To develop a cancer of some kind is a fact that one in two people on average can look forward to. Although tragic, developing the disease in the modern day is probably the best time in history to get the big C.   One such form and the one covered in this video is breast cancer. Treatment can involve surgery which permanently alters the body and as such can cause significant psychological trauma. Chemo is another heavy one for treatment and another is radiotherapy.  The machines are complex and today's subject is about when that complexity causes a disaster. In our case today sadly the machine used in the hope of treatment will end up causing far more suffering. The L-Stock radiotherapy overexposure event. Forward. So today's video will be based on the IAEA report into the incident. If you'd like to go into a further deep dive into the figures then check out the report and as always the link will be in the description below. I won't go too much into the history of radiotherapy today which is only because if I do then the video will be way too long but I will touch lightly on the particular machine involved. Right, let's get started. Bialstock. So this is Bialstock. Going on population is the 10th biggest city in Poland. Like most big cities it has an extensive healthcare network which deals with many things including with those who have cancer. This was dealt with by the Bialstock Oncology Centre which I'll call the BOC from now on to minimize your exposure to my abysmal attempt at Polish. Anyway the BOC is as described by the IAEA as reasonably well equipped and staffed. The centre treated in the early 2000s over a thousand patients per year in its tele therapy department using its three tele therapy machines. But for today's video we'll only be looking at one, this one to be precise, a Neptune P10. A domestically produced machine under licence from France by the nuclear centre in Swerk. It is a linear particle accelerator. This type of tele therapy machine accelerates charge some atomic particles into a radiation beam which is then fired at the patient. The dose level is vital as too much can actually cause more damage than good. This is achieved by two transmission chambers inside the radiation head at the exit of the beam. They monitor the dose to see if the beam's flatness and symmetry are in spec. The signal from the two chambers is fed into the machine's control system which will then make sure the actual dose matches the pre-selected dose amount. The Neptune machine control system offers five different dose rates. The power for these vital transmission chambers is supplied from one power supply in which the current runs for a fuse. It will later be found that the defective fuse could cause abnormal readings from the transmission chambers which in turn could make the tele therapy machine give a dose higher than anticipated by driving the filament voltage to its maximum. But for the time being this was not known during the machine's operation. Now starting up the Neptune machine requires multiple steps to ensure its safe operation. First of all once switched on a minimum of five minutes is needed to pass to allow for proper warm-up. Then a check process begins. This involves the operator pressing certain buttons to initiate each system's self-check. After the step is complete a green light is displayed on the control panel and the next step can be initiated. Of course one of the checks is of the dose monitoring system. If it fails then the signal is sent to an interlock which will stop the initiation of the radiation beam. The signal sent to the interlock uses a diode. However this system has a flaw. If for any reason there is a break in the diode's wiring the signal is not sent to the interlock and bizarrely will give a green light allowing the next check to be undertaken. This leads the machine to be able to administer a dose of radiation without the proper checks. Anywho after startup an output measurement should be taken and this includes even after an emergency shutdown. The Neptune's manual stated a number of reasons for a complete startup checkup. This mainly covered events relating to equipment malfunctions but not for the case of a power cut. Now remember that for later on. So the BOC when treating patients always had at least two radiographers on shift at the radiation unit and at the beginning of any radiation treatment program an oncologist and physicist are also present. The overexposure. On the 27th of February 2001 the centre would be operating as normal. During the treatment of a patient the BOC experienced a power cut. The patient who was lying down on the treatment couch at the time was being dozed with 2.5 grey. This would be a total of 155 monitor units. But at the moment of the power cut had only received 5 monitor units. Now power cuts were a semi regular event at the BOC and as such wasn't seen as too much of a serious issue. Although the Neptune tele therapy unit would need to undergo the restart process. Previously the machine had operated just as good as pre power cut keeping the selected dose rates. The operator of the tele therapy machine called his boss the chief physicist and they restarted the machine. After the warm up time had passed he did some checks with the panel and power supply and these seemed to come back okay. But a full check including an output measurement wasn't undertaken because the power cut wasn't listed in the manual. The patients remaining 150 monitor units were administered however a small asymmetrical radiation field was noticed. So the patient completed their treatment and the next one was set up for their dose. She as well was due to receive a couple of greys in dose. During her treatment the chief physicist was called out for an emergency in another part of the centre. The next three patients received their doses and each reported skin irritation around the treatment site. The last of the three raised concerns with centre staff after experiencing severe itching. Something that shouldn't have happened after only a couple of greys. The patients were examined by the radiation oncologist and they discussed their concerns with the chief physicist and the decision was made to stop treatment and investigate. A Siemens dosimeter was used to check the output of the machine and it read 37 times higher than the selected amount for an 8 MeV electron beam and 17 times higher for the 10 MeV electron beam. Obviously something was not right and further investigation would be needed. It was disassembled on the 28th and an engineer discovered a failed fuse in the AC to DC power supply and on top of that the diode responsible for sending a signal to the interlock was also faulty. These were replaced and afterwards the machine's output tested within spec. It was rather confusing but the freakstorm of two fail components had caused the overexposure. Clearly a more in-depth investigation was required and this would result in the IAEA being called in. So after the overexposure the IAEA were informed. This is the International Atomic Energy Agency. They are called in for these types of incidents to assist local authorities in their investigation. So let's first of all talk about the patients. All five had received many times the prescribed radiation dose. They were initially prescribed vitamins. By May they had been re-examined and it was initially thought that they may not need to have surgery. However the progressions of ulcers into necrosis on their bodies would change this. Eventually all five would require surgery in 2002. Three remaining in Poland and two being sent to the Institute Curry in France and this was to remove decaying affected areas. All experienced reduced blood cell counts and severe discomfort and sickness. Their exposure was severe but survivable albeit with a reduced life expectancy. The IAEA set about trying to reconstruct the series of failures that led to the overexposure. They found that if the diode had failed and a fuse had also failed that the output monitors would fail to correctly read the radiation beam causing the filament control voltage to rise and cause doses up to 100 grey over the course of a treatment of 150 monitor units. Well over the 2.5 grey that was intended. It would seem that the shortcomings in the machine's design in which it wouldn't fail safe was a pretty big oversight. This failure could have still been caused if a more robust restart process was in place that would have required a dosimeter check. This would have caught the high dose of radiation but sadly missing this resulted in five serious overexposures. So it's the time for my new disaster scale. No one died. Thankfully. So it's going to be the most serious in the lower end of the scale at a number two. Do you agree? This is a Plainly Evcourt production. All videos on the channel are created because we can share our license. Plainly Evcourt videos are used by me John in a currently wet and windy corner of southern London UK. I have YouTube membership as well as Patreon membership so fancy feel free to go over there to financially support the channel. I also have a second YouTube channel and Instagram and Twitter or X, whichever one you want to call it. And all I have to say is thank you for watching and MrMusic, play us out please.


Well, we're back alive and we have Senator Brian Campion Sheriff I'll say Senate Education, excuse me and they have Provided us and it's on our web page a rewrite of section six and Which is the intercollegiate sexual harm our sexual prevention Council so Senator campion you want to go through I'm assuming the Educational committee will be offering the amendment on the floor Thanks, Senator Sears. Yes, and thanks for having me and I'm glad Michelle Child is here What I would just like to say and then I'll stick around I'd like Michelle to walk through it and then take questions as she she goes through it But the short of it is yes, we will we did hear from the University of Vermont the State College is A sexual violence task force. We also had written testimony submitted And we feel as though we're hoping and we hope this committee agrees that this would be Put into H 183. We did make some changes Senators in particular Lions Kerslick and Hooker were Took the lead on this and really worked and made some some edits and some more I Don't know if I'd say significant changes, but some additional changes that Miss Charles would walk and walk you through And I thought as we go through it. I'll be here to Address any questions that might come up with the language. How does that feel to you? Sounds good? I should we have four different colors Yeah, I thought that was very helpful It was great And so you have I don't know if it matches the senator's recommendations if that's still on there But lions is in yellow virtually. Okay, good. So Hooker pink and UVM is green. It's green In gold should yeah, it should have been catabined, right? so if so, yeah, I'm happy to stick around and The dance, you know, why don't you thank you senator camping Michelle? Why don't you walk us through? Sure. And and so you have a clean version and then you have that marked up Is your preference for show you the marked up copy? Yeah, I like to see the marked up so we can see are these the the marked ones like using the term harm prevention council, that's a change from the house version Yes Yes, there's here's reworked from the from the house version Changes from the house. Yes. Yeah, what what version is this please? one three point one One is the clean version that they voted. I'm just showing you Their markup process because senator wanted to kind of see that. Yes, very good That's helpful so starting with the term harm Sure, so we're so we're looking at draft 2.1 with the little coding color coding. So you'll see change the previously said sexual violence prevention console and members prefer to use the word harm because it's a little broader and when you're talking about the issues That are involved here around Around campus sexual harm. It's it can be it's involves harassment and other issues not just violence and so I think in That it is a more appropriate term based on the the recommendations of the task force, which is What's to have this council? Subsection a that's just a little technical I think so nothing substantive there the next change so you'll see the the section on Subdivision one is the members of the council Change is at the top of page three adding a new subdivision to at the suggestion of senator Hooker That to ensure a council that is reflective of Vermont's college campuses appointing authority shall consider diversity when making appointments to the council So that's just kind of an aspirational statement, you know, some folks are going to be Tied into having to pick a specific person because of the the type of appointment it is So like the title nine coordinators and like that it's going to be who it is, but it's to encourage Diversity on the council So subsection C on duties, this is just reworked a little bit the first one Added there was strong support for this and Sir alliance suggested it is that the first thing that they do is to review the recommendations from The task force report and develop prevention solutions to sexual harm based on those recommendations so Senator Perchlich had specifically really dug in and read the whole report and was looking at it and was interested in Kind of looking at in deeper at some of those recommendations And so what they wanted to that have the council do is to follow up on some of those The next change is on subdivision four and this is the language that I think Wendy Koenig submitted from UVM as a recommendation And I think this committee thought I think Jeanette was the one who actually forwarded it to me And so that is the exact language That UVM had proposed and it's just like tweaking semantics very in my son in my Opinion very minor, but it wouldn't thought they felt more comfortable around that Around sharing effective practices as opposed to best practices The next change is the top of page four subdivision five Senator Lyons Identify campus-wide activities publications and services that promote a campus culture of respect to support in the prevention of sexual violence And you know, I'm looking at that and I'm thinking I should probably change that word to harm No, okay So and the next one is something that was a specific recommendation of the task force and Senator Perchlich had recommended that they this kind of be highlighted for the for the council to report back at the end of this year So that the legislature could if it chose to take action on this particular thing Remember the council is only authorized to meet four times a year Right, and so there's a lot of things that they would be looking at but this one is to recommend statutory protections By November 1st to ensure that there's a sexual harm similar to the good Sam that we just passed on Exactly exactly same exact concept is that you it's Would be this would be for the universities right that they wouldn't be able to or is it for crimes I'm not sure I could the University of Vermont for example punish somebody who reported something right them I understand that That under this it would not you maybe that's something that should be in that study should the University also protect from Consequences right well, let me let me look at the underlying task force report. My guess is that it's talking about any kind of repercussions whether that be Yeah, I would I you know We've got plenty of time because this bill still in appropriations need to be voted out hopefully today, but So So I'll follow up on that Kind of related to that subdivision six is so the the house version had the network calling the first meeting no later than September 15th of this year If you are requiring them to report to you by November 1st and that really arguably only allows them to have one meeting Prior to that you'll probably you know, it's their first meeting setting their agendas and figuring that out And so they thought that if you have them meet for the first time at least in the summer then you can squeeze in a second meeting in the fall To to ensure that they have adequate time to be able to recommend some suggestions on subdivision six And then Effective date has those sections has the has the establishment of the Of the of of the council and the appropriation for the staffing take effect on passage And then the rest would would continue to take effect on July 1st something I do want to mention and the center Sears mentioned And I have to look at it is that I think I made an error so the the Still has a has a seven year Sun because that's typically what they do for any kind of Council board that's established That would have been 2028 and I think I unintentionally while looking on something for someone else related to this In 2025 so and I and I didn't highlight that or discuss that with senate at and so that is three years shorter so it would have a four year sunset instead of a seven year sunset so Can I just my apologies for that? Can I just clarify there? Yeah, senator campion So did you all discuss changing the sunset? We did not discuss changing the sunset could could you do that absolutely Okay, could I also comment on that All the boards and commissions now all the boards and commissions we and I realize this is a task force or something else but All the boards and commissions that we set up now have a five year sunset unless They're just as reports do I personally would favor 2025 Yeah, I think it's sort of like our DAP we came back and looked at it and said yes, we should continue it, but at least it forces You know Hopefully some of some of you will still be here in No, I like that change as well. I would just like send it head to yeah, we're happy to take another look at that this afternoon The only the only question I have Michelle is effect if you can make the appropriation effective on passage when the bill if the bill were to pass before the budget You need to check with Stephanie on that one Okay, because I am assuming it's in the house budget. It's not in the Senate budget at this point and If we made it effective on passage, I don't know if that's a problem or if it's nothing I mean, it's it's not it's for FY 22. So the money wouldn't be happening until July 1st. Anyway, so right I'm happy to put that as July July 1st I think you probably check with Stephanie, please I don't okay Michelle could you scroll up To the UVM language. Yep Yeah, right there So this uses the term tertiary violence. I I am familiar with tertiary prevention primary secondary tertiary prevention And I'm wondering if that's a reference to prevention because if you unless there's a Discussion of sexual violence in primary secondary and tertiary forms So I'm I'm just flagging that I I've never heard tertiary violence, but I've often heard tertiary prevention. So I believe that language has been in there since introduction and I and it hasn't really gotten any Discussion until then about that particular term so We can flag that also if you want us to look at that would be great. Yeah, I don't know whether Is Sarah you know Sarah might be able to address that because some of this language, you know came from Came from the network. Yeah. Yeah, I think the UVM language is just on the Identify and share the effective practices it okay, they just made a couple small changes to that paragraph Either way it's And and I also don't understand If it is tertiary violence As opposed to a mix up with tertiary prevention Why tertiary and not secondary As well so You know, it's it's referencing a Three-part classification scheme which I've seen used for prevention efforts With tertiary being long-term prevention So I just feel like we need clarification about violence versus prevention there and Why Only tertiary I guess we can have Sarah Robinson into committee this afternoon And have a conversation with her if and then come back to all of you that'd be great. I actually, you know, I I really appreciate Senate ads work on this. I think you did a terrific job And Thank you. Thanks. I agree. I think You know it addresses Several of my concerns. I think there's just a couple of technical questions outstanding Can I just ask a question on the tertiary Violence so is that expanding it to all kinds of violence on campus or just related to sexual Violence Looks like it could add in every kind of violence on campus. I'm sorry. I was stop. I'm gonna stop my screen. So I'm just one to be able to address that because that that that term of art was not something that I selected So did it come from education? No, it was it was in the house version and Senator Nicko we're going to have Sarah Robinson from the network in this afternoon to she's here actually. Oh, she is oh Maybe it'd be a good time to open this up to witnesses for the next few minutes Who might want to comment? Only commenting on The changes from house that Senate education not not that we've already voted out the bill Sharon go ahead. Good morning. Thank you all Sarah Robinson deputy director at the Vermont network against domestic and sexual violence Thanks very much to the committee for being willing to reconsider this Section and for the good work of the Senate Education Committee who had some really excellent conversations about this So I can speak to Specifically that section section four or subsection four I think that the concerns may be Allayed by simply reflecting the language of sexual harm In that section so saying sexual health education strategies for mitigating sexual harm and tertiary Sexual harm on college campuses in Vermont Or tertiary harm just generally so the idea is to Limit the amount of harm that happens after the incident or violence occurs And so that could be retaliation from somebody who has harmed them. It could also be Institutional harm or harm that people experience while going through the process of reporting. So I think that Yes, if I could just ask So tertiary is is third stage And primary I understand but what is the secondary then in that scheme So secondary prevention would be following There I think there's a confusion between violence and prevention So here it's the the primary violence. I understand And then I know you're you're talking about a A follow-on violence, but that seems like a two-part thing whereas prevention. I've always heard talked about in primary secondary Tertiary, so I'm wondering if there's a confusion here between Violence and prevention in the use of tertiary I think you could easily use secondary violence on college campuses in Vermont There I don't think it would change the meaning of that and I think that would make sense Okay, you could replace the word tertiary with secondary And I think that would be fine great Thank you. Are any other comments or questions About this is that Something that Senate Ed can look at this afternoon. Absolutely. We can Miss Robinson if you're available to come into Senate Ed, but I don't know how much will actually need you but just on standby and we'll have Miss Childs and come in I'm thinking 15 or 20 minutes just to talk about that and review the sunset to make sure everybody's on the same page. That would be great Happy to be available if the committee needs me Rebecca Turner or Matt Larry Do you have any comments on this section Morning Thank you Senator series for the record Rebecca Turner Head of the appellate division of the Office of the Defender General I wanted to just focus on one piece of this and appreciate the opportunity to weigh in I don't believe I've spoken to This committee About our thoughts about this one of one of first was was introduced in house tradition there. I shared Concerns relating to the membership of the council and I'm happy to see that the most recent changes of course include a seat at the table By someone by someone designated by the Defender General and that that was a request and I appreciate that and I wanted to bring the committee's attention of page three Lines one two three the the new proposed language Highlighting Highlighting the aspirational goal that the membership be diverse diverse reflecting Vermont College campus And I wanted to share that that I really that I'm happy to see this languages is in line with my earlier express concerns, not just that the Defender General's Perspective Highlighting Highlighting the aspirational goal that the membership be diverse diverse reflecting Vermont College campuses and Not just that the Defender General's Perspective wasn't included in the original drafting and now it is but where that concern really live was just having more diverse perspectives and making sure that those voices were heard on this council as well. And I shared earlier before House judiciary that we know anecdotally that black and brown boys and men are disproportionately accused of these offenses and I wanted to ensure that those perspectives are brought to this forum as well. And so I rec I appreciate lines one two and three recognizing that diversity. I worry, however, that Well, Michelle Childs framed it as an aspirational goal. The current makeup of the membership as described in page two really prevents That perspective of a college student or others from the community representing, you know, You know, students who stand accused from having their voices heard. I understand that the Defender General's appointee provides An aspect of that but that is a much more specific and specialized perspective working within the criminal justice system and certainly not standing in for the voices or perspectives of the students themselves. So I wanted to bring that to the table that while this is great, there really isn't a way to actually achieve that diversity on this panel is currently set up. I would recommend considering expanding the number of student college students who are To be on this council right now it's just two and of the two I don't see an assurance that diversity of perspectives from the college students perspectives are captured there. The second point on this was I was I was sitting on the term diversity and I think that it isn't clear what that means in this context what's intended. Certainly I could throw in wet my two cents of what I think right age gender race ethnicity is the intent to include those those pieces of diversity gender identity household income. Is it that we want to ensure there is representation from both public and private schools student body is it the non traditional student perspective diversity. So I thought that it could weren't particularly where there is such so important to capture these voices in in this in this area. So that those are my comments for the for the new changes here this morning. Thank you. I don't know how to. I don't know how to. But there's delicately but there's. I mean it would be helpful to have somebody that's mostly accused. Would be. I don't know how you write that in as a college student. Because that's the show I was watching about the teenagers.  Gang rape at Central Park. It's a net. The name of it. Anyway. I don't know if they're. There's a way to. Express that wish to. If I could just speak to that. Mr. Chair. So I sat on the sexual. Violence prevention task force a couple of years ago. And we. I'll just be blunt. We were sort of hamstrung because the membership of that group was set up to be oppositional. And it was set up to have. For every person who was. Arguing about. What what I considered a positive change in the system. There was somebody. In the. In the oppositional. Chair. And ultimately we we. We literally. Our report on the most. Important aspect of it. We almost deadlocked. And so I would be very hesitant to add. Somebody or to try to add somebody. Who has. Or who claims to have been falsely accused. Because it seems what it would. What it would start is a conversation about whether this actually exists. Or whether the problem is. False accusation rather than sexual violence on. College campuses. So I was glad to see the makeup of this panel. Be. Composed very much primarily of. People who agree that there's a problem and are working on it title. Title nine coordinators. I think all agree that there's a problem. And they're, and they're working on it. So. Having. Or trying to write in that representation would include. False accusation. Seems to me to start that. Discussion about is there. Is there a problem or is the problem. One we're creating by falsely accusing people. Just my. Just my opinion on that. My. My experience in this chair tells me that a lot of people. That have been. Sent afterwards exonerated. And many of them are. I don't disagree with you that it might make that. All more difficult. I don't think there's anything wrong with. At least asking for a third students. Oh no, I. I think increasing the number of students would be fine. Can I ask you though? So if you. So right now. You have on the student case. On some division of two college students, at least one of whom has lived experience as a sexual violence survivor and one who represents a campus based racial justice organization. So if you wanted to add an additional student. I mean, do you just want to say three, three, and then specify. The two. My suggestion. My suggestion to the education committee is to have three students. Two of whom are defined and one of whom could be. Any member of the college. Okay. Got it. As long as they're a full-time student. So. Could I just comment on Phillip. And Senator Bruce comment. I can see that you don't want to set up the committee to be. To. Be deadlocked, but I do think you need to hear from those voices. I. I just think that. We often. Do things. Well, meaning, but. Not listening to. Voices that have a different. Perspective or a different experience. And I think it's absolutely. Important that those voices be heard. Well, we do have the defender general. Well, I. I realize that, but. I think as. Rebecca pointed out that. That's very different than having. Just. Because we need to get to the floor. Sorry. I appreciate the conversation and I. I take it that it's the sense of the committee to. That when the amendment is presented by. The Senate education committee that we would support that. And Senator Sears. You will review this afternoon with Ms. Childs and others. Those. Three areas that you just pointed out. And then, which I think. Senator will be comfortable with adding a student. The sunset. And then going over. The change to. Tertiary. Yeah, I don't. That's more. That came from UVM. So they want to. No, the tertiary didn't. I got the green on it. I know, but they, they had made a couple of comments at the very. It was in the house. Bill. All right. Well, thank you all very much for a great week. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. It was in the house bill. All right. Well, thank you all very much for a great week.


Hi and welcome to Nursing School Explained. This video will go into basic cardiology as well as electrophysiology and will be the basic foundation of a series of videos to come that will go into cardiac rhythms and cardiac dysrhythmias as well as EKG interpretation. But in order to really understand where the dysrhythmias come from, we need to understand the basic electrophysiology and how things happen in the conduction system of the heart so that we then know how to interpret the dysrhythmias. So first of all, let's go back to reviewing the basic principle of cardiac output which equals heart rate multiplied by stroke volume. And cardiac output is always something that we worry about because the cardiac output is the contraction of the left ventricle that supplies the rest of the body with blood flow and is therefore super important to understand these electrical conduction problems when they occur. And then stroke volume can be broken down into preload, afterload and contractility. So preload is the ventricular filling of diastole, in diastole. So when the ventricles are not contracting when they're at rest, they get passively filled by the blood that flows into the heart. So depending on how much blood volume they get filled with depends on how strong that cardiac output will be. So for example, if the patient is dehydrated or has anemia, then that preload will be less and therefore the cardiac output will be less. Afterload is another important principle and that is the pressure that that left ventricle has to pump against to get the blood out of that left ventricle and into the body. And there are two determining factors that determine the afterload. And that is first the arterial blood pressure. The higher the pressure in the blood vessels are that go away from the heart, the more of a pressure or of a force the left ventricle is going to have to overcome to pump the blood into the body. And then the second factor is the arterial distensibility. So remember that as we age, our blood vessels get calcified. That means that they become less pliable, less stretchable, and they kind of harden. And so when the blood vessels, they usually are able to kind of expand and contract, they are very elastic, but as they harden, they are not able to expand so much. So now when the pressure comes through, when the blood comes through is ejected from the left ventricle and the arteries only distend so much because they've become hardened, then the left ventricle again has to overcome or has to pump harder to overcome that pressure and pump the blood out into the body. And the third principle here is contractility. And this is really what all relates to the cardiac conduction system. So contractility refers to the ability of the heart of that muscle fibers to lengthen and to shorten in order to produce that cardiac output, just like you would a skeletal muscle. So the ability to contract and then produce that cardiac output. So all these three times the hard way to produce that cardiac output. And when we talk about contractility, we have to talk about action potential. You might remember that from basic physiology class that there are three different stages which are polarization, depolarization and repolarization. And starting with polarization is also known as the resting membrane potential. So there is no electrical activity at all. This is a cardiac muscle cell here and inside we have positive charge and outside there is a negative charge, but there is no electrical activity. The plus remains within the cell. The negative remains outside of the cell and nothing is happening. No electrical activity is taking place while during depolarization. The cardiac muscle cells get stimulated by sodium flowing into the cell. And then this action potential kind of goes down like a wave. So sodium kind of flows in and causes that cardiac muscle contraction. And but this is only the electrical event. So this is the electrical event from the positive and negative charges that are expected to cause a mechanical event and the mechanical event being the contraction here. Now there are certain dysrhythmias where there is an electrical event, but it's not causing the contraction. And that would be PEA, also known as pulseless electrical activity, which is why we learn in basic CPR class that we always have to check the patient's pulse when they become unresponsive. Because on the EKG monitor, we might see a waveform. We might see this electrical activity, but because no contraction is happening, we are not able to fill a pulse. So this pulseless electrical activity, electricity is flowing through the heart, but it's not stimulating these muscle cells. And therefore the patient doesn't have a pulse, there's no circulation, and then certain measures will have to be taken. And this depolarization here on an EKG, the P wave represents atrial depolarization and the QRS complex represents ventricular depolarization. So the contraction of the atria comes first, followed by the contraction of the ventricles. And of course the ventricles are going to have a stronger and longer contraction because they are much bigger and they are the ones that produce the cardiac output. Now repolarization is when the influx of sodium into the cell stops and the potassium flows out. Remember whenever something goes in, something else has to come out in order to maintain balance between the positively and negatively charged ions. And the membrane potential returns to a negative resting level, which is the polarization also known as that resting membrane potential. So there is no activity, then every then the sodium flows in, eventually potassium flows out and then we're back to square one until the next beat hits. Where repolarization on an EKG strip is represented by the T wave, and that is ventricular repolarization, and we'll go into that a little bit more when we look at the actual wave forms. And then other important principles here are the refractory period. So a refractory period is the cell's ability to respond to a stimulus.  So the absolute refractory period happens from the onset of the QRS to the peak of the T, so right between ventricular depolarization and repolarization, where the myocardium cannot respond to a further stimulus because it is currently in this depolarization phase and it hasn't quite repolarized yet. Now in the relative refractory period is when the downslope of the T wave hits and some cells may have repolarized, so they might have returned to the resting membrane potential, and they are therefore able to respond. And when another beat hits at that time in the relative refractory period, there is a high risk for dysrhythmias. So that's when it becomes really, really dangerous. Okay, so let's look over this here on the graph. So we have here, this is a normal EKG with our P, QRS, and T waves. And then here represented we have atrial depolarization represented by the P waves, ventricular depolarization represented by the QRS complex is what it's called. And then ventricular repolarization is the T wave. And then remember I said that atrial repolarization happens, but the atria are smaller chambers and they repolarize right after they depolarize. But on an EKG strip, we're not really able to see that because the ventricular depolarization has so much more strength in the conduction system that the atrial repolarization is kind of hidden behind this QRS complex. So we can't really see that. But remember the atria are not as important as the ventricles when it comes to dysrhythmias and production of the cardiac output. And then here we have the absolute and relative refractory periods that we talked about over here. So the absolute refractory period is from the onset of the QRS to the peak of the T wave. And then the relative refractory period is from the peak of the T wave to the end to the downslope, the entire length of the downslope of the T wave. So what that means is that when electrical impulse hits during the absolute refractory period, that means the ventricle is still depolarizing and we can't really expect the ventricle to be contracting again. However, if there's an additional impulse coming in through the relative refractory period, through this very short period of time, through this downward slope of the T wave here, then that's why dysrhythmias can occur. And then these properties of cardiac cells are super important to understand and that will really help you in understanding the different dysrhythmias that we're dealing with. So first of all, we have automaticity. And that means that cardiac pacemaker cells' ability to initiate an electrical impulse without a stimulus by a nerve. So all the cardiac cells are specialized cells. They are all pacemaker cells. We typically just think of the heart pacemaker as the SA node, the sinoatrial node. But every cardiac cell has the ability to take over as the pacemaker. And that can be without a stimulus by a nerve because we're thinking usually stimulation has to occur from a nerve. So whether that is moving your arms or your legs, we have to stimulate the nerve first in order to get the contraction going. But the automaticity, all the cells of the cardiac muscle have the ability to stimulate that impulse without a nerve being present. Now next, we have excitability and that goes hand in hand with irritability. And the way I like to remember that is we all know the excitable friend that we have, but sometimes we cannot get irritated with them because they're so hyper excitable. So think about this in terms of cardiac physiology. All cardiac cells have the ability to respond to an external stimulus that can be chemical, electrical or mechanical. So this relates back to the membrane potential. So chemical and electrical might be an imbalance that's due to potassium or magnesium imbalances or even sodium and calcium. If the level is abnormal, that can be the cause of dysrhythmias. And we have to have a certain level so that the cells are excitable, but not quite irritable. And we'll look into that a little bit in more detail after here. And then conductivity. So the cardiac pacemaker cells can receive an impulse and conduct to the adjacent cell, which means that an impulse anywhere in the myocardium can spread. And we'll go into that when we look at this graph up here. And then contractility is the ability to shorten causing a contraction in response to an electrical stimulus. So remember, when the cardiac cells get stimulated, they shorten, which then causes the muscle fibers to shorten and then lengthen. And actually that shortening causes the contraction and then produces that cardiac output. And the contractility can be enhanced by certain medications. And those are, or examples of those are digoxin, epinephrine, and dopamine. And those are very important medications when it comes to dysrhythmias. And we'll talk about that in the following videos. Now this graph over here is basically just the four chambers of the heart, the two atria and the two ventricles. And then in green, we have the conduction system. So typically we have the SA node, sinoatrial node as our inherent pacemaker. Then the impulse travels down through the atria to the atria ventricular node, which is between the atria and the ventricles, the AV node. Then we have the bundle of his that travels down through the left and right bundle branches and then up the ventricles to the prokinjee fibers. Now all these different systems, the SA, AV and prokinjee fibers, they have an intrinsic heart rate. So the SA node usually conducts the electricity at 60 to 100 beats per minute, which is the normal heart rate for an adult. Whereas the AV node or the bundle of his that comes a little bit further down in the conduction system have an intrinsic heart rate of 40 to 60. And even the prokinjee fibers, the last part here of the conduction system, they have an intrinsic heart rate of 20 to 40. Now when we see a patient with a heart rate in the 50s, for example, we have to think, did something happen with their SA node where the impulse is not coming from the SA node, but the AV node now has taken over and the heart rate is 50. Now certainly there are a lot of other factors that can determine the heart rate being 50. Then we have to look at the underlying rhythm. Do we have a PQRS and T wave that represents the atria and ventricular depolarizations in order to determine where the breakdown is in the conduction system? And then coming back to the principles that we talked about over here. So the conductivity, any cardiac cell can get excitable and then conduct an impulse. That means that a cardiac cell, for example, up here in the left atrium, can become irritable for whatever reason. Electrolyte imbalances, problems with circulation to the coronary arteries, whatever it might be, any cell in the heart can become irritable and then they want to take over as the pacemaker because of this intrinsic ability of every cardiac cell to have the pacemaker ability. And that then will show as a dysrhythmia. So that would be, let's say, a premature atrial contraction, for example, because now we might still have the conduction going through as normal, but now we have an extra beat or an early beat that comes from somewhere from an irritable cell in that atrium. Now, this can also happen in the ventricles. Of course, ventricular dysrhythmias, as you can imagine, are more dangerous than atrial dysrhythmias because when the ventricles are not pumping efficiently, then we're having a true problem. So even a cell down here in the ventricle can become irritable, but because it has the principle of automaticity, excitability with irritability and conductivity, so it can initiate an impulse. So now if this cell here in the ventricle is irritable, then it will conduct an impulse to the adjacent cells that then might travel down to the pockinji fibers and up here again. So we might not have an impulse that starts all the way starting from the SA node represented in that P wave, but it might be showing up somewhere later on in the prolongation of the QRS or the T wave because now we have this extracellular that's become irritable. So remember, these intrinsic heart rates are very important, as well as these four principles to really know where the cardiac dysrhythmias come from to understand how the heart functions and the innate ability of the cardiac cells to be a cardiac pacemaker cell. So this is the first video of this new series that I was mentioning in the beginning of the series. I will have some additional videos that go into sinus rhythms, atrial rhythms, AV blocks, atrial ventricular blocks, as well as ventricular dysrhythmias. So we're basically gonna cover all the different parts of the conduction system where something can go wrong. And remember that in nursing school, you're not expected to know the details of every single dysrhythmia. This is more advanced, which you will learn in your ACLS or Advanced Cardiac Life Support once you take these classes. And then you also learn, of course, how to treat these dysrhythmias. This is a very basic overview and also on NCLEX, you're not expected to know the depths and details of all of the different dysrhythmias. And my videos will show the most important ones. And if you understand these very basic principles, you should be able to really understand and how to interpret the dysrhythmias. I hope this video has helped you get a better understanding of the very basic electrophysiology and how it applies to the heart and dysrhythmias. Please also watch out for the following videos on the different types of dysrhythmias. Please subscribe to my channel if you find it helpful. Leave some comments below and share with your friends. Thanks for watching Nursing School Explained. We'll see you soon.


What's up everybody, Jason here for jaspyscasebreak.com. 223 Tops Crumb Update Breakers July 10 box case break. Picker team number seven just sold out. And again guys, Jason, those one-on-one I'm gonna be debut patch autographs. So here we go guys. Appreciate you guys helping sell it us out today guys. Some people bought straight up, other people got those through fillers. Little team randoms. Here we go. Breakers July case right here. All right guys, so thank you guys so much. And again for people that are tuning in. Today is the last night of those giveaways, or not giveaways I should say, but discounts. Cyber Monday, Black Friday Cyber Monday. 15% off the entire website. So again, even if it doesn't look like a break it's gonna fill just by tonight. Because tomorrow, no more 15% off. Goes back to normal price, which again, I tell people at the time, we still have great prices. You know, so it's not like you're still entirely losing a lot, but could save just a little bit more. Now the next break I wanna just keep it kind of base bullish, just because definitive is in the R&B and the second break at definitive number 11 is already down to six. So we can definitely run those back to back. So let's try to sell out a definitive R&B. That way we can work on some definitive tonight. And the R&B is not at that expensive guys. A good amount of teams in there. Diamondbacks one of the biggest teams for like 175. Now if you use the discount quote from 56 bucks it turns out to be like 47, 60, 47, 30. So pretty cheap. All right, here we go. Actually that's, get the three cards on the back first. Alexander, Jolts, Weissley, Rosario. Brett Weissley for the Giants. Giants is Steven, Burrito, and a Kevin Kiermeier. So a 299, that's for the Blue Jays and Barry. And then behind Jordan Walker Youthquake is a Jason Delay for the Pirates who's going to Charles. And then we have a Levi Stout for the Reds going to Brad to 150. All right, here we go. Edward Juli, your show. Then Christian Vazquez. And how about this little Adley Rochman or the Oral Zack from that filler to 150. Nice sit right there. Schmidt for the Giants to 399. And we have two color autographs back to back. One's like a ray wave. First one is Max Mayer for the Marlins, which is going to Steven. And how about another one for the Marlins, Soriano. Back to back Marlins hits to 250. Purple there and then Max Mayer it is out of 150. Quick to breathe though. Next one. Man, my work has just had two car accidents and I do lots of legs for three months for speeding in the space of 10. Jesus, what's going on, man? Oh, this seems like way more cars than normal. Stubbs, Rodriguez, Pascantino. All right, we got Yipez, Ohapi. And we got a Noah Cindergarde pink to 399. Jared Kellan at gold to 50. And how about another Kalanick? Orange this time, already halfway through the rainbow out of 50 and out of 25. That's for the Mariners and X-Line. And then we have Shuster, Youthquake, Wodeo's Waldo, Cabrera, sorry. For the Yanks going to Tristan. And then a Chris O'Kee to 199 for the Reds. Reds is Brad. Yeah, yeah, I don't know. Well, yeah, I'd assume so too. Jesus, Tagy Yoshida, Fairchild, and I's Gunnar Henderson. Zika Tovar, Colby at a 250. Joey Ortiz to 299. Yorba or a blue. And then behind Michael Bush, we have two color cards. First one we go with the back with. Kevin Kelly to 299, Speckle. Then we have a gold wave for the Texas going to Grant Anderson. And that's going to Alexandros. Phillips, Levi, Talos. And that's nice. Minnesota twins are going to Michael. Duvall, Emmanuel Valdez for the Red Sox. That's number to 199. Behind Marvis is a Evan Lee for the White Sox, sorry for the Nationals going to Ryan Pressnell. And then Israel Pineda, back to back hits there for the Washington Nationals going to Ryan. And Duvall's number to 299. Julian to 125. Bellinger, Bebe Youthquake, Green to 99. Grissom to 250. Ryan Walker to 125. And then Cooper Hummel to 399 for Seattle. We got Bobby Miller. And behind Bobby Miller is Jake Berg. And Vinny Pascantino, nice one there for the Royals. Chris Parent with that one. Yeah, very busy day, man, honestly. Kind of slowed down the second half after my lunch, but it's just because we pretty much did most of the stuff earlier today. But yeah, it's always good to be a little busy. We got a Christopher Morale, nice one there for the Cubbies. What a desk. Juggers of Provar to 399. Joey Ortiz to 150. And then behind this Youthquake, we're going to go to the back card, which is Soriano. And then behind Vientos is a Jose Caballero for the Mariners, excellent. Hoby Harris for Washington to 75. And then we got Blake Perkins for the Brewers, going to X-Line. And Bobby Miller, very nice to 199 for the Dodgers. I'm a Valon. All right, two more boxes, guys. Kind of feel like we're missing a wowser hit, man. This has been kind of a little underwhelming case. But we still have two more. Come on, give me something nice. Allen's Miller Perkins. Gold, Tyler Alexander to 50. Detroit, going to Charles. We got Trevor Williams to 75. And there's a Radiator Ricky, shortstop. And it's Zack Nieto for the Angels, going to X-Line. Miguel Vargas, Youthquake. We got Tanner Beebe for the Guardians. And Ben Joyce for X-Line and the Angels. Guys, hopefully we can get something really nice to end this off, but it's been a pretty bad case. I feel like the biggest hit. Ruchman blue? I feel like, damn. All right, boss, I mean, I have no control over it, man. I mean, I just try to hope to get a better case. We got one box left. This is one of those cases where you load it up with a freaking MLB debut patch or something to make up for all of it. But it looks like that's not going to happen here. All right, Casey Smith, Soto. Miguel Maya, Van Winker. Rich Hill, Poshmere. Negative Dominic Smith in a manual with all this. Brett Beatty? Well, I guess that's not that terrible. That's going to you pups. So Metz is going to Alexandros. Wish they had more color to go. And then another Ben Joyce. Refractor this time to 4.99. Another one for Slime. All right, well, sorry guys. Nothing super crazy out of this case, unfortunately. But like I said, sometimes this does happen. Again, a definitive is a fresh case. I definitely know that's going to be a little bit hotter. I really doubt it would be that bad, but a definitive is one I want to do tonight. Already an R&B and a fresh case on that one. But again, sometimes it's going to happen. Beatty. I've got great colors though, right? I mean, a lot of nice colors. Just not the craziest players after all. Thanks guys, appreciate it.


Hi, this is our first tutorial session. In this session we will try to solve some important problems given in our notes especially from the mathematical preliminaries and also from the chapter on arithmetic errors. Let us see how to solve this problem. Here we are given that a sequence A n is going to satisfy some condition. What is that condition? Mod A n minus L is less than or equal to some constant mu times A n minus 1 minus L and this happens for sufficiently large n that is what the assumption says. Not first few terms, but after certain term say for some positive integer capital N all the terms A n's for n greater than equal to the capital N we have this condition. And further the question also says that the constant mu is something lies between 0 and 1 that is very important. Now we are asked to prove that the sequence A n converges to L as n tends to infinity that is what the question is. Well let us see how to prove this result. To prove this result first we have to obtain this inequality. Let us see how to obtain this inequality it is not very difficult. It goes with an idea which is quite often used in our course therefore it is important for us to understand and keep this in mind. The idea goes like this see we are given this inequality. Now the same inequality can also be applied to the right hand side. For that let us take n sufficiently large then you can apply the same inequality for A n minus 1 minus L that will be less than or equal to mu times A n minus 2 minus L. In this you have to also make sure that n minus 1 is also greater than or equal to n that is why we have taken n very large when compared to capital N. And now once you have this you can see that A n minus L is less than or equal to mu times mu into A n minus 2 minus L and that can be written as mu square into A n minus 2 minus L. Remember I am putting equal to sign here because this term that is the right hand side term is equal to this term. It does not mean the left hand side is equal to this often students get confused whether this is equal to this. No this is still less than or equal to this we are writing only because the right hand side is equal to the second step of the right hand side. And now what you can do is you can again apply the same inequality for now A n minus 2 minus L and that will give us less than or equal to mu cube mod A n minus 3 minus L like that now you can keep on going up to what term we can go well we are given permission to use this inequality only up to n is equal to capital N. Therefore we can go only up to A n minus L here. So, when you go up to A n minus L your mu will have n minus capital N on the power. Therefore this will be less than or equal to this that is how we landed up with this inequality. Once you establish this inequality the conclusion comes almost trivially because mu is less than 1. Now you take n tending to infinity and see what happens when you take n tending to infinity n tends to infinity you can see that n minus capital N will also tend to infinity and that implies mu to the power of n minus n tends to 0 why since 0 less than mu less than 1 because of that we have this property. Now you can see that this term is going to 0 and this term is a finite quantity and therefore the entire term will go to 0 on the left hand side you can see that we have taken modulus for this. Therefore this is surely greater than or equal to 0 now if you recall in the sandwich theorem if you have two sequences A n and C n and you know that A n is less than or equal to B n is less than or equal to C n and if this goes to say 0 and this also goes to 0 as n tends to infinity then this will also go to 0. In the sandwich theorem we have stated it with any limit here we are using it for that limit as 0 and you see by using sandwich theorem therefore you can see that this term also goes to 0 as n tends to infinity that is equivalent to saying that A n tends to L. Now let us go on to the next problem. The next problem is a discrete version of the second mean value theorem for integration. The problem says that you have a function F which is continuous on the interval AB and you are also given some n points taken from the interval A to B and also you are given some values G 1, G 2 up to G n they are given to be real numbers and more importantly they are of one sign. It means either everybody is positive or all these G's are negative there is no sign change among these G's that is what it means then we have to show that sigma i equal to 1 to n F of x i G i is equal to F of xi into sum over i equal to 1 to n G i where the xi is some number lying between A and B that is the problem. How to prove this? This is a very simple application of the intermediate value theorem. What you do is just take the minimum over all the values of F at the points x i call it as F x suffix star and similarly take the maximum of all these numbers call this as F x super star. Now what are we going to do with that? Well we have the left hand side i equal to 1 to n F of xi G i. Now if you replace all these terms by the minimum then you will have this is less than or equal to F of x star it will come out of the sum because now it is independent of i into sigma i equal to 1 to n G i. Similarly if you replace all these by the maximum then it will be less than or equal to F x super star and since this is independent of i this term will come out of each term and you will have sigma i equal to 1 to n G i that is very simple to understand. So, therefore, we have this remember for this we have used the fact that G is of one sign and we assume that G is greater than 0 otherwise if all G's are less than 0 you will have a reverse inequality that is all. Otherwise the idea of the proof goes exactly same as in the case of G i is to be greater than 0. So, here itself we have to assume that G i's are greater than 0 and then we get this inequality. Now what we will do is we will take these terms and define a function G of x is equal to instead of x subscript star and F superscript star we will take it as F of x into sum i equal to 1 to n G i. You can see that G is a continuous function why because F is given to be a continuous function and this is something which is a fixed number positive number as per our assumption right. Therefore, G of x is constant times a continuous function therefore G itself is a continuous function. Now if you recall you have a continuous function G and you have G of say a and G of v then given any number between these two numbers say n you can find a xi such that G of xi is equal to n that is what the intermediate value theorem says right. So, we will just use this now to get a xi such that now you see you take this as your n G of xi is equal to this i equal to 1 to n F of xi G i right. So, that is what precisely we wanted to show that this term can be written as F of xi into sigma i equal to 1 to n F of xi is equal to 1 to n G i right. So, that is what we wanted to show here and that comes directly once if you write this inequality it comes directly from the intermediate value theorem. Similarly, if G i is less than 0 then as I told the inequality will reverse that is all the same idea for conclusion will go through even in this case also. Let us go to the next problem again this property is often used in our course especially if you go through the proof of Taylor's theorem and also the theorem for polynomial interpolations we will use this idea. What this problem says you have a continuously differentiable function G and we know that the equation G of x equal to 0 ok. This is a equation it has at least n real roots then the equation G dash of x equal to 0 will have at least n minus 1 real roots. This idea is used as I told in the proof of Taylor's theorem as well as in the proof of the error analysis of the polynomial interpolations. What is the idea behind this well you know that the equation G of x say it has n roots say for instance these are the roots of the equation G of x equal to 0. Let us say this is the graph of the function y equal to G of x and you have x 1, x 2, x 3 and x 4 are the roots of this equation then you have to show that G dash has at least n minus 1 say for instance if this equation that is G of x equal to 0 has 4 roots then G dash of x equal to 0 should have 3 roots. How will you get well you use the Rolls theorem. Rolls theorem says that in between these two points you have a point xi such that let us call it as xi 1 such that G dash of xi 1 equal to 0. Similarly here also you can apply the Rolls theorem between x 2 and x 3 and you will get say xi 2 such that G dash of xi 2 equal to 0 and similarly here also you have xi 3 and G dash of xi 3 equal to 0. So, that is the idea it is just a direct application of the Rolls theorem. I hope you can write the solution for this problem now. Well now let us pass on to the discussion on the order of convergence if you recall we have introduced two notations one is big O and small O. When will you say that a sequence a n is big O of b n if you recall you should be able to find a constant c and a n such that you mod a n is less than or equal to c times mod b n for all sufficiently large n's right. So that is what we have to show in order to show that a n is big O of b n. Here a n is n plus 1 divided by n square and b n is 1 by n. One way is to directly take this term n plus 1 by n square divided by 1 by n and see that this is bounded as n tends to infinity this should be a bounded quantity. This is obviously equal to 1 plus 1 by n and that tends to 1 as n tends to infinity right. Therefore, this is correct that this sequence is a big O of 1 by n. You can also directly use the definition in that case you have to write n plus 1 divided by n that can be written as sorry this is n square and that is written as 1 by n plus 1 by n square which is equal to 1 by n into 1 plus 1 by n right and that can be written as less than or equal to 1 by n I will just replace this by 1. I just want a constant here right that is the idea and b n is nothing but 1 by n. Therefore, I am having already b n here right 1 by n here this I have to somehow freeze this n and make it a constant for that I am dominating 1 by n by just 1 you can dominate it by 2, 3 and so on anything any finite number but I am just dominating it by 1 and that gives me 2 times 1 by n. Therefore, in this case my c is just 2 and that shows also from the definition that this sequence is a big O of 1 by n. Let us take the other problem here we have a n is equal to 1 by log n and you want to show that this is small O of 1 by n. Therefore, b n is this if you recall we have to here show that for every given epsilon greater than 0 we have to find a n such that mod a n is less than or equal to epsilon times b n for sufficiently large n right that is what we have to show. Now, one way to see is to directly compute the limit and see this log n into 1 by n which is equal to n by log n right that goes to infinity as n tends to infinity. Therefore, this is actually a n is not a small O of 1 by n. Now, if you want to see it through this definition how will you see well we can see by contradiction assume that 1 by log n is less than or equal to epsilon into 1 by n for some sufficiently large n and for some epsilon or rather we should write for every epsilon because for every given epsilon this should happen right. So, for every given epsilon I will find a n such that this happen that is what I am assuming and I will show that it leads to a contradiction. How it leads to a contradiction this implies n is less than or equal to epsilon times log n right and that implies n by n by n log n is less than or equal to epsilon well I can directly write it from here for all n greater than or equal to capital N right. You can see that the right hand side is tending to infinity as n tends to infinity this should hold for all n sufficiently large right. So, that cannot happen because this side is going to infinity whereas, this is some very small number if I take then this cannot happen right. So, that is a contradiction. Let us now solve some problems in the chapter on arithmetic errors here let us take this problem. The problem says that we have a computing device that uses n digit rounding binary floating point arithmetic show that 2 to the power of minus n is the machine epsilon. Let us recall what is mean by machine epsilon machine epsilon means it is a very small number which we denote by delta such that you take that delta add it with 1 and then take the floating point approximation whatever the floating point approximation that you want to take well in this problem it is the n digit rounding is the floating point approximation ok. Then that delta will actually give some number which is greater than 1. However, if you take any number less than delta whatever may be the number it is if you take any number less than that delta then the floating point approximation in our problem again it is n digit rounding should actually give 1 it should not give anything greater than 1. Only for delta it will give that is the last number for which it will recognize it as a non-zero number anything less than that the computing device will recognize it as 0 only that is what is called the machine epsilon. Now, let us see how to solve this problem well if you see how to represent this number in the binary form we can write it as 0.000 0 up to n terms and n plus first term is going to have 1 and then 0 into 2 to the power of 1 ok. So, if you recall it is floating point approximation is 0.1 if you write and then into 2 to the power of E. So, whatever may be the E that comes here you have to write but I am just writing it in the direct form and then you can see that the 1 is sitting at the n plus first position right. Now, any delta that you take which is less than 2 to the power of minus n will have 0 in first n plus first position even in this position it will have 0 and then it will have 1 somewhere else right that is how delta which is less than 2 to the power of n will look like ok. Therefore, if I add 1 plus that delta what I will have well 1 can be written as 0.1 into 2 to the power of 1 right and that delta will have first many terms 0 at least n plus 1 terms are 0 and then you will have 1 somewhere after n plus 1 term. Now, if you see this will be equal to 0.1 then 0 0 many 0s at least at least n plus 1 terms right that is what we know because 2 to the power of minus n has 1 at the n plus first term. Therefore, any delta will have 0 at the n plus first term at least and have 1 somewhere else into 2 to the power of 1. Now, what I will do is I will take the floating point approximation of this thereby I will do the rounding up to here when I do rounding up to here that all these are 0s right and the non-zero term is actually truncated here and thereby the floating point approximation of 1 plus delta will remain as 1 because I have truncated up to n plus first term and up to that there was no non-zero term in the representation of delta and therefore, you have 1 that shows that 2 to the power of minus n is the machine epsilon for the computing device that uses n digit rounding binary floating point representation. You can also understand from here why the definition of machine epsilon demands that the floating point approximation of 1 plus delta should be equal to 1 right because if you do not have that if you just say that f l of delta should be equal to 0 if you say then the floating point representation of that will actually push that non-zero 1 to the first position and thereby when you do the n digit rounding you will not be losing that non-zero information in the floating point level that is why in order to lose that information you are actually adding 1 to it here and that is how this information is lost otherwise this would have written as 0.1 into 2 to the power of some e right and therefore, this 1 would have come to the first position and when you do the n digit rounding of that you will not be losing this information. So, you are adding 1 to it and checking that is the reason why we have given 1 in the definition of the machine epsilon here this machine epsilon is a very important concept in computation one has to understand this. Let us take the next problem here we have the number x a that is given as 3.14 and y a is given as 2.651 these are given to us as approximate numbers generated from some true numbers x t and y t we do not know what are these true numbers all we know is that we got this approximate numbers by using 4 digit rounding ok. We are not given these information y t and x t are not given to us we are only given that x a is obtained by rounding 4 digits from x t and similarly y a is obtained by doing 4 digit rounding of y t. Now, we want to find the smallest interval that contains this number and the second subdivision is we want to find the smallest interval that contains x t by y t remember we do not know x t and y t right. Therefore, we just have to find an estimate of x t and y t in terms of both the lower bound as well as the upper bound ok. So, how to get the lower bound and upper bound of x t plus y t let us see for that first we have to understand what is the range for x t and what is the range for y t that is what we have to understand. You can see that x t can be any number greater than or equal to 3.1395 you have to tightly find this number that should be the smallest number which when rounded should give you 3.14 you can see that that is the smallest positive possible number that gives you 3.14 when rounded to 4 digits right. 4 digits after writing the floating point approximation right. So, you have to do 4 digit rounding it means 1 2 3 4 this is 5 therefore, it will be rounded to add 1 here and that will make this as 3.14. Similarly, the largest number that can lead to 3.14 is actually 3.1405 because you can see that 3.1404 also gives us when you do 4 digit rounding it gives 3.140 then 4 1 4 2 4 3 4 4 and so on all this is the largest number that can be this numbers when you round to 4 digit rounding it gives you 3.14 therefore, x t should be anything less than this number that is the maximum possible that you can think and once you get this idea now it is very easy to solve this problem you can see y t will lie between 2.6505 and that is less than or equal to on the upper bound you have this is less than 2.6515 right because 2.6514 will also give 6.65141 and then 4 1 4 2 and so on any number will give this number right. Once you have this now it is just a matter of adding this 2 number x t plus y t and that is less than or equal to 5.792 and this is less than or equal to what 5.79 roughly right. So, that is what we get let us go to the next problem next problem is to estimate x t divided by y t again we have 3.1395 less than or equal to x t is less than 3.1405 and similarly y t lies between 2.6505 and this is less than 2.6515 and that implies right that implies 1 by 2.6515 is less than 1 by y t is less than or equal to 1 by y 2.6505 right and just doing the reverse of this inequality and therefore, x t divided by y t will be less than or equal to no this is less than therefore, it is less than 3.1405 divided by 2.6505 and this side it is less than 3.1395 divided by 2.6515 right that is the answer for this problem. Finally, let us solve this problem where again we are not given what is the true value x t we are given the approximate value of x t as 2.5 with an absolute error of utmost 0.01 that is what is given to us. Now, we want to evaluate the function f of x equal to x q actually we want to evaluate it at x t, but unfortunately we have only x a right therefore, we are evaluating it at f of x a right. Now, what is the absolute error involved in f of x a when compared to f of x t is the question. So, we have to estimate f of x t this is what we want to actually find, but we actually found x a because we are only given the approximate value. Now, we want to find an estimate for this what is mean by estimate of anything you either have to find the upper bound that is you have to find some fixed number say k such that this is less than equal to k or it may also be that you have to find a lower bound say small k such that small k is less than equal to this number, but here we will only find the upper bound. What is given to us given condition is x t minus x a is less than or equal to 0.01 right that implies that minus 0.01 is less than or equal to x t minus x a is less than equal to 0.01 right we know x a. So, just substitute that you will have 2.49 is less than equal to x t is less than or equal to 2.51. Therefore, we have an estimate for x t from here as lower bound as well as the upper bound. Now, let us use the mean value theorem that gives us mod f of x t minus f of x t minus f of x a which we want to find can be written as f dash of xi modulus into x t minus x a what is xi, xi lies between x t and x a. Now, what is this this is nothing, but 3 times xi square and this is 0.01. Well, if I have to substitute 0.01 for this I should have less than or equal to right. And again we know that xi lies between x t and x a and we already know that xi lies between these two numbers the maximum that it can take is 2.51. Therefore, we can roughly estimate xi to be less than or equal to 3 into 2.51 square into 0.01 right and that is approximately 0.189003. So, this is an approximate estimate for the error involved in evaluating the function f of x equal to x cube at the point x a when compared to f of x t. So, these are some of the important and interesting problems from our classes covered in week 1. With this we will finish our tutorial session 1. Thanks for your attention.


In this video, we're going to be talking about why Beck couldn't help Peach and just a warning there's going to be talk about suicide in this video. What is up everybody? This is Chris from the Rewired Soul where we talk about the problem but focus on the solution. And if you're new to my channel, my channel is all about mental health and what I like to do sometimes is pull different topics from pop culture like shows on Netflix you might be watching to teach you how to improve your mental and emotional well-being. And in this video, we're actually going to be talking about how to help a friend who might be struggling with their mental health, alright? So make sure you subscribe and ring that notification bell. Before we get started, you guys, we at this moment in time, we are only 1700 people away from 10,000 followers on Instagram. You guys are amazing but we're so, so, so close. So if you haven't yet, go follow me on Instagram after Rewired Soul. I'm trying to help you all out and help myself by making things easier by getting the little swipe up feature for Instagram stories. So go follow me over on Instagram, tag your friends, tag your friends and tell them to follow me too. And we'll do this thing together, baby. So yeah, we're going to be talking about the show You Over on Netflix. Great show. Tristan and I actually have one more episode to watch. We're about to watch it as soon as I record this video. But if you have not watched the show You Yet or if you haven't gotten to episode nine, there's going to be spoilers. So if you're in the middle of the season or you haven't watched it yet, turn this video off, come back later. If you're not playing on watching the show and you just want to learn some stuff about mental health, stay tuned. All right. But anyways, yeah, we're going to be talking about Peach and Beck, mainly Peach. Yeah, mainly Beck. All right. But yeah, so what we're going to be focusing on is Peach threatening suicide or even attempting suicide, right? So this is something that comes up quite a bit and that's why I want to talk about it. So just a little quick recap of the show. When Beck got into a fight with Peach, Peach ended up taking a bunch of pills, calling up Beck and saying, Hey, I just took all these pills. Beck races over with Joe and they go over there and Joe finds out that she didn't really take like anything that could really kill her. And Joe had to have this awkward conversation with Beck about how she didn't take anything that would actually kill her, right? But what Beck tells Joe is that, you know, this isn't the first time that Peach has done this, all right? And this is something that a lot of people deal with, okay? I've made videos about suicide before and things like that. But a question we get a lot is like, like, how do you know someone's serious? How do you know if somebody's telling the truth and all of that? So as we find out later in the season, like, Peach is manipulating Beck a ton. And by the way, I put up a poll over on my community tab about what topics you want me to cover. Like everybody chill out. I'm 99.9% sure I'm going to cover all those topics as well as more. I just want to see which ones you wanted first. But anyways, I'm going to do another one about Peach gaslighting Beck. But yeah, Peach was manipulating Beck. And this is what we call holding somebody as an emotional hostage, okay? So this might be your friend. This might be a significant other.  All right? This happens a ton. A lot of you came to my channel for my elimination videos, right? And one issue that elimination had was that that dude Harris kept threatening to kill himself, right? And this is a way that people keep control over us, okay? So here's some tips on how to deal with this. The first major important thing to understand, and it's going to sound harsh at first, but bear with me. First important thing to understand is you cannot save anybody, okay? You are not a licensed therapist. You are not a psychologist. You are not like a doctor or an EMT or anything like that. You cannot save anyone. So one of the things that we do is we take way too much responsibility for other people's emotions and actions, all right? So you have to remember that you cannot save anybody. Now, this is something that I had to learn. Some of you who have watched my videos about how many people I've lost, most of them are former clients. Some of them are people I knew outside of work and outside of my clients. But as of recording this video, I've lost about 76 people in the last three and a half years or so. I could not have done that job if I took responsibility for every single relapse, every single overdose, every single suicide. I would have drove myself insane. Now, one of the ways that I got out of that way of thinking was coming from a 12-step background, I had a sponsor who I would talk to because when this started happening, I was going nuts because I would sit there and rack my brain around it and be like, what could I have done? What could I have done more? What could I have done more? Now, that's a good thing that I felt that way because that means I care, but my sponsor had to remind me that I only have so much power, right? So what I did with my job, and this is something I advise all of you to do, I came in every single day the same way I do this YouTube channel and I give it 110%. I do the best I possibly can, all right? But I would drive myself insane and for an addict like myself who's in recovery, that could lead me to relapse if I took responsibility for every single thing every single client did, all right? So just remember, you have no control over what somebody else does. Once you get rid of that illusion of control, it can start helping. Now, the reason why that sounds harsh is because some people who are watching this video are going to say, oh, well, does that mean I just shouldn't care? It shouldn't matter? No, that's not what I said. Everything, everything is about balance, right? But we can't focus on the actual solution until you get it out of your brain that your captain save a person, all right?  Like this isn't the movies. OK, it's not a show on Netflix. You are not saving anybody. OK, so you can help get them on the right path. And that's the best thing that you can do. OK, so I'm not telling you don't care. I'm not telling you ignore these suicidal threats, but you need to focus on what the best options are. OK, a huge issue throughout this show is enabling. OK, so looking at Beck's relationship with Peach and going to run and try to save Peach every time Pete's throwing suicide and everything like that, like this is the form of enabling. That's enabling that behavior. OK, now, because they wanted to keep it secret, this is something I see, like I see it in shows and it's so disheartening that this is something that actually happens like you guys. That's why I make these videos. This stuff actually happens like Beck in that scene where they show up at Peach's house. She talks about to Joe like, oh, we can't tell anybody. We can't tell anybody. Her family will think this. Her family will think that. It's like what what again? You are not the person to save people, right? But this is also something that we see when Claudia is detoxing in that basement, right? So let's let's talk about this. Like this is why Tristan and I always talk about everybody needs a healthy, a healthy type of anxiety, right? Like what if what if after throwing all that stuff up and let's say Peach did take some stuff, what if Peach ended up dying in that bed right next to Beck, right? What if Claudia while detoxing in that basement even though Karen was a nurse, what if Claudia died in that basement? You want to live with that? I sure as hell don't. You know what I'm saying? Like we need to quit doing this thing where we're going to keep secrets. Like here's the way I deal with this. Like when people like tell me to keep secrets or whatever, I ask myself, if this person dies, am I going to be able to live with that on my conscience? Right? So here's the thing. Like they didn't show it in this. I don't know if it's different in the book, but if this was a real story, I guarantee you, I guarantee you Beck would have so much regret in her life and it would take her years of therapy, okay? To get rid of the idea that maybe, maybe Peach would be alive if she actually got Peach's professional help, all right? Like think about that for a second.  But Beck thinking that Peach did commit suicide, any actual person would sit there staying up at night hating themselves, wondering what could I have done more? What could I have done differently? And one of the first thoughts in her head was, maybe I should have told her family, maybe I should have called 911, maybe I should have got a professional help, right? Same thing with Claudia in that basement. Like you gotta quit covering up for people who are sick, okay? You are not a licensed professional. And even in the case of Karen helping Claudia, Karen is not the person to help, right? For example, when I was getting clean and sober, my mom, even though she has a PhD in psychology and was the clinical director at a rehab center, she was not the person to help me. We're too close, okay? That is not how this thing works. So a real quick story. My best friend who I grew up with, he has been sober for over three years now. And he used to call me up drunk, suicidal and all of that. And the one thing he would always tell me is don't tell my parents. Don't tell my parents. Cause his family was like my family. He's like, don't tell my parents. And what happened? This is the first time I thought it. But one night when he was drunk and suicidal, I sat there thinking and said, if this dude goes out and kills himself, am I gonna be able to live with myself knowing that I didn't tell his parents, which might have saved his life. So I had to weigh the options. I had to weigh it, okay? On one hand, I tell his parents and my best friend in the world hates me, hates me for that, right? But on the other hand, I tell his parents and maybe it saves his life. Now, when I look at it like that, when I look at this thing very life and death, black and white, the decision was simple.  It broke her heart and she was crying. But guess what? We got my buddy into rehab.  So I want you guys to remember that. Like, again, I'm not saying don't be there for your friends who are struggling with depression, who are suicidal, but too many people out there are suffering far too much because people like you and me think that we're gonna save them rather than getting them professional help, rather than talking to their parents about it or their family about it.  Like don't do that. But I just wanted to kind of set in the groundwork. Like if you need to, like what I would recommend is like, if you have a therapist, talk to your therapist, talk to a mental health professional, hell, call the suicide hotline and be like, yo, like I have a friend who's doing this. What do you think I should do? Like they're 24 seven, call them, ask them what youth they think you should do to help your friend. The best thing you could do to help your friend is to guide them to a place that will help them, okay? Like it's almost like addiction. Like do not do anything that will enable them to keep doing this thing, but do everything in your power to help them get the help that they need, right?  I will go with you to a doctor. I will go with you to an ER. You know what I'm saying? Like part of what they were afraid of was Pete's was like, oh no, they're gonna put me on a 72 hour hold. I don't give a, I'm trying to keep this PG, but I don't care. Like yeah, you need to be on a 72 hour hold if you're threatening suicide. You know what I mean? But anyways, anyways, I hope this video helps you out and understands what you need to do if you have somebody A, in your life who is threatening suicide or B, who is trying to keep you as an emotional hostage by threatening suicide.  You need to get some help. You need to learn how to set up these boundaries, okay? All right, but anyways, that's all I got for this video. I have a bunch of more you from Netflix review videos coming up, breaking down characters and all that. But if you liked this video, please give it a thumbs up. If you're new, make sure you subscribe and ring that notification bell because I make a ton of videos. And a huge thank you to everybody supporting the channel over on Patreon. You are all amazing. And don't forget, please go follow me on Instagram at the Rewired Soul, it's real easy. All right, thanks again for watching. I'll see you next time.