I think let us get it started now. The next presentation from me is about enhancing safety culture through organizational learning. In the previous session, Peter was talking about the safety culture. And we had seen a lot of principles, safety culture is a culture which is evolving in an organization if we follow certain principles. So some of the principles he was telling like people or the trust permeates the organization. You know everybody is accountable for nuclear safety. So like that there are several principles which support a good safety culture in a nuclear organization. And there are many good documents available about safety culture. And those principles you can see from those good documents. But each of these principles are supported by several attributes. If we see these attributes in an organization we say that that particular principle is well maintained or well established in those organizations. So in my presentation what I am going to talk about is how organizational learning is helping to promote nuclear safety or rather performance in an organization. So organizational learning is one of the important principles if it is embraced in an organization can derive significant benefits for promoting safety culture and safety performance in an organization. And if you look here there are four points that are given four attributes. If these four attributes are present in an organization we can say that that organization has a good organizational learning. It has seriously taken organizational learning into picture and they wanted to improve. The first one is the organization values operating experience. They give good importance to operating experience that's coming from their own organization. That's coming from the fleet of their organization and from external to those organizations. And the important thing is the underlying lessons learned from significant industry and station events are used effectively to improve performance. What does it mean? What does it mean they use operating experience? They need to identify the underlying causes behind those events whether it is a significant big event or a minor event. What are those underlying causes and what are the lessons that can be learned from those events and how that can be incorporated into the organizational processes and programs. The third one is there are established processes to identify, resolve and improve from latent organizational weaknesses. You will come across several organizational weaknesses, latent weaknesses as you progress through the nuclear power program and how they are going to be captured, how they are going to be analyzed and how the results are going to be implemented for successful performance improvement. And finally, how the organization cultivates a continuous learning environment. If these four attributes are present in any organization, we would say that it has a good organizational learning. So in this presentation, I'm trying to give you two examples. We are going to see how two examples of an event that happened in the industry and how they analyzed, how they identified the causes and how they learned the lessons just to give an idea that how industry is using the operating experience to learn, learn these, learn from these events. It's not going to be that easy to understand the whole scenario behind these events, but don't bother about it. I'm trying, I will try to make it as simple as possible for you to understand the important aspects of the event evolution. And finally, you will be able to appreciate the, how they arrived at the causes and the contributors for this event. So the first example is about a reactor's cram and safety injection caused by human errors during a maintenance activity. This happened in one of the PWR units. And the task is a very simple task. They were trying to measure a voltage across a safety system battery. There are safety systems used in the, you know, in a nuclear power station for many purposes. One of the maintenance requirement is to periodically test the voltage across those terminals to make sure that those batteries are having the, you know, the remaining life or required performance standards. A simple system, they use a multimeter, typically if you see a simple meter, two terminals put it on the battery and see how much voltage. Very simple task. The lead technician was giving direction. There are four people in this scenario, two lead technicians and two trainee technicians. The lead technician was giving directions and the trainee technician was actually performing the task. And the trainee technician connected the terminals to the multimeter terminals to the rectifier. The rectifier is the, a component associated with the battery. And after this, they saw loss of power supply to the safety related switch board. The entire switch board lost power supply after just connecting these two terminals to the, to the rectifier. And followed by that, there was a automatic reactor scram, the turbine trips and the station loses the 400 kilovolt power supply, electrical power supply. The reactor coolant pumps, which circulates water to the reactor coolant, also trips after this. Immediately seeing that the loss of power supply to the safety system switch board, the technician resets the power supply to the switch board. There is a, you know, there will be a circuit breaker which trips the power supply. The technician immediately tries to reset it. And he, when he resets, safety injection actuates. At the press, the next, what happens is the primary system relief wall opens several times and a diaphragm and a relief tank ruptures. The entire thing calls for 12 days of shutdown to investigate and normalize the plant. So I will go in detail about how this event happened in more detail.  Then only you will be able to understand the, this event. In a nuclear power station, we have different classes of power supply. This is the, you know, the high voltage power supply, the 6.6 kV. This is normally derived from the grid. The station transformer supplies or the grid supplies this power supply. We would say this is the least reliable power supply available in the station. Normally the reactor coolant pumps, the heavy loads in the system, non-safety loads are driven by this power supply. So you can see this also has a backup. It has, it can be fed from the station generator or it can be fed from the grid or it can be fed from the another safety source. Next we have, next level we have as, you know, the diesel generators, the blue ones here once. Here another diesel, two diesel generators. They supply power to this, this, you know, the switch board or the bus. We call it a bus. And these are normally fed by the grid. If the grid power supply fails, the diesel generators come online and they feed the power supply to this. We say this is an emergency power supply, much more reliable than this power supply. The next level, the highest level is, you know, the DC power supply system, 48 volt DC, some industry uses 110 volts, but generally a DC power supply is used for control and protection purposes. You know, in a nuclear power station we have several critical control functions, several critical reactor protection functions. All those protection and safety functions are controlled by, I mean, provided by power supply from this source. And they normally take power supply from the grid. The diesel generator feeds it when there is no power supply here. And even if the diesel generator fails, there is a battery backup here. The batteries are designed to provide for sufficient number of times so that the plant is brought to a safe shutdown state. So in this particular scenario, the maintenance technicians are working on this battery. They're trying to measure a voltage across these batteries and find out if they're healthy or not. So it's just a five-minute check they're going to do. Now let's see in detail what happened in detail little bit. Unit was operating at full power. It's a periodic test, means once in three months or once in six months, means it's a routine job. It's not a new job or anything, the people are used to this job. And on a 48 volt DC power system, as per procedure, normally they measure the voltage across the battery terminals. But in this case, contrary to the procedure, voltage measurement was performed on the energized rectifier. If I go back to the picture, you can see they're supposed to measure the voltage here, but they choose to measure in this rectifier because it's same. If you measure the voltage here or if you measure the voltage here, it's one and the same. It's correct. But the procedure calls were measuring it on the battery terminals, but these guys were doing it on the rectifier. We'll see what's the consequence of it later. Then as I told you, there were four people, two lead technicians and two trainee technicians. So the trainee technician was performing the job and the lead technician was giving the directions. So the lead technician asked him a question, but the trainee thought it's an order for him to execute. You remember, he's asking a question, but the trainee misinterprets or misunderstands that it's a direction for him to perform. The question is, what will happen if you put this multimeter into the current mode and measure? You know, this small meter which is used for measuring voltage, it has several buttons. You can measure voltage, you can measure current, you can measure resistance. So these guys are going to measure voltage, but if you put it in the current mode, what happens? He was asking a question. So he thought it's an order, put it in the current mode and measure. So what he does is he puts it in current mode and then attaches to the rectifier terminal. So it's little electrical, don't bother about it. If you put it on the current mode, it actually short circuits the two terminals of the battery. Don't do it anywhere in a high voltage battery, it's harmful. There are several incidents that happen. If you wrongly put it in the current mode and measure the voltage, it short circuits and then the protection trips the power supply to the circuit. This is what has happened on the day the power supply caused a short circuit and resulted in normal power supply to the switch board was lost. The people are immediately they realized it's a mistake they have done. So what has happened is the battery power supply lost for an unknown reason. There is a battery which is backing up because now this the electrical, you know, the rectifier trip and there is a battery backup, that is also stopped for an unknown reason. So there is a complete loss of power supply of the safety related 48 volt DC switch board. So the total power supply is lost. And this caused the following, automatic reactor scram, opening of the strip down transformer circuit breakers. Because I told you this DC power supply controls and protects many functions. It feeds power supply to many things. So because they all lost power supply, we lost the 400 kV power supply. And there is a normal pressurizer spray is also lost. That means the pressurizer spray means it's used for putting a spray into the pressurizer and then reduce the pressure of the system. You add more spray, the pressure comes down. So you lose control on maintaining the pressure in the primary system. And the last one is loss of CVCS let down system. It's a controlled volume system. It allows some amount of water being taken from the primary system to maintain purification and to maintain the chemistry and also to maintain the pressure. So once this is lost, you again lose the function of maintaining the pressure in the primary system. So a simple event of just measuring a voltage across two terminals. Imagine it has resulted into a significant problem for the operators. But the maintenance team is not aware. The maintenance guys are working in a different area from the, they're disconnected from the control room. They're working in a different place. They are not aware that the reactor had scram. They are not knowing that there is a loss of 48 volt supply and that has caused all these problems to the plant. So they started re-energizing the switch here. They started resetting the switch here and started closing it back. Because they know that because they put it on the wrong side. That's why it got tripped. So you want to reset it. But when you reset it, this is the, you know, you can look at the picture here. The work area is like this. This is the rectifier on which they work. And these are the two circuit breakers which are providing the power supply from the rectifier and to the rectifier. So they trip, so they're very nearby. But there is a red label there, you can see red warning that says that if you reset this breaker, there is a chance for emergency injection or the what do you call that in a water injection into the reactor is possible. That's what is written there. But they did not realize this. They just went for resetting it. And then as a result of that safety injection, CVC has let down line closed, primary pressure increased. Don't bother about it, why it happened. These are all the consequences. And the pressure is a relief valve open several times because the pressure is increasing because you're not able to maintain the pressure in the primary system, the relief valve open several times. And because of that, one of the two diaphragms and the relief rupture tank, relief pressure tank. There is a pressure vessel on which all these relief water goes. And that tank pressure is increasing because of that the rupture disc failed. And finally it resulted in 12 days of outage for even the investigation and rectification and coming back. So what do you think are the main causes of this event in your own opinion? If you are, I just explained to you what has really happened. Using your own judgment, can you tell what are the probable causes for this event? Pardon? Human error? Yeah, good human, human error. Communication gaps? Communication gaps? Can you be more specific? What is, where is the communication gap here? Yeah, okay. Pardon me? Very good. Procedure is not followed or I mean rather going out of procedure, yeah? And control room, yeah? Of course, we do not know what was the communication, it could be. Need to? Need to be trained well. Need to be trained well, okay. What's the training because it's just measuring, it's over? Yeah, but then you mean to say the lead technician is aware. He was just asking him a question, what would happen? Yeah, he was trying to teach him, actually. But then he misunderstood, the problem is not lack of training. The trainee technician is trying to do the job under the control of the lead technician. The lead technician is very smart. He knows if he puts it on current mode, it's going to trip. But he was asking a question to him, if I put it on current mode, what would happen? But the trainee misunderstands it as an order and then he does it. So it's not a problem with training, it's a problem with communication, as somebody said. He understood the communication in a wrong way. That's what I would put it, okay? Like, yeah, it's a good point, actually. It's one of the things. They reset it without communicating with control room. Do they have authority to reset the safety system breaker without knowing what exactly happened in control room? Does he have authorization to do that? He is authorized to do maintenance. Is he authorized to do this work? That's a good point. I think a lot of inputs you have already told most of the things. But one of the most important thing is lack of risk assessment. If you look at the morning lecture which Peter was talking about in a nuclear industry, there are activities, you know, how do you, the risk has got two factors, you told. One is the consequence or the other one is the probability. In this case, the probability of error is very, very less. It's a very simple event. But the consequence is very high because he's working on a safety system. But did they do a proper risk assessment on this activity? Did this job receive the attention that deserved received in a nuclear power plant? That are the question. We'll see it in more detail in the next slides. The next one is a distracting environment. I mean, distracting environment in the sense you answered it in a different way. There were four people. Why do they need four people in such an activity? You just need measurement and then two people are good enough. When you have too many people in activity, there is chances of distraction. Two guys would be talking and two guys would be doing and they may not be knowing what's happening around. You know, that's one of the reasons when they analyze, they identify human error reduction tools. You said that already there is a human error. Why did human error happen? They were not using any human error reduction tools. I will get into that little bit in detail in my next slides. So let's look at lack of risk assessment. The test was conceived by the station as a low risk activity. They didn't think that it's a, it's just measuring a terminal voltage. They were looking at it. They were not looking at the consequences. And no pre-job briefing and contingency plan was in picture. You know, what is a pre-job briefing? Any of you are aware of a pre-job briefing typically done in a nuclear industry? Any idea? Pre-job briefing is before an activity is started. All these stakeholders, all the people who are involved in the job meet together for about five minutes, 10 minutes, depending on the intensity of the activity. And then they discuss on two things. What is to be achieved? What is to be avoided? Or what is to be accomplished? And what is to be avoided? And what are the error likely situations that can happen here? In this activity, there is an operation team. There is an maintenance team, electrical maintenance team. Two teams are involved. Did they talk to each other? No. Was there a pre-job brief? No. If only they talked, they told the control room that I'm going to work on this. If it trips, what should I do? Yeah, it would lead to a safety injection and you should not reset it, right? This information was known to them. Probably this event would not have happened. Industry has a practice of pre-job briefing and having a contingency plan. If something goes wrong, what we should do on that? Deviating procedure, somebody told yes. The procedure calls for measuring it at the battery terminals, but then they measured it at the rectifier, maybe for convenience or ease of doing or something. But then that had an element of problem for this event. Oh, sorry. Performing voltage measurement in wrong location. Posted warning sign was ignored. We know that. Distracting environment. Four people, instead of two peoples. They were trying to conduct a shadow training. They're trying to make them get trained into this job. But then you can do them shadow training, but you cannot involve them in doing it. And if you do it in a way that you want to train them, their role should be very clear. So unclear roles and responsibilities of lead technicians, workers and trainees, these are the contributing factors under distracting environment. Finally, the human error prevention tools not used. No pre-job brief, which we have seen. Procedure adherence, procedure was calling for measuring in the terminals of the battery, but they did it in another way. There was no procedure adherence. There was no three-way communication. You know what is three-way communication? We were talking about communications. Three-way communication or repeat-back communication, which is very well used in the aircraft industry and the nuclear industry. It's a very good communication tool. Repeat-back is like, if I want to say something to you, say for example, I'm talking to a doctor on an emergency situation. I want to know his phone number or clinic address. I ask him, what is the address? He says, x, y, z, so on and so forth. Then I repeat and then tell him, is it x, y, z? Then he says, yes. So I send the communication. He sends the communication, I acknowledge it, and then he confirms it, three ways. So a nuclear power plant, the good practice is that people follow repeat-back communication or three-way communication to make sure that we understand it correctly. If only the lead technician used a three-way communication to the trainee technician, probably you would not have understood the question as a wrong one. Does it make sense to you? There is something called self-checking and time-out when sure. And I will not go into that. It's too much. Some of the self-checking is checking ourselves, making sure that I'm everything what I'm doing is correct, coming out of all my daydreams and other activities and making sure that I'm on the right place, I'm on the right equipment before I start doing it. Industry typically calls star, stop, think, act, review. So we'll not go into that. And another one is the time-out and ensure. Whenever you are not sure, take some time, think and then act.  In this case, if you see when the power supply was lost, he was immediately hurrying to reset it. He wanted to restore the power supply without knowing what would be the consequence of resetting it. If only he had taken a time-out and then consulted the control room, what would happen if I reset this? Probably safety injection would not have taken place. So what are the contributing causes? There are weaknesses in nuclear safety culture. You can see it's not using human error prevention tools. Acting outside of normal, I mean operating equipment in recovery attempt without approval of operators. He was operating in equipment which is not under his domain. And lack of situational awareness and insufficient questioning attitude. Nobody was questioning. Morning we started questioning attitude is very important for nuclear safety culture. People are not challenging the actions of each other. Operating experience, very important for the topic on which we are discussing. There are several fleet experiences because there is no time, I'm not listing them. I can at least list some 10 to 15 events which had happened before this event had actually happened. And they were not aware or they were not using this operating experience. Similar events which doing such battery maintenance and they had loss of power supplies. It was not used correctly. And there was no common cause review. They were not doing a common cause analysis why it had happened. Lessons learned. Briefly, we'll see what are the lessons learned from this. Reinforce compliance with maintenance procedures, rigorous and timely methods for procedure revision including risk assessment for change requests should be in place. This is one of the recommendations after the incident they followed. Define clearly role and responsibility of maintenance workers, lead technicians and supervisors. Systematically use human performance error reduction tools during maintenance work. Take timeouts when facing unexpected situation before taking any action. And have safety culture as one part of maintenance fundamentals in a continuous way for an effective line of defense. And they review the risk of electrical work on safety related power supplies. The last one during risk assessment consider potential human errors. These are the lessons they learned from one. There is another one. Make sure what supervisor and line manager have sufficient knowledge of operational risk of the component and system they work on. Probably the supervisor or the lead person who was working, he was not having a good idea about operational risk. What would happen if I do? That's also possible. And lastly, the review and reinforce more rigorous evaluation of industry and fleet operating experience for applicability because they did not consider several incidents or events that had happened in the industry. So now they wanted to consider them. Why is this event important to us? This is a complicated event resulted from human errors that demonstrated weaknesses in nuclear safety culture. Operators were unaware why abnormal events were occurring. Impulsive non-violated actions were taken without considering the possible consequences before attempting corrective actions to reenergize the switchboard. What is, while this event occurred at a pressurized water reactor, do you think is it applicable only for pressurized water reactor? It's equally applicable to all type of reactors because the power supply system, the electrical systems are more or less similar in all type of designs. They all have a battery-powered emergency supply system. So this event can be used by almost all the units as an operating experience. So this even highlights the importance of a healthy nuclear safety culture at all levels of plant works and the need for rigorous and consistent use of human error reduction tools. That's about the first event. If you have any questions or anything you want to understand about the first event or you want to add something to the first event before we go into the second one, no? Okay, yeah. What is pre-briefing, you want to know? I think I will talk about that in the lunch break or something to you, maybe because of time I wanted to, it can be, I can tell you a little more elaborately what's a pre-job briefing, how is it done? That would be good. Okay, I move on to, yeah. Very good comment, excellent. In fact, industry uses such instruments for such critical applications. The instrument has no provision to selection. You block them, you make it only available for, in fact, I have no time, I can share in my own plan we had an incident in which one fellow lost two of his eyes. He was measuring a, in a battery directly he was maintaining, the battery has an acid, hydrochloric acid, he was measuring the voltage, and then the hydrogen gas is produced when the battery is charging and discharging. So the short circuit exploded the battery and the impact part into the glass. I think he lost one nigh or part of one nigh or something. Based on that, industry has learned that to block it whenever you measure a voltage on high capacity batteries they always use only the voltage mode. Thanks for the comment, yeah? Yeah, you see, when you are analyzing an event sometimes it's not possible to find the causes. That's the reason it's written unknown reason. When it's not so easy, an event has happened, you're trying to analyze it, why it has happened, how it has happened. There are thousands of interactions of components and you look at many, many event scenarios and then try to find out the causes. Based on this event, they could not establish a cause for why the battery also lost its power supply, failed to provide the cause. Now the second event, it's about inadvertent draining from the reactor vessel while at mid-loop conditions.  In a refailing shutdown, they open the top cover for taking out part of the fuel and putting new fuel. And during the time, they also, you know, this is the reactor pressure vessel. They take out the cover, top cover and the fuel, the entire thing is flooded with water and then they take out the fuel assemblies partly and then put new fuel assemblies. Okay, the water level will be maintained somewhere here. And these are the two connections which connect to the circulating pump and the steam generator and the pressurizer. There are two connections, there are no valves here. So if I want to work on this pump, let's say I need to do some maintenance on the pump. So that means I need to drain water up to this. Otherwise, I'm not able to, I have no access. So what they do is typically lower the level in the vessel so that it allows maintenance here. It's a very critical activity. They monitor the level very carefully, but still it will be having a lot of margin. This picture is not very exact to the drawing. It's just showing, although only a few centimeters, there is more than a meter of a distance would be available. So this particular event when it happened, the plant was on refilling and it is on mid-loop operation. They were doing some maintenance on the steam generator or possibly on the pump. So I'll go back to. So the maintenance was being performed on a motor operated valve in the residual heat removal system. That means there is a, this is the main loop on the primary system. There is a residual heat removal system, which is safety system. Suppose these pumps and these heat exchangers are not available. You remove the heat by a residual heat removal system that takes connections from here somewhere. It takes water from here and puts back the water somewhere here through another system. So there are valves connected to this. So they are working on a valve which is attached here. You can imagine where the work is being done and when the reactor is on a mid-loop operation. Sorry. So the maintenance was being performed on a motor operated valve in RHR system. The maintenance is taking out the driver, the actuator, electric actuator, doing some replacements could be some bearings or replaced, gears are replaced and then they are putting it back in good condition. So the actuator was installed on the valve after completing the shop tests. You know, once you put back the actuator back into the valve, they need to set the limits, the open position and closed position. There are limit switches in the actuator. So they need to be set to the correct position to make sure that the valve is fully shared and fully open. So this can be done and actually you need to, in the field, you need to set it. So they were, the workers start beginning to stroking the valve to set the limit switches. At that time, control room observed there is a drop in pressure, reactor pressure was a level and about nine cubic meters of water was lost. Two field operators came to field for investigation and then again the level was restored by the gravity flow from a tank or from a low safety injection system. What's the consequence if the level goes below? Any idea? What would happen if the level goes further below? Pardon me? Yeah, that's good. You expose the core, the core can, the heat removal will get effective, very, very important. So this picture I put to make, give an explanation for that. So if you look at the reactor pressure vessel, this would be the connections. You can see the fuel, actually you can see the fuel and how those, you know, the connections are there. You can see good amount of distance is there between those connections. Even summary, in a little more detail, unit was at mid-loop operation. Maintenance was performed on a motor operated valve on the primary circuit, which is a first isolation valve. So first isolation valve means if this valve is open, chance of water to get out of the reactor pressure vessel. It was installed on the valve after the shop testing was completed. The work supervisor, there is a supervisor and technician. The technicians are performing and the supervisor is giving direction. He left the work area to call the main control room for permission to stroke the valve to set the limit switches. So we went to the phone to talk to the control room. I'm going to open or close this valve to set the limit switches. But before that, the contract workers, before the contract workers, before I mean began stroking the valve open to adjust the limit switches without permission from the supervisor of the control room. Before they could get the permission, the contract workers started stroking it and this action led to unexpected drop because the water was going out of the reactor vessel and the level dropped. The mid-loop level, special alarm actuated in control room and they immediately acted and they took some action to put back water into this. So this is how they restored the water back to the system. It's not important for us. What are the important aspects? What do you think in this situation, what went wrong here? Communication, obviously, control room to the plant without proper communication distorted, yes? Procedure, they didn't follow the procedure or rather a communication or procedure, okay? Let's go a little more deep. Risk assessment performed on outage maintenance work before the outage did not identify any task specific risk associated with the work on this one. Normally in a nuclear power station, they do outage planning six months or one year ahead. You know the refilling outage is hardly less than a month, three weeks or four weeks maximum. But the preparation and planning starts almost six months to one year ahead. So they list all activities, there will be thousands of activities done in an outage. So they do a risk assessment of each and every activity and then they sequence the activity in such a way that the risk is always maintained low. For example, you have three safety trains, nobody gives permission to work on all these three safety trains at a time. The boundary valves, for example, in this case a boundary valve, people look at it carefully, can I give a boundary valve maintenance when there is a refilling outage going on? So that did not identify this activity as a risk involved activity. And they have a nuclear power station, they have a work planning system. There are many, many works coming up. It's a computer controlled work management system. It tracks what are all the works issued. If a work is issued on a train A and it would not allow you to issue a job on train B and train C. So in this particular station, they have a computerized work planning system, but it's not integrated with the planned lockout tagging system. Tagging system means, when they take an equipment to a different position, a valve, say for example, a valve is closed and then it should not be open for isolation purposes. They give and kept it closed condition. They put a tag in there, a red tag or a caution tag. That is to make sure that nobody operates it and make sure that it gives you safety for working on a particular equipment. So the tagging system and the work planning system are not integrated. This means the person who is going to tag the system was not aware that already it's a boundary valve. If they are integrated, you would know that they are together and they would not have acted on that. But many stations have an integrated tagging and work management system. Yeah, this is important point. Contract specialists may be unfamiliar with planned systems and not aware of planned rules and administrative processes that must be followed to help ensure nuclear safety. This is one of the important causes. These contractors who are working on the valve, they are specialists on the valve. They know how to do the valve in a very perfect condition, but they do not know the consequence of opening a valve or closing a valve. What would happen if they opened this valve? They do not know the importance of nuclear safety. They did not have an appreciation for the consequences that would result. They are the same thing which I was telling you. The supervisor thought, he assumed. He assumed that the specialists understood they were not to proceed with the limit switch. He did not reinforce them. He did not tell them in a pre-job briefing or in a clear terms that you must not work without my permission. He assumed that they know they should not operate the valve. And also this is another important thing. Many times it really happens in nuclear power plant.  This is the end of a maintenance schedule. You know, the eight hour period is going to get over. The guys are very much interested in finishing this work and go home. So he is in a hurry. So he knows that he's going to get permission. Let me start before by the time he gets permission, nothing is going to happen. Let me start. So the time pressure because it's a closing ship duty, that's another factor that has added to it. Why I'm listing all these things where you used to have an appreciation that how industry uses the information, the cost analysis, how depth they go to do the analysis. Because these are important for promoting nuclear safety. You can do a very shallow operating experience analysis that doesn't bring out underlying causes in any event. But if you do a very clear thorough analysis, you can bring out all the underlying causes in an event. At the time of the event, it was accepted practice that work was allowed and blocked valves as long as the valve remains shut. I mean, there are some industry guidance and expectations that if blocked valve in the sense, it's a first isolation valve of an isolation valve. The first isolation valve, you can do maintenance as per this particular station's expectation that you are allowed to work on the valve as long as it's remained shut. You are not opening it, but you have a risk on that. But some stations don't allow it. They have very clear guidelines. They have some extra conditions for that. Workers were allowed by the procedure to operate the valve as long as they had permission of the main control room staff, even though the red blocking tag remained attached to the valve. This is another important point. I told you there is a red tag attached. It says, do not operate the valve. But still the station expectation or station procedure allows them to operate the valve if they have permission from control room. So this gives you a little bit cushion for you to go towards unsafe situation. Pre-job briefing of the work crews prior to beginning important of our hazardous work were not routinely performed. They were not having an expectation that a pre-job briefing should be done for hazardous work or works which has potential for events. The corrective actions following the previous event were not effective. Previous experience, similar events were not followed up or not regressively implemented to improve the performance. What can we learn? Are our risk assessments are needed prior to authorizing outage work on reactor coolant systems or safety system components? Pre-job briefings could have helped work better understand conditions of the reactor coolant system and the valve that they are working on. If there was a pre-job briefing, it gives an opportunity for the supervisor to tell the contract workers, it's very important for nuclear safety. We should not operate the valve without control room permission and it could have prevented a near miss event. Yeah. Except for unique or unusual circumstances, dictated by system design, work should not be allowed on system boundaries. This is industry practice. Except, there are certain very rare exceptions in which they put lot of contingency measures. They put additional people to make sure that they don't operate it. Otherwise, industry doesn't allow people to work on boundary valves on critical systems. So clear rules must be established that provide guidance on how boundary isolation valves are identified and for the actions that planned workers and operators may perform. Yeah, that's about the two events. Now I go a little about how this can be used for improving safety culture or improving the performance. This is operating, learning from experience improves your performance. You know, as a small kids fall dozen times a year and as we grow old, we learn from our own mistakes and we don't do that. We learn from our own mistakes. Same way, most animals, most creatures in the world do the same thing. We learn from our own experience. But also, this is experienced or invented by some genius Pythagoras many, many years ago. We don't learn it from our own, you know, knowledge or our own efforts. We just use it from some part of the world. There are many inventions, many such inventions available from many places. We don't reinvent it, rather we inherit them. So if you try to use those experiences, your growth is going to be like this. If you're going to learn from your own experience, you will only reach this height. In our industry, people can learn from the following. In nuclear industry, people can learn from their own in-house experiences. There are many, many experiences in their own station and also they have a lot of external operating experience they can learn. It could be from decades ago or it could be recent ones. You told about three events this morning, Fukushima, you know, the Three Mile Island and Chernobyl. Also, we talked about the David Busse. There are many, many events, recent ones and old ones. They teach a lot of lessons. There are many things that can be learned to improve our performance. So this is a famous quote by somebody. He says, fools say that they learn by experience. I prefer to profit by others' experience. So you choose what you want to be. There is a famous law, Heinrich's law. Anybody is aware of this Heinrich's law? Probably you've seen this, but the name is not familiar. You know, when people analyzed the accidents or something happening in an industry, they have a relation with the reference to the minor events and near misses and unsafe practices. So if some event has to happen, it has a relationship with the minor events. It has a relationship with near misses. It has a relationship with unsafe work behaviors. So if you control this part, if I try to make this base much smaller, I can prevent an accident. That's the basic philosophy of this triangle. So let's see an example. It's very easy to explain a lifting and rigging example. A guy is hit by a load, a fatal accident could be one. There are broken hand and by load injury. If you see, before somebody dies due to a fatal accident, you can definitely see many minor injuries or loss of limb, the loss of other parts. And also there could be load drop. Fortunately, no injuries are damaged to the components. That's near miss. Actually a load is falling, but still nobody dies, no injuries. It's a near miss, we call it. Something similar to the previous event. But if you look at the worker behavior, there are several things, four or five things listed here. Deficiencies in worker skills, lack of pre-job briefing, workers entering under load, use of deteriorated rigs, inadequate communication. It could be many, many more. So if we focus on the bottom part of it and try to reduce that, we have a control on reducing the accident. That's what this Hendricks law is trying to say. The root cause is common for all of this. So how industry uses this? As I told you, we have a lot of in-house operating experience. We also have domestic operating experience. We also get overseas operating experience from IAEA, from Vano, from any vendor organizations. A lot of information is available. Industry organizations use this operating experience to reduce their base of this unsafe work behaviors. And also to reduce their near misses. They also learn from their own near miss incidents. And one other thing comes here is that they do a job observation, which I will come in my next slides. How can you identify these unsafe work behaviors? Unless people go to the field and then see what's really happening in the field, you will not be able to capture them. Many stations have a very good job observation or work observation programs. They systematically go to the field and see how workers' behaviors are there in the plan. They take note down and have a database and analyze it. Tens of thousands of information they analyze and then come to know that what behaviors will promote in safety and performance. This is the last part of my presentation, which will tell you how we can use the observation operating experience for improving performance or how rather industry uses it. So this is what typically an observation process in a nuclear power plant, where they use select an activity for observation and they conduct an observation. They also provide coaching to correct the, correct the reinforced bad behaviors. I mean, correct bad behaviors and reinforce good behaviors and input it in a database every time. Whenever whatever you see, this is most important unless you capture them in a database and analyze, you will miss all those, the value behind those information and analyze them periodically and then they will tell you an identity area for improvement. There is some potential for weakness in this area. We are finding a lot of people are not wearing hard hats in this operating area. You're finding a lot of people not using procedures while working in batteries. These are the information you will get from these observations and then you can revise your management expectations and processes to improve it. This is typically followed by industry to improve performance. So if you look at it here, we have in a station how work is done, there is a management expectation, what we want, how people to behave and the people are provided with training and experience. We provide them training because they need skills to do the job and the experience also gives them the ability to do a good work. And finally there are processes like procedure, mechanisms or work control processes or work management system. These are all called processes in the power station and they help them to implement the work in a systematic way. The process plus behavior finally gives you the result. You may have an excellent process, you have the best work control process or work instructions, tools, everything. But if the worker behaviors are not good, your results are going to be problematic. You need to have both right. If you have good worker behaviors, if you have a bad process, then also no use. If you have, you need to have both of them right. So this is one method of triple loop learning we call it. So what is happening is we are observing basically the training and experience of the people. You can find out when you observe a work, if there is a weakness in the training or experiences. You can also observe if there is a weakness in the process. You can also observe a weakness in their behavior. Most important is behavior. You're looking for behavior. You're also looking for process and training. So you take these observations and then giving a full feedback to make your management expectations changed or in a better way to make sure that the performance continuously improves. So this is done in a three levels. In the first level, it's called a coaching. You work on the coaching mode to improve performance. In the second level, you work to make better ideas. How can you develop better ideas to improve performance? And the third one is most important, wherein you generate what would affect the values and beliefs of the people. You can, that's most important. Let's briefly see what is it. In the first loop, you are observing the work. You are seeing a behavior. Let's say he's not wearing a helmet. He's not wearing a safety shoe. He's not following procedure. You correct them immediately. So it gives you some improvement, but the improvement is very incremental, very minor improvements, and it continues. So loop one helps, is useful in people achieving expected performance. You can achieve a performance what you expect. Examples, a worker use personal protective gear. Workers adhere to procedures. Workers self-check and peer-check actions and demonstrate a questioning attitude, procedures are revised and improved, et cetera. In the second loop, you are observing the, your observations are looking for a change in paradigms. You're not, you're not looking, you're looking for people are, people are following in the first loop. You are seeing people are not following safe practices. You're correcting those practices, but still the improvements are not substantial for you. You are not able to reduce the accidents. That means whatever you have achieved in the first loop is not good enough for improving your performance. Now you have to look for different ideas, change your paradigm. What else I can do for doing this, take it to your next higher level. That is what is the second loop, improve the process. Here we look at improving the process of the practices, not just the behaviors. So you get a greater change here. So loop two is an improvement path to use when continuing to do the same thing does not improve performance. So you look at, you know, there is a, you can improve the way you use procedures. Actually industry come up with, if you go to a nuclear industry, there are three categories of procedures. Procedures for continuous use, procedures for, you know, routine use. And the third one is for information use or something. The continuous use means activities which are very significant to the nuclear power plant, which has a safety potential. People have to have the procedure. Each step has to be read and then it has to be followed and then tick mark. You know, verbatim, it has to be followed. So these practices all came because of the loop two improvements. So I'll not go into that. One of the thing is the arc flash clatting. I would like to say that, you know, arc flash clothing. In an electrical equipment, when you work on a high voltage equipment, six KV or 220 KV high voltage equipments, there are, you know, 30 years, 40 years people, I mean, not even 30 years, 20 years ago, people used to have several burn injuries. People lost life when there is arc flashing when there is a short circuit in an electrical thing. It gives out the flash and then it burns the skin and many incidents were there. So industry invented an arc flash clothing and now there is no such incident. This is a shift in paradigm. They just wanted to, you know, earlier days they were just using all protections. They were using the gloves. They were following the procedures, but still people are getting burned because of this. So they thought industry invented a new thing called arc flash clothing. The third loop, the last one, this is most important, the third loop. When you want to make a significant improvement in the performance, we need to work on the third loop, which is going to affect the values and beliefs because this is affecting what the workers or the people of the nuclear power plant are thinking about an activity. So this is very difficult to do. It's not so easy to change my belief. I have certain belief. It's easy to change my belief. So industry leaders do some examples, actions to do this. For example, industry leaders created Vano to promote excellence in nuclear power plant operations. You know, Vano is a, I mean, previous speaker Peter was also talking about Vano and he was quoting about the nuclear safety principles from Vano. Vano was the organization founded in 1989. It was born because of Chernobyl accident. After the Chernobyl incident, they realized that there is not so much communication among the people around the world to promote safety and the performance of the nuclear power stations. Like INPO was formed, INPO is an Institute of Nuclear Power Operators in the US. It was founded after the three mile island accident. These are all big changes which affects the total industry a lot. So that is a big change. So Vano or INPO or such organizations, they promote safety and then take the safety level of the plant to a very high level. If you look at the safety of the plants 20 years or 30 years ago and what is today, there is a significant improvement and because of all these changes which have been contributed into the industry. Yeah, so finally, I mean, I just wanted to make a few conclusions that in a nuclear organization like a nuclear power plant, there will be a lot of opportunities to learn from internal and external operating experience in all phases of its life cycle. Though I was focusing my presentation only on an operating plant perspective, the examples, everything, there are plenty of opportunities when you are constructing, when you are commissioning or when you are decommissioning or doing any activity. So in every phase, you should have a mechanism to capture these operating experience and learn from those experiences. Effective implementation of an operating experience and a work observation program helps in significant improvement in safety and performance. There are many aspects of safety culture. There are many attributes for the safety culture but this is one of the most important one, the learning organization or how you use your own learning for improving performance. So if this is implemented, substantial improvement in safety culture can be achieved. So the last one is again, the repeat of the previous one in a different way. Ordinary men learn from his own mistakes and wise men learn from others' mistakes. So with that, I conclude my presentation and if you have any questions, I can take for few minutes, questions. Thank you very much. Thank you very much.


This study produced a high-quality de novo genome assembly of white clover, trifolium-repens, at the chromosomal level using pack bio-hi-fi sequencing, a third-generation sequencing technology. The resulting genome is a valuable resource for further research into the biology, evolution, and genome-wide mapping of quantitative trait-locky associated with the relevant agronomic traits of white clover. This article was authored by Hongjie Wang, Yongcheng Wu, Yonghee, and others.


A warm welcome to the 24th lecture on the subject of wavelets and multirate digital signal processing. In the previous lecture, we had looked at the admissibility condition for the continuous wavelet transform in depth. The admissibility condition was essentially a condition for reconstructibility from the continuous wavelet transform as we saw. The continuous wavelet transform we noted was extremely redundant to use a continuous scale and continuous translation, meaning essentially a two dimensional representation when what we are dealing with is a one dimensional entity is extremely redundant, very wasteful. And therefore, we began to ask the question of discretization. Can we discretize the scale and can we discretize the translation parameter? We first addressed the question of discretizing the scale and in that context, we had noted what happens when we change the scale. We shall proceed in this lecture today to build on this discretization of scale in greater depth and to consider one particular kind of discretization of scale with which we have been dealing in the first half of the course namely dyadic discretization. Therefore, I intend in the lecture today to talk about logarithmic scale discretization in general and dyadic discretization in particular. With that little background, let us look once again to what the continuous wavelet transform does. We had noted that a continuous wavelet transform essentially operates like a filter both in synthesis and in analysis. So, we had noted that the continuous wavelet transform at scale s is essentially a filtering operation. A filtering operation with a frequency response given by psi cap s omega with some constants of course, at the moment let us simply ignore the constants. So, you see the output independent variable here can be interpreted as the translation. The output independent variable is tau here. Well, then if we take an ideal filter or an ideal wavelet so to speak, we had taken examples of ideal frequency responses that were admissible and those were strictly band limited. They had a psi cap which looked something like this. Of course, I am assuming that the wavelets are real and I am looking only at the positive side of the frequency axis. So, we had noted that the admissibility condition is essentially a statement of band pass character. Therefore, if we consider an ideal band pass function like this and take a dilation of the same, we again get a band pass function. So, for any s greater than 0 as we should have it psi cap s omega. This was of course, the Fourier transform psi cap omega psi cap s omega would look like this and we once again note that there is a contraction or expansion a dilation in general both of the band and the center frequency and that is the reason why we had argued that logarithmic discretization makes sense. Logarithmic discretization means s should be discretized, s should be discretized according to a naught to the power k. So, where k runs over all the integers and we said as long as a naught is positive and greater than 1 and k runs over all the integers, we do not need to take a naught less than 1 also as a possibility because after all when k runs over all the integers, the less than 1 possibility is taken care of. I had given you the example of 2 for example, 2 raise the power of k over all integer k is the same thing as saying half raise to the power of k over all integer k. With that little recapitulation of our discussion, let us go again in depth to analyze what would happen when we discretize the scale. So, in other words when we discretize the scale what we are trying to ask is what do you do to each of these filters and how do you recombine what you have done to each of these filters to get back the original x of t. In other words for each such k, we have a filter and you see how the frequency response of this filter looks. Let us start with the ideal situation and then let us degrade to the practical situation eventually. In the ideal situation the filter the k th filter so to speak would have a frequency response like this. So, it would have a band going from omega 1 divide by a naught to the power k to omega 2 divide by a naught to the power of k where s is of course, a naught to the power k. Now, it is obvious how we can reconstruct this part after all if things are ideal and in fact, if you do pass x t the input through an ideal filter like this to get the continuous wavelet transform here. The reconstruction should also proceed by doing the same thing. So, in fact the k th branch of reconstruction should essentially have the continuous wavelet transform coming in here. The k th branch I mean the continuous wavelet transform being fed to the same ideal filter and if we add this overall k we should get back x t. So, in the ideal situation the answer is very simple. What each branch so to speak each k th branch in some sense of this continuous wavelet transform does is to extract a particular band on the frequency axis and now we can also see very easily interpret very easily what each branch should do. Each branch should have a separate non overlapping band just to take an example. Suppose you had a band pass filter of the following kind. So, if you had psi cap omega looking something like this suppose this were psi cap omega 1 between pi and 2 pi and 0 everywhere else and naturally mirrored on the negative side of omega. Then the k th branch will essentially do the following. The k th branch would cover the band between pi divided by 2 to the power k if a naught were equal to k. So, I must also specify what a naught is k th branch with a naught equal to 2. So, essentially the k th branch would take the frequencies from pi by 2 raise the power of k to 2 pi by 2 raise the power k and we can see that in this particular case for different integers k these bands would be non overlapping. So, it is easy to fix our ideas. In fact, what I have done is to put before you the very idealization of the dyadic multi resolution analysis which we have been looking at all this why. In fact, let us look back at this frequency domain here. You see take for example, k equal to 1 k equal to 1 would take you over the band pi by 2 to pi and if you look at the original band its pi to 2 pi k equal to minus 1 would take you from 2 pi to 4 pi again non overlapping with pi to 2 pi and you can continue in a similar way k equal to 2 k equal to minus 2 and you can proceed k equal to 0 need less to see keeps you in the original band pi to 2 pi. So, now we are beginning to understand what the continuous wavelet transform does in an idealization equations. You see in that case are we really just talking about doing things only in the frequency domain well we must not forget what we are trying to do and which we can never do because of the uncertainty principle is to do what I have just shown you on the frequency axis ideally, but do it with time limited functions. And alas if you look at the inverse Fourier transform of this psi cap homogenous function omega that we just drew here it is far from time limited in fact it decays as slowly as the reciprocal of time terrible anyway. So, this is easy now to interpret and understand and now it is also easy to see that if you take the ideal situation then you could simply put the same filter on the analysis side and the synthesis side. This also makes it clear how we get the notion of filter banks when we discretize.  A filter bank is a collection of filters either with a common input or with all the outputs sum together to get a common output and of course more subtly the filters are interrelated. Now all these qualities are satisfied in the k th branches that we are talking about here. In fact in the particular k th branches that we speak of here our analysis filters have the following pattern. The analysis filters are the ones that create the continuous wave led transform strictly speaking we should put a complex conjugate here as was the case with the continuous wave led transform. So, these are the analysis filters and this is the frequency response if you ignore the constants. The synthesis filters again if you ignore the constants have a frequency response that looks like this. This is the k th branch and therefore, if you analyze what you are doing all over the k th branches for k going from minus to plus infinity you are doing the following. On the k th branch if the input signal x of t has the Fourier transform of omega then we are actually constructing x cap omega times psi cap a naught to the power k omega complex conjugate and therefore, this is on the analysis side I mean and on the synthesis side the k th branch multiplies this again by psi cap a naught raise the power of k omega which essentially amounts to multiplying the original Fourier transform by a modulus squared of psi cap a naught raise the power of k omega and on the output side one is going to sum up all these outputs of the branches. So, the final output or overall output is going to be x cap omega multiplied by a summation on all k psi cap a naught raise the power of k omega modulus the whole squared and a minute ago we saw what this was for the ideal situation ideally this should be one one for all omega of course, that is where the challenge is we wanted to be one for all omega with time limited functions and that is the whole challenge. Anyway, how do we relax in the frequency domain if we want to meet this challenge well relaxation means do not quite insist it must be a constant allow it to be between two positive constants. Now, I shall insist on strictly positive constants and we will see why what I am saying is to relax this requirement for design for design ability let this quantity psi cap a naught to the power k omega mod squared summed over all k all integer k be between two constants. So, be greater than or equal to a constant let us say c 1 and less than equal to a constant let us say c 2 and we are told that c 1 is of course, less than equal to c 2 c 2 is less than infinity and c 1 is greater than 0 note this is greater than not greater than or equal to and of course, this is strictly less than not less than that is this cannot go to infinity. So, here there is the possibility of equality here there is not these are strict inequalities that means, c 1 is strictly positive c 2 is strictly finite and of course, it is not difficult to see that this is a non negative quantity. So, it cannot possibly become negative. So, all that we are saying is instead of insisting that this be a strict constant allow it to be between two constants. Now, this is the case then can we make a small change to the synthesis filter and reconstruct that is the first question that we shall answer that is very easy to see. You see in that case let us define another function psi till day from psi now psi till day shall be defined in the frequency domain. So, let psi till day t have the Fourier transform psi till day cap omega. So, we will show that you know even if the wavelet psi t does not quite obey this strict constancy of the sum we can still build a reconstruction approach that is what we are trying to show. So, you see suppose this is the definition of its Fourier transform define psi till day cap omega to be psi cap omega divided by the sum here and please note that since we have this condition here this sum lies between two positive constants and what is important here is the fact that it does not go to 0 the c 1 constant is important here because the c 1 constant this denominator never goes to 0 and therefore, this is valid because of c 1 being greater than 0 otherwise this definition would be meaningless. So, the c 1 is required for this reason to be able to build this psi till day cap. Now, we will show something interesting you see we will show that we could use psi on the analysis side and psi till day on the synthesis side and we will first show that if psi obeys this requirement then psi is admissible. So, we will show that now we use c 1 to define psi till day we will use c 2 to prove admissibility. So, once we have ensured this we also have admissibility let us prove that by admissible I mean we need to consider this integral and we of course, agree that psi t is real. So, let us make the remark here psi is real I mean the it is a real wavelength. So, you see let us break this integral into partial, but finite integrals of the following form summation k running from minus to plus infinity integral from a naught to the power k to a naught to the power k plus 1. Now, let me take an example suppose for example, a naught is equal to 2 then the integral from 0 to infinity is the same as the integral from 2 raise the power k to 2 raise the power k plus 1 with k running over all the integers as k takes negative integer values you are covering the range below 1 as k takes positive integer values we are covering the range from 1 and above 1 that is the interpretation here. So, for example, k equal to 0 would cover the range 1 to a naught in general or 1 to 2 in particular if a naught is equal to 2 and k equal to 2 will cover k equal to 1 will cover the range from 2 to 4 and so on so forth and k equal to minus 1 will cover the range from half to 1 and so on so forth in particular with a naught equal to 2 anyway with that we keep the integrand as it is, but as usual we make a substitution on the integrand. So, put alpha equal to a naught raise the power of k times beta and make a change of variable in the integration now when alpha is equal to a naught raise the power of k times beta this limit simply becomes 1 and this limit becomes a naught. So, we have a naught raise the power of k beta here and of course interestingly d alpha is also a naught raise the power of k d beta and therefore, one can easily see that d alpha by alpha is equal to d beta by beta. So, in place of d alpha by alpha I can simply write down d beta by beta. So, now we have a beautiful summation coming in what it means really is that the integral from 0 to infinity psi cap alpha mod square d alpha by alpha is equal to the integral from 1 to a naught summation if I interchange the order of the summation and the integral which I can do simply because this is a finite integral here summation from k running from minus to plus infinity. In fact, I could interchange this order because I am guaranteed that I have a finite integral here and I am guaranteed that this is converged for all beta it lies between two positive constants. So, it is meaningful to do this and in fact, now we have a condition on this. This is a non-negative integrand here and this is of course, you know integral over a non-negative quantity 1 by beta between 1 and a naught. If I can put an upper bound on this the upper bound on this is known to us it is c 2. So, the summation k running from minus to plus infinity psi cap a naught to the power of k beta mod squared is upper bounded by c 2. And therefore, the so called admissibility integral as we call it we shall now introduce this term the admissibility integral is upper bounded also by integral from 1 to a naught c 2 t beta by b beta and this is a very easy integral to evaluate it is essentially c 2 integrated log natural beta from 1 to a naught and that is c 2 log natural of a naught a neat and elegant result. So, once I have the upper bound on this summation I am guaranteed admissibility. So, we have shown that if psi obeys this requirement and now we will introduce some terminology we shall call this quantity which we are talking about all this while the summation we shall call this quantity a sum of dilated spectra and we shall abbreviated by s d s and just as in the case of the continuous wavelet transform we have primary and secondary arguments for this sum of dilated spectra. The secondary argument is psi because it is for psi that we are constructing a dilated dilated or sum of dilated spectra and of course, the primary arguments are a naught and omega. Well, actually a naught is a grey area you could treated a secondary or primary you know in the continuous wavelet transform for example, we distinguished primary and secondary by calling those arguments primary which did not change in the discussion in a particular context and secondary for those that did or rather the other way around primary for those which did change which were important in a particular context and secondary for those that did not. So, for example, in the continuous wavelet transform the primary arguments where the translation and the scale those were important in a given context they changed in that context and we were looking at the variation of those in a context and the secondary arguments were the essentially the wavelet with which we are constructing the C w t or the continuous wavelet transform and the function on whom the continuous wavelet transform is being constructed. So, here too we shall talk about s d s with secondary arguments of psi and a naught and primary argument omega but of course, we could shift this and what we are essentially saying is s t s s t s psi a naught as a function of omega needs to be upper bounded and lower bounded and the upper bound guarantees admissibility. Now, we will soon see in a minute that this C 1 guarantees reconstruction and in fact we are going in that direction. We have already constructed a psi tilde where psi tilde cap omega is essentially now with this language psi cap of omega divided by s t s psi a naught omega and it is very easy to see that if s t s obeys the upper lower bound condition psi tilde is also going to be admissible. So, we show that psi tilde is admissible and to prove that all that we need to do is to try and look for bounds on the sum of dilated spectra of psi tilde. So, we need to consider for this purpose the sum of dilated spectra psi tilde a naught as a function of omega and this is not at all difficult to compute. Indeed, let us in particular construct psi tilde cap a naught raise the power k omega which is the typical term required or rather the modulus of this squared and the modulus of this squared is very easily seen to be the modulus of psi cap a naught raise the power of k omega the whole squared divided by that is the interesting thing. Let me expand the denominator. I will first write a summation on L to distinguish it from this k. Summation on L going from minus to plus infinity psi cap a naught raise the power of L. Now, in place of omega I need to write a naught raise the power of k omega. So, I will write a naught raise the power of k omega there and now this is easy to evaluate. In fact, you can see that this becomes a naught raise the power L plus k and please remember the summation is on L and k is fixed. So, for a fixed k when L runs over all the integers as it does here L plus k also runs over all the integers. So, what we have in the denominator is once again the sum of dilated spectra of psi a naught evaluated at omega. So, that makes my life very easy. What I am saying in effect is psi tilde cap a naught raise the power of k omega mod squared is simply psi cap a naught the power of k omega mod squared divided once again by s d s psi a naught evaluated at omega. It makes my summation very easy to do. So, what I am saying in effect is that the sum of dilated spectra of psi tilde with parameter a naught evaluated at omega is in other words summation only on the numerator. You see the denominator is independent of k. In fact, the little correction which we need to make here you see here I need to put a square. So, although I had discussed this in the context when I took the modulus squared I should also put a square here. I do not need to put a modulus because this is anyway non negative. So, with that little correction what I have in the denominator in fact, here also I need to make the correction.  So, here we have psi a naught omega squared and now this is familiar this is essentially s d s psi a naught once again. So, what I have in effect is that s d s psi tilde a naught evaluated at omega is just s d s psi a naught evaluated at omega divided by s d s squared and this is where the lower bound becomes important. Since this is lower bounded by c 1 never goes to 0 and it is also upper bounded by c 2. So, never goes to infinity it is valid to cancel. Cancellation from the numerator and denominator is valid because of the bounds and on cancellation we shall get s d s the sum of dilated spectra of psi tilde evaluated at omega with parameter a naught is just the reciprocal simple. In fact, now I can go a step further I can use the bounds on the sum of dilated spectra for psi to come up with bounds on the sum of dilated spectra for psi tilde let us do that. So, let us come back to this expression you see all that we need to do is to note that if s t s psi a naught omega is bounded between c 2 and c 1 this one greater than 0 and this one less than infinity then I can take the reciprocal on all sides because these are all non negative quantities and I can get infinity is greater than 1 by c 1 is greater than or equal to 1 by s t s psi a naught evaluated at omega is greater than equal to 1 by c 2 which is in turn greater than 0 and this of course is the sum of dilated spectra that we are looking for here this is nothing but s t s psi tilde a naught evaluated at omega. So, we have a bound the bounds on the sum of dilated spectra of psi give you the bounds on the sum of dilated spectra of psi tilde and the same arguments that we used to show that psi is admissible can be used to show that psi tilde is also admissible. So, psi tilde is also an admissible wavelet and therefore, I could now construct an asymmetric analysis and synthesis paradigm on the analysis side I would use the wavelet psi on the synthesis side I would use the wavelet psi tilde. So, all that I am saying is use psi tilde on the synthesis side that means the kth branch is as follows it has a filter with frequency response given by psi tilde cap a naught raised to power of k omega and now we can see what happens to x when it goes through the analysis and synthesis side with this analysis and synthesis together would produce x cap omega times psi cap a naught raised to the power of k omega complex conjugate multiplied by psi tilde cap a naught raised to the power of k omega and this is easily seen to be of course, this is summed over all k this is easily seen to be x cap omega times sum for k going from minus to plus infinity psi cap a naught raised to power of k omega complex conjugate psi cap a naught raised to power of k omega divided by the sum of dirated spectra psi a naught evaluated at omega and once again you can see what all this is leading to this is independent of k. This simply gives you x cap omega into sum of dirated spectra psi a naught omega divided by the sum of dirated spectra psi a naught omega and once again because of c 1 and c 2 we can cancel for all omega and that gives us just x cap omega. So, we reconstruct now we have also brought in a new notion here if we have made this relaxation namely that the sum of dirated spectra can lie between two positive constants we also need to generalize our notion of analysis and synthesis a little bit. We need to generalize it by allowing a different wavelet on the analysis side and on the synthesis side. You have psi on the analysis side psi tilde on the synthesis side. So, we are slowly leading to a different paradigm in the context of filter banks all this while the wavelet on the analysis and the synthesis side has been the same. Now, we are allowing them to be different if we want to relax the context of design anyway that remark apart. Let us come back to one specific case the specific case of a naught equal to 2 in the specific case of a naught equal to 2 which is also called the dyadic case dyadic refers to this a naught equal to 2 what we are asking for is that the sum of dirated spectra of psi 2 omega must be upper and lower bounded now in particular if one considers the higher wavelet one can show that this is true I do not wish to go through the details, but rather to leave it to you as an exercise. So, exercise for the higher wavelet for example, show that the sum of dilated spectra as we have constructed lies between two positive bounds. Now, you know to give you a hint it is clear that the upper bound essentially gives you admissibility and it is not very difficult to show the higher wavelet is admissible. So, first if you can simply show the higher wavelet is admissible then this is kind of done the lower bound is a little more tricky and that I leave as an exercise for the class to do and of course, this also holds for the Gaussian wavelet for example. So, I also put down the following exercise for the Gaussian wavelet or the derivative of Gaussian one can once again show a very wide range of a naught is possible. So, one can show that the sum of dilated spectra in the context of the derivative of Gaussian kind of wavelets is always between two bounds for a very wide range of a naught and I encourage you as an exercise to find out what that range of a naught is. Now, one more remark in case the sum of dilated spectra is 1 is constant for all omega. So, in other words c 1 becomes equal to c 2 then we have the situation where psi and psi till they are the same and that is essentially the situation of orthogonal filter banks the kind of filter banks that we have been talking about all this while. So, in other words the specific situation where analysis and reconstruction proceeds from the same wavelet is the case where the sum of dilated spectra well it you know please remember here we are talking about a continuous translation parameter. So, we have not yet discretized the translation parameter. So, it does not follow that the higher wavelet has the sum of dilated spectra equal to a constant because we have discretized the translation parameter there, but if you are not to discretize it then those wavelets where c 1 is equal to c 2 give you an orthogonal filter bank that means the wavelet on the analysis and the synthesis side is the same and in particular when a naught equal to 2 it gives you a dyadic and resist synthesis system. With this then we conclude the lecture today and we shall build further on the dyadic case in the next lecture. Thank you.


Hi everyone, Joe for jaspyscasebrakes.com coming at you with 2019-2020 upper deck credentials hockey That's a one box ram team break number three, and it's the last one. We did it. We have filled up the hockey mixer We're gonna give away those final eight spots right there So as you know, we're gonna do the break itself first and then at the end of the break will randomize all 31 names The eight names on top gets into the hockey mixer And if you're in the hockey mixer, it'll be part of that Mahomes promo too, which is gonna be happening a little bit later tonight A very big thank you for all of these folks for digging into this break for rallying around it. I appreciate it All 31 hockey teams are in let's roll it. So names and teams first different dice roll at the end for the giveaway Snake eyes for names and teams. That's easy one and two Mike tower down to Matthew Mike and Matt Two times for the teams Sharks down to New Jersey Devils. That's way too small All right, so here's the first half of the list right here Here's the second half of the list right there No trade windows for these filler breaks or mini breaks Let's sort by team. Let's print and rip Let's rock and roll. Thanks. Once again everyone for getting into it There you go. TJ's happy with the draw. He's like I like the caps. It's actually pretty pretty good pretty good box for For a filler box Ryan loves the caps too. Hope I can get some games next year. Yeah, what's the hockey restart plan? Has that been announced yet? NBA obviously has gotten their They're kind of schedule going NFL grinding through COVID issues and trying to finish off a season as well I feel like I've not heard Anything about hockey Ryan saying late January early February for a hockey restart So it's free agency and trading and all is that is that window all open and Happening and well, there's our first autograph and it's a good one. Look at that 25 out of 49 kale mccar For Peter and the Colorado avalanche Wow Out of a filler break. I don't know hockey, but I know that everyone freaks out when this guy gets pulled So I know he's a good hit. I guess that's his debut right there too on card autograph as well Nice very nice We've got out of 699 debut ticket access Martin fair very that goes to TJ in the capitals Think it's just one auto a box right here. We got Vancouver 43 out of 199 we got Brock Besser Think he's pretty good too, right? Vancouver that'll be for Ryan Harrell last-bought mojo. It's the acetate card put all these numbered cards here That John Tavares is to 199 that'll be for Toronto. That's going to go to Allen And we got debut ticket access Colton white to 999. That'll be for New Jersey That's going to go to Matthew and then we've got for the st. Louis blues Mackenzie McEatry St. Louis Mike Grzinski with that one got Connor McDavid. We got another numbered card. We got a fox in the box We got debut ticket access It's a lower number. That's 99 So this is for San Jose That'll be for Mike Tower gets the your your tycoon Gonna be a rough one Adam Fox for the Rangers that'll be for Ryan Harrell Ryan and the Rangers 401 out of 499 debut ticket access Jacob Middleton to 999 Kate's brother, maybe sharks Mike Tower and the star of the night Credentials card Connor McDavid. That'll be for Jack and the Edmonton Oilers Is it you? Is that how it's pronounced? You're taken? All right, there you go. Nice nice autograph popping out of here out of a filler break. That's pretty solid Let's flip back to the screen right here Yeah, not at all right Russell down to Adam and everybody in between Let's get all those names in here. Let's roll it. Let's randomize it four and a one five times So after five, it's gonna be top eight After five or in the mixer which is coming up next in a separate video One two three Four and fifth and final time after five times now first off my apologies to everyone from nine Down to 31. We'll get them next time Congrats to the top eight though. You're in the mixer Mike Russell Mike Ryan two different mics Steve Ryan Ryan Ryan Look at that. There's the top eight right there So three Ryan heralds one Ryan case and a Steve birch two different mics Mike T Mike G and a Russell in the hockey mixer Thanks for watching everybody. I'm Joe for jazby's case breaks.com. We'll see you for that one in another video. Bye. Bye


I also made another prediction six years and half ago. I said the United States and China both need political reforms. But in the case of China, small reforms have been going on all the time in the political system. We fixed problem here and there. But I said problem is the United States. Your political system was a product of pre-industrial year. And I made a forecast. I said result significant, substantial political reform. My concern is in your next elections you will produce a leader worse off than George W. Bush. So it was you, it was not the Russians. So this is the Chinese humble advice we can offer. China is a civilizational state. I remember when Harry Kissinger wrote his famous book on China. He started with this quote. He said, my goodness, look at this China. It's different. China used this unique language which started 3,500 years ago.  But these two European languages were dead languages. China still used the same language. This line of culture and continuation of civilization uninterrupted. So this is why we have indeed, you know, for instance, this whole idea of meritocracy. Why say confidence? I said with my debate with Professor Fukuyama. I said, if you look at the top leadership in China. We've just had people's, the party's Congress. Minimal requirement, two terms of provincial governor or similar position, which may have to govern at least 100 million people given the size of China before you came to one of the top seven positions, decision making bodies. I said to Fukuyama, I said, with this Chinese methodology, meritocracy-based system, we can say with certainty we can improve the system. There are problems. We can fix it. But we will not produce any leaders like George W. Bush, you know. It's way below the Chinese bar, you know. That's my point. I respect deeply more than respect. I admire Chinese civilization. I admire Chinese history. I have been all my life an admirer of Chinese art since I was a very young man. China has been one of my, the compass of my life. But I don't admire your political system. And I feel, I find much more admirable and worth of respect. A system when you have the right to make a strike, when you have the right to be paid decently, when you have the right to speak freely, when you have the right to not to be contaminated by terrible pollution, and so on. So I will not say in the name of relativism and so on that every political regime are equivalent. I don't believe so. I really think that Europe invented an idea which does not belong to Europe, that migrated to America, that has been adopted by a lot of parts of Latin America that is incarnated in part of Asia, which is an universal idea, which is the idea of freedom, of equality, and so on. And China of today is not worshipping these values. And that's why I do hope, I hope. I would be happy, I would not say that with surprise or not with surprise, if there was one day a real Chinese spring, a real cultural revolution as the one I saw in my youth of Chinese people saying it's good to have wealth, it's good to have gross products, it's good to have exportation, but it's good also to have human rights, I think that this would be a great news for humanity. You said that Wei Wei had this equivalence between political systems, but he does not have equivalence, he has a clear preference. He believes that authoritarian systems are superior to democracy. He explicitly said that democracy yields to bad governance, if I'm not mistaken. So my question to you, there are millions of people today in the world that live under bad governance systems, which are democracies. China has a different view, and therefore countries tend to like, tend to be very tempted to export their models. They like to see what they do replicated elsewhere. So would you recommend to your government to go out in the world and promote what you think is good governance and promote the cause of less democracy or non-democracy? Actually it depends on how do you define democracy. I like this nexus foreign, because you said at the very beginning that we discussed the real meaning of democracy, real democracy, but unfortunately so far what we see as shown in Arab Spring about one person, one vote, a multi-party system, that's the best procedural democracy. That's not necessarily the real democracy. Remote democracy is far more important as you said about education than many other important ideals. In terms of China, let me quote from everybody knows Confucius. He said, people are like water. Regime or leaders are like boats. Water can carry the boat, can also overturn the boat. So if you look at the China model in particular, the key message is stay in touch with your people. It's so easy.  I respect your preference. It's understandable. But you do some surveys. What are they about most? Fighting poverty, fighting disease, street security, safety, et cetera, job creation. You do this accordingly. That's how China did. Would you recommend the rest of the world to go that way and repress the options that he described? No, it's not his definition. It's really people should sit down and discuss what kind of political system with your people. We're doing that. Yeah, we should experiment. China of an option, which is very interesting because we have the four decades of successful experience. In your opinion, that China should export that view? Xi Jinping said in his report, China's experience can offer an entirely new alternative for those countries and nations who desire for quick modernization and complete independence. Is this going to be a state-supporting export? No, no, it's not. I'm joking. Actually, China is very modest. I'm being slightly less modest. China does not export its model. Do not advocate its model. But once you're successful, you go to Africa, people talk about looking east. They have tried the western model for decades, not working, you know, look to the east. May I just talk here about the oppressed Muslim minority? So don't tell me that everybody is fine. There is an oppressed minority in China. And then I want to bring up something else here in terms of terrible things that are happening today like in Syria. And it's what is happening to the Rohingya Muslims. And the way I look at it is I thought it was never again. And to me, never again meant a Muslim or a Christian or Jewish or Yazidis or black or white or any color. But today we are seeing a genocide. And I don't see China has also quite a lot of influence in a place like Burma, like Myanmar. Apart from, I don't want to even talk about North Korea. But I don't see anybody doing anything for the Muslims in Myanmar or the Muslims in China. Let me answer you this question first. No, because I do believe it's important in order to know. Because I do believe we go in a conversation in which you are saying how good you are. We are saying that you are not very good. But in a certain way, the problem is that part of the Western democracy is also a problem today is that we lost curiosity on the others. Obviously, China's legitimacy is not based on caution only. And if we are not seeing this, we are basically playing a game. But on the other side, I do believe what you are also giving is actually a critical story because every political regime is successful under certain conditions and not others. I do believe one of the biggest problems that we have, we forgot what are the real advantages of democracy. The real advantage of democracy is not simply rights, but this is that when people are disappointed, you are giving them a mechanism through which they can react. Democracy is not famous for doing the right things, but democracy is famous for changing the governments that people don't like without violence. The question is the following. The Chinese system at the moment, in my view, works fine based on an incredibly important economic performance. How strong is the system if economic performance is not there? So if we want to be serious, we should be open to the vulnerability of both regimes because otherwise, we go in a rhetorical story which is probably a good opera performance, but it is not helping us more. And just on Bernard and Olivier, the government should be very happy that you went to Kurdish regions and didn't end up in Catalonia at the same moment. I think that China will not go so far as you think and maybe as China deserves if she stays on this path. If you really believe that the Rohingya problem is a problem of faith, if you really believe that the Uyghur problem is a problem of religion, it means that really your leadership has not understood how really a great power has to work in order to succeed because it is a human rights question. It is a democratic subject and it is not NGOs of the West who are... This is a plot theory, it's absurd. It is people who are in despair, the Rohingya. It's so terrible, nobody knew. No, no, no, let me finish. Nobody knew in the West, except a few of us, who the Rohingya were. They are the most miserable people in the world. They have no rights. They have nearly no identity. Have you been to that region? Have you been to this region? Of course I have been. My friend, I have been, alas, I am elder than you. And I went to this region. No, no, no. I went in this region. I will give you another figure. I spent my youth between Bangladesh and Burma. I know exactly what is the face of a cursed Muslim people in this environment. I know who the Rohingyas are. I know that they are men deprived of any rights and I know that in front of that, you cannot feel something else than despair and they are despaired and that's why they revolted and the way in which they are treated is scandalous. Okay, mind your own business first. I don't agree. It's 89% versus 12% satisfaction. Who does speak in China anyway? You know really too little about China, little knowledge is dangerous. We have 130 million visits abroad, three million students abroad. Don't attack me about my knowledge because that's not the right way to go about it. Even with that we cannot agree to your interpretation. I would like to bring in something different.