Now, we get to hear from Ben Simmons. Christian? How's it going, Ben? Good. How you doing? Doing good. Thank you. I guess, first of all, how are you feeling physically? Are you ready to go? Yeah, physically. I feel great. You think you could, I guess, hypothetically play in the first few games this season and be good? That's the goal. That's the plan. Copy. And second, just what was it like being a part of this organization while everything was falling into place during the offseason when you had kind of the trade requests, the contract negotiations? Was it like just watching all that, wondering where you would be in all of it? There was a lot going on, but for me, I got to focus on, the first thing was my health, getting back on the court. So that was my priority. Besides that, I worry about what I can control, and everything else, that's where it was. So for me, I had to prepare for the team. Ben, I got two for you. Just starting with training camp tomorrow, will you be fully cleared for everything? Ready to go.  I mean, can you just walk us through how quickly it went from feeling good enough to maybe play to ending up needing surgery? Pretty quickly. I'm glad I got it done. It was much needed. I don't think people really realized where I was at. That day, I was supposed to play game four. I woke up on the floor, couldn't move, could barely walk. So I'm glad to be in this position, this situation. We have myself and got myself into a place where I can compete now. So I'm excited. You had said on JJ's podcast that you were feeling the glutes. I want to say, is that the day of game four? Just to correct? Down the glute, down the calf, in my foot, all of that. The physical ailments, the back, I guess that's essentially only maybe half. I don't want to put a percentage on it, but you were dealing with both physical and mental issues last year. You said you're physically ready to go. Do you expect you'll be in a proper head space to compete or would not know that until you're out there? I put myself in a position. I've been working on myself this past year to get back on the floor and play at a high level. So I deserve to take this opportunity by the horns and get back on the floor. So I'm excited to team up with these guys and these coaches. I'm looking forward to it. Ben, to your left. Good to see you. In the past, taking a lot of pride in your ability at your size to play point guard. What have been your conversations with the coaching staff and some of your teammates about where you fit in on both ends of the court and are you willing at this point in your career to compromise and play off the ball or play a different position? You know me. You know my game. For me, I just want to go out there and impact the game in any way I can, whether it's setting a pick, passing the ball, scoring the ball, getting a stop, rebound the ball, getting a block. So there's so many ways you can affect the game and it's not just scoring. It's not just defense. And for me, I feel like I cover most of those things. Obviously, I have weaknesses in my game, but that's everybody. Can I be the first to ask how many threes you're going to take this year? Who knows? Hey, Ben, over here. Obviously, it's been 18 months, I think, give or take, since fans, everybody saw you on a court last. And so all the doubts that go with that, no one's seen you play. You've obviously been through a lot physically, emotionally and otherwise. Just kind of open-ended. Like, what do you, what's different about you the next time NBA fans see you on a court? What are you expecting from yourself? That's up for everybody else to decide. That's not to me. I'm going to go out there and play. I'll let everybody else talk. I know it's your job to ask questions and stuff like that, but for me, my focus is going out there and doing what I can for my team to win in any way I can. So expectations, that's for you guys. Ben, in terms of just the way you now fit with, obviously, two of the big stars on this team, Kevin Durant and Kyrie Irving, three of you have never played together. So do you have any sense of, have you been in that? We've been playing all week. Yeah. How's that look? Incredible. Ben, right here in the middle. I remember in February when you mentioned or disclosed to us that you had dark days and a lot of people didn't really know what was behind the curtain. How are you mentally now and what can you do to make sure that those feelings of frustration and that darkness doesn't resurface during the season? That's just working on yourself. And I feel like everybody has dark days, but you know, when you're able to address it and work towards getting to a place where you need to be, that's where I am. So for me, I work on myself every day. Is there any part of frustration that there still is a narrative out there that? No, I don't care about narrative. I don't care about people making or saying certain things because I can't control that, you know? All I can do is focus on what I can do in the court, win games, help this team win a championship. So, you know, that's the end goal for the Nets, obviously. You know, we're here for one reason. Hey, Ben, it looked like at one point you were maybe a day away from finally getting to play with Kevin and Kyrie, and it didn't happen in the summertime. Were you ever at the point like, come on, give us a chance. This guy might leave. This guy might not come back. We're never going to get to see what we can actually do. I can't. Yeah, I know that.  Like different things were going on, but I can't. I don't worry about that stuff because I can't control it, you know? Obviously, it's a blessing to be able to play against a lot of talented players or play with them. Sorry. But I just focus on what I can contribute and do for this team. And in that moment, it was getting healthy. You mentioned you feel like you're in a good headspace right now. What gives you the confidence that not only you can stay there in the moment, but stay there throughout the season, no matter what happens? Because I put a lot of time and effort into myself. What went into that? We could be here all day talking about this, but a lot of time and energy has been spent on getting myself to a place where I want to play. But then in terms of, you know, back injuries can be tricky sometimes, right? And this has flared up for you a few times. Is there like a maintenance portion of it where you have to just like routinely make sure that you're not overloading it? How does that work? Every day. It's a lot of core, a lot of maintenance pilates, manual work, massage, taking care of my body. Just normal stuff. Just staying on top of it and going the extra mile. Does the recurrence of back issues give you any, I guess, precautions on how you play or are you just going to go out there and play? I don't want to be on the court if I can't play, you know? Ben, right here. You said that you can't be concerned with what the media says, what the public thinks, all of that. That's too much for you. But what about your peer group, guys you play with, guys you play against? Do you feel like that there's questions from them about you that you want to clear up with your play on the floor, your availability? Do I play against? Yeah. I don't care about people I'm playing against. I'm worried about my teammates here, my coaches in this organization. Ben, to your left. This is kind of a different looking roster than what ended the season last year. They're getting you back in the mix. Joe Harris and some additions over this summer.  I think we got a team that wants to run.  And obviously Guard, too. We got some great new additions. Then defensively, I think we're going to be great. Ben, there were some games in Philly when Joel was hurt. And you basically played the five. There was a couple of games out west, especially on the road trip where the ball was just kind of flying all over the place. You had some huge scoring nights. Does this seem like maybe roster-wise this could be a little similar to that, the way you guys played then? Yeah, I think obviously not having a guy like Joel on the team. He's so dominant in the post. Allows us to get out and run more, move the ball a lot more. And obviously the weapons we have from the arc is incredible. So I'm looking forward to playing with these guys. And I think the chemistry is going to grow. I think the best example I could probably give is when we had that team in Philly with Marco, JJ, or Sonny Liasova. I think we won like 15-14 games in a row. So I'm excited. The roster, I like the roster. I'm excited to play with these guys. I think it's a good opportunity for us. We have a lot to prove. Ben, is there a deeper right here in the middle? Is there a deeper meaning to changing your number? Are you trying to leave what happened in the past? I know you said on the podcast you were excited, just with the jersey changing everything. No, I wasn't that deep. I would have 25, but I think it's retired. Thanks, Ben. All right, thank you.


Is it good to go? All right, thanks for coming. I'll be talking about Pareto optimal solutions for smooth analysts, and this is based on joint work with Ryan O'Donnell of CMU. So thanks to Shanghua for giving a nice introduction to why we should study Pareto optimal solutions in terms of capturing trade-offs between different objective functions. Let me actually give a different motivation for studying Pareto optimal solutions. It's that it can actually be an important complexity measure for understanding the performance of algorithms. So let me give a motivating example. Suppose we have the knapsack problem. So we have a vector of values and a vector of weights, and some upper bound capital W on the total weight that we can support in the knapsack. So our goal will be to solve this problem optimally and to do so by building up optimal solutions to larger and larger sub-problems. Now what if I consider the universe on just the first i items? There are two to the i candidate solutions, one for every choice of which items to put in and which items to leave out, and each of them in turn has some total weight and total value. And actually I'll plot these solutions on the xy plane with the value, the total value along the y-axis, and the reason I'll use w minus the total weight is that throughout this talk, the goal will always be to maximize objective functions. It'll be better to have larger total value and it'll be better to have larger remaining residual weight in the knapsack. Now if these are the solutions that we get from looking at the entire universe, the first two to the i candidate solutions, then there are going to be some solutions which are clearly dominated by others. For example, this solution right here, well there's another solution up and to the right. So there's another solution which has larger total value and smaller total weight. So in this case we'll call this original solution not Pareto optimal. If there's any other candidate solution, that's simultaneously better on both objectives. And conversely, if the region up and to the right is empty, if there's no other candidate solution better on both objective functions, we'll call the point Pareto optimal. And the full set of points will be the Pareto curve. Actually in the specific case where I'm considering all the solutions on the first i items, I'll actually refer to this as the i-th Pareto curve. So now the goal will be to solve the knapsack problem exactly by building up Pareto curves for larger and larger sub-problems. And actually the size of the largest Pareto curve we encounter will actually be a measure of the runtime of this algorithm. It'll be the main bottleneck in this algorithm. So now suppose we were trying to build up the i-plus-first Pareto curve from the i-th Pareto curve. Well, if we extend our universe size to now include the i-plus-first item, there are new solutions we have to consider. For every solution on these first i-plus-one items, it really comes from a solution on the first i items and a choice of either include or not include the i-plus-first item. So in fact, all the new points that we get, well, they come from an old point and a shift left and up. So for each old solution, if we don't include the item, well, it's total weight and total value state put. But if we include the item, then we shift over the point by the weight of the i-plus-first item and up by the value of the i-plus-first item. So actually you can check from this picture now. Unfortunately, gray is not coming out too well, but this point that was not Pareto optimal, while the shift left and up, this point will also not be Pareto optimal. You can see in this figure there is another candidate solution occupying the region up into the right. And in general, this will be true that any point that we've thrown out to form the i-th Pareto curve, well, we don't have to worry about what new solutions arise from it. Those solutions will also be irrelevant. So this point is not Pareto optimal. And there can be cases where we had a point which was Pareto optimal on the i-th curve, but is actually no longer Pareto optimal on the i-plus-first curve. So if we encounter these types of solutions now, we can also throw those out. And in general, the set of remaining points will be exactly the i-plus-first Pareto curve. So the approach now is to build up these curves one by one. And what I was hoping to get across this discussion, this algorithm, by the way, is called Dynamic Programming List, in the specific case of NAPSAC, it's called the Namehouser-Allman algorithm. Well, what I was hoping to get across in the previous discussion is that the i-plus-first Pareto curve can be computed from the i-f1. And actually, if you implement this intelligently, it can actually be done so in linear time. If you maintain these lists as sorted orders, these Pareto curves, then actually you can compute the next Pareto curve just by an appropriate merge of two different lists. So in fact, pO of i-plus-1 can be computed in time linear in the size of the i-th Pareto curve. And a relatively trivial observation that actually solving this problem, finding the n-th Pareto curve, actually solves the problem exactly that we're interested in. If we had the n-th Pareto curve, we could actually compute an exactly optimal solution to the NAPSAC problem. All we'd have to do is check all the candidate solutions in the n-th Pareto curve and find the one which has the largest total value while still having non-negative residual weight left over. So in fact, in this algorithm, this is something that's used in practice in operations research even though it's exponential in the worst case because the sizes of these Pareto curves can blow up exponentially. In fact, this is a fairly typical example of when an algorithm as an intermediate stage enumerates the set of Pareto optimal solutions. And that's actually the main bottleneck in the algorithm. Understanding whether or not the algorithm performs well in practice is equivalent to understanding how large these Pareto curves can be. So this was used by Byron Baching who first showed that actually in the model of smooth analysis, even though the number of Pareto optimal solutions can be exponentially large in the worst case, they were able to show that in the smooth analysis model, they're actually polynomially bounded in two dimensions. So I won't get into the formal model just yet because it's a little bit notation heavy, but an immediate consequence now is actually that knapsack can be solved in smooth polynomial time just by the algorithm that I explained on the previous two slides. And interestingly enough, this is actually the first example of a problem that's NP-hard and yet is easy in the model of smooth analysis. In fact, moreover, there results even generalize a long line of results on random instances. For a long time, people had studied things like what happens if in a knapsack instance, the weights are distributed uniformly at random on some interval. Can I solve it exactly in expected polynomial time? And that becomes a very difficult probability question, even understanding what the optimal solution value looks like, yet here they were able to generalize all of this work on specific cases of random instances and were able to show that as long as the density functions of the weights and values were themselves bounded, they were never too concentrated, then in fact the namehouser-Allman algorithm runs in expected polynomial time. So let me now formally introduce the model and then I'll start to talk about what the previous results are and where we can go from there. But the model will be a little bit notation heavy because it'll be a generalization to the one that I described for the knapsack case and actually all these little bells and whistles will be important for various applications. But for now you can imagine a model where an adversary is trying to force many pre-optimal solutions in expectation. So the adversary will get to choose quite a few things. The first thing the adversary gets to choose is the set of candidate solutions. This was easy to describe in the case of knapsack because it was in fact all of 0, 1 to the n. It was every choice of which items I can put in the knapsack and which ones I want to leave out. And more generally, you can actually choose combinatorially interesting families. So for example, if n were the number of edges in some graph, then I could just as well choose this set if I were the adversary as maybe the sets of edges that form a spanning tree in my graph. Or even more, I could choose the set as the sets of edges which form Hamiltonian cycles. The adversary will be interested in then choosing D linear objective functions and trying to force many pre-optimal solutions in expectation. The first objective function the adversary will actually he'll be allowed to choose it adversarily. So even in the case of knapsack, the fact that you're allowed to choose one objective function adversarily and it's not perturbed means that you can perturb either of the weights or values in a knapsack instance and it still runs in smooth polynomial time. The remaining objective functions will actually be linear. So the adversary will choose some D minus 1 linear objective functions from the 0, 1 to the n space to r. And in fact, in general, these random variables the adversary will even choose the distribution of them. Not just the value and then perturb them by gaussians. He'll even be able to choose an arbitrary perturbation where these random variables just are random variables on the range plus minus 1 and the density function has to be bounded by phi. So actually this level of generality is important in some context where you want to consider more than just gaussian perturbations for things like applications the mechanism design is all elude to later. So in any case, this is the model. I apologize for all the notation but it's good to get this out of the way. Are there any questions that I can answer now? Okay. Is there a question? No, it can be arbitrary nonlinear. So that's what allows it to encode a lot of combinatorial structure. So a lot of the bells and whistles in this are what allow you to move to models which are somewhat more realistic of how you might measure data. So allowing one arbitrary one allows a lot more freedom in the expressive power of the adversary. Okay. So if I let P O be the set of pre-optimal solutions, as I mentioned, Bayer and Valking showed that for the two-dimensional case the expected number of pre-optimal solutions is polynomially bounded. And this is what had implications for knapsack in particular. And this was later improved to a tight analysis by Bayer, Roglin and Valking and actually showed that a matching upper and lower bound that the answer should be n squared. That an adversary can force n squared pre-optimal solutions in expectation and he really can't force more than that. Fee is just the bound of the density. Fee is the bound of the density function, that's right. And Roglin and Tang then showed a very strong generalization of this and showed that actually for any constant number of objective functions it's still polynomially bounded. So even if you want to solve multi-objective optimization problems which you want to find multi-dimensional predo curves, you still can do so instantly in the smooth model for a constant number of objective functions. But actually the dependence was not so great on this number of objective functions. In fact, the exponent of this polynomial itself depended exponentially on D. So actually a lot of bounds and smooth analysis can be sort of slack in what actually the polynomial is. So actually the focus of this talk will be on getting a much tighter analysis of this through an interesting approach, let's say. So one other result I want to mention in this line is that a recent paper of Dugme and Ruffgaard actually used the results in this line, not exactly the number of predochemical solutions, but used the stronger property to actually show a black box reduction in mechanism design that any FP task can be transformed to a truthful and expectation FP task. So our results we end up getting a much stronger bound on the number of predochemical solutions. We show that in fact the exponent's dependence on D can actually be improved to linear in D. And it's a somewhat technical proof, so I'll just say something somewhat cryptic for now and then I'll get into why we're able to make this work later. But the key in all of these works, these previous works, is actually in choosing the right definitions. You choose the right definitions to analyze these random events and actually the whole thing becomes easy. The difficulty is the definitions become very convoluted. Even for the case of dimension 2 as you go up they become even more complicated and you get worse and worse bounds on this exponent. So part of our contribution is actually finding more principled way to get the definitions. We do it implicitly through an algorithm that actually constructs the family of events that we analyze. And I'll explain that more in detail and then to be clear right now. So I'll mention that this answer is a recent conjecture of Tang and just to compare and contrast this to a distributional model, what if I took all the power out of the adversary? What if instead of having all this combinatorial structure that allowed me to capture things like perturbations to napstack instances, what if instead I just asked what happens if you take the same number of points as random uncorrelated samples from a D dimensional Gaussian? So there's no more combinatorial structure across one of the 0, 1 vectors of these different items. Instead if I hit the sample button two to the n times, it's been known actually since the 70s that the expected number of pre-dopimal solutions is exactly n to the D minus 1. So actually what our result is is it actually shows that it's a square factor off from this purely distributional model where the adversary has no power and it's totally Gaussian distributed. The strange thing is that for the case of D equals 2, well if you recall I said that actually in the smooth analysis model the matching upper and lower bounds were n squared. And here in this Gaussian land the answer is actually n. So actually the square factor is already necessary for the case of two dimensions and in fact this is why this was conjectured n to the 2D minus 2 as exactly the right answer all the way up. Although no lower bound better than the Gaussian case is known right now. Are there any questions? Okay so I'm not going to be able to explain entirely how this result goes through, but to make some of my statements a little bit less cryptic we have to get our hands a little bit dirty. My goal is to explain some of the previous proofs, the Bayer-Rogland Vockingproof, and then I'll actually give a reinterpretation of this result. So the first goal is actually to come up with a slightly, I'll only work with dimension 2 until the very end of the talk. Now the first thing is I want to give a slightly easier characterization of when a point is Pareto optimal. I can imagine if I took all my candidate solutions, they have some objective 1 value, some objective 2 value what if I start all the way on the right from the largest objective 1 value point and I sweep from right to left. Well as I encounter points when will they be Pareto optimal? Certainly the first point that I encounter will be Pareto optimal. It has the largest objective 1 value of all points. So it's clearly Pareto optimal. And in fact now any subsequent point that I encounter as I sweep from right to left will actually be Pareto optimal if and only if it lands above the highest point that I've seen so far. So for example this point is not Pareto optimal it doesn't cross this barrier and this point is Pareto optimal it crosses the barrier and it causes us to move up the barrier. So now this point is not Pareto optimal because it doesn't cross this new barrier when we encounter it. There is another point that's up into the right. So let me work with this condition now and let me explain the general pattern. So I mentioned that all the work in these previous papers is through definitions. So at a high level our goal is to count the expected number of Pareto optimal solutions and in fact the pattern that these papers use is we first define some complete family events. Some family events which has the property that every time there's a Pareto optimal solution there's some unique event that I can blame there's some unique event that occurs because of that Pareto optimal solution. So if we had this type of domination condition it would mean that if we could bound the expected number of events that occur we could bound the expected number of Pareto optimal solutions. But this is actually a rather easy condition to satisfy. I could for example choose a complete family events that for every possible solution it just asks is that solution Pareto optimal? That's certainly a complete family but it's useless to us because it doesn't make the task of bounding the chance that the event occurs any easier. So in fact that's what I mean by all the work is actually in the definition. This will actually become quite convoluted just for the purpose of making this last statement easy to do. So for example, you know now let me explain the events which Bayer-Rodl and Evoquing use for the two-dimensional case. These will be the easiest events to explain. Suppose we have some Pareto optimal solution X. Well we want to define an event based on something that must have happened if X is Pareto optimal. So we can imagine that we started sweeping from right to left when we encountered X that had to be above everything else we'd seen so far. And actually similarly the common case is that if we continue this sweep starting at X, we actually expect that at some point we'll encounter a point even above X. We expect that we'll encounter some point Y that's above X because if not X really has a unique identity is the largest objective two value of any point. So I won't worry about that case. And the common case is that I can take some Y that's actually the first point I encounter when I sweep from right to left starting at X that's actually above X. So this region in space between X and Y should actually be empty. But now X and Y themselves are different solutions in 0, 1 to the n. So they have to differ in some index. Let's say it's index I. And for simplicity let's say X of I equals 1 and Y sub I equals 0. So this is almost the picture of what the event looks like. There's one more technical detail that if you don't want to don't worry about it. It's that we can actually draw some interval around X which if we draw it narrow enough it'll actually not contain Y. Y will be above it X will be inside the interval but the rest of this interval will be empty. You can think of really what we care about because this interval becomes very, very small because we really want to perform an integral to understand the expected number of period optimal solutions. But now this is actually a complete family of events. Really let me try and formalize just saying that the event is what I drew on the last slide actually occurs. So the event is some interval I where it has with epsilon and the event that we're interested in now is that there's some period optimal solution X. Well it has to land inside the interval but moreover if we let Y be as in the picture it's the first point when we sweep from right to left starting an X that's above the interval with that Y and X they have to disagree on this index I. Y sub I has to be equal to 0 and X sub I has to be equal to 1. So you see already that even in the case of two dimensions in order to make this analysis work I need these events which have this conditional chain of things that happen. Y is the first point which is above this interval and so on but the virtue of choosing this sort of convoluted definition is that it actually makes the analysis become easy now. It's almost just an immediate consequence if you work out what the real definition is. For example suppose we had that event E and we're interested in does it happen? So we have some interval I and this is really the operative interval that we care about this X land in here and does all that chain of events happen but now what we can do is we can actually sample all the randomness out of objective 2 except for one missing random variable. That missing random variable will still be enough for us to show that this event is unlikely. So now suppose we had all these other variables in for objective 2 except for this one missing one on this index I that we really care about for this event. Well, now if we pretend that this missing random variable is 0 for simplicity then every point is mapped to some objective 2 value and every point is mapped to some objective 1 value and actually some of these points locations in the plane are already fixed. We know that among the entire set of K and 8 solutions some have their I and X equal to 0 some have their I and X equal to 1 and these blue points that have their I and X equal to 0 they don't actually depend on the missing variable in the second objective function. So actually this remaining randomness we have these blue points are actually frozen in the plane. What that means is we know among the blue points which ones are above the interval which ones are below the interval and we in fact know what's the rightmost point that actually that identity of that point actually has to be the Y in order for our event to occur so what we're actually doing is we're being able to deconstruct the event to figure out who Y is and later who X is that's the basis of this analysis now we know that X if the event occurs actually has to happen to the right of Y so it has to be among these green points conceivably we might be worried about any one of these green points landing inside the interval but actually it turns out that there'll only be one green point that can actually cause our event to occur because all these green points and these black points too essentially these non blue points will they move up together with this missing random variable so for example if you know I sampled this missing index and all these green and black points moved up together what happens if some other pretty optimal solution lands inside that interval well even though X actually has landed inside that interval and there is a pretty optimal solution in that interval we're actually not worried about it because we know that X actually has to be above the interval yet X by design agrees on the Ith index with Z so this means even though there is a pretty optimal solution inside this interval we actually should be blaming it on a different event we should be blaming it on some other index which these two points are different on so actually the only point which can land inside the interval and cause the event to occur is the unique green point that's highest up so I hope you can at least get the intuition behind the analysis but now let me actually just give a reinterpretation of what this is actually doing so there's one interpretation which is just based on a complete family of events and analyzing it which sounds fine because it's a union bound actually what we're really doing is we're defining these events implicitly through an algorithm there's some transcription algorithm which what it can do is it can take all the randomness after it sees everything and for every pretty optimal solution it finds an event to blame so there's an algorithm I mean it doesn't need to be efficient but there's an algorithm which given a pretty optimal solution X will find some interval that X is contained and it finds some Y which is you know up into the left of it and it finds some index where they're different this algorithm spits out the description of the event and what we're actually doing that so this already defines a way to see that this family of events is complete the statement that it's complete is just that on input any pretty optimal solution this algorithm outputs something that's some event that we can blame but now the analysis is actually like a speculative execution of this because what we're actually doing is given the description of the event given the index I given the interval given X sub I and Y sub I well we're actually able to look at just some of the randomness we're able to look at everything all the randomness and objective to except for this one missing random variable and we're still able to figure out who the X is that we should be blaming we're still able to recover a unique point that must land inside the interval in order for the event to occur but since we only looked at some of the randomness in fact that remaining randomness that we have left over is enough to show that the event is unlikely that it's now unlikely for X to land inside the interval so that's how this pattern of analysis is going to work is that for the case of as you go higher and higher dimensions the events become much more complicated the chain of conditions that you need to verify but at the end of the day you can actually write down a simple algorithm which you're just saying that you know given some pre-diplominal solution and output some description and the entire analysis then is that given those clues about what's occurred another algorithm can take that as an input and look at just some of the randomness and actually step by step it will have the same output as the original algorithm method of analysis is actually through invariance of algorithms so the algorithms themselves are page to the scribe or something but it's much simpler than the family of events that they actually implicitly define so the last thing I want to mention is I'll just give you an idea for what the family of events now looks like in higher dimensions in dimension 3 even so for example now in this case for three objective functions we can imagine sweeping according to this first objective function we take all the candidate solution and we start from the largest objective one value and we consider them in decreasing objective one value order now a point occurs the first one is again clearly pre-diplominal it has the largest objective one value for a new point that occurs to be pre-diplominal it just has to be pre-diplominal on the two dimensional objective two objective three plane so for example this next point is pre-diplominal when we encounter it this next point is as well and this point is not because now when we encounter it it's not on this two dimensional surface there's another point that's better in objective two and objective three that occurred earlier and hence has larger objective one value so in fact now if we encounter some new pre-diplominal solution x we need to define some notion of the common case what events happen in order for this point x to be pre-diplominal and the common case we actually expect that there'll be some later y that we encounter which will be up into the right of x this again will be the common case otherwise we'll actually be in a lower dimensional instance and the trick ends up being that if you look at all the points before so x and y first of all differ on some index i because they're different zero one to the n solutions so in fact what we'll output from our algorithm well one of the things we'll output is what's the index i where x and y disagree and we'll in fact output whatever the values are of x and y but we know that actually of all the points that occur before y which have larger objective one than y, x has to be on the two dimensional pre-diplominal surface that I've drawn here in a dashed line in fact even if we take the points from z which are different on this i-th index so it includes x well this restricted set of points x is still Pareto optimal so what this means then is that we can essentially recurse now because we can imagine since x is on this lower dimensional pre-diplominal surface but now all these blue then this blue and this red point they all agree on a new index so you can actually recurse to another case where we try and sweep along objective two and we know that now in the common case exactly as before there's some later point z that's actually up into the left so what we end up outputting is actually for the index j that x and z differ on we output this full table of first of all what's the i-th index, what's the j-th index and what are the values of x, y and z that are the sort of key agents in this entire argument and the trick behind all of this now is that there's some way to actually speculatively execute this algorithm outputs enough information that it can look at just some of the randomness and still be able to figure out first who y is, then who z is and then turn who x is and that's how the analysis works so that's actually all I really wanted to say about this are there any questions I can answer? thanks first oh thanks you seem to have a question so you give this really nice application application at the beginning of the 2D case with knapsack seems like they're really proof from the book about why in particular average case versions of knapsack are fast and stuff so I mean what would be the killer applications to sort of jack up d a little bit say d equal 3 so there, so as long as the objective function you're interested in is some monotone increasing function of these different objectives if it's an arbitrary really complicated non-linear function but it's still monotone then people actually, the way they end up solving this is by building up the Pareto curve for higher dimensions and then just checking only those solutions and just outputting the best so the knapsack was one case where the objective function was something simple like maximize one subject to a threshold constraint on another but there are other examples where things like you know, Poppenmeacher and Yanukakis initiated some study of you know approximate Pareto curves and there they had examples where in some web services you actually had a couple different objective functions and really what you're trying to optimize was some very strange function of those so in those cases there's really, I mean there's not too much structure in the objective function other than it's monotone and in those cases you still have an approach because you know that points which are dominated are still not optimal solutions so that would I would say is maybe the canonical sort of example for Pare dimensions yes


by miles or so and I may be there on the mileage but in any event it bottomed and the allegation is that the chart was an error and that according to the chart it was a substantially above the bottom. The certain damage occurred to its steering apparatus and some of its diving planes but it was on the surface about a half an hour ago and no one was injured there was no leak each so far as we know to its nuclear plant salvage ship was standing by and to assist it moving into port we anticipate no problems but for a time it looked like we might have another nuclear incident on our hands. The result is Mr. President I'm really not up to date on Southeast Asia. What is the story behind the well what was your evaluation yes down I want to ask you to go in the office now I've got you thought I thought you said damn tired you better go home do you know we had started that breakfast but I just didn't know I'm sorry I would love to come in well I I I think it shows two things Mr. President first that they have more power than some credit them with I don't think it's a it's a last gas but action I do think that it represents a maximum effort in the sense of they poured on all of their assets and and my guess is that we will inflict very heavy losses on them both in terms of personnel and material and this will will set them back some but that after they absorb the losses they will remain a substantial force I don't anticipate that that we'll hit them so hard that they'll be knocked out for for extended period or forced to to drop way back in level of effort against us I do think that it is such a well coordinated such an obviously advanced planned operation that it probably relates to to negotiations in some way I would expect that were they successful here they then move forward to more forcefully on the negotiation front and that thinking that they have a stronger position from which to bargain I don't believe they're going to be successful I think that in case on where we're going to have the real military engagement I believe we'll we'll deal them a heavy defeat I think in the other areas it's largely a propaganda effort and publicity effort and I think they'll gain that way I mentioned our people across the country this morning well we'll feel that they're much stronger than they had previously anticipated they were and in that sense I think they gained the question my mind is how to respond to this is there anything we should be doing we're not doing I've talked to the chiefs about some kind of a reciprocal action retaliation for their attack on our embassy or in retaliation for their attack across the country there just isn't anything they have come up with it is worth a damn they talk about an area bombing attack over Hanoi the weather is terrible you can't get in there with with the pinpoint targeting the only way you could bomb it at all at the present time is area bombing I wouldn't recommend that to you under any circumstances they just haven't been able to think of retaliation that means anything my own feeling is that we ought to to depend upon our ability to infect very heavy casualties on them as our proper response and as as the message we give to our people I think it one thing well to do is try to keep Westmoreland in the news I ever twice a day I quite agree you do that I think you I haven't I haven't built it to talk yesterday to our people aren't have that was to make I said one today but I'll make it twice a day you're quite right thank you all to to I don't think they get enough information I think you become sensitive and we all pull in and I meet with them once over two three months yeah you meet with them once a month if there's something big but if you'll remember you see I remember home all day late and I can choose the difference and I think in this campaign here the other crowd is cut to three committees grinding out things their only interest is to find something wrong yeah people look for something wrong unless you've got so much choking them that is happening just back to that Jerry Ford last night I want your evaluation of that I thought it was a disgrace I really thought it was a goddamn disgrace that's why I stepped in at one point I didn't know whether to open up earlier or not I didn't want to reduce your reaction to him because I thought it was very effective but damn when I was annoyed at that I thought it was discourteous and absolutely irresponsible it seemed to me that he was so determined to find something wrong and he had nothing that he could find wrong although there might be much that was wrong we all said that first thing we do it save the fifty-two minutes they didn't respond would respond in light of what we knew now but at that time it didn't and he just so determined to find something that was wrong that he wouldn't even listen to the other things look like to me I thought maybe I was just prejudiced but he started pounding the table I thought he was just came in temperate it was just a disgraceful performance now I do think that when he left he'd cool down some and and I think the unanimous front that he faced and particularly Buzz Wheeler's strong support out that cooled him off and I doubt very much he's gonna make many speeches about this subject they're going to find something anything they can find though that's wrong what do you think our reaction ought to be should it be different from what it was last night we're going into other meetings I thought that I was rather willing to admit the possibility of error all along I kept saying that sure if you ask me now today I change a lot of things I would respond immediately instead of waiting fifty-two minutes I think that I take exactly that track with other meetings except that I wouldn't initiate it and I don't think you're gonna get that kind of partisan criticism in some of these other meetings I'd be surprised if Aaron's for example did that he's not strong enough to do that but but if he does I'd respond exactly the same way we were too strong with Jerry oh no oh no no no no I thought it was frankly I thought it was just right Mr. President I thought when he left he'd cool down some and he found that there wasn't a chink in our armor that he'd been able to break through I would have layered it just been more that's right that's why I didn't want him there Mr. President he's impossible to do you can't argue and he's a bright guy and he's brighter than Jerry for one thing how did you evaluate to Dirksen I don't know I I I concluded that he was just keeping his powder dry and preserving his options he was very anxious to go in with all flags flying all guns blazing until I talked to him a long time the other day at the Security Council luncheon or something he called me one of the old noticed it but I had a long talk with him and on the phone and he wound up he said all right what do you want me to do and I said I just want you to say that the president is reviewing this matter and will give the leaders a report and whatever the nation needs will be supplied and will be supported he said all right so he said something along that line didn't say much yesterday he said a little more but what I thought maybe last night what he was doing I was hoping that you'd have this reaction but I guess it's not justified I was hoping he was just utterly disgusted with Ford's performance and didn't want to go against him and same time didn't want him well Mr. President I thought that for a time but then he remained silent so long initially I thought when Ford was getting angry and his face was contorted with anger I thought Dirksen really was feeling contempt but then it went on and on and on he didn't say a damn word and he could have very easily well yes but what he would be charged with undercutting him and I just thought he couldn't say anything in the displays like your wife tears up those over the maybe so but I thought there were several openings when he could have said well buzz what do you think about this now surely there's something we could have done differently or is it but would it have made any difference this is what he this is the line average ever should have taken sure there's certain things here we must have been able to 52 minutes but suppose you hadn't done it 52 minutes would the end be any different than the cancer courses no there were several openings he had he didn't see them and that's why I felt he was preserving his options and also I I haven't read the the record it's on my desk right now but of yesterday but the newspaper reports weren't particularly good on what he said yesterday it seemed to me Dirksen yeah now one thing about McDonald Bob I thought if we got in deep trouble he is a little better witness I believe than most of them in he better than more yes he is look sharper to me and more modern clearer and cleaner actually I think you got scared hell out of McDonald and get him into this thing and his Navy and his skipper it's his operation in a very real thing that's what I know you're absolutely right and I get him up to it up in his ears and I picture him as Mr. objective and Mr. fire and Mr. so and so Mr. President I knew you were disappointed with the briefery yesterday but I did it purposely if you saw all his metals and you must have Christ he has 14 campaign ribbons and metals there and he has three stars on his shoulders and quite frankly I did it purposely to put him forward instead of me not that I'm trying to get out of the line of fire but I just thought that in this situation those people would be more impressed by a man with a suit on his eyes all right and crime but this morning we'll do it differently I'm sure you get to leave in the more mission and I just there's not anybody in this government that can say as much in his little time as you can I said I quite frankly I've tried to I thought he was just I just didn't think he's up to this morning I thought we'd have buzz do what he did last night and then I'll take the questions okay mr. president one thing you might like buzz first this morning to start with South Vietnam he'll feel very quickly covered two or three minutes the events of the night good tell him Bob and you too you don't ever had trouble but tell him to talk louder from that of the room yes the echo that's right I can't hear what's going on thanks


Tim, you have 11 new emails, 7 are promotional, I'm going to sort those under promotions. One requires an immediate response. Dr. Graham needs to reschedule your exam on Tuesday. I have checked your calendar and Dr. Graham's availability and it looks like we can schedule you for Thursday at 3pm or next Tuesday at 4pm. Which do you prefer? Next Tuesday at 4 would be best. Consider it's done. Thanks, my craft.


As we have addressed earlier, our stock market is a business. It was a wonderfully effective business for those who initiated it, and it served to substantially support the development of corporate business in our economy. In the negative, it also proved to be a means to further separate business performance from both owner authority and accountability to owners. Our challenge in addressing this area is a massive support that has been given to economic privilege, promoting business model stability. It developed a funding system with leader reliance upon what people do in the stock market instead of what it is able to accomplish for us. The key, of course, is that we the people are the owners of our economy and the ultimate owners of everything in it. We the people are also the owners of government that it is able to manage the economy and it is to serve the welfare of the people. The stock market is not some bastion of privilege. It is just a part of our economy, a part of the economy that we own and that only exists to serve us. We have great interest in how it functions and what it does for us. The stock market was a business, a very good one. It was a very productive and successful support for our nation's recovery and reset in reaction to our industrial revolution. It was a business that brought corporate investors together with those who would own and operate corporate businesses. The need was for businesses to grow. We were shifting from family business and us and them venture to corporate business operations where everyone could benefit through business investments. Business was shifting from family to corporate concepts. Corporate business needed access to far more resources than were commonly available to any family. The stock market provided the connection between investors and corporate authorities. Corporations were one type of stock market customers. The stock market provided access to investor owner funds as a service receiving limited and shared ownership generally called securities as payment. This was a highly valued service to corporate customers. The other customers were the investors who purchased interest in corporate stocks and bonds through action of the stock market. This was accomplished through the market managing the transactions and it was an extremely effective business. Market activity has even been used to measure the success of our economy but this is a measure of what people do, not what they accomplish. Accomplishment is in terms of what is delivered to customers that they get to value. Performance approach provides a clearer understanding of value to us as people who own the economy. What does the operation of the stock market both deliver to us and that we get to value? We get to have limited ownership in corporate America. That is great value to us as investors. Investment is a way to accumulate our wealth, storing our prosperity for later use. It is a way for us as people to maintain wealth but then it also separates ownership from some of the benefits of ownership. It is impersonal ownership. It supports massive populations of investors so that our ownership is effectively reduced to a way to gain income from investments. Not support for the authority of ownership but a requirement to trust those who run corporations to see to our joint interests in corporate profits. The first warning bell goes off. Corporate leadership functions on privilege, not on earning profits. Modern leadership assumes that properly running the organization will best assure its performance. Of course the ultimate witness is the division between management and labor, a subject we have already addressed. Working together in coordinated effort is far more effective at performance than proper use of authority. Performance orientation provides a new understanding of the market, not that common to either the students of management or economics. We have value in establishing a new vision of the operation of the market and how it relates to operation and purpose of our economy. What we see in the operation of a business is that the real decision makers are the customers. They are the only ones who really determine what the business earns and they do it as individuals and in accord with how the product of the business, whether goods or services, satisfies their needs and wants at an acceptable price. They rarely even know whether the business is properly running or not. Let us take a new look at the business of the stock market with its commercial customers, the businesses that issue stocks and bonds for purchase by investors. These are like a government issue of money. They are tokens that have the promise of value. What then does the commercial business get for selling an interest in itself? They get investments. They get another type of token. Like money, the stocks or bonds pass through the market without being converted into anything. The stock market takes a cut of the transaction that passes those stocks and bonds to investors. It is performing a vending service. It is much like a temporary employment agency in this operation, but selling the interest in corporate America instead of the time and effort of workers. It is delivering a vending service to its corporate business customers, selling them profitable potentials. Where regular employment assures that workers are paid for their efforts, the stock market assures that these businesses are paid for the tokens they deliver for sale. Like a temporary employee, these businesses do not work for the stock market, but it markets their potential profitability for them. That is the service provided. On the other side, the stock market serves those who invest. They get to buy an interest in corporate America as token interest in businesses. The service the stock market provides is the sale of interest in businesses as a potential for earning income. It trades stocks and bonds, private tokens, for business ownership, for dollars which are government tokens of value. For a product, the stock market produces for investors is a vending of these tokens. There is no change on tokens as they pass through the market and the money that passes through it is unchanged. These are not part of the operation of the stock market business model. It is selling services only and collecting some of what passes through it to pay for its profitable operation. For our corporate business customer, the stock market is renting out its internal profitability and the price for this is a cut of that profitability. For the investor, it is passing that rental out to them as its service and maintaining the system of tokens for harvesting some of that profitability. The warning flag should go up for us. Tokens are sold to investors, tokens of ownership, but not the ownership itself. And between the ownership that is sold to the investors and the business that rents a part of itself out, there is this vending business. It is ownership stripped of most of the natural authority that is common to being an owner of something. There is essentially zero accountability of the corporate business to the investors. Separation of authority and responsibility is a known bad management practice. It leads to problems of abuse and waste. In the case of stocks and bonds, it was a disconnect between the value of the business as an operating entity and the value of its tokens. That value was speculative. The value of the tokens was not the value of the business. Enter the initially puzzling differences between the price of these tokens and what they were supposedly worth. It was soon recognized that the value was what investors were willing to pay for them. They could be bought for one price as sold for another. All it took was change in opinion as to what customers expected them to be worth. It wasn't their current worth, but their speculative worth in the future. Enter a new type of player, the freighters. These were professional gamblers intent on buying tokens at one price and selling them at a higher price. It is here that the true economic waste is uncovered. The trader does not produce anything that is valued by the business that issues the stocks and bonds. There is also no product for investors, nothing that they get to receive and value from the activities of traders. There is no valuable product for the stock market itself beyond increased sales activities from which they can harvest their income. The effect achieved by professional gamblers and stocks and bonds is waste. It is intentional harvest of wealth as a market product from the operation of the stock market itself. It is waste that returns no goods or services to the market's customers, but rather takes a cut from the value of stocks and bonds that are bought and sold. Due to the speculative nature of the stock market, traders get to harvest wealth from the earnings of those who would invest in corporate businesses. Their harvest devalues the stocks and bonds for the investors. The more successful the traders become, the lower the return on investment becomes for those who would invest. This is not good for our economy. Gambling and stocks and bonds has become so lucrative that it has all but forced those who would invest to purchase their own professional gambler help as a way to preserve wealth in this investment arena. It has all but removed banks, those highly regulated, as to their investments from major participation, eliminating a large part of their former business, which further limits the dollars that are available to invest. So let us summarize this situation. First, the corporate leadership is intent on running their businesses and delivery of stock and bond tokens to the stock market for sale is an effective way to gain working assets for the businesses they run. The market separates them from those who buy at interest so that the leaders are able to run their businesses without the inconvenience of owner demands or directions. It serves privileged corporate leaders, giving them unregulated access to investor assets. It gives those who operate the stock market as a business by having traders significantly increase the buy and sell activity, which is the service that earns income for the stock market. It serves the traders who gain a living and a profit from their gambling with what investors would put into corporate America. And what about the investors? The investor is the only one who is putting money into investments. The others are harvesting from the investments that are made. This arrangement was like that in feudal England. It was where only the ones who earned anything were the peasants who worked the landfished or had businesses that could be taxed to support the aristocracy. It was where a class of privileged people could live well off the productivity of others. But original feudalism recognized the value of the peasants as the source of all wealth. The landed barons were pretty much aware that they needed to protect their peasants, they needed to maintain their satisfaction as peasants, or they might abandon the feudal land and serve other barons. With the stock market, the traders prospered from a temporary stake in the market with the intent to just sell it back for a profit. It was a new type of privilege. If investors lost what they invested, it was perhaps a concern, but not a great one. If businesses lost the value of their resource base, that was their problem. These were professional gamblers. They were not functioning as an effective part of the economy. Once again, we have support for the nature of privilege. It creates structure and stability, not performance. It discourages change. In this case, it promoted corporate businesses that were inherently stable. The greater the speculation as to the future of a specific stock or bond, the greater the harvest for gamblers. It discouraged investments in business startups. It discouraged investment in businesses that had fluctuations in value. The stock market favored large corporate businesses where there was little product change and therefore little advancement. It attracted investors to utility providers and mining companies. It attracted people to invest in banks and publicly supported or highly regulated businesses. It favored businesses like the automobile, whose products would continue to sell strongly because it had effective capture over its customer base. These are businesses with securities that are less likely to suffer from gambler harvests. It is in the nature of privilege that it spreads. The ability to harvest income without having to earn it by productive effort was obviously valuable to common investors. There was a new class of traders, investment houses. They could sell a trading service to investors, optimizing what they could earn by competing with the traders. The investment houses would gamble just like the traders but on behalf of investors. They would gain the same sort of expertise that was exhibited by the traders but would exercise it to support their customers. In our performance perspective, this is just another business that harvests from what the investors would put into stocks and bonds. It is one more flow of value out of the stock market business. It promotes wealth for the people who return no product to the market's customers. It is another version of selling protection but this time from trader activities. The threat is one of gamblers taking the value out of investments. It is truly amazing with all these privileged parties feeding at the trough that there was still a good flow of investor dollars into the system. Perhaps the best vision for this is that there is little good alternative, even starting up a new and productive business is discouraged as funding is hard to come by when funding for startups is subject to gambler manipulations. And then we have to include the interference of government. For public management, it interferes to prevent openly criminal behaviors by traders but otherwise supports them as a matter of privileged earners. The government collects its taxes from everyone. For government action, we also have to include the support of modern economics. It is there measuring the activity of moving money. Every increase in waste is addressed as an economic improvement. We have the performance vision that puts this into a working perspective. What the government takes out through taxation is funding that does not flow to the investors and what the investors are able to harvest is also taxed. We have an incredible performance potential for wealth generation in our economic system. Even with all these people harvesting their own income from the investments of common people, it still is able to provide some income. The true potential is staggering. The potential benefit from eliminating investment system waste is likewise incredible. It just needs the vision to gather people to effective change efforts. Are there things in here where we can identify specific sources of waste? Places where we have a good basis for bringing people together to benefit us all by actions to eliminate it? Our most immediate need is recognizing that we are not alone. We are not some other group of customers who are trying to find their own way to get ahead at the expense of others. We, as we the people, are the owners of the economy. It is we the people who are looking at how best to handle the public purposes that we recognize in having our economy serve us. Having special people harvest from this system at the expense of others is a challenge rather than something to be preserved. What is the value for us, for all of us? We value a way to both preserve our personal wealth and a way to support the economy that will serve our purposes. First we need to kick out the idea that this is some sort of private business that can do what it wants with its customers. Preserving wealth is a matter of public concern and even those who have no money to invest today are looking for where to invest what we will earn through our future economic commitments. Our personal potential for investment is what we can all value. It is not just a place for private citizens to invest. It is a place for our banks and other financial businesses to invest our funds. It is a place for our retirement systems and unions to invest our funds. It is a way to fund corporate America to better serve us as owners of this economy. The stock market may well have been initiated as a private enterprise but its function has become an endemic part of our economy. Our general direction of change will be to establish citizen-based management of the entire stock market business. We the people of the only real party in interest. If we find our agreement and set a demand upon it, the stock market will respond. Our general challenge is investment waste. It is some people who are privileged to harvest from potential returns on our personal investments. It is people finding wealth by taking it from us by people in businesses who do not deliver us any value goods or services from what they do. It is actioned by those who believe they are privileged to use our investments for generating their personal or business income. The rule is both simple and consistent. Those things that do not come to us as customers or as owners, and we are both, are of no value. The fact that there are also people relying upon or receiving that waste and working for it is of no consequence. If they are not investors who decide to commit their resources to earn a return on their investment, it is waste. Consider the stock market indexes. A look at the value of stocks in terms of what our professional gamblers can get for reselling their holdings. The current selling price of securities has little to do with the value of the business that we choose these securities, or the return on investment that these businesses commit to secure base of investors. This is where we start with government now regulating what is an effective corporate casino. Government is harvesting its share from the operation and is unlikely to support any changes based on seeing to the welfare of investors or corporate America. The government that should be serving us has become a leech upon the market. Suck in the life out of it. We all, with government leaders intentionally included, see the wonderful potential for benefit that is not being supported by current political interference. That is part of the benefits that are available to us to initiate effective improvements. We need to start with a new and more effective vision. For government, we common citizens are the only real party in interest. Our potential direction of change is what we learned in our history, setting up an alternative government investment service where business investments are only available for long-term purchases, probably only being brought back by the company that issued them. Should the government initiate competition with a private business? The answer, of course, is that we the people are the nation. There is no competition. There is no us and them to be served. The challenge is serving someone other than we the people. The government has a constitutional purpose in serving the welfare of we the people and no basis for protecting some specific business as its operation harvests wealth for privileged traders. In our current environment, the change costs associated with our directing this would be very high. It would be especially high as there is a large population of heavily rewarded traders who have special access to government leaders. We do have a far less expensive change alternative through harvesting the conflict of purpose inherent in our current operation. The foundation for change was encapsulated and, I quote, attributed to President Ronald Reagan. You tax what you want to go away. We have a fairly simple picture for the operation of the stock market. You should note that I have annotated the investors as citizens when the investment in our American economy is primarily through buying an interest in corporate America. It behooves us to recognize that there is very much a public interest in addressing systemic waste. Waste is a flow of value out of the performance cycle without returning anything that has value. What traders or investment businesses are able to harvest reduces the investors' return on their investments. The management technique would be to tax short-term trades so heavily that professional traders and investment houses can no longer earn effective income. The securities would have to be held for perhaps two to five years to avoid the tax. There would, of course, be exceptions for court-ordered actions and heritances or the like, but turning off the manipulation would quickly change the very nature of the securities markets. It would stabilize the price for stocks and bonds and assure that the return on investment goes to the people who invest to own a piece of their national economy. As to what happens to the investors when some businesses fail and all their value is gone, we have the obvious answer, and it is common insurance. It is selling a service of spreading the risk that something goes wrong with some specific investment. The business of stock market is sales, and these would drop dramatically with the absence of manipulation. With that, we have identified who it is who can sell investment insurance. Insurance for investors is a potential business product for the stock market itself, and it could replace much of the loss of vending income when short-term trades were abandoned. What about the people who have been making a very good living? Are we just going to abandon them, kick them out of the only employment they know? The economic answer is that ceasing to pay people who do nothing for you is not some interruption in their entitlements. Perhaps the government can use some of the tax income from short-term trades to establish retraining opportunities. The simple truth is that these traders produced value only as their efforts are valued by investors. If the investor gets the return on investment without their involvement, why would investors maintain them? One option is offered in the government providing an investment support service, a public service alternative to the private stock market. Another is taxation of waste and active discouragement to the business of investment as a casino effort. Either of these will strengthen and support investor ownership in corporate America. Those who invest to own will be the ones most benefited by the change, and we see the owner investment as beneficial to citizens in general. Also, where the investors become more effective owners, there is encouragement for those investors to act to secure their own benefits through exercise of that ownership, taking a personal interest in the operation and profitability of the corporate entities they own. Where the welfare of the investor is less determined by manipulation and more by actual value of the corporate business, there is increased potential for investors coming together to assure that value. Wasteful practices by corporate management could well become an issue that would bring the investors to find agreement. Political donations of the like would be seen as reducing the pool of funds that would otherwise flow to the investors, encouraging their interference with leader privileges. The change benefits would likely be immediately limited to the value of securities, but would almost certainly have long-term value effects in both investor wealth and corporate operations. We have another lesson to be learned, and it is in communication rather than performance itself. Our common reaction to this level of improvement potential, a reaction that is trained into our general behavior, is that eliminating waste is somehow damaging. That is privilege-based thinking at its worst. That loss of stability is a threat that justifies continuation of waste. The way to get beyond it is to make it personal. If you have been hiring a local youth to mow your lawn, but find that more than half of what you thought was your lawn is actually owned by your neighbors, they are the ones who are responsible for mowing it. You would farm your lawn mowing youth that you are no longer going to pay him to mow that lawn, only what actually belongs to you. You suggest that he address this also with the one who really is responsible for its maintenance. Have you shorted this young man? Should you continue to pay him for a time because you have lowered his income from no fault of his own? The harsh answer is that you have others who depend upon you, taking from them to continue supporting this neighborhood youth just makes no sense. The change in your priorities may affect other people, but the choice is still your own. If he complains that he was able to buy many good and useful things, even helping his parents out by paying for his own clothes, and you are cutting him down without good reason, what is your response?  The answer is that the decision of what you do with what is yours is not even his concern. If anything, his creation of additional costs by how he acts is likely to convince you that ceasing to support him was a good decision. What we are suggesting is taxing away the waste or replacing what we have with a public service. Either is just a choice, as is not making any changes at all. They have different values and they incur different costs in terms of the commitment of citizen time and effort to bring them about. They face different challenges to change actions. Decisions on whether to take action or simply support action or to let things continue is a matter of personal commitment to a benefit that all can see. Having that choice is empowerment. My presentation of the options and focus on costs and benefits is just my technical support for your decision. In this lesson, we have addressed a single, very important, semi-public institution. We have looked not only at how it operates, but the impact it has on our economy. Still more to our purpose, we have identified areas of significant waste that can be addressed for their elimination. It is also instructive that this is just one institution. It is not the larger economy. While it is most certainly an important aspect of our economy, it is still just one little piece of the larger effort. If there is this much waste in this one piece, consider how much opportunity awaits our larger examination of our commercial environment. In our next lesson, we will expand upon the role of our government in seeing to our needs and wants through its impact on our various elements of its larger economy. Instead of just looking at the good and proper operation of government, we will shift to the impact that we can have on government operations with recognition of the common value that can bring us together to have that effect.


So, we have been discussing about features which are exclusive to Fourier transform NMR. We talked about various important parts in that one. So, we will continue with that discussion with regard to the special features with our exclusive for FTNMR. In that one we now come to the 10th point which is phase correction. Typically we know that NMR signals are of two types. One we have a signal which is like this and this we call as absorptive signal or you may call this also as a spectrum with a zero phase or the other is the dispersive signal which goes like this and this is a dispersive signal and this we may call it as 90 degree phase. In the FTNMR we collect the data as let us say we collect the data is cosine omega i t and e to the minus lambda t, lambda i t suppose we have the signal which is like this. When you Fourier transform this it generates two components one is the real component and then you also have the imaginary component time domain function this is my FID. If FID is like this the real part will have a pure phase absorptive signal this is absorptive and the imaginary part will have the dispersive component. Now similarly if I have if my FID is of the type sin omega i t e to the minus lambda i t if I have this sort of a function FID this is my FID then after Fourier transformation I will get again a real part and an imaginary part. The real part will have the dispersive signal and the imaginary part will have the absorptive signal. So therefore we have to see what is it that we are going to get in FTNMR spectrum. Now often we find that the signal is not exactly dispersive or absorptive sometimes we get sometimes we get signals which are like this. So this is a mixture of absorptive and dispersive signals. So therefore this is known as phase error. So this is called as phase error and this has to be corrected. So now what is the source of the phase error? What causes the phase error? This we have to understand. Now as I explained to you suppose I have experiment done like this I have the initial magnetization here this is the M0 initial magnetization which is here if I apply a norm like 90 degree pulse along the x axis which is exactly correct 90 x then my magnetization will come along the let us say the y axis whether it is 90 x or minus x if it comes exactly along the y axis then my signal will be cosine omega it e to the minus lambda it this will be my signal if I collect the signal starting from the exactly magnetization aligned along the y axis. But often it so happens that this is not achieved and what happens is you get the magnetization which was initially a rotating to somewhere like this to some other position so then it will be oriented here in the transverse plane. If this is the case then you have the x, y and z so the signal which you are going to collect will have the contributions coming from this as well as from this. So if it is not 0 phase this is let us say this angle is theta then theta is the phase at time t is equal to 0. So in such a situation your signal will have real component which is the cosine component cosine omega it and also sine omega it so signal will have both the components. So if a Fourier transform this what I should get of course this will have a certain amplitude here this is the coefficient let us call this as a1 and call this as a2 there are two coefficients depending upon what is the error here theta error depending upon that the components along the y and the x axis will be different whatever is along the y axis will have a cosine omega it whatever is along the x axis will be the sine omega it. Now if I do a Fourier transformation of this sum together which is collected here I will have a mixture of in the real part it is also true in the imaginary part also this is the absorptive component and then I will also have a component which is coming from the x part which is the dispersive component this plus this will give me a signal which is like this. So this is because of the error in the initial pulse application the pulse is not applied exactly along the x axis but slightly deviated from the x axis. So RF phase is not exactly 0 but slightly away and that is a theta therefore when the 90 degree rotation happens it does not come exactly along the y axis but it comes somewhere in the xy plane and that if the angle is theta 0 the certain mixture of these two things will happen. So this is this is this has to be corrected okay and this is called as a 0 order phase 0 order phase error because this is not dependent on any frequency entire magnetization is rotated so at time t is equal to 0 all the magnetization components have the same angle at t is equal to 0 all the all the components the same phase error and in the this is in the real part the imaginary part similarly we will have a this portion will have pure dispersive component and and also a small absorptive component okay the trick in correcting the phase will be to mix these two appropriately so that the dispersive component from the absorptive signal will vanish and likewise the absorptive component from the imaginary part will vanish okay so that is the idea okay. Now there is another source of phase error and that is the following. Suppose my FID is supposed to be like this right and my data points my data points are should be like this here here here here here should be like this okay so therefore at time t is equal to 0 the magnetization is entirely along the y axis or whatever that is okay see in this case the magnetization is entirely along the y axis if I am collecting the y components but suppose I cause a small delay in the acquisition of the time so in this situation where will the magnetization be all the components of magnetization will be along here all the components so this will be all the components will be here in this case the normal case this is but instead suppose I do not start collecting the data from time t is equal to 0 this is at t is equal to 0 now if I collect the data this is my FID but I do not start collecting the data from the first point but I start collecting from here okay here some delay for various practical reasons I do not collect this so this can be a small time also it can be few hundred nanoseconds that is it has nothing to do with the dwell time it has some hardware limitations so you may want to give a small delay here this is a small delay we may call it as t0 so your actually data's collection starts from t0 so therefore your signal here will be cosine omega i t plus t0 okay so what does that mean in if I were to represent this in the transverse plane like this the magnetization where it will be to start with to start with we are because the t0 is a delay during this period time the different components will have processed to different extents right so during the time t0 the various components would have processed although I applied a 90 degree pulse correctly that it came to the y-axis the magnetization came to the y-axis why I did not start collecting the magnetization from that point I started collecting when the different components are moved to different extents that is t0 so let us say one component has moved here and another component has moved here okay and the third component would have moved here okay these are different spins different lines in your spectrum they are corresponding to different spins so they all have moved to different extents let us call this as 1 2 3 and all of these now have different thetas right they all have different thetas compared to the previous one it was a 0 order phase now in this case because of the delay in the data acquisition the different frequency components in your magnetization have moved to different extents therefore the first line would have a mixture something like this okay let us recall this as 1 and the second one the second one may have had some more here and the third one would have even more third and so on so different ones will have different mixtures therefore this is what we call it as frequency dependent phase shift and this is what we are talking about these are all in the real part of the spectrum similar thing will happen in the imaginary part of the spectrum so in order to correct for this here as well as in the previous case the strategy is to mix the real and the imaginary components okay so therefore phase correction phase correction would imply mix the real and imaginary parts appropriately eliminate the admixture the computer does this there are various kinds of knobs over there so this you just keep moving the knobs and in real time actually you can monitor on the screen how the phases are changing so these are the algorithms are there this is the mathematics behind this all that is all programmed into the computer it is all programmed how to mix the real and the imaginary parts and what should be the coefficients for the mixing all that is then you can manually adjust it so this can be manually adjusted okay to obtain the phase correction then we will have after you have done that you get pure absorptive line for the real part and pure dispersive part for the imaginary part you generally do not use the imaginary part for other purposes in when you want to represent your spectrum you only plot the real part you only plot the absorptive spectrum right imaginary part stays there in the computer but you do not you do not really look at that however it is used for phase correction so that is the important part of the Fourier transform NMR and this does not exist in case of conventional spectroscopy okay so now move on to the next important concept and that is dynamic range so what is dynamic range let us say we have a small signal and a huge signal like this this may be a solvent this may be from your sample and you notice in Fourier terms of NMR we excite all of them together okay in FT NMR all these are excited together and signal is digitized so when I collect the data in the digitized form it will be superposition of the contributions from all of those okay suppose this signal has the intensity of 1 this signal has the intensity of 100 then what I will be collecting will be 101 if this is 5 and this is 200 or it will be collecting will be 205 okay so that is what will be representing in my in my FID so this is what happens in the FID the FID which you have this you have the various points at various places and in every point we will have this summation represented okay therefore in every point the data has to be represented correctly this sum has to be represented correctly how it is stored how it is stored in the data the data is digitized right as I told you data is digitized and there is this device which is called as analog to digital converter analog to digital converter also called as ADC okay this collects data in the binary form okay so it gets collect data in the binary form because that is what the computer understands right and let us say we have analog to digital converter which has the resolution of about let us say 4 so there are 4 bits there are 4 bits in the analog to digital converter what is what is this this will be 2 to the power 0 2 to the power 1 2 to the power 2 and 2 to the power 3 so what is the largest number that can be stored here 2 to the power 0 is 1 this is 2 this is 4 and this is 8 this is equal to 15 this is a 4 bit 4 bit digitizer each one of them is called as a bit the 4 bit digitizer the largest number is 15 that is 2 to the power 4 minus 1 this of course is the very small number typically our intensity ranges will not be so small they will be much larger than this we would like to as a large a range as possible okay so therefore typically one uses what are called as 12 bit digitizer 12 bit or 16 bit 16 bit digitizer so in out of these they also have to account for the sign 1 bit is kept for the sign plus or minus 1 bit is kept for the sign so therefore what will be the number in this a 12 bit digitizer okay in a 12 bit digitizer 1 plus 11 this is for the sign and 11 bits what it will give you 2 to the power 11 minus 1 2 to the power 11 is 2048 minus 1 that is equal to 2047 okay so this is the largest number that you can store therefore in your FID the digital point should you when you add up the intensities of the small signal and the large signal it should be below 2047 or let us say if you scale it for some reason you have a possibility of scaling it down I multiply everything by scaling factor like 1 by 5 or 1 by 10 or some that is a scaling factor even so that scaled number should be less than this in other words the ratio of larger signal to small signal should be less than 2047 then the whole thing will be represented and this is where the problem comes let us consider that you are collecting a signal in water consider a sample sample in water and we are recording the proton spectrum proton spectrum what is the what is the concentration of proton here in water so this is approximately 110 molar water concept proton is 110 molar and if you have a sample which is 1 millimolar what is this concentration this is 10 to the minus 3 molar and therefore what is the ratio the ratio is equal to 110 divided by 10 to the minus 3 this is approximately 1.1 into 10 to the power 5. So therefore it is impossible to represent this number in this 12 bit digitizer and this is called as the dynamic range in such a situation the small signal gets lost only the big signal is represented and the small signal is not represented this is called as dynamic range problem this is the problem so what should we do to avoid this we have to devise techniques to suppress the strong signal most of the most often the strong signal is from your solvent it is not of much use for you to collect your water signals solvent signal therefore you can suppress that strong signal and so that you can observe the your actual signals and there are various strategies to do this so therefore you would come to the next topic which is called as the solvent suppression there are various strategies to do this I will take you some of the very simple ones there and of course there are very elegant procedures which are there we will see or use them the simplest thing is first the pre-saturation so what is the strategy here let me represent my FTNMR experiment in this manner this is my 90 degree pulse and I am actually collecting the signal here as a FID this is my FID so what I will do is before I apply the 90 degree pulse I apply a soft RF another RF I do not use the same RF which is here I will use the soft RF here on water on water that is the solvent signal that means it will excite only the water it will not excite anything else so this will saturate the water signal this will saturate the water and it won't affect anything else because it is soft so it is applied exclusively to the water signal therefore it will only saturate the water now before that water saturated water returns back to equilibrium before it comes back you apply 90 degree pulse here or whatever the flip angle you want to use and then you direct the signal you finish your experiment before the water comes back so therefore in this area the solvent contribution will be reduced so this is the simplest of the experiments and there are other methods what we will see what is called as the inversion recovery we will see the next experiment which is called as the inversion recovery let me call this as A okay then I will say B B is inversion recovery inversion recovery technique so what we do here is the it has actually uses more than one pulse here so the strategy will be like this you apply a 180 degree pulse a hard pulse you a time tau wait for a time tau and then you apply a 90 degree pulse or flip angle whatever flip angle you want to give and you collect the FID here how does this work let us try to understand this in a vectorial manner vectorial picture inversion recovery means 180 degree x plus meaning what the magnetization is rotated from here to here right initially magnetization was here and that gets rotated to this point when you have a 180 degree pulse so let me draw that as here now this magnetization contains contributions not only from the water but also from your other signals for my other samples as well let me represent them with a different color so let us say I have another one here for two is enough for purposes of understanding now both these will try to recover back to equilibrium okay now what you do is suppose my red is water and the green one is my sample okay so in that situation what I will do is I will adjust tau such that water has come here because it is recovering as it is recovering water has come here at 0 point and but the green one has come here okay so which means they have different relaxation times the red water and the sample water and the sample have different T1 values because this is T1 relaxation right this is a longitudinal magnetization longitudinal magnetization is what is happening here this is here what is happening here is T1 recovery during the time tau there is a T1 based recovery so the if the two have different T1 values I adjust the time tau in such a way that the red signal which has come down to 0 but the green one has gone up or go either down either way it is possible it may not have reached there or it has crossed that okay now after this if I apply a 90 X pulse I will not get any signal from the water ideally I will get only signal from the sample however in practice this does not happen some signal will always come because the recovery is not all that very very precise adjustment is not so precise so this is a strategy this of course requires that have distinctly different values things which are very distinctly different values only then you can suppress the water if they have similar relaxation times then this will not work okay because if the water has relaxed to 0 your sample also relaxed to 0 okay so then you may lose it and then of course if the difference is not very large in T1 is not very large then your sample also will get will get attenuated sample signal will also be attenuated okay so this is an important technique okay now then we will stop here and in the next one we will continue with this and take more


Thanks guys. I'm with Nestor Cortes.  How did it go? It went great through three innings about 40 pitches Everything felt great. Obviously no PMPs involved, but you know body feeling great aren't feeling good What do you take away from that session? Just staying ready staying staying up to par with all the other starters to make sure I can start the season with them Any doubt in your mind that you're gonna be ready that first week of the season? No, no doubt I think I've prepared well enough so far this spring and hopefully to get into live games here soon There was that hiccup before the team even reported with your hamstring. You had a drop out of the WBC I know you were so looking forward to pitching in that. Just how disappointed are you that you weren't able to go? Yeah, I was bummed. I was you know, obviously it's something that only occurs every four years And I was excited to represent, you know the country that gave me the opportunity to be here and to live out my dreams So I was super excited for it, but obviously with the injury It made no sense to push it and go over there as people know I'm pitching and doing lives now So I might have been ready, but Also hamstrings are a little tough You know recuperating so I didn't want to go out there and you know pitch meaningful endings and not be ready for the season Is there anything additional you're doing as far as preparation to try to help ensure that the hamstring doesn't pop up again? Yeah, we're we're activating every morning. Make sure my hips are in line Making sure that I'm getting ready before I actually go out there and do what I have to do In the past I've just I just been the guy to go out there and stretch at the team and then go about my day, but This spring I'm making sure that like I said everything's activated before I actually go out to stretch So there's no there's no worry there. Let's look back to last year first time All-Star absolutely fantastic season. What stands out to you about that season? obviously the All-Star I think It was a dream come true Something that I would have never imagined Even even last year going through like my first 10 or 12 starts still doubts that I was gonna make the All-Star team But it was such a good experience Something that my family and I will will hold on to forever. How do you duplicate? Last season and is there added pressure because of the year you had? I wouldn't say I wouldn't say there's pressure. I would say It would just be fun to try and replicate that again I know last year, you know, I got injured for a couple starts May 28 starts And this year I'm looking forward to making all 30 starts 31 starts whatever the case may be And going north of 158. I think that's the the biggest goal for me Hopefully we can we can do that pitch clock has been a big topic of conversation so far this spring But you're always been a guy that's worked fast when you hear the discussion to just kind of laugh inside saying that's not gonna affect me Yeah, we were going through the meeting inside like the first day of spring and I'm like this has there's nothing But this doesn't imply to me, but no definitely.  Do you know when that date is gonna be? I don't have a day yet I think we're looking for another live next time around So hopefully after that, I'm here to pitch in a game. Well, that's sure. We're looking forward to it Thank you so much