic one. So they started with a deterministic system and they proved that it is as random as you can expect. Okay? So the first, I don't know if it was the first, but the first I want to mention here was an Osov and Sinai. And they proved that if you have a Riemannia manifold, well, if you are in the case of an Osov flow, so you have negative sectional curvature and you consider the Liouville measure, then the flow is K. All right? I might come back to this. The main tool that they used for proving this was Roth-Linz and Sinai theory of measurable partitions. But, well, that's what I want to say right now. So the second result I want to mention is by Einstein and Weiss in which they develop a condition that is checkable to see if a flow is Bernoulli or not. And they apply this to the situation of geodesic flows on surfaces of constant negative curvature. So phi geodesic flow on surface with curvature constant and equals to minus one and the measure being the Liouville, the Lebesgue measure. So they proved that in this case the flow is a Bernoulli flow. So this is a totally deterministic system, but after a change of coordinates it becomes the most random as you can expect. Okay? All right. So this is a main result because it introduced this notion of very weak Bernoulli partitions and it's a notion that is checkable and if you prove that there is a sequence of very Bernoulli partitions that generate your sigma algebra, then your flow is going to be Bernoulli. So this result was later extended by Rettner exactly by checking the very weak Bernoulli condition and she showed that if you have a nozzle flow and if you have a measure which is good in some sense, in this case it has a Gibbs property, but it has also some other regularity properties that I don't want to mention right now, then what she proved. She proved that if the flow is a K flow, then it actually is Bernoulli. So in this setting there is no space for a flow being K and not being Bernoulli. Okay? This regularity implies that actually has to be Bernoulli. All right. So I wanted to say a few sentences on the approach of Rettner for proving this. So Rettner implemented as far as I understand CNI's program and CNI was interested in analyzing measures, relevant measures for fiscal systems and how did he do that? He realized that if you have a symbolic description of your system, things become easier to do it. So what Rettner did was exactly that.  So you have a symbolic model and that will be more precise in a few minutes what it means to have a symbolic model, but things become easier to analyze in the symbolic model. So at this level here she implemented these properties plus Onstein-Weiss idea. So Mil being a good measure and she used Onstein and Weiss. Actually I'm going to write here Onstein's theory because that's how it's known nowadays. And she was able to get the Bernoulli property, to analyze the Bernoulli property. So why am I mentioning this? Because I'm going to write a result right now or in a few minutes. And the approach for proving this result is exactly as Rettner's approach. So I'm going to give a setup on which we are able to say many things about the system. It's going to be Bernoulli or basically a Bernoulli times a rotation. And the way we are going to prove this is exactly as this. You start with your system and you get a symbolic model for the system and after that you use in our case instead of having a measure like that you're going to have an equilibrium measure. So we are going to use thermodynamic formalism plus this very weak Bernoulli condition to get the Bernoulli property. So what is the result? We prove a theorem following the same approach of Rettner. And what is our setup? So our setup unfortunately at the moment we are not able to deal with all the dimensions. So you have a three-dimensional sinfinity closed compact without boundary manifold. You have a flow and I have two assumptions on this flow. The first assumption is that it doesn't have fixed points. So without fixed points. And the first assumption is a regularity one. It is the assumption that the vector field that generates this flow is at least of the order c1 plus beta. If x is the vector field of phi. And I assume that this is of class c1 plus beta. In terms of the vector field saying that the phi doesn't have fixed points the same as saying that the vector field does not vanish anywhere. So you are in the situation. Well, we have a dynamics. We need a measure. So we're going to have mil. It's going to be an equilibrium measure in the sense of the Hombuses talk yesterday. So it's an equilibrium measure of a holder potential. I'm going to assume it as ergodic. And I'm going to assume it has positive metric entropy. Okay. So this doesn't seem similar to what has been done before about another flows. But note, as long as I am assuming that the positive metric entropy is positive, well, by who else in the quality, since we are in low dimension, this means that I have, well, I have a flow. So I always have a Lyapunov exponent that's equal to zero is the flow direction. Having positive entropy tells me that I have a positive Lyapunov exponent as well. If I do the same thing for the inverse flow, well, the inverse flow also has to have a positive Lyapunov exponent. This means that the flow actually has one Lyapunov exponent, which is zero, another one, which is positive, and another one, which is negative. So I am exactly in the situation of non-uniformly, non-uniform hyperbolicity. And I'm happy because if I have non-uniform hyperbolicity, I can use passing theory. Okay? So we are going from something that's uniform hyperbolic to something that's non-uniform hyperbolic. All right, so this is the setup of the theorem. And what is the theorem? The theorem is a joint work with Le Drapier, François Le Drapier and Omri Sariq, is that in this situation, my triple here, m phi mu is either a Bernoulli flow or it is the product of a Bernoulli flow with a rotational flow. Okay? That is a second part of the theorem that if in addition we impose an extra condition on our flow, and the condition is that the flow is a red flow, if in addition phi is a red flow, I don't want to define what the red flow is right now. If I have time towards the end of the talk, I will. So in the case of the red flow, you should think of the red flow is the most non-integral situation. So a contact structure, giving a contact structure is just like giving planes, in this case, you are two dimensions, so you give planes, tangent to the space that are non-integral, so you don't have an integral foliation of these planes. And a red flow is something that is associated to this contact structure. So in the case that you have the red flow, you cannot have the situation of Bernoulli times rotation, you have to be Bernoulli. So if in addition phi is a red flow, then only the first case happens is Bernoulli. Okay? In the geodesic flow is an example of a red flow. So in our case, we don't have Bernoulli times rotation, we have to have Bernoulli. All right. So now let me mention to you this thing that I just erased. How do you use this same sketch, the same scheme of retina to prove this theorem? So the first part as I wrote here is that you have to have a symbolic coding of your system. So remember that the system that I'm dealing with is this triple here. I have this three-dimensional manifold, I have a flow without fixed points, and I have a measure with positive entropy. So this first part here was made in a joint work with Omri Sariq is that if M5u is as above, then there is a symbolic model. And in this case, then there is what we call topological Markov flow. And I'll define what it is and a map which is actually holder. Well, I need some notation here. Topological Markov flow is going to be sigma r, sigma r. I'll define this right after I write the theorem. There is a map pi r from sigma r to the manifold such that it commutes the diagram. So pi r composed with sigma r is equal to pi composed with pi r. And you should think of the diagram here exactly as Pablo Carrasco said last week. So what is the goal of symbolic dynamics is to obtain some extension that intertwines the dynamics, but the extension itself is not much more complex than this thing here. So in the sense of not being much more complex, I mean that it is basically finite 2 1. So pi r is finite 2 1 in a set of full mu measure. So why is it good to have an extension which is finite 2 1? Well, we all know that whenever we have a measure here, we can project the measure here. But when we have a measure here, it is more complicated to lift the measure. Well, in some situations, you can lift the measure, but the measure that you lift is going to be much more complicated. If you have a finite 2 1 extension, you are always able to lift your measure in a way that the metric entropy of the lifted measure is the same as the metric entropy below. Why is that? You have this Abramov-Rochlin formula which tells you that the entropy on the top is the entropy below plus the average of the entropy on the fibers. If the fibers are finite or countable, they carry no entropy, so the entropies are the same. All right? So this is one of the main goals of constructing these finite 2 1 extensions of your dynamics, because you can analyze ergodic theoretical properties, not here, but here. You can lift measures. I just want to mention two corollaries of this theorem. One of them is again in the setup of Jehovah's Witness talk yesterday. So one of the corollaries that we get, we don't get finiteness still, but we get countability of the measures of maximum entropy. So there are, at most, countably many measures of maximum entropy. And the second corollary is in the terms of counting the number of closed orbits. So the symbolic model is much easier to analyze closed orbits. And by doing that, we are able to prove that the number of closed orbits of length of period at most t grows at least as a constant times e to the t times the topological entropy divided by t. Okay? I have a measure that's positive. So the topological entropy is also by the variational principle positive. So this is a positive number. So it grows roughly as an exponential after you divide by this t here. All right? And we cannot expect much more in this setup, because our conditions are very weak. I mean, you could have countably many closed orbits, and this would, well, this tells you that you cannot expect to have an upper bound for this thing here. All right. So this is the symbolic part. And what does it allow us to do? It allows us to consider this measure, mu, here, on M, and lift it in a way that the entropy is preserved to a measure nu on sigma r. But what is sigma r? I still didn't define what sigma r is to you. So before writing this, let me tell you what is sigma r and sigma r. Okay. So let us say that you have a graph oriented graph with countably many states, countably many vertices. You can consider the paths on this graph, and this gives you a symbolic space, which I'm going to call sigma. So paths, two sided paths on G. So what is the graph that defines the two shift? Well, you have zero, one, and you have all possible transitions allowed. You can consider a more complicated graph with countably many vertices and do the same thing here, paths on G. And there is a dynamic associated to this, which is the left shift. And this is a topological mark of shift. What is a topological mark of flow? Well, it's just like we defined on Totoki's flow. You need a roof function, so you need a function from the basis to the positive reels. So you can consider the suspension space and the suspension flow. Sigma r, the suspension space. What is that? All the points below the graph of r with the identification that x r of x is the same of sigma of x zero. And sigma r here is the suspension flow. You flow at unit speed vertically upwards in this space here. When you hit the top, you consider the identification and you come down. So this is our model. It's a suspension, but the condition that we have to put is that instead of having finitely many states on our symbolic dynamics, we have countably many. Okay? But this is not bad. This is actually good. So what I want to do right now, well, I want to tell you more or less the scheme of the proof of the theorem. So we start with a measure on n. And because we have a finite one extension, we can lift this measure to the space sigma r. And it is easy to check actually, because the entropies are preserved that if this guy is an equilibrium measure, this guy is also going to be an equilibrium measure. Okay? So we are with an equilibrium measure with respect to the flow, but we can consider the flux measure. So every measure here is associated to a measure on the... Yes. I'm proving the theorem that I just erased here, that I want to get Bernoulli-City or Bernoulli-City times rotation. So this is the first part of the proof. You get the symbolic coding. Now you need to do the Einstein's theory and thermodynamic formalism analysis to be able to prove Bernoulli-City or Bernoulli-City times rotation. Okay? In the end, we are going to prove that this thing is Bernoulli. And two Bernoulli flows, they are the same. So all flow is going to be the same as Totoque after a change of phase. Okay? Okay. My time is almost done, right? I have five minutes? Three? Four minutes. Four minutes, okay. So you get this measure which is leaving the suspension space and you can project it down to the flux measure here on the basis. So you are with a measure on your topological Markov shift. This guy is an equilibrium measure. I just told you that this guy is an equilibrium measure as well. There is a lame of Perian polycott that shows that if you have an equilibrium measure in the suspension space and you project, what you project is still going to be an equilibrium measure for the basis with respect to another potential function. But the conclusion is that we have a topological Markov shift and we have an equilibrium measure on the basis. So Perian polycott tell us that this guy here is equilibrium measure. And what is good is that Boozian-Sarig analyzed equilibrium measures for topological Markov shifts to accountably many states. So we have two properties of these measures that it has local product structure and the Gibbs property. Some Gibbs property. So this is the thermodynamic dynamical formalism part that I need. And this allows me to, to the following sketch of proof. We can see our suspension flow.  And the tool that we are going to use to start to analyze the ergodic properties of this flow is something called the olonomy group. It has been used by Brin, by Pessin and by many other authors in the literature. What does it do? Let us fix a point here and let us consider all SU paths closed centered at this point with respect to the basis. You can lift this SU path with respect to the basis to SU path with respect to the flow with what happens when you lift. Well, you do this, you do this, you do this and you do this and you come back to something here. Not necessarily X again, but some, but X plus some displacement vertically. Let me call this vertical displacement to be the P of my curve gamma that I start with. And I can look at all of these P of gammas here. So the olonomy group is the closure of all of these P of gammas where gamma is a closed SU path at X. Why do I do this? Because I have to understand the ergodic properties in the flow direction. And how do I do? I do by means of the hyperbolicity in the basis. So for example, if I have something that is a constant suspension, these guys here, they are always going to be multiples of the same number. And this is what we analyze. Analyzing this G here, how do we analyze this G? It is easy to see that G is an additive subgroup of R. And it is closed. What are the closed additive subgroups of R? They are either zero or discrete, non-trivial, or they are the whole of R. If it's zero, we can apply Katak Kononenko's construction for Liftschitz theory, Kononenko, to conclude that actually the roof function has to be a co-boundary. But roof functions cannot be co-boundaries, right? They have to be positive everywhere. So how can it be a co-boundary? So this does not happen. If G is discrete, non-trivial, again applying Katak Kononenko's construction, we conclude that R is columnologous to something taking values on this closed subgroup. So in this case, our flow is almost the constant suspension. So let me conclude here. So our flow is something that the roof function is a constant multiple, is a multiple of some constant number.  So what do you do? You just change your section by completing this thing here. And if you see your flow with respect to this section, well, how long does it take for it starting in the section and go back to the section? It takes a constant time. So this thing here implies that by the streak of bowing that this thing is a constant suspension, which is almost Bernoulli times rotation. So if you apply, again, non-steam theory, we obtain that in this case what we get is Bernoulli times rotation. So we are already in one of the cases of our theorem. We just have to analyze what happens when g equals r. When g equals r mean what that means is that you can go in the full direction as much as you want by doing sq paths. There is the Rochlin-Sinai theory, and that's when I say it again, of measurable partitions that says that in this case you can actually prove the k property. So having this saturation in the full direction tells you that the flow is a k flow. So we only need to analyze what happens when it's k. Remember Ratna's theorem that she allowed us to go from k to Bernoulli. So we apply her ideas in this case are these properties of Boozian-Sarig, so thermodynamic formalism, plus the notion of very weak Bernoulli partitions. So I'm going to put on this thing here to conclude that if the flow is k, then the flow is Bernoulli. So this is a rough scheme of the proof that goes with the with the head of this Holognomy group. This Holognomy group allows us to get three very rigid situations in which starting from them we can conclude that this case does not happen. In the second case what we get is Bernoulli times rotation. In the third case what we get is a Bernoulli. And I think I'm going to stop now. Thank you.


The objective of this study was to analyze the results of emergency surgery to oncological patients in both general surgical and oncological hospitals in Sogd Region. Methods included analysis of data from 122 patients with complicated forms of malignant neoplasms treated at SRSC in the period from 2012 to 2016. Results showed that 41 patients had colorectal cancer, 21 had gastric cancer, and 87 had tumors of the reproductive system. Additionally, 15 patients had symptoms of a locally advanced process and 21 had distant metastasis. Surgeons did not always perform the appropriate volume of intervention in non-core institutions. Among the 209 patients, 122 received specialized care at SRSC and 87 at general surgical hospitals in the region. Severe complications during tumor progression were not necessarily indicative of non-receptible tumors, and the implementation of emergency operations in general surgery hospitals had several drawbacks. This article was authored by J.R. Sanjanov, Z.H. Huzinzoda, and F.S. Mancharov. We are article.tv, links in the description below.


So the sync thing has two control buttons, which are located down here at the bottom of the panel. Mic set. Mic set is fantastic. It lets you set your gain staging of your mic. So when I tap that, it says, hold set mic gain, so you hold it. And then it says, sing your loudest, yes! That's really helpful for when you're performing in live situations. It's going to prevent you from peeking out and feeding back. Tap tempo down here. For every song that you're doing, if you're going to be using a delay, I recommend getting the song to start and then you just start tapping along to the beat of the song. And that's going to make all of your delays work really nicely with the song that you're performing. And those are the control buttons. Thanks so much for watching. If you have any questions, please leave them in the comments below. And don't forget to like the video and subscribe to our channel.


Obesity has been a growing health concern across the world. Obesity can make one more susceptible to developing all kinds of diseases, heart disease, stroke, high blood pressure, diabetes and cancer, all kinds of cancers. But exactly how obesity increases your chances of getting cancer is not entirely clear. So what if we could understand what aspects of obesity contribute to a specific cancer in order to prevent the development of cancer in obese individuals and treat obesity independently, while learning something about our own biology? The scientists of this paper wanted to understand if and how obesity contributes to cancer. Their findings are published in their article titled Obesity-Induced Gut Microbial Metabolite Promotes Liver Cancer Through Siniscence Secretome Published in nature in July 2013 by the Otani Lab, the Japanese Foundation for Cancer Research. In order to do this, the scientists fed either obese mice a high-fat diet or lean mice a normal diet and examined the development of liver cancer. Diet alone was not sufficient to cause cancer, but when this treatment was combined with a cancer-inducing chemical, 100% of obese mice fed a high-fat diet developed cancer compared to only 5% of lean mice fed a normal diet. But the question is, is this due to the fact that the mice were obese or to the fact that they were eating a high-fat diet? To answer this question, the scientists looked at mice that were obese due to changes in their DNA sequence, but that ate a normal diet. These mice were also more likely to develop cancer with a cancer-causing chemical than non-obese mice. So this suggests that obesity can promote the development of liver cancer when a trigger, in this case a cancer-causing chemical, was provided. So what could explain this? The scientists noticed that the cells around the tumor were producing lots of molecules that promote cancer. These cells were in a state of arrest that we call senescence. When the senescent cells or the molecules they secreted were removed, obesity did not cause mice to develop cancer in the presence of the cancer-causing chemical. So this suggests that obesity is somehow making the cells in the liver senescent and causing them to produce all kinds of pro-cancer compounds. So the next question is, how can obesity affect the state of cells in the liver? To answer this question, the scientists looked at the intestine. Our intestine is full of microbes, including bacteria, that form communities that play important roles in our health. Some bacteria are important in promoting health of the intestine, while others can be detrimental. The scientists found that obesity can greatly influence the types of bacteria that live in our intestine. Let's say, for example, that obese mice have more red bacteria in their intestine than lean mice that have more green bacteria. So they wondered if the different bacterial communities in obese versus lean mice could influence biology in the liver and explain the fact that obesity promotes liver cancer. But how could something in the intestine influence the liver? Well, it turns out that bacteria produced by products that leave the intestine, enter the circulation, and travel directly to the liver. So the scientists wondered if bacteria from obese mice produce different byproducts than bacteria from lean mice. Well, it turns out that bacteria from obese mice produce lots of DCA, a compound that damages cells and can even cause colon and liver cancer. That's a very interesting finding. When the scientists reduced levels of DCA or removed the bacteria from the intestines of obese mice, these mice no longer form tumors in the presence of the cancer-causing chemical. So what did this study show? First, this study shows that obesity can promote liver cancer development. Second, the scientists take this a step further to describe a mechanism by which this can happen. It goes like this. Obesity alters the types of bacteria that reside in the intestine. Now, obese mice have more red bacteria and fewer green bacteria. These red bacteria produce lots of DCA, which enters the bloodstream and travels to the liver. In the liver, DCA causes liver cells to enter a state of arrest or senescence. These senescence cells in turn produce compounds which promote liver cancer development in the presence of a trigger, in this case the cancer-causing chemical given to the mice. So the scientists have come full circle, starting from their interesting discovery in the liver that took them all the way to the intestine and back to provide a theory that explains how obesity can promote liver cancer. So what does this mean for you? This study shows that obesity can influence liver cancer and has broader implications than initially thought. Of course, it still remains to be seen if this result stands in humans. I'd also like to find out if DCA produced by intestinal bacteria could be causing cancer directly without acting through senescence cells in the liver. It would also be interesting to find out how the microbiome changes over time as one becomes obese and why. Is it because of the food that we eat? Is it because of a general state of body-wide inflammation? Overall, we should take away that it's important to live healthy lives. What we eat and how we treat ourselves influences biology all over our body. So as you can tell, scientists are studying cancer not only at the organ level but at the organism level By trying to understand how biology in one organ can influence biology in another we are developing powerful tools to understand our complex physiology and tackle these resilient diseases. This video has been provided to you by Eureka Science. To stay in touch with Eureka Science, like us on Facebook, follow us on Twitter, subscribe to our YouTube channel or visit us at www.eurekascience.com Thank you for watching!


We can continue our discussion of force diagrams or our free body diagrams by looking at specifically what you have to do if you're given a diagram, but you need to construct your equations. So how do we construct those equations from our diagram? What I'm talking about with a diagram is let's say you're given a particular problem where you've got some mass, let's call it mass one for right now, and then you're given a diagram showing you a series of forces acting on that object. Now in this case we've kept it nice and simple by having all of our forces up and down or left and right. So when we do this we're trying to construct our set of equations. Some of the forces in x and some of the forces in y from this diagram. One approach is to start if they're named F1, F2, F3, F4 just to make sure we're not missing anything, is to start with F1. F1 is over here to the right so that means that's going to be in the positive x direction. Similarly F2 is in the positive x direction. F3 however, well that's down so our up and down direction gives us our y equation and down is negative so we would plug in a negative F3. When we come to F4 that's up so that's going to give us plus F4 and then our last one our force 5 here is in the negative x direction because that's pointing to the left. Now our equations aren't entirely complete because we don't know yet is this object in equilibrium or is this object accelerating. So it's possible that there's an acceleration component in the x direction and an acceleration component in the y direction and this gives us our full force equations for this diagram. Now this was a complicated diagram that I had 5 forces but it was a simple diagram and that they were all either up or down, left or right. So let's take a look at a little bit more complicated diagram. Let's say we've got a diagram where we're given various quantities. Weight, attention, maybe a normal force, maybe a friction and then maybe there's somebody helping it out so we have attention 1 and attention 2. So this is a fairly complicated diagram as well. We still want to come through here and describe our equation. Now this might be the diagram for a box sitting on a table being dragged by two people and there's some friction in the system. So in this situation we would expect that the box is moving, possibly accelerating to the right. It's probably not accelerating up and down. So this is our sort of physical sketch. This diagram over here is our force diagram. We want to use this equation, not our physical sketch, to help us through our equations. So for this particular situation again we want to start with each force and figure out what we have to include in each of these equations. If I start with T1 it's directly to the right and so I've got a plus T1 in the x direction. T2 is a little bit more complicated. It goes to the right but it also goes up. So we could take this and think about it in terms of our trigonometry. We've got an x part and a y part for that equation. So the total tension 2 is not in either equation but a part of that tension 2 is in the x direction and a part of that tension 2 is in the y direction. The rest of our forces are a little bit easier. Normal force points upwards, positive y, weight, negative y, friction, negative x. Always a good idea to come back and check and make sure that you've included each one of the forces somewhere in the equation in terms of making sure that I've got everything in these equations. We're not quite done yet because we still have to consider whether or not it's accelerating. Again for this situation with the box going along a desk in that particular case my MAy becomes zero because it's not accelerating up and down. MAx, it could be accelerating to the right or it could be moving at constant velocity. We'd need a little more information. You're always safe putting MAx and MAy in there as long as you're keeping track and later come back to evaluate what those particular accelerations might be.