So if you can un-share your screen, create, share mine, and I will be presenting this talk. Yes, good. So my talk will be about a recent result on the non-equilibrium thermodynamics of uncertain stochastic processes. And you will be able to find this presentation at my website, slides.com. And it's related to a recent paper that is posted to archive. I just submitted a revised version that is hopefully better to understand, and there are some more examples. So it will appear tomorrow. And I'm glad if you will go through it. So what is the basic idea? The basic idea is that in, and this is not only in stochastic thermodynamics, but in any thermodynamic or any system, what we basically do is that we have our system of interest. And in case of stochastic thermodynamics, we consider that there is some uncertainty in the states of the system. So basically, if we have a trajectory or we have a set of states, we basically consider that we model it as a through the theory of probability. So there is a probability distribution over the state or over the trajectory of the system, et cetera. But on the other hand, when we talk about the system, typically it's coupled to a heat bath or particle bath or there are some parameters of the system. And in this case, we very often consider that we know these parameters like temperature, chemical potentials, et cetera, with infinite precision. So basically what we hypothesize is that we know it exactly. But in reality, what an experimenter does is that if we want to make an experiment like that, if we want to make an experiment like that, we try to measure temperature and there is maybe some uncertainty or we prepare the system. And of course, the device is not perfect. So we prepare the system and the temperature, for example, can slightly change. Or there are some external things that we cannot affect. So that might, for example, change the temperature of our system. Or basically there are some other external things that come into the game. And in this case, there are two very different approaches to the system itself where we can acknowledge that there is some uncertainty and we cannot model the system deterministically. On the other hand, we require that for the bath and the system parameters, we have to know them exactly. And in our case, what we consider is that as a typical experimenters, as typical experimenters, we do not know the exact value of many things. So we have to know the exact number of heat baths, temperatures, chemical potentials, energy spectrum or control protocols, transition rates, initial distributions. And there might be various reasons for that. But in general, this is something that is worth investigating also from the practical point of view, that there are some uncertainties about the system and its environment. So let's start a simple example. So let's have a system that has three states. And let's say that the system evolves stochastically. So there are some transition rates between three states, let's say with different energies, E0, E1, E2. And then we say we couple the systems to three apparatuses. And these apparatuses affect the exact form of the transition rates. So the question is, do we know this or can we somehow say something about the apparatus? So now we want to measure the distribution at the final time and there are two possible scenarios. So either we have the apparatus, then we can run the experiment many times. So we run the experiment and we want to measure, for example, a probability distribution at time tf. So what we do is that basically we let the experiment run, stop it at tf, measure a position of particle, repeat the experiment and do it so many times that until we get a decent estimate of the probability distribution. And in the case that if we know that the apparatus is the same for each run, then what we can measure is this conditional distribution of, for example, energy, given the apparatus. But sometimes we, and this is what we call effective scenario. And then we can do many measurements for the apparatus, alpha 1, many measurements for apparatus alpha 2, many measurements for the apparatus alpha 3. And then for each of these, we can measure this probability distribution. And then if we want, we can also make an average over the apparatus and make the average value over the each apparatus, averaging over the probability distribution of each apparatus. But very often what happens is that we don't know exactly the apparatus and each apparatus is randomly chosen each time you run the experiment. The temperature slightly changes because the sun is shining on our experiment, or there is some air conditioning that changes the temperature, something that we don't know. And then in this case, we can only measure the, let's say, the, the average of all the apparatuses at once. And this is what we call phenomenological scenario. And one can think, okay, so in one case I can measure the quantity for each apparatus. In one case, I cannot. But the question is, does it change the experiment? And the answer is yes, it might change the experiment. So, because in the case where we know that we are coupled to a single apparatus, and then we can adopt our control protocol, for example. So then we can basically adjust the experiment to the conditions we have. So let's say we have a simple example of a moving optical tweezer and the moving optical tweezer has this stiffness function. This is this, but basically it's quadratic potential. And this k is a stiffness. And let's say we want to move the trap from zero to some finite value lambda f in time tf. And we can calculate the optimum protocol and everything. Let's say we choose the optimal protocol so that it minimizes the average work. And the problem is that if we know the apparatus, if we know the stiffness, then we can change the protocol for each value of the stiffness. And if we do not know this, then we basically measure the stiffness many times and then we, for example, say, let's measure the stiffness of many times and just use the average value that we have. And we think that this average value is due to the imprecision of the measurement, but the imprecision doesn't have to be due to the measurement but due to the fact that the real stiffness changes in every run. So one can calculate the work in case of this we call it adapted scenario where we can change the protocol for each stiffness and unadapted when we cannot change the protocol and we have to use a single protocol for all cases. And then this is expected that in this case, there is some extra dissipated work that we have we spare we are spending in this unadapted scenario, because we cannot adapt our protocol to the, to the, to the environment. So, and then the question is, what is then the optimal protocol for this unadapted scenario. And how we can deal with these quantities. In this case, so let's start with a simple definition. So let's say we have set of apparatuses. And here we use this, let's say, generic one generic description apparatus but it can be really set of temperatures set of chemical potentials set of whether it's connected whether the system is coupled to one. One reservoir or multiple reservoirs and all of these details. So, the only assumption is that in each sense, in each case for each apparatus. Let's say that the system satisfies the local detailed balance so that we can interpret the quantities from the terminal point of view. And let's say that we consider a probability distribution over the apparatuses. And then of course the effective value of any terminal make quantity is basically just the average over all apparatuses. In this case, the effective distribution that can be calculated, fulfills this equation. And unfortunately this is non Markovian equation so this is the first complication in our case because the averaging over many apparatuses causes that basically there is a coupling between the probability distribution of an apparatus and probably distribution of the system. So then the evolution is not anymore Markovian in this effective case. So we can investigate the first and second law of thermodynamics. The expected first law of thermodynamics is as expected so basically the change in the internal energy, the effective change is equal to the effective change of the heat and effective change to the work. For the kind of second law or let's say the, the, the composition of entropy into the entropy production term and entropy flow term, this still works. So there is this expected entropy production that is not negative. The problem is that the expected entropy flow that is normally equal to the inverse temperature times the heat flow is not valid anymore because the expected entropy flow is the average value over the beta times the Q, which is this is just for the case of one heat bath. So there is no explicit relation between the entropy flow and the heat flow, which is the cornerstone of the second law of thermodynamics so here the thermodynamic description or interpretation is a little bit more complicated. Okay, so now we were talking about these two scenarios so basically for the adapted scenario for each apparatus we can choose the optimal protocol that minimizes the work. What we do is that for each apparatus, we choose the optimal protocol that minimizes the work, and then we average. And for the unadapted, unfortunately we cannot do that we can we have to use the single protocol. And then of course, the difference between these two things that is telling us what is the difference between the work in the unadapted scenario and adapted scenario. Basically, this is what we can call an extra dissipated work due to this lack of knowledge of apparatus. Let's now just focus on a very specific scenario because one of the one of the uncertainties that can be is just the uncertainty about the initial state so let's say that everything is fixed everything is known temperatures are known. Temperatures are known. Chemical potentials are known everything is known, except for the initial distribution. And let's say we have a set of possible initial distributions. And each distribution has some probability to appear. And let's say we have a distribution that minimizes the expecting the expected work. We know that any other distribution for any and for any other distribution there is a formula for the dissipated work that is the minimum dissipated work done by this optimal by this optimal distribution. And there is this drop in the scale of the virgins, which is called mismatch cost that that basically tells us what is this difference between the dissipated work for non optimal distribution versus the optimal distribution. And one can show quite, quite a nice fact quite interesting fact that this average dissipative work dissipated work. And in the case where we average over the all possible initial distribution can be calculated as a so called Janssen Shannon divergence where we basically take the, all the distributions way done by their probabilities. And this is the KL divergence. And as a, as a, this new model, the average distribution. So then we can easily calculate the dissipated work that is justice in Shannon divergence. The last thing I want to talk about is the way that it also in this case we can formulate some fluctuation fluctuation terms, and we can also decompose the entropy production into two interesting terms so let us know now just basically that we are in this case of phenomenological approach that where we cannot measure the probabilities for each apparatus, particularly trajectory probabilities but only the probabilities average overall practices. And here we denote the trajectory probabilities as follows. And of course the effective ensemble and production is the KL divergence between the forward tragic forward probability of the trajectory versus the backward. This is the standard standard result. And by using the chain rule for KL divergence we can show that this can be decomposed into two terms. So this is the KL divergence over the average probability of the trajectory with respect to the average backward trajectory. And there is a term where the role of this x and alpha is changed so is the probability of observing alpha given the trajectory. And basically we have now three types of the entropy production. So one is the effective one. One is the phenomenological one. So this is the effective that is average over all apparatuses. This is the entropy production over the average trajectories and this is something that we call likelihood entropy production. And if you look at it, it's interesting to see that here in this case you don't calculate the probability of the trajectory given the apparatus. You are calculating the probability of the apparatus given the trajectory. So basically you do the reverse thing so you are learning about the apparatus from observing the trajectory. And in the case of phenomenological entropy production you can basically rewrite the express the KL divergence versions of this. And in this case you get the trajectory entropy production, which is simple to show that it fulfills the detailed fluctuation theorem. And of course the conclusion from this is that this phenomenological entropy production is the lower bound of the full effective entropy production. So by observing the only the average trajectory probabilities over the all apparatuses, you can estimate lower bound of the effective entropy production. And for the second quantity this KL divergence or P alpha given X, you can also calculate likelihood trajectory of entropy production. And if you look at it, it really looks like look like likelihood function that you are trying to calculate the probability of parameters, given the trajectory. So this is your data, and this is this is your parameters. And then again, it fulfills a detailed fluctuation theorem. And interesting is that from integrated fluctuation theorem, you get a result that the average lambda this is the average trajectory entropy production, given the trajectory is still for one trajectory is the larger or equal one. What it means is that basically the detailed fluctuation trend tells us how much we learn from observing the forward trajectory versus learning from versus how much we learn from observing the backwards trajectory in the in the backwards scenario. So basically, it's determining the difference between observing the trajectory forward and learning from it and observing the trajectory backwards and learning the parameters from it. This is one example how it can be calculated. So basically if we have, let's say a distribution of temperatures and we have a simple system of two states, then basically we observe a trajectory and this is, this is a sample from some unknown temperature. So we can then update the the probability of temperature observing the trajectory X. Let's say that the prior distribution over temperatures is uniform from this zero to three. By observing this trajectory, we can calculate the probability of observing T given X. This is what we get. This is the probability of serving T given the forward trajectory. This is the probability of observing the temperature given the backwards trajectory, I can calculate likelihood entropy production. And this is again given the X and you see that for some temperatures, there is a slightly negative value. But if you calculate the overall value, it's positive. So here it's very much larger than zero. Here you see that there are some cases where some temperatures where it is smaller than zero, but it's just a small region. And I just want to say that I didn't have time to go through all of the details that are all of the results mentioned in the paper. There is also a section on maximum work extraction with uncertain temperatures, also dynamics of the thermodynamic value of information when there are some uncertain thermodynamic parameters. And this is just a very first step to the whole new field of processes with uncertain environments, where you can consider systems with uncertain energy spectra, experiments with uncertain control protocols, extension to time dependent apparatuses. So basically then you say that your temperature can change in time, but you don't know how you can have some probabilistic equation on that. And you can maybe try to calculate the trajectory probabilities of these temperatures and other things also extension to a hidden mark of models that would be very convenient for several systems. And that's basically all from me. So thank you very much. And now it's time for questions. And I will try to open the list of participants. And please raise your hand if you have a question. Yes. Hello. Thank you for the very wonderful talk. As you can see at the end you're talking about if you have the environment is not only uncertain, but it's fluctuating itself. I was wondering if you thought at all about environmental parameters that not only are they uncertain fluctuating in time but but they themselves are affected by the dynamics of the system. Yeah, that that will be another interesting step. Here I just want to mention that basically the difference between all of these great field of, let's say time dependent temperature or time dependent parameters is the fact that we consider that we there are fixed or can be maybe even time dependent, but we do not know the exact value. So, in this case, there would be another great, basically great interplay between the system and the environment where you just know the part of the environment, like the part of that is your system and you have only some information about the environment and there can be some some some feedback loop for example in this, you haven't considered that that will be great. Future step. Thank you very much. Thank you. Are there some more questions. I could have a, I would have a question. Yeah, picture. So, you show these two scenarios. Right one scenario the adaptive area where you know, you measure also you know what it is and then you carry out the optimal protocol for that and the other is where you only know the average. And then you do your work extraction for the average. But I was just wondering, so suppose that you know the distribution of alpha. And then you do your experiment for extract work for example, is then, but then you're only allowed to choose let's say one alpha from that distribution. And the optimal alpha is that necessarily the average or I guess. Yeah. So, so, so that's, that's the, that's the thing so that what we see typically is that choosing just the average is not the optimal. It's not the optimal one. Also, it's true for the protocol. I didn't have the time in the paper we have a simple example of a bit ratio where you basically couple the system to a bath of uncertain temperature, and then you choose your protocol that raises your bit. And then it shows that the protocol is not simple average of the two protocols. Also it's not average of the temperatures or something like that. It's really very complicated and in general very difficult to find. Yeah, I can I can understand. Yes, thank you. Yes. Are there some more questions. Yeah, maybe I can also mention that the devil be also next interesting step where you don't know the protocol you observe the trajectory, you try to estimate the apparatus and then you try to change adapt the protocol. Regarding to your information you gain from serving the trajectory and in this case you would have the feedback loop and then there would be a natural question. What is the, what is the trait of between observing the trajectory and changing the protocol and this well known exploration versus exploitation problem from reinforcement learning. That would be great next next step so exactly. Rohit was the next one. Yeah, yeah, my question is pretty simple, I didn't understand how you got the non Markovian feature through averaging in the beginning when you are averaging over the effects of all the apparatus. Yeah, that's that's the problem that basically if you look at this. If you look at the transition, then if, if this equation would be Markovian, it would be on the right hand side you would have some function some some transition matrix, some rate matrix time the average distribution. Unfortunately, you cannot decouple this integral into the product of the some rate matrix times the average distribution so basically the integral of a product is not the product of integrals, and that's why you get this non Markovianity in general. Okay, okay. Thanks. Okay, so next question by Sungela Chen. Hi, my name is Sangela thank you for the talk. Could you repeat. What was the, what, what are the apparatuses are they just different bats that you can couple to yes yes so so we had this this abstract term for any kind of parameters that you have it can be temperature above. It can be chemical potential. It can be even the stiffness parameter everything that is a parameter of your of your experiment. So then I'm a little confused about what the protocol and how this is just like choosing different. So if an apparatus is some parameter, then you're choosing different apparatuses meaning you're choosing different parameters in some order and that's what you call your protocol. And in this case, the protocol means changing the energy spectrum so that you do what you want. And of course you do it in some way, depending on the parameters but if you know do not know them you have to somehow deal with all of these scenarios that might happen. Okay, thank you. And, okay, and the last public question by John. Yeah, thanks. So, if I understand the uncertainties that you're considering are all parametric in the sense that I have a stiffness of a potential and I don't know. Have you thought about kind of less structured types of uncertainties like maybe I have a potential and it's almost parabolic but you know differs a little bit in shape. Sure. Yeah, so for example you have a, you have a class of potentials, and they are parametrized. I mean, at the end of the day. It's always that you can parametrize them somehow or this is the typical approach that you use somehow label them if you want. And in our case it can be discreet can be continuous both of them. So basically you have some set of these, let's say potentials or apparatuses. You have a potential average over them. And, and this goes a little bit into your direction of stochastic control protocol. It will be interesting to see how this whole business changes when you don't know the parameters exactly, and you have some uncertainty about them. Great. So thank you. I think we are going to the next talk. So thank you again. The next speaker is alias from Max Prang Institute and


Tired of the everyday routine? Ever dream of a life of romantic adventure? Want to get away from it all? We offer you... Escape! Escape! Transcribe to free you from the four walls of today for a half hour of high adventure.  Today with Paul Dubov starred as Pascal, we escaped to the Arizona desert and a lost treasure of a million dollars as Ralph Bates told it in his most unusual story. When the man comes, follow him. What's wrong? I know that now. But what goods it do? How could you tell dead men that it's all your fault and you're sorry? No matter what you tell them, they're still dead. So what's the use? It never would have happened if we hadn't got mixed up in this Superstition business. We was going along fine. All the other boys in Frisco respected us, stayed out of our territory at least most of the time. That was on account of the boss, Mr. Heinemann. He was too smart for him and they knew it. Smart and a great guy along with it. Of course some people might call him an ordinary racketeer, but he wasn't like that. Nobody could have treated me no better. And he was cultured too, loved music. Played a violin almost as good as his fellow hyphets or whatever his name is. By one time he sent me clear to New York to pick up a strat of various he'd heard about and I had to hang around the dealer's store for two weeks before I got a chance to lift it. He wouldn't have trusted a job like that to any of the rest of the boys. He trusted me more than any of them. Me, Pascal. That's how come I feel so bad about what's happened. Because he trusted me. And he had to trust somebody, you understand? Because for 15 years the boss had been stone blind. Come on, Pascal. Eyes, man. Give me eyes. When it's foggy down there, boss, I can't see the bay at all just the end of the bridge. And I'll talk to Golden Gate, there's nothing but just fog. I guess it's gonna rain. What about the street below us, Pascal? What's going on down there? Nothing. Just street cars and taxis going up and down with a few people. Not very many. I'll tell you, boss, there's nothing doing at all. It's a very dull day. All right, forget it. You can come away from the window. Why don't you play the violin a while? No, not today. I'm too restless. Something's gonna happen, I think. Happen? What's gonna happen? I don't know. Something. Are any of the boys here? Brian and Deleon are next apartment playing gin rummy. You want us to call them? No. I wonder if you know what it's like, Pascal, to live always in pitch darkness, depending on somebody else to tell you what's going on around you. Ah, forget it, boss. You got me. I'm the eyes, you're the brain. We're doing all right. Maybe only sometimes I wonder... I'll get it, boss. I'll get it. Mr. Heinemann's apartment? Who? Well, I'm not sure whether Mr. Heinemann... Who is it? Oh, I see. All right, thanks. That was the manager. Your brother's here from Phoenix. Mark? He's downstairs? Yeah. He's on his way up. The manager couldn't stop him. He says he looks like he's in pretty bad shape. Ever see a desert rat that didn't? No. Well, so I'm to be honored by a visit from my sanctimonious brother. I wonder what he wants. No money as usual.  I wouldn't give it to him, boss. Why not? As long as it keeps him over there on the Arizona desert, for the most of the year, I can stand one or two visits from him. You can hear the elevator stopping, but open the door. I still say you ought to crack down on him. Open the door. Hello, Mark. Help me. Come in. Boss, he's hurt or something. Help me. What is it? Eyes past the cow. Quick! Hasn't shaved for four or five days. He's weak, trembling. Holding on to the door frame with his right hand, holding his chest with the other hand. I think he's been shot, boss. Yes, shot. Come here. Help me. Take it easy. Take it easy. Come on, come on. Over on the couch. Okay. Come on. Here we are, boss. Easy now. There. What happened, Mark? I had to get here. I want you to have it. So he can't... He's out of his head. Get Brian and Daley over here. Brian knows a lot about gunshot wounds. All right, boss. What happened, Mark? Who shot you? Shot. Connect me with 907. I have to get here. Come on, come on. Hello, Brian. All the glitters is... All the glitters is... All the glitters is... All the glitters is... All the glitters is... Fools. Oh, fools. Trages of kings and princes. Dying. Mark, you've got to get hold of yourself. Dying. I have to get here. You get it instead of him. Watch out for him. Oh, Mark? Map. Old map. And a new map. He doesn't even make sense. Look, look. Eyes, Pascal. He's raised up a little, he's pointing with his finger at the carpet about four feet away. When you get there, watch for it. When the man comes, follow him. Understand? Sure, Mark. When the man comes, follow him. Yes. When the man comes, follow him. What's he mean? I don't know. Follow him. What's up, boss? That's the guy that said you wanted me. Come in, Brian. This is my brother. He's been shot. See what you can do for him. Let's have a look. I've got to think, I've got to think. What could he possibly have stumbled into? Yeah, this happened a couple of days ago, at least. Should have had a doctor right away. He wanted to get here for some reason, but why? It's daily, boss. What's coming off in here? You're not cooking up something and leaving a little daily out of it. Ain't I in this, Mom?  Don't get so smart now, Pascal. I've got as much right to talk around here as you have.  The boss's brother is here. He's been shot, he's in bad shape. Yeah, you're not kidding, Pascal. Matter of fact, he's about in as bad shape as he'll ever be. Boss, he's dead. That was the start of the thing. When a doc came, he said Mark should have died 24 hours earlier. Said he stayed alive long enough to get the frisco on sheer nerve, nothing else. Mr. Heinemann, he don't say much. He let the doctor take charge of everything. It was a wallet and some other stuff in Mark's pockets. Mr. Heinemann, he took it with him and went into his own room and stayed there. After a while, the other boys drifted back to their rummy game and finally about 10 o'clock I went to bed. At two in the morning, I woke up to find Heinemann shaking my arm. Pascal, can you hear me? Pascal, come on, come on, wake up. OK, boss. I'm awake. What's the matter? I've been thinking. That's some ideas I'd like to talk about. All right, I'm listening. It's about Mark, the things he said. They begin to make sense. Oh, maybe to you but not to me. Look, is this what I think it is? Oh, wait a minute, boss. Let me give it some light. Oh. Yeah, it's a map of a mountain range, I think. There's a lot of wavy lines like they use for valleys and ridges. There's some faded writing on it, brown ink. I think it's pretty old. 60 or 70 years at least, judging by the feel of the paper. Go on, Pascal. Describe it to me. Well, it looks like a road runs across the bottom along the basin of mountains. And there's a spot on it marked Red Hill. And there's a wavy line starts there and runs about halfway up the map. It runs past some dots marked Three Trees. And off on one side is a little drawn of a shovel with a broken handle. And it ends at another spot marked Camp. It's probably a trail. Yeah, I guess so. Well, a camp is beside a line that looks like the edge of a ridge or a cliff. And there's some writing that says, if no answer, go down. If no answer, go down. What else? Well, about a third of the way to the left from the camp, there's an X marked. And it says, man lives here. I thought at the top there's another X. That's marked Thunder Peak. And at the very top, there's the word superstition. I guess that's about all. Good. Later, I'll have you take my finger and trace over the whole thing until I know it by heart. But this is enough to start on. To start what on? A search for whatever caused my brother's death. Something rather valuable, if my thinking is correct. All right. Only, how do we go about finding it? Mark told us how. When the man comes, follow him. You know what it means? Not yet. Well, if the map's 60 years old or more, how do you figure this guy's going to be there? Because my brother found him and followed him and then died for it. We're going to follow him, too. You and I and Bryant and Daley. We're going to Phoenix. Boss, I think maybe it's a kind of mistake to take Daley along. Why? Because he's a double crosser. That's why I've been trying to tell you. You can't trust him. Don't worry. I can handle him. He's not the one who has to be watched. Then who is? Bryant? Let's leave it for now. Call the ticket office and get four reservations on the next plane out. I've got the feeling we'd better move fast. By the next afternoon, we checked into the hotel Westwood, Hoenn Phoenix and started trying to get a line on Mark Heineman's recent activities. After two days, we still didn't have much to go on. He'd apparently hooked up with some new partner about six months before and gone into the desert. No one had seen anything of him since. An old man who ran a hardware store where Mark had bought tools and supplies finally gave us the tip-off without knowing it. You see, Mr. Heineman, your brother was one of the fellows around here who believed in the legend of the Lost Dutchman Mine. I figured that's what he was really prospecting for. What is the Lost Dutchman Mine? It's supposed to be a deposit of gold. Richard and then it's ever been found. A real treasure of kings. Treasure of kings? Boss, that's what he said. Clive Pascal. According to the stories, there's supposed to be a map in existence somewhere showing the exact location of the mine drawn by the Dutchman himself. During the last 50 years or so, a lot of prospectors have gone back into the superstitions, looking for it, but none of them. What do you mean by superstitions? Superstition mountains out on the desert east of town. That's where the mine is supposed to be located. Why are they called superstitions? Yes, because so many fellows have gone up into them and never come back. They're supposed to be in a patchy curse on. Anybody goes in there. The rains used to be sacred. They ended in God of Thunder. I see. And why do you think these men never came back? Heat, thirst, got lost, snake bite. Oh, it's awful rough country. And there's no water. Then too, there might be a kind of curse on the place of that double cross. Meaning? Well, blaze and sun and a lust for gold can be a bad combination on a man's nerves. A lot of partners have come back out of those hills alone. Double cross, huh? At least that's one curse that isn't limited to the superstitions. You'll find it in a lot of places. Well, we'd better go. Many thanks for your information. Well, not at all, Mr. Ironman. Sorry, couldn't be more help. So that's what Mark found, a gold mine. A rich one, maybe? It must be. Mark was dying, and he knew it, and yet all he talked about was treasure of kings. Gold, in other words. He didn't even tell us who shot him. Maybe his partner did it. Maybe. Pascal, I want you to buy a pair of binoculars and rent a car. We're going to drive out and try to locate that red hill this afternoon. All right, boss. The one thing we've got to watch out for is that curse. That's what happened to Mark. It's only an Indian superstition. I'm talking about the double cross. Mark wasn't the first man to die from it, and I don't think he'll be the last. Here, Pascal, let me take your arm. I rented a Nash sedan from the garage at the hotel, and we headed out across the desert east of town. It was late afternoon before we finally found it, the only red hill on the east slope of the superstitions. Mr. Heinemann told me to take the binoculars and try to locate the three trees that were marked on the map. I left the car, worked my way around the far side of the hill and almost to the top before I could see the trees standing close together on the shoulder of the ridge about six miles away. Just the way they were shown on Mark Heinemann's map. I stared up at the pale blue peaks in the distance, watched the lightning flashes from near the tops of them, and shivered a little. Finally, I turned and started back to the road. Dust had fallen fast like a dozen that did it, and it was nearly dark when I reached the car and opened the door. Mr. Heinemann was slumped over in the seat with blood running from a cutness forehead. He was unconscious. In just a moment, we will return to escape. But first, Ozzie and Harriet are back on CBS, coming to you on most of these same stations every Sunday evening, just before the Jack Benny show. You'll find the more delightful, more welcome than ever. Ozzie and Harriet's own two boys, Ricky and David, are now playing themselves in the CBS series. So make it a family party with Ozzie and Harriet tomorrow night. And now with our star, Paul Duvall, as Pascal, and with Herb Butterfield as Mr. Heinemann, we return to the second act of escape. And when the man comes, follow him. Boss, come on, I'll wake up. You're not hurt bad.  Come on, come on, boss. Come on, Pascal. Yeah, yeah, yeah, yeah, it's me. I'm here with you now. Can you hear me? Yes, I could hear you, Pascal. Did you see him? No, no, I didn't see anybody. Who was it? What happened? Oh, man. Talk to the Texas draw, wearing heavy boots with hobnames, came up on the side of the car next to the hill and poked a gun at my face. You knew who I was and that I was blind. He wanted the map. Did he get it? No. I put him under the floor mat and I heard him coming. Good. Tried to grab his gun. He slugged me. It was out of going through my pockets. Ran off in the rocks when he heard you coming. Well, it's dark up there now. No good trying to follow him. Never mind. I know who he is. Oh, did he tell you? No, but it fits together. Mark had a partner. This guy? Sure. Who else could he be? Then this is the guy who shot Mark. I think so. I imagine there was a double cross and he got even, but wait. No, of course not. What's the matter, boss?  What do you mean? I had figured all along that Mark double crossed his partner and got shot for it. It was the other way around. Oh. It was Mark's map. And this partner doesn't know the secret of it. He probably knows where the man lives. But 10 to 1, he doesn't know about following him. Pascal. Yeah, boss?  We've got to get an outfit together and start up that trailer tomorrow morning. There's no time to lose. Let's go. At 9 o'clock the next morning, the four of us passed the Red Hill and started up the rocky trail that led toward the far off heights of Thunder Peak. Brian and Daly each led two mules loaded with food and kegs of water, and I took care of Mr. Heineman. It was already hot even at that time of morning. And boy, it got hotter. The line drawn on the map followed the crest of a ridge, but there wasn't really any trail. We wound around through tumble masses of rocks and bolers, climbed over cliffs and gullies and stubble across crumbling slopes of debris that slid away beneath our feet and crashed down into the ravine. By noon, we were stopping to rest every 10 minutes. Even the rest didn't do no good, because there wasn't any shade. By late afternoon, we'd covered only six miles and we were done in. None of us had known how hot a desert sun could get. We were ready to turn back or fight one another at the least excuse. Yeah! Yeah! Come on. Move, you full-legged devil. It's no worse for you than this for me. What's the matter, daily? Your tongue's hanging out. I let it hang. When I get back to Frisco, I never want to see the sun again. It's good for you. Nuts. It'll give you a tan. Get rid of that fish-belly-sank quite in complexion of yours. How would you like to have a bullet in a stomach, Pascal? Go ahead and draw, if you feel lucky. Pascal, daily, that's enough. Now cut it out. Now, Pascal, start it. I don't care who started. That's enough. I took close to $1 million worth of gold to have the whole thing loused up because somebody lost his temper. You said $1 million? That's right, Brian. According to the story, that's how much the Dutchman is supposed to have dug out of the mine and hidden before he was killed by a patchy without ever getting back to bring it out. $1 million. Boy, what a man could do with $1 million. Not a million daily, 25% of a million. That's the amount of your share, you know. Yeah, sure. I know. I was just thanking. Hey, look. Right ahead of us. We couldn't see him on account of the ridge. Trees. Three trees. Oh, boy, a little shade of sugar. What's wrong? Eyes, Pascal, what is it? The trees, boss. The ones marked on the map. Only they're dead. Been dead for years, they look like. Yeah. There's not a square foot of shade under all three of them. Well, can't be helped. Least it means we're on the right trail. Well, it's still the easiest way I know to get $1 million. Let's push on. Two hours later, we came across a shovel with a broken handle stuck on the top of a pile of rocks. So we knew we were still heading in the right direction. The shovel had been drawn on the map. We stopped there for the night. While at the dock, the boss heard somebody in the rock, so we put out the fire we'd built and took turn standing guard. And later when the moon was up, I thought I saw something moving a short way off, but I couldn't be sure. Yeah, it was a creepy feeling thinking I was being watched, not seeing anybody. All night long, I could see the flares of lightning and hear the low thunder from the top of the shadowy peak ahead of us. I was glad when dawn finally came and we hit that trail again. But two hours later, I was wishing for sundown again. It was even hotter than the day before. And on top of it, all of us were so stiff and sore we could hardly move. We cursed and sweated and stumbled through the long blazing day. Finally at dusk, we reached the spot marked camp on the map. It was close to the edge of a straight walled cliff that yawned over a deep box canyon below. There were signs of campfires and burrow tracks. This place had been used before. Yeah, we were too tired to care. Not even bothering to unsaddle the mules, we drank from one of the kegs and dropped down in the shade of a rock ledge. Not able to move any further. After about an hour, the sun slipped behind the ridges to the west and left us in a shadow. The boss got us out of our feet, put Brian in search for something to use for a fire and told Daley to unpack the mules. He took me with him to scout along the rim of the cliff and try to find out what was meant by the words on the map, if no answer go down. After half an hour, we found nothing. When we were ready to decide, there was no way to go down that thousand foot rock wall when suddenly, Pascal, that was a shot. You see anything? No, no, it was back toward camp with this ridge between us. I can't see a sign of anything. Come on, Pascal. Yeah, take hold of my arm. Okay. Let's get back there fast. Who is it? Come on, come on, speak up or I'll shoot. Relax, Brian. It's us. That's Pascal and the boss. Did you see anybody? No, what happened? Somebody took a shot at Daley and he got all spooked up and fired off half a clip. It was that guy that's been following us, boss. I saw him airing the rocks, not more than 100 feet away. And you missed him, I suppose. Well, it was dark. Hey, what happened to the mules? They're gone. Yeah, they stampeded when Daley fired off that gun in their areas. That's great. We'll have a fine time packing five kegs of water and all the supplies on our backs. Yeah, well... Boss, we don't have five kegs of water. There's only one here. What? I hadn't unpacked the mules yet, boss. I was going as soon as it got a little cooler.  That's what I've been telling you, boss. All the brains this dope's got...  One more crack, and I hope you'll... That's enough! Daley, I could kill you and love it. I could stand here and pump bullets into you and love it. Do you know how long a man can live up here without water? 24 hours at the most. But we still got five gallons of water.  How could I...  It's done. That's that. You'll see if there's any chance of finding them. And try to keep from getting yourself shot. Then I go with him, Brian. Okay, boss. Come on, smart boys. If you don't find them in 20 minutes, come on back. Five gallons of water for four men. We'll take it a full day to get down into that canyon and find the spot where the man lives. Another day to get back here, if we're lucky. Then two more days back to the road. I guess we can just barely make it. There's only one thing, boss. There's no way to get down into that canyon. I think I've got the answer there. At least that's one thing that shooting didn't. Listen. Hello! It's an echo. If no answer, go down. Yeah. I think we'll find a spot some place along the rim of that cliff where there's no echo. When we do, I think there'll be some way to get down to the bottom. We'll try it in the morning. And one other thing, Pascal, before they come back. Yeah, boss? From here on, keep an eye on Bryant. I think that gold is beginning to look pretty big to him. I think maybe you're making a mistake. I think Daley's a lot more likely to try something. He's a born double-crosser. No.  But Bryant's the one who's dangerous. And he'll do as I tell you and watch out for him to understand. All right. Sure, boss, whatever you say. An hour after dawn the next morning, we found a spot on the edge of the cliffs where there was no echo. Slanting downward from it was a narrow, steep crack in the wall. The four of us took turns packing our one last keg of water and inched our way down toward the canyon floor 1,000 feet below. We made it finally rested, then struck out to the west following the map. Great chunks of rock lay tossed about it, though giants had played there. And thorn and cactus grew everywhere among them. The sunlight curled and blistered on the surface of the boulders, and always from above us and nearer now came the sullen and ominous roller thunder. At noon we stumbled across the bed of the ravine, nearly missing it from being half blinded by the heat. And three hours later, we found the place where the man lives. It was marked by a monument. Bill of broken rocks stacked up higher than our heads. Mr. Heineman felt all over the surface of it with his hands and then told us he knew the meaning of the words, when the man comes, follow him. But he said it wasn't time yet. We'd have to wait. We sat there by the pile of stones, not talking much. Just waiting, two hours passed. I think it was Daly who noticed it first. Look, look there on the ground. There's somebody here. He's behind us. Hit the dirt! I don't see any. So that's it. Boys, I'm a little disappointed in you. Scared by a shadow. Look at it. It's a shadow that pile of rocks. Looks just like a man would have had on holding a gun. Yeah. The rock pile don't look like a man, but the shadow does. Well, since he's apparently come now, I guess we'd better follow him. Huh? How do you mean follow him? The sun's going down. The shadow must be getting longer, stretching out over the ground. So get going. Follow the direction it's pointing. Yeah, boys. The scowl will stay here with me and keep you on line. Watch for signs of something buried. Rocks laid over to a cleared space, something of that kind. We're not more than a few feet from a million dollars. Let's get it. Two of them worked their way along through the rocks while I stood by the monument and waved them toward one side or the other. Part of the time, they were out of sight behind a ledger bullet. An army could have hidden in that broken mess and never been noticed. I kept describing everything that was happening to the boss. And about 20 minutes went by before I heard Daly shout. We found it! Found it! He scrambled over. A legend came running toward us, calling out and holding something in his hand. Then about 100 feet away from us, he stopped suddenly and drew his gun. Pascale, what is it? What's happening? Daly's pulled a gun on his boss. Drop it, Daly! Drop it or I'll shoot! No, Pascale! He's here between us! You're fooled! He's hiding in the rocks! All right, Daly. You asked for it! Pascale, no! I got him, boss! The Daly double-crossed it! You're fooled! He was going to kill us, boss. He was coming at us with a... Wait. Wait, somebody staggered out of the rocks there and fell. Somebody I never saw before. My brother's partner, the man who's been following us. But then Daly killed him and I killed Daly. Boss, I thought Daly was shooting at us. I didn't know there was anybody else there. Well, you know now. I told you to keep an eye on Bryant. What's happened to him? Pascale, where's Bryant? Right behind you, sucky. Look out, boss! How's he shooting, Bryant? I got him, boss. He missed me and I got him! Good. Only he didn't miss me. Boss! No, no, no, no, boss! Pascale, can you hear the thunder? Yeah, yeah. Sure, it's real loud. It's funny. Same old curse, double-crossed. My fault, boss. I should have done like you told me and watched Bryant. A million dollars in gold for somebody else. Don't talk like that. It's for us. For us, for you and me. I'll get you out, boss. You're not really hit bad, you know? Man, I'm dying. I knew too, Pascale. What?  What? What do you mean? The water keg. Bryant's bullet smashed it. I heard the water running out. No, no, no. Am I right? Yeah. It's all gone. It's three days out to the highway, Pascale.  You don't have one single drop of water. Escape is produced and directed by Norman MacDonald. Today, we have presented transcribe. When the man comes, follow him by Ralph Bates, adapted for radio by Les Crutchfield, with editorial supervision by John Dougal. Stardust Pascale was Paul Dubov, with Herb Butterfield as Mr. Heineman. Featured in the cast were Harry Bartell, Jeff Corry, Barney Phillips, and Junius Matthews. Special music was arranged and played by Ivan Dittmar. Next week, you are standing on the rolling deck of a pirate junk in the China seas. And facing you is the sinister figure of the most feared man in the Orient, a general who has just doomed you to death. Next week, we escape with an unusual story that general died at dawn by Charles Booth. Be sure to tune in at the same time next week, when once again we offer you escape. It's wonderful, truly amazing, how much you can get from just one radio program, the unbounded passion of the world's greatest Don Juan, the unrivaled music of the world's most eminent soloist, and unsurpassed lesson in philanthropy. Also, some of the greatest laughter you'll ever hear, for the program is the Jack Benny show. Be sure to hear Jack Benny and his gang again Sunday at 7 o'clock Eastern time over the same CBS stations. This is Roy Rowan speaking. Now, stay tuned for five minutes of the latest news to be followed by the Let's Pretend program over most of these stations. This is CBS, the Columbia Broadcasting System.


Consumption of dairy products, and particularly the fermented dairy products as yogurt and cheese seem to have some protective effect on cardiovascular disease, but also on type 2 diabetes. And we know a lot of information we have from epidemiological studies, from observational population studies, and we used to analyze the studies in a way where we looked at those who have a high consumption compared with those who had a low consumption. Today we have a different way to analyze it because those who have a low consumption of dairy, what do they eat instead of the dairy? Some will have something fruit and vegetables and others will maybe eat some refined carbohydrates. So it really, whether it's good or bad to have a high or low, it really depends on what you compare with. So it's much more a food based analysis in the research, and I think generally we can say from all the population studies that a high intake of dairy products are associated with a small but significant decrease in the risk of cardiovascular disease, and it's particularly stroke where it seems to be reduced. And we know that there are many properties of dairy products that assist in doing the job. We used to simply say take a cheese and look at the label and say, oh it's high in saturated fat so therefore it's bad. But today we know that there are also a lot of protein and very high in content of calcium that are important. So there's a lot of nutrients that actually exert difference effect on both for body weight regulation, for type 2 diabetes, but also for cardiovascular disease. So I think that we have gained a lot of new information over the last 10 years that actually have diversified our view on dairy products and also on the different nutrients that are typical for dairy products. We can also see from some of the population studies that for dairy products it looks like that the fermented products such as yogurt and cheese seem to be more healthy than others. And it's probably due to some of the byproducts in by the box in the bacteria in the yogurt and cheese that they produce some different maybe short chain fatty acids and other products that have some health benefits. And it may vary from what kind of bacteria it is, but generally when we look at those who consume yogurt and also from randomized trials that there are some of these bacteria strains that have some health benefits and that's also today we have recognized that all the billions of bacteria we have in the gut are extremely important for our health. So instead of having a capsule with bacteria it's much better to have it in a yogurt and it can be very tasty and you can keep it in the fridge and for many people it's also you know you medicalize them if they're going to take drugs whereas to have yogurt is something that is very normal and it also provides them with other benefits. So as long as you don't add too much yogurt into the yogurt I think it's very healthy and it's a good way to facilitate some bacteria strains that can be useful for many people who need some improvements.


Welcome. I welcome you all to this lecture in the course, Samasa in Paninian Grammar. And this is the first course on Samasa. We begin our lecture with the recitation of the Mangala Charana. In the previous lecture, we studied the rules in the Grammar of Panini stating certain important steps, certain processes required for the derivation of compounds or samasas. We continue to study this aspect in some more detail even in this particular lecture. So far, we have studied the semantic condition which is Samarthahapadavidhi. We also saw the name of the process stated by Prakkadarad Samasaha. We also studied the necessary condition stated by Suha Supa. Then we studied the Purvapada Nirdharana stated by several sutras in the section that begins with 2 to 30 onwards up to 2 to 38. Then comes an important stage where we add Samasantha Pratyayya. The Pratyayya that is added at the end of the Samasa. So Samasantha Pratyayya is a suffix. These are suffixes and they are added at the end of the Samasa. That is why they are called Samasantha at the end of the Samasa. Samasa and Anta. This also implies that they are part of the Samasa. They are not just placed at the end of the Samasa having no relation whatsoever with the Samasa. That is not the position. The theoretical position is that these suffixes they are part of the Samasa. Their function is to determine which formal processes the Samasa will undergo when it becomes part of the sentence that means an output. As we have already seen that the input for the process of compounding is a sentence. We need two or more interrelated words and then the process of compounding can start and then we do lots of operations and then generate the output in the form of a Pratyapadika which becomes a part of a sentence. So when this Pratyapadika becomes a part of a sentence, what other formal processes it will undergo? This is triggered by this Samasantha Pratyayya. That is its main function. For example, ending of the word. So if an original word listed in the lexicon ends in a consonant and after adding the Samasantha Pratyayya, if the word becomes a vowel ending word, now the Samasa will be treated and will be considered as a vowel ending Pratyapadika. And in accordance with this, the Samasa will take the next derivational stages and then it will be able to produce the final output in the form of a Subanta. So the ending of the word will be determined by the Samasantha Pratyayya. Also addition of the suffix which indicates the feminine gender, this is also dependent on the Samasantha Pratyayya. Whether the feminine suffix A is to be added or whether E is to be added is determined on the basis of the Samasantha Pratyayya more specifically on the basis of the markers attached to these Samasantha Pratyayya and we shall see the examples. Also the Samasantha Pratyayya functions to determine the accent of the generated compound output. These are some of the functions of the Samasantha Pratyayya and therefore it is accepted that this Pratyayya is part of the Samasa. Such an important part of the Samasa called Samasantha Pratyayya, they are stated in the section governed by the Adikara Sutra, Samasantha. And this is 5468 and this goes up to 54160 that is the final sutra of 5.4. So what this means is that end of the compounds of excess are stated in these 90 plus sutras. So end of the compounds of excess are stated to all major four types of Samasas in this particular section from 5468 up to 54160. And the Samasantha Pratyayyas with respective Samasa are stated in sutras with the tag of that respective Samasa. So for example, Avyai Bhave Sharadprabhratibhyaha. The sutras beginning with this, they will tell you the Samasantha Pratyayyas that are added at the end of the Avyai Bhava Samasa. Similarly, you have Bahubrihau Saktyakshnoha Swangaj Satcha. This sutra states the Samasantha Pratyayya Satcha in the Bahubrihi compound alone and so on and so forth, Dvandva Chudashahanta Samahare. This will tell the Samasantha Pratyayya which is added at the end of the Dvandva compound that too when it is in the sense of Samahara. And similarly also Tat Purusha compound. Now the most important thing is that these suffixes are also termed as Taddhita. So the bigger Adhikara that begins with 4176 and comes to an end in 54160 is Taddhitaaha. So all these Samasantha suffixes are also termed as Taddhita suffixes for specific purposes which are common to both the Taddhita formation as well as the Samasa formation and the statement of the Samasantha suffixes in this Adhikara also goes to show the interrelation between the Samasa and the Taddhita which we have already studied in brief. What that means is that given any sentence a particular meaning can be expressed using the interrelated words in the sentence. Now these interrelated words can be compounded and the same meaning can be expressed through a compound and further these interrelated words can be processed and Taddhita suffixes can be added and the Taddhita formation can also express the same meaning. This we have already studied. So this is the interrelation between the Samasa and Taddhita. Here are the examples. So if we have the meaning at the beginning collected by the speaker in his Arthakasha king of men Porushanam Raja. So you have Alau Kika Vigraha in the form of Porusha plus Am plus Rajan plus Su. Since Porushanam is Shasti, Shasti is placed in the initial position because this is Shasti Samasa prescribed by the Sutra Shasti and so this will be the Alau Kika Vigraha. And now we have the Sutra Raja Sakhibhash touch 5489. This Sutra states the suffix touch. Touch means a and it has got a as a marker as well as a marker. Now this suffix touch is prescribed by this Sutra after the word Rajan at the end of the Taddhita Porusha Samasa of this kind. So we have Porusha plus Am plus Rajan plus Su and here itself we add the suffix touch. So now this becomes the part of the Samasa and it is at the end of the Samasa. So this is the Samasanta Pratyayaya. So we have Porusha plus Am plus Rajan plus Su and a. Touch is a. Once we place these elements side by side, now this is an entire Samasa indicated by these two long square brackets. Then we begin the process of compounding. Obviously then the Suhbhakti is dropped. So we have Porusha Rajan a and then Porusha Rajan a. Then we apply 64148 which deletes the an of this Rajan. And so we have Porusha plus Raj plus a and finally we derive the compound output in the form of Porusha Raj. Now this word although has got Rajan at the end of this compound still because of the Samasanta Pratyayaya the compound ends in a. So now this is a vowel ending Pratipadika. The Pratipadika occupying the second position or the final position in the Samasa is Rajan as listed in the lexicon. But now because of this Samasanta Pratyayaya the Samasa ends in vowel a. So this Pratipadika becomes a vowel ending Pratipadika and Akaraanta Pratipadika. And it will take its forms in accordance with this Akaraanta ending and it will have the declensions in the similar form of Devah, Devah, Devah, Devah, Porusha Raja, Porusha Raja, Porusha Raja. Now because of this a suffix the Samasa with Rajan being the final constituent becomes now a Pratipadika ending in a. Accordingly the behaviour in inflectional morphology is determined. This suffix by the marker t also determines that the Pratipadika will be added with the feminine suffix e stated by 4, 1, 15 which is. So this sutra says that if a Pratipadika ends with a suffix that has the marker t at the feminine suffix in the sense of the feminine gender and so we will add this suffix e and we will get the necessary feminine form. Also because of the marker ch the final vowel accent is also determined by 6, 1, 163 chitaha. Let us take another example of the Samasa Pratyayaya where the same sutra Raja Sakhibhash touch applies. So if you have a meaning friend of Krishna at the beginning as thought of by the speaker and where he or she wants to make a compound out of it, Krishna Sya Sakha. The alokika vigraha of it is Krishna plus Gnas plus Sakhi plus Su and then we add the Samasa Pratyayaya touch over here, touch is a. So we have Krishna plus Gnas, this is the Purva Pada, Sakhi plus Su, this is the Uttara Pada and we have the Samasa Pratyayaya a over here. Then we delete both the subs, we have Krishna plus Sakhi and there are zero suffixes over here plus then this Sakhi has this a deleted and we have Krishna plus Sakha plus because of the application of 6, 4, 1, 48 and finally we get the compound output in the form of Krishna Sakha. So Krishna Sya Sakha is the input and Krishna Sakha as a Pratyapadika is an output. So the word Sakhi ends in E but now the compound Krishna Sakha ends in E and accordingly the inflectional morphology will take its own form. The final constituent of this Samasa is Sakhi ending in short E but after adding the Samasa Pratyayaya the Samasa ends in short E and then its behavior in the inflectional morphology is determined accordingly and you will have Krishna Sakha, Krishna Sakha, Krishna Sakha, Krishna Sakha and so on and so forth having the forms derived in the same fashion as that of Rama also. Now this Samasa Pratyayaya will also determine the addition of the feminine suffix Nyev and also the accent which is the final accent determined by the Sutra Chitaha. Now after having seen the Samasa Pratyayaya and the Sutras which prescribes Samasa Pratyayaya let us proceed in understanding the Sutras which prescribes the Sublook which is an extremely important process in the derivation of a compound. So Sublook is a very crucial operation in the derivation of a compound. What happens in this operation is that the sups which are part of the Samasa they get deleted. This operation acknowledges the sentential base and at the same time removes that base at least formally from the process but it does not remove it semantically. It does not remove it cognitively that remains there and that is the reason why a linkage between the compound form and the sentence remains uncut. So this particular process acknowledges the sentential base and at the same time removes it from the process of compounding so that merging into one Pratyapadika of the two elements becomes smooth. But this process of Sublook obviously highlights the underlying structural presence. So if you want to go back, if you want to fall back upon this you have a choice, you have a system systemic support to do so. Now this process is stated by the Sutra 2471 Supo Dhatup Pratyapadika Yoho. What this Sutra means is that in place of sups which is a part of the verbal root namely Adhatu and also the nominal root or a Pratyapadika is substituted 0. So the meaning is in place of sup which is part of the verbal root or Adhatu and also the nominal root substitute 0. What this means is that the sup is deleted. Now instead of stating it as mere deletion Panini has stated the 0 substitute. So it has given this deletion the status of an entity and Panini has used this particular technique throughout his grammar and scholars have also studied this aspect and have noted and have commented upon this concept of 0 in Panini and grammar. So this 0 suffix underlies the semantic implication that we were talking about a while ago. So what this means is that even after deletion it still retains its historical status as a further and Panini has used this in Sutras like Nala Upap Pratyapadika Antasya where we have seen in the derivation of the compound Raja Purusha Rajan which is a Purva Pada is stated to retain its historical status of being a Pada and so this Naa occurs at the end of the Pada and therefore the Sutra says this Naa gets deleted because right now as we see Rajan occurs at the end of a Pratyapadika but it also historically occurs at the end of a Pada so to speak and such a Naa is deleted that's what Nala Upap Pratyapadika Antasya says therefore Naa is deleted and we get the compound form Raja Purusha. We have derived the compound form Raja Purusha earlier and that is what is being referred to now. So here we have the same derivation process Purusha plus Aam plus Rajan plus Su this is the Aalavkika Vigraha Purushanam Raja that is the Aalavkika Vigraha and we add the suffix touch over here and so we have Purusha plus Aam plus Rajan plus Su plus A touch is A and then at this stage this Aam and this Su because they are the soaps they get deleted. So in this stage when we add Purusha plus Aam plus Rajan plus Su plus touch these two external square brackets indicate that this is what is a compound so this is a Samasa. The process of compounding has begun because this is the Aalavkika Vigraha and so this one unit is called Samasa and because it is called Samasa it is also called Pratyapadika immediately by the Sutra, Kirtadhita, Samasa Aschha or Arthavadadhatura Pratyapadikam and because it is a Pratyapadika now this Su and this Aam they become part of a Pratyapadika and so Supadhatapadika applies at this stage immediately after the Purvapada Nirudharana and also the addition of the Samasaanta Pratyaya has happened and so we have the sub-look over here so we have Purusha plus 0 plus Rajan plus 0 and then we add the suffix we have already added the suffix U which is a Samasaanta Pratyaya and then we do the next processing by applying 64148 we delete this Aam of Rajan and finally we get Purusha Raju as the compound but the point is that 2471 applies at an early stage by removing the sentential context in the form of the Sups it then facilitates the compound generation. This is a very crucial stage in the process of compound generation. Let us also observe this in the derivation of the second example that we have studied earlier where the meaning is friend of Krishna or Krishnasya Sakha and the Alawkika Vigraha is Krishna plus Ghas and Sakhi plus Su and then we add the Samasaanta Pratyaya here Krishna plus Ghas plus Sakhi plus Su and this touch U is added and now after we add this obviously this Alawkika Vigraha itself enables it to be called a Samasa and this Samasa becomes Pratyapadika and these Sups Nasa as well as Su they are now part of the Pratyapadika and so they get deleted by 2471 and so we have Krishna Sakhi and then Krishna Sakha by the application of 64148 and so we finally get the form Krishna Sakha. So Krishna Sakha is the input and Krishna Sakha is the output and we do not see any Sups over here neither after Krishna nor after Sakha but even though formally we do not see any Sups which is what is the highlight of the Samasa process otherwise it would not be distinguishing itself from the sentence in the sentence you see Sups here as well as this Su but in the compound they are missing even though they are missing their meaning obviously remains even though they are noted down as 0 obviously their meaning is there and that is the reason why this compound Krishna Sakha has got correlation to show with this Alawkika Vigraha. So we can dissolve this compound in the form of a sentence of this kind using these case endings because they are implied even though they are not visible. This is the theoretical implication of this process called sub look which is extremely crucial and very very important and we need to pay serious attention to this particular part of this important process namely sub look. Similarly when we have another example Kingsman goes to Kashi this is the sentence and we have Radhnyapurushaha kashim gachhati so Radhnyapurushaha are the two words which are semantically related and now we start the process so we have Rajan plus Gnas plus Purusha plus Su as the Alawkika Vigraha so the term Samasa applies over here the term Samasa does not apply at this stage because this is Alawkika Vigraha this is not Alawkika this is Alawkika Vigraha. Once we convert it into Alawkika Vigraha of this kind this takes the term Samasa and now this becomes a Pratipadika by the sutras mentioned earlier and once this becomes a Pratipadika these sups Su and Gnas they are now part of the Pratipadika and that is why Supo Dhatup Pratipadika Yoha applies and deletes both these sups and we have zero suffixes over here 2471 does this and then we have Rajan plus Purusha as the next step in the derivation process all these steps they are rule governed right now we are highlighting only 2471 in this particular process so we have Rajan and Purusha and then we apply 827 and by the application of 827 this Gna at the end of Rajan gets deleted and the output generated is Rajan and Purusha and the final output is Rajapurusha this is the Samasa output now this Samasa output becomes a Pratipadika it is already a Pratipadika and so then it also becomes part of the next sentence and the Suprataya etc can be added to this Rajapurusha and you can have Rajapurusha, Rajapurushau, Rajapurushaha etc as the forms generated of this particular Pratipadika so this is how Sublook plays an important role and these are the theoretical implications of this Sublook so Rajan over here is considered as a Pratipadika but it is also a Padha given the status of the zero suffix so Nalopapratipadikaantasyas says Pratipadikasavnikam yathpadam padantasyanasyalopasyat so then this Gna is deleted by 827 with these conditions so to summarize the suffix is added at the end of a compound immediately after the process of compounding begins it is to be noted that this suffix is part of the compound and affects the form of the compound in multiple ways ending of the compound feminine suffix as well as accent are the three main functions of the addition of this particular suffix and such a suffix is added in all four major types of compounds in Sanskrit. Similarly, Sublook reflects a very crucial stage in the derivation of the compound process as it acknowledges the sentential base and at the same time removes this sentential base at least formally for the smooth merging of two elements into one Pratipadika the constituent words retain both properties that of a Pratipadika as well as that of a Padha and both of them get used by sutras in Panini, Panini's grammar like Nalopaparadipadikantas here and we have seen an example of this sutra in the derivation of the compound Rajapurusha it is this base which the compound falls back upon for various purposes and that is what is the significance of this Sublook Panini has achieved this very delicate bridge construction which is a semantic or which is of semantic nature through the stage of this Sublook these are the texts that are referred to they are from the Panini and grammatical tradition and we shall study some more processes and the sutras stating those processes in the coming lecture. Thank you very much.