Lipton Tea and Lipton Soup presents Inner Sanctum Mystery. Welcome to the shadowy borderland of the squeaking door, all you hearty adventurers. Into the land of the grisly, ghastly, gruesome, horrid, shocking and monstrous. I mean Inner Sanctum. Of course I assume that we're all old friends here, but if by any chance there's a stranger among us, perhaps I should state the purpose for which we are here assembled. Our object is to make your spine tingle and your hair stand on end. That's right. When we're through, you'll discover that a fiend indeed is a fiend indeed. Heavens, you stop talking so scary. Our folks will tune us off their radios. Oh Mary, I'm just trying to scare them into the chill, so they'll have to drink Lipton Tea. Well that isn't necessary at all. For a great many years, people have been enjoying Lipton Tea without any persuasion from you. That famous Lipton flavor has won the praise of tea experts all over the world. And you know folks, these experts describe the Lipton flavor by saying that it's brisk, B-R-I-S-K. Now brisk means that Lipton Tea always tastes fresh and full-bodied. Yes, tangy and vigorous. Never flatter, wishy-washy. That's why I always say you don't know how good tea can be till you know how good Lipton's is. And now friends, let's go from tea to terror. Yes, the title of tonight's story is Terror by Night. It's an original radio play by Amel Tepperman. Tell me, have you ever been alone with fear? Alone in the night and frightened? Well here's Anne Shepherd and the role of Linda Dixon to tell us what happened to her. It was a Friday night and I think I was already a little nervous as I drove north into the mountains. It was the first day of my vacation. I started from the city early enough to arrive before nightfall, but my car was six years old and developed motor trouble. So now I was driving through the night with fifty miles more to go. And I was tired and nervous and irritated. And then I heard that siren in the distance. At first I couldn't place it. And then I remembered the state prison was somewhere in the vicinity. A siren. That meant... That meant a prisoner had escaped. He reached over and turned on the radio. They were broadcasting an alarm. I repeat, motorists are warned to be on the lookout for Lee Hartley who escaped from the death cell at state prison at 9.15 p.m. He has five foot ten dark haired, regular features, no distinguishing marks. Hartley is a confirmed killer. He is believed to be armed. Beware of Hartley.  And that man was loose. I stared ahead at the lonely road spinning toward me through the wind here. It has been established that Hartley was helped to escape from the outside by a sweetheart, Helen Hearn. A red-headed woman just as vicious as Hartley himself. It is thought that Hartley and the Hearn woman may have separated after the escape. All motorists are warned to beware of a dark-haired man and a red-haired woman. Alone or together. My hand was shaking a little as I turned off the radio. I looked in the car mirror and shivered. I too have red hair. A storm coming up and I was driving into it. And the night was black and I felt small and lonely and frightened in the car. Then I saw in the mirror the headlights sweeping up behind me a car. It had come out of nowhere. It was pulling alongside cutting me off. I crawled behind the wheel and then watched the door of that other car open. A man stepped out. I breathed a sigh of relief. It was a state trooper. You're driving all alone, Miss? Yes, officer. Sorry I scared you. We're stopping all cars. Where are you heading for, Miss? Oh, I'm going up to Seven Lakes Hotel. That's near Carstairs. You see, I started out late from the city and I'm having motor trouble. Yeah, sure. Can I see your driver's license, please? Oh, yes, my driver's license course. Here, I've got it somewhere in my purse. I seem to be all fingers. That escaped prisoner Hartley. What about him? Oh, well, I heard the prison siren. Then it came over the radio about Hartley and his red-haired girlfriend. See, you've got red hair, too. You don't think I'm that woman? You find that license yet? Well, I'm sure it's in here. So many... oh, here I've got it. Here's my license. Thanks. What time do you see you left the city? About five o'clock. Took you a long time to get this far. Well, I told you I had motor trouble. Oh, sure did. Okay, Miss Dixon, here's your license. You can go ahead. Thank you. Oh, darn. There it goes again. Or motor trouble. No, it's the same thing. The mechanic said it might happen. There it started. You want to get that fixed first chance you get? It's late, so all the service stations are closed. There's one that's open all night about two miles up the road. You better stop there. Bill Slater's place. He's a good mechanic. He'll fix you up. Tell him Joe Nesbit sent you. Thanks, I will. Listen, Miss Dixon, you be careful. Don't stop to give anyone a lift, man nor woman. Don't worry, I won't. The night closed in on me again, but I didn't feel quite so nervous knowing that the trooper was somewhere behind me on the road. And Bill Slater's service station ahead. In a few minutes I saw the lights on the service station. I swung into the open space in front of the pumps. I stopped. There was a rumbling of thunder and the west storm was moving up fast. There was another car, a coupé parked at the pump. But there wasn't anybody in it. And I didn't see any attendant around either. I pressed the horn button. No one answered. No one came out of the office. Still no response. Everything seemed so quiet and suddenly ominous. I found myself shivering. I had a curious feeling that someone was watching me. I've got to get away from here fast. It started when I worked. It started. No, it started. The wrong time I sat behind the wheel. Listening. Listening for the sound of footsteps. Stealing up behind the car. There were none. Then I could bear it no longer. I had to get out of the car. I had to see what was in that office. I opened the door of the car and stepped down on the gravel. Anybody in there? No answer. I clenched my fists and stepped inside. There on the floor at my feet lay the body of a man. His mechanics jumper was stained red with blood. And his throat was cut from ear to ear. How long I stood there I'll never know. I was petrified. Unable to move.  Someone coming downstairs. He must have been hiding somewhere upstairs. I've got to get away outside. I don't want to run. That other car, the coupé, I could jump into that. Yes. If I could reach that coupé before he comes down. Anything wrong, sister? Too late. Anything I can do for you, sister? Yes, it's my car. It won't start. I thought someone here might help me. Sorry. There doesn't seem to be anybody around. That's my coupé over there. I stopped for gas and no one came out. So I went in and looked around. Did you find anyone? There isn't a living soul in there. Oh. You look kind of tired. Oh, no. No, I'm all right. My name is Taylor. John Taylor. I'm Linda Dixon. Linda Dixon, huh? Glad to know you. Travelling far tonight? Well, I'm going to Carsh Stairs. A seven-likes hotel. They're expecting me. Now, what do you know about that? What? Carsh Stairs is the town I'm heading for, too. Isn't that a coincidence? Yes, I'm sure it is. Your car won't run. Tell you what, we'll put your baggage in my car and I'll give you a lift to Carsh Stairs. You can send for your car in the morning. Oh, no. I'll have your bag switched in a jiffy. Please, no, I would rather not. We are all switched. Ah, come on. Get in here. He took my arm and helped me into the coupé. His hand was strong. His grip was hard. It hurt me. There you are. Snug as a bug in a rod. We'll drive away into the night, leaving behind us the dead man in the service station. From where we sit, it looks as if pretty Linda Dixon has gotten herself into an awful jam. And believe me, she's shaking like jelly. My goodness, that poor girl. And just think this is supposed to be her vacation. Why, Mary, she's in the country now, isn't she? In fact, it looks to me like she's going back to the soil. Horizontally. Oh, dear. Why do you always look on the dark side of things? Seems to me you're always pessimistic. Of course, lots of folks feel that way at times, like when they've been working too hard and they're tired. But you know, I think there's nothing better than that down feeling than a good hot cup of Lipton's. The tea with the brisk flavor. That brisk flavor really perks you up. You see, that word brisk, B-R-I-S-K, is just another way of saying that Lipton tea tastes full bodied and vigorous. Yes, tangy and spirited. Never flat or wishy-washy.  Well now, let's go back and see how pretty little Linda Dixon is making out. All alone in the car with a strange man. But after all, she shouldn't be too scared of him. He's just a felon who needs a friend. The storm broke a few minutes after we left that service station. We drove through sheets of rain. I sat stiff and tense beside the man who called himself John Taylor. He had both hands on the wheel. He stared out through the windshield. My eyes focused on something on his right hand. It was a stain, a small stain, but it was wet and rare. I couldn't take my eyes off it. What are you looking at? What? Oh, nothing. Nothing tall. Think I'll turn on the radio. Did you know there's been a jail break? Five foot ten, very dark hair. Don't be fooled by his pleasant manner. He is a killer by instinct. Killer by instinct. I looked at the man beside me. Helen Hearn is a clever and dangerous woman. Five foot three, red hair, very pretty. I caught Taylor looking at me out of the corner of his eye. What are you looking at? Is that your hair? It's red. The street of lightning. And looking out of the rain swept window, I glimpsed a signpost. The lightning illuminated the sign, and my heart skipped a beat of what I saw. That sign we just passed. What about it? Well, it, it, uh, said Kerhawkson ahead. We're going the, the wrong way. What we should be on the cost is, not on the Kerhawkson road. Funny. Must have taken the wrong turn. Well, aren't you going to turn back? Sure. Whatever you're saying. We'll turn right around and go back. We're in the ditch. In the ditch? It's no good. She won't budge. Well, it looks like we're stuck here for the night. You look scared. Oh, no. Um, I think I'd better get out and walk. Perhaps there's a house nearby. Walk in this weather? Oh, I don't mind the weather, really. I don't. You can't walk in this storm? Well, uh, nevertheless, I'm, I'm, I'm going to try. Not on your life. Staying right here, till I get the car out of the ditch. Get pneumonia walking in this storm. But I will. Let's see. Where's that flashlight? Oh, here we are. Got some tools in the trunk compartment. You stay put. Stay right where you are. I heard him open the trunk in the back. I listened for further sounds. But there was nothing. I didn't hear him moving here. I didn't hear any tools. I had to find out what he was doing. Slowly, carefully, I got my door open. I stepped out into the ring and sneaked back to the rear. I saw him there. Not moving. In front of the open trunk compartment. Fending over with a flashlight in his hand. The ray of light was focused on, on something curled up inside. It wasn't baggage or tools. It was a woman's body. Just then he saw me snap the flashlight off, but not before I caught a glimpse of red hair. Then I must have fainted. When I came to, I found myself seated inside the car again. My face and hair were wet. My clothes were dripping. John Taylor was driving. His face as he stared ahead through the night was dark and bleak. The storm was over. Night was quiet. Oh, so you're awake again? I, I don't feel well. Is it because of what's in the trunk compartment? She's dead. I told you not to get out of the car. What are you going to do with me? What do you think? Please. Sorry, sister. I've got to take your medicine. Oh, no. Do not make any trouble. I'll try to make it as easy for you as I can. They say that when a person loses all hope, subconsciously he seeks refuge in sleep. That's what must have happened to me. I must have dozed or perhaps I fainted. I don't know. But I awoke with a start at the sound of breaks. I sat up straight and saw that we stopped in front of a small field stone house. Why are we stopping here? I'm out of gas. Oh. Come on. We're going in. Then on the door I said, Roger Bryce, MD. In the spark of hope. I'll do the talking. Is that clear? Uh, yes. Where's the bell? Oh. Must be awake. There's a light in the parlor. How'd it do? Good evening. Dr. Bryce? Yes. Can I help you? I'm terribly sorry to disturb you, doctor. But my sister and I were heading for Costes and we seem to have gotten lost. And we're out of gas. Oh, sister. He was passing us off as brother and sister. Now I knew why he hadn't cut my throat as he had that service station lens. He was carrying me for protection. I was his passport through the police court. I'm afraid I can't be of much help to you. I'm seven miles from the nearest town. And I haven't any spare gasoline. Come in, won't you? Why? Yes. Thank you. We will. I wonder if I could offer you my hospitality for the now. That would be imposing. Not at all. I have two rooms that aren't being used. Really. Oh, come. I insist. I'd hoped for a chance to talk to Dr. Bryce alone. Just a word to warn him. But Taylor never left us alone for a minute. He insisted, insisted, insisted coming into my room to make sure he said that it was comfortable enough for me. Then he took the doctor by the arm and went out with him. Good night, sis. And sweet dreams. I was alone. Free of the presence of John Taylor. I had another lease on life. I waited. My heart pounding. Give them both a chance to retire. Then I slipped off my shoes. And in my stocking feet, I stole across the room and inched my door open. Slowly, carefully, I stepped out into the corridor and turned right toward the doctor's room. What's the matter, assistant? You weren't thinking of going anywhere, were you? I wanted a drink of water. A drink of water, huh? In case you didn't know it, there's a water pitcher on your dresser. Well, I didn't see it. Good night, sister. I turned around and went back into my room. It was no use.  I turned out the light in my room. I knew he was watching my trances. Then I lay down on the bed. How long I lay there, I don't know. Perhaps I slipped, perhaps not. But I heard that slight creak as my door began to inch open. The blood chilled in my veins. Slowly the door came open. I lay fascinated, unable to move. Immediately I saw the outline of the hand and the knife it held. I wanted to scream, but I couldn't. Slowly he came toward the bed. Now he stands over me. He raises the knife. I rolled over on the bed just as the knife flashed down. I fell off the bed and cowered in a corner. That horrible figure came around the bed after me with a knife. I had no strength to think, not even to hope. All the life seemed to have gone dead in my veins. And then it was over. Who, who had won? In the dark I strained my eyes to see. There was a vague shape on the floor. And another, weaving around the room, who, which one was it? Doctor, Dr. Bryce, is that you? No, Linda. It isn't Dr. Bryce. It's I, John Taylor. John Taylor. Standing there at the light switch. And on the floor lay Dr. Bryce unconscious with a long gash in his head. I had to hit him with a water pitcher. My eyes turned to Dr. Bryce. I saw the knife still ripped in his right hand. That's Hartley, Linda. Lee Hartley, the killer. It was he who came in here with a knife? Right. I was down the cellar just now. The real Dr. Bryce is down there. Dead. And this fellow posed as Bryce when we came to the house. Then, then you, you're not Hartley. Oh, isn't that rich? All the time you thought I was Lee Hartley and I thought you were Helen Hearn on account of your red hair. The, the body, the, the body, the red-haired woman. That's Helen Hearn. This fellow must have killed her back at the service station and stuffed her body in my trunk apartment while I was inside. That all happened last summer. In time I think I'll manage to forget that night of horror. But it won't be soon. Sometimes in the night I dream that I, I see that awful figure with the knife poised above my throat. And I wake up screaming. But then John takes me in his arms and holds me tight and tells me that everything's all right. You see, I'm Mrs. John Taylor now. Oh. You know, a happy ending. As for Mr. Hartley, that pleasant killer, he got what he deserved.  He should have stayed in jail where they never raised your rent, where they make no charge for meals or for electric current. You see, when you're in jail, everything is free, except you. You know, Mr. Host, that's the first happy ending we've had in a long, long time. And I must say I enjoyed it. Ah, those lovebirds shouldn't have gotten married. It's bad for business, Mary. Now when she wakes up screaming from her nightmare, she reaches for her husband instead of a hot cup of ellipt and tea. Well, I'm glad she has a husband to comfort her. There are plenty of other occasions, Mr. Host, when Lipton's tea is welcome. And I don't mean just at mealtimes either. Lipton's is grand between meals. And, of course, it's the perfect beverage to serve when friends and neighbors drop in to visit you. Yes, I guess that's why more people serve Lipton tea than any other brand. And now a word of caution to all amateur detectives.   Oh, by the way, this month in a sanctum mystery novel is Puzzle for Wantons by Patrick Quenton. Yes, and next week's in a sanctum story directed by Hyman Brown and brought to you by Lipton Tea and Lipton Soup. Next week's story is about a lonely man who falls in love with a mannequin in the store window. Oh gee, fellow wants a real girl. So he tries to make her come to life. And what do you know? He finds he has to kill her first. Well, now it's time to close the squeaking door. So, good night. Pleasant dreams.  Folks, these busy days we all want to save time when we prepare meals, and yet we don't want to sacrifice that good homemade taste. Well, the answer to that is Lipton's noodle soup. You see, Lipton's takes no time to prepare and yet it has a real fresh cooked chickeny flavor. Yes, it tastes just like the chicken noodle soup you'd make right in your own home. Lipton's is economical too. It costs less and makes more than canned soups. So folks, don't forget to serve Lipton's noodle soup. And don't forget to tune in next Tuesday night for another inner sanctum mystery. This is CBS, the Columbia Broadcasting System.


Assalamu alaikum. My name is Ismat Shah. I'm a professor of material science and engineering and physics and astronomy at the University of Delaware. So I'm going to be teaching this course in energy economics and you would wonder why would a person who has a background of physics and material science be teaching economics course and it is a very legitimate question. The only thing is that while I was a professor of physics and astronomy and material science and engineering, I also directed a program at the University of Delaware which is related to energy and environmental policy. So as you can imagine that all the things that are necessary for policy, the knowledge of economics is very important for that. After that, I learned economics for six years and the result is that I am standing in front of you and recording a course on energy economics. So first, there are some introductory slides. There are a few slides that are a little bit a bit too much but don't worry about that. I'm just going to very quickly go over the main content of the material so that you know what is coming up and then we will go into the real material of the course a little later. So let's start with the section one. Section one basically introduces the energy fundamentals. Not just that which energy is available, renewable, non-renewable, all the things are described. In fact, apart from this, what is energy? We don't have any idea what energy is for the name but what is its physical concept? There is a spiritual concept and a metaphysical concept but we will restrict ourselves to physical content of energy. So we will talk about what is energy. Then if you talk about energy, you will have to understand the units of it. So I will describe in detail all the units of energy, power and everything, force and whatever else that is related to that. Apart from that, then we will also talk a little bit about the economic fundamentals. Like this Kuznet curve. The interesting thing about Kuznet curve is that it was used for something else, equality or GDP per person, but now it is used in environmental issues as well. Yes, let me tell you that energy is only necessary to understand what the effect of energy is. Not just on society but on all the environments. So we will talk a lot about the environmental effect of the energy. So we will talk about that. I have also mentioned here, Canadian economics. It is a very interesting idea that you quickly become rich and the rich people do not need to fight them. So it is better that everyone becomes rich. So you will only get to know the basic understanding of how much there is in it. So we will talk more about that. We will talk a little bit more details into that. Then we will get into the nitty-gritty of what kinds of energy, what kind of fuels, right? We talk about fossil fuels. The biggest problem these days is that we are using fossil fuels with so much effort. And due to its use, we will see what is the problem of the environmental problem. But where are the fossil fuels? The fossil fuels have not come from above, right? The fossil fuels are made in the ground. So we will look into how the fossil fuels are made. Coal and oil have different origins. Oil and gas have one origin and coal has a different origin. So we will talk about the origins of both. What are the origins of the three? And then the history of where it started and where it is at this time. And how much coal and oil are saved. That is a very important thing to understand in economics. So we will talk a little bit about that. And apart from that, the prices of these things, oil prices, you know that if you live in Pakistan, you will be sure that it keeps rising and coming down. And all the reasons for that are externalities. Political externalities, weather externalities, right? Sometimes it happens that if the storm comes, then the refinery will be closed, then the price of gas will be more. If it is not here, then it is outside. And some reasons for political externalities, that import has been reduced from outside, then the price will be more. So we will understand all of those externalities where the oil prices are very much dependent. Coal is not so sensitive, but it is still sensitive. Now if you imagine that the coal in Balochistan was half the price five years ago, now its price has become low. So why is it low? So it is necessary to understand what are the factors that relate to the price. Then there is a small section on electricity. Although electricity itself is an energy source, but it is not a primary energy source. Primary energy source is oil, gas and coal. But it is necessary to understand that because for our life, there is nothing more than electricity. Transportation and electricity are two things that affect the life of a common man. Industry also affects it, but in day-to-day life, when we need electricity, then we will have to see how the price control is in Pakistan or outside. And then there is supply and demand economics, for all these things. How much did it come in the market? It was your supply and how many people bought it, it was your demand. What is the use of all these things? Transportation is the biggest thing, but there is no major use of 30-40% fuel, it is used in transportation. Oil is used in transportation for 80% of the time. So you have to see how it is used. So you have to understand the internal combustion engine. So for that, there are some principles of physics that can be understood very easily. There is no need to worry about it. There are thermodynamics principles. If you understand them, then life will be very easy. Not just for this, but for other things too. So I will try to explain it in an easy way. So we will read it in a good way. The internal combustion engine is not a wide engine. There is also an external combustion engine. Like the old engines of the rail cars, they are external combustion engines. We will also see them because they still need it in their industry. And apart from that, we will understand the other things that are on the roads, the trucks and all the other things. And with that in mind, then we will see the need for oil. And why and what is the effect of it on a normal person's life.


As an emergency medicine physician, lots of residents would ask me if I had had a helmet on when I crashed, would I have avoided an injury. And there are lots of studies to suggest that helmets make a huge difference. They reduce the severity of injuries that we do have when we fall doing recreational sports and they can prevent much more serious injuries. I see the results of head injuries from recreational sports like bicycling, skateboarding, razor riding, helmets really do make a difference in preventing serious injuries and lessening the severity of injuries across the board in recreational sports. They're as important as seatbelts for basic safety when you're riding your bike or your scooter or your skateboard, when they can pick up that habit and change that life habit to wear a helmet when they do these sorts of things and we like to pass that message on to these young kids.


Hi everyone, Thomas here. I'm glad to present you some new results on first-term polynomial time lattice reduction algorithms This is joint work with my colleagues Paul Kirchner and Pierre-Anna Fouff-Romin-Riaren So first of all, let me make some recalls on lattices and on the LL algorithm So what are we working with here? So to set up some Setting super that we are taking the Euclidean space here R2 and take a bunch of linear independent vectors in this space then consider the sets of all possible integral linear combination of these vectors you get a very regular structure which is in the sense of a grid in high-dimension and it has actually the structure of group such it's a subgroup of the Euclidean space and by construction it's a discrete this algebraic structure is called a lattice In a lattice you might want to measure the density of points in your structure and for that you use a geometric invariant which is called the covolume it can be computed from your basis vector as a root of the Determinant of the cram matrix that is to say the matrix of inner products of your vectors It also corresponds to the volume of the parlippi bettys spanned by your vectors. I say it's a geometric invariant because it's invariant under a change of basis independent Actually, so I'm speaking of having multiple bases in your lattice So that the question is how can I get from a screw on a very bad one to a nice one like the first one I showed A solution to do that at least in dimension 2 is to use the shortest vector to reduce the length of the longest one more precisely you take the shortest element in the coset which is spanned by the short vector and get through the long one and Then you get a shorter vector and then you repeat as long as you can and at one point this process will stop This is in substance the so-called Lagrange-Gauss reduction algorithm and this algorithm has very interesting properties in particular the output basis Satisfy that the first vector is one of the shortest vector of a Zalates Moreover, you can prove from that that the length of this shortest vector is Smaller than four-third of the co-volume of Zalates, which is a constant which is independent of a Zalates itself More generally speaking in any dimension in your rank We get the following theorem, which is Minkowski-Hermes theorem for first minima Which asserts that for in the lattice lambda of rank D The length of the shortest vector will be smaller than some constant which only depends on the dimension multiplied by the normalization of the co-volume so We know that such short vectors exist. However, finding them algorithmically is a hard problem has been proved to be NP-hard However, in 82, Lenzfra, Lenzfra and Lovac Show that there exists some polynomial time algorithm with given any lattice lambda will give you some Lattice vector of lengths at most two to the n times longer than the length of the shortest vector It might seem pretty big But actually this LLL algorithm is quite useful For instance, we can solve the Simultaneous-Tayefanthian approximation problems, which is finding an approximation with rational of real numbers with common denominators From that you can use the same method to find the minimal polynomial of algebraic numbers You can factorize over rational that was the original application of Lenzfra, Lovac And of course you can do cryptanalysis with that and that might what interest me the most in the context of this conference For instance, you can solve knapsack problems in very specific settings. You can break RSA with public exponent And you can also of course Attack lattice-based cryptography Moreover, you can also Help computation in algebraic number theory in particular. It's very important in a normal form computation Working with ideals and also to control the size of elements appearing in your computation and ensures polynomial time So let's see how we can construct this or reconstruct. Let's say this LLL algorithm So first of all if you take any basis Let's say v12vd of your lattice lambda then you get a filtration from that basis Constructed as follows you start from the sublattice 0 and then you can see a lambda 1 which is the lattice spanned by v1 then lambda 2 spanned by v1 v2 and So on until you reach the full lattice. So you get an increasing sequence of sublattices Now you might want to quantify the quality of your filtration and to do so we do a bit of quantization how we do that we basically Use this co-volume actually we're using the degree here Which is the logarithm of the co-volume of each of the sublattices appearing in the filtration. So in turn you get Some bunch of real numbers which corresponds to the degree of each element appearing in your filtration Now We've seen that the Gauss reduction algorithm Helps to reduce lattice in dimension 2 but given a filtration We get a bunch of rank 2 lattices actually all of the quotients lambda i plus 1 over lambda i minus 1 actually of Rank 2 so that we can use Gauss reduction algorithm on these quotients more precisely what we're going to do is to use the Gauss Gaussian algorithm on the Projective sublattice corresponding to this quotient then lift the result and replace in our basis and more generally replace in the corresponding filtration If we look at the effect of this operation, let's say I place i Then we can easily see that the all the degrees are invariance Except the degree of lambda i which is replaced by say lambda i prime and in particular We can show that this new degree lambda i prime is smaller than the previous one so at all in all the Gauss reduction is a Local tool because we're only applying it in a very specific position of the filtration to densify it so that reducing the co-volume Okay, so now from that operation we can construct a simple iterative algorithm that will do Gauss reduction steps as much as it's possible and From that we just start from the beginning of the basis So let's say the first two vectors and then we move on to the third second and third and so on but maybe doing so Will had to reduce the already previously reduced first second and third vectors so that maybe we need to redo a step of reduction earlier on and So we then continue go on and might be go back and go on and so on but in the end We will finish by reaching the end of the basis and no more Gauss step can be done anywhere else in that case. We say that the basis is a little reduced if we analyze this algorithm we will find some dependency which is six stick in the rank and which is cubic in the size of the integers However, if we are precocious enough, we can use floating point arithmetic instead of exact arithmetic and It was first step made by Ingrid and then still a in 2009 Where they show that we can do LLL reduction which dependency which is quadratic in the logarithm of the size of elements appearing in your basis more Recently, no major and still a showed that with some recursive strategy You can go down to some cardiac or quasi cardiac dependency in the dimension and quasi linear dependency in the logarithm However, this algorithm is purely theoretical and the constant periods of ego are too big to be concretely implemented The question is now How can we improve these quasi quadratic dependency in the rank because quasi linear dependency in the size seems already close to be optimal So let's try to focus on the rank dependency So how to get some faster type lattice reduction? so we're going to completely change the structure which is Used and instead of doing these iterative back-and-forth strategy as you didn't LLL we're going to use parallelization and regression on the rank So let me explain that a bit more So I said that all the reduction boils down to doing some gauss steps on projected sub lattices What we can do first and this was already hinted by the line 93 was to is to Do parallel gauss step Everywhere is possible when it's non overlapping. So basically taking the first two vectors and the production of third and fourth and so on Then you do all your parallel reduction like that But if you do stop there, then you don't Interleaving relation between let's say second vector and third vector and so on so what you do is shift all your windows and Do the same parallel gauss reduction at the Intersection of the produce blocks and then you continue again and again and again, and you will in the end reach a reduced basis So if you take a full round of local reduction So all let's say the odd steps and all the even step today two of them if you look at the effect of this operation on the on Degree space then whatever is you're basically applying some discretized version of the laplacian operator And by that I mean that each Degree is now replaced by the average of its neighbors ancient degrees It's very reminiscent and to the diffusion property of the solution of the heat equation because heat equation is Basically that infinitesimal Increase increment of time you are playing the laplacian operator on your space and here at each time step We are playing a discrete laplacian operator onto the profile space So since we know that the characteristic time of the Diffusion of the solution of the heat equation is quadratic in the diameter of the space will get exactly the same kind of property In substance it means that the number of steps you need to reach a stable stable step is Roughly quadratic in the diameter of the space which is here actually the rank of the lettuce. Okay So now we can Remark in addition to that that all the operation are actually local So we can do the same but with big blocks instead of blocks to and recourse inside the blocks so for instance here we take like big blocks and for them for instance and We will apply parallel reduction on each of these blocks and each of them consist in the same Recursive calls so we're starting by even odd steps and even steps and so on when it's done We do we shift all our window by half a block and we do the same reducing and calling recursive recursively on the range and we do it again on D-shifted windows and again and again and again So we want to make some big algorithmic design by exploiting this locality property and to do so it will amounts to Makes an algorithmic design with the only block matrix operations So let's now see More in more details. What are these precisely block operation? First of all, we need to invert triangular matrices. This will be used everywhere. So as Warmer, let's see So take a triangular matrix. Let's say block AC D and if you you can write directly the inverse of this matrix using Schroes complements And it's pretty easy. It's a minus one D minus one and some Block here minus a minus one CD minus one Okay, so formula is pretty explicit so we can construct recursive algorithm for that and the complexity of this algorithm Amounts to basically matrix multiplication. So you can inverse for the cost of matrix multiplication Okay, so now let's see how we can compute. It's a so-called periodic composition by blocks. So um Curated composition is an algorithmic new to handle filtration because I said previously that we were directly using filtration but in practice what we are doing is to have an algorithmic grip on it, so we want to work with matrices and to do so We want to find some say normal form of The basis and it amounts to finding some orthogonal transformation to put the basis in triangular form because triangular form is the Way to encode filtration as matrices So basically it just means that we are looking at the lattice Modular any kind of rotation of the space and we take a good rotation so that your matrix is just triangular It's nothing much more than that. So how we can do this computation by block so Instead of working directly with a basis we're working with a cram matrix, which is a symmetric And we work it we were divided in three blocks ABC Then the first corner we can just Super that we can directly Find the decomposition. So let's suppose that we find a triangular matrix La such that la transpose la is equal to a okay Then we construct as before the source complement of a into matrix G So it's C minus B transpose a B and we can decompose it Directly using let's be recursion and we find L transpose s LS is equal to s and we know I can show with a bit of computation that the Sure, let's get a composition C our part of security composition is la LS and La minus LS transpose minus one B here from that we can directly work some Block Cholesky algorithm, which is the transposition of this Construction here once again the costly step Except the reduction step is a matrix multiplication here and you can prove that it amounts to matrix multiplication once again Now the Final tool we need to do our reduction is so-called size reduction. So what size reduction? Size reduction is a process which will reduce over diagonal elements using some let's say lattice compatible Transformation that says to say unimodular transformation. It's Transformation matrix which has integral coefficient and determinant. Why? so How we can reduce over diagonal elements here I did normalize the matrix R we construct with QR decompositions just dividing the rows by this lengths of the diagonal Okay, so how we can do that? We can use a block structure idea by start reducing the upper part of the over diagonal elements Okay, let's suppose we can do that then we will reduce the lower part before and like for the curriculum for the inversion it remains to handle correctly the upper diagonal part here like the upper right elements So how we can do that? So if we write the transformation, let's say U is U1 U2 and X X being some unknown for the moment integral matrix the effect of U on the triangular matrix with that we write by block a CD is Applying some transformation U1 on a a plane transformation U2 on D and then doing AX plus C U2 on the upper block So if we support that U1 and U2 are correctly chosen so that a U1 and D U2 are small as we want then we just want a X plus C U2 to be close to zero with X being integral and And basically we get a recursive algorithm from that which amounts on size reducing a size reducing D and Finding like that if you take a minus one C U2 for the matrix X and you're basically good This is in substance a block variant of a reduction which has been introduced by Seisen, so we call that let's say Seisen size reduce So we can move on to the actual reduction procedure which will amounts to use our big design by Applying parallel reduction and recursion and all of our block tools So once the dimension is two, then we use the Gauss algorithm or if you want to be more efficient acceptably you can use Schenegger algorithm, which is quasi linear in size B Then for a certain number of iteration, which is basically quadratic in diameter as I said We will do some reduction and we start we start start by Compting the curative comparison with the block shoulder scale with them I showed and then we say Seisen reduce as a basis to reduce the size of all coefficients appearing and then we do this window strategy and We will apply the reduction recursively to all the blocks So here we introduce some condition Which is reminiscent to the lavage condition in the original algorithm Which will basically says if you need or not to reduce And so that if you're reduced enough you just move on to the next block and so on so that you will eventually stop So if you look at the running time and where the Most computation is done You can see that for free when the dimension is small enough It's with regards to the rank with regards to as a size of the question appearing then you can actually Don't go All the way down to the leaves of the recursion tree But you can stop a bit before and use a more costly reduction such that the big easy reduction and The overall running time of the algorithm will remain unchanged So basically for free you can use something which is a slightly more powerful than a Gauss algorithm And something which is slightly bigger dimension and so you will get in the end vectors which are slightly shorter than before So all in all with this little trick we can heuristically Conjecture that in time which amounts to matrix multiplication So D omega multiplied by the condition number of your basis We can find some vectors, which is within 2 to the D log log C over log C multiplied by the normalized co-volume so this D log log C over log C is basically because we use this big easy instead of going up the way down to rank two with Gauss algorithm Otherwise, we just get 2 to the D like LLM. So for the running time This is a conjectural right now, but we made a lot of experiments and in particular Here you have on the left some traces of execution So the abscissa is the log of the dimension of the lattice we're considering from 2 to the 7 to 2 to the 11 and in Ordinates you get the log of the running time in second So we also we increased linearly the condition number of the matrix we're considering and we see that all the Slopes of this of these graphs are Almost all equals and around 2.7 which was the exponent we use for matrix multiplication Um, so just before moving on to other Experiments and results. I just like to point out that we can reduce this D omega dependency for knapsack like lattices


Hi, on NPI. OK, I on NBI is brought to you by Digi-Key and Adafruit. Every week, we look at the latest, newest stuff from Digi-Key and more. Lady, what is this week's I on NPI? This week's I on NPI is a Raltron crystal oscillator kit that I saw pop up on digikey.com slash new. They got a cool logo, Raltron. Apparently, they're in Miami, Florida. So it's cool to have really great weather there. It's like Tron's uncle. Raltron. Yeah, and they've also got great crystals. So why not? It's a Rami technology company. I guess they're somebody. But they're small business. And they do manufacturing. And they're here in the US. So let's check out this week's new product. OK, so the new product is the crystal resonator design kit. So chances are, you've used. This is like the best trapper keeper ever. It's basically a trapper keeper. Crystals, if you've never used crystals in your electronics, they're not necessarily the bedazzli type crystals. Instead, they're the kind of crystals that come in a metal tin. Usually, you have to have two capacitors with them to stabilize the oscillator.  It's a crystal. It's not like a amethyst type crystal or like a quartz crystal. But it is a crystal material. And when voltage is applied across it, it vibrates. And it will oscillate back at a certain frequency. And so by setting up in a feedback loop and you kick it once, you can get quite precise oscillations out of it. So what these are used for is creating a timing signal for microcontrollers and other chips that need to have a precise measurement of time. Because you can make an RC oscillator, but RC oscillators, they're not very precise. They have plus or minus, maybe 5% or 10%. Maybe you can sometimes tune them to get 1%. But a crystal oscillator is going to work much, much better. You're going to get maybe 20 to 50 PPM. That's pulses per million, or parts per million error rate, which is pretty good for a timing oscillator. And so oftentimes, your microcontroller will use a crystal also as a source for a multiplier, like a PLL, to multiply that frequency. But we'll get to that. So the most common crystal used in any electronics is the 32.768 kilohertz crystal. The reason it's an odd number like why 32.768 kilohertz? Well, because that is a 2 to the 15 number. And so if you have a binary counter in your microcontroller, and binary counters are very inexpensive, as it counts from 0 up to 32.767, when it gets to 768, it will flip over. And that overflow will let you know that one second has passed. So it's a very easy way to count one second. So it's used for timing. So in this case, this board that is shown here has a real-time clock. So it's something that keeps time. It runs for years on a coin cell battery. And it can do that because 32 kilohertz is quite slow. It's a common crystal value, but it's slow enough that you're not running very fast electronics. It sips power, like microamps or less. So there's a lot of different values. So this kit, and I'll open up the kit, of course, and show you the pages inside, it has the most 32 kilohertz crystals. It has all sorts of different sizes and packages and also the load capacitors.  Like, if you look here on this Arduino board on the left, you see there's kind of the metal tin. And then above it, there's two little yellow dots. Those are the load capacitors. Sometimes you pick them. But actually, sometimes I've noticed certain chips or devices. They actually have the load capacitor, like a tunable number inside the micro. Or you kind of have to pick a certain loading value. And so that's why they have multiple, even though I tend to use a 12.5 picofarad for 32 kilohertz, and maybe I use 18 picofarad for 12 or whatever, they do give you a full range with multiple sizes and also load capacitances. So I showed you the 32, I call them 32 kilohertz, but they're 32.768. They also have a lot of microcontroller, common microcontroller values. If you have a USB microcontroller, you're going to have 6, 12, or 24 megahertz because USB is a 12 megahertz protocol. And so you're going to have something that's like a multiple or a divisor of 12. A lot of microcontrollers also like to run at like 8 or 16 or 20 or 40 megahertz, those are pretty common values. The microcontroller sometimes runs at that value. But again, it's pretty common for inside the microcontroller there's a phase lock loop. And so there's a non-precise higher speed oscillator that they then tune against the precise lower speed oscillator. And that way you can, a lot of my controllers these days you may have noticed you can actually change the clock speed, sometimes even on the fly. So original AVR microcontrollers, I think you could maybe clock divide only, but in the SAMD 21, you can clock up and you can even overclock if you'd like. So the SAMD 51 you overclock it to 200 megahertz, even though it only has I think a 16 megahertz crystal on it.  Next up, there are a couple of weird values in here too like 27.12 megahertz. You're probably like, okay, that's an odd value and it's not even like a multiple of two. What is up with that? This is a RFID board. So this is a PN532 and it's an RFID transceiver board and RFID for like NTAG and my fair chips is 32, sorry, 13.56 megahertz. That's the frequency. And so multiply that by two, you get 27.12. So that's another thing. If you have certain RF work you're doing, you'll need to really get that crystal to be the exact multiple. Also, if you're doing video stuff, old NTSC video, you had to have the color burst crystal and it was like 3.96 megahertz. The crystal actually does matter. You don't round up or down. You wanna get the exact value and again, you wanna have the loading capacitors match because that'll get your value as close as possible to the stated. So inside the binder are all these pages and I think that these are like, I'll show them also in the overhead but I think they're pages that are used for like baseball cards or something. Yeah, this was clever. So each inside there's five, there's a five piece tape of each crystal and they're in the little clear pockets and behind it is a printed out piece of paper that goes that, you know, is behind the clear part and it has the part number, the frequency, the stability, the load capacitance, the ESR operating mode, operating temperature and size. And then there's also a short URL that you can go to to get the data sheet and also a QR code. One nice thing about the short URL, they got their own URL shortener. Big ups for that because it would have been really easy to like use the Google one or Bitly. They actually got their own, which is very smart. Don't rely on other people for your URL shortening. What are the chances of like a giant global network going down and no one being able to communicate? I know. Probably not. Okay. Unlucky. Well, it's available on Digikey. That's right. So you can pick this up. Digikey also has capacitor kits and resistor kits. I always recommend having a resistor kit and capacitor kit. I use them all the time. We sell some, you know, in the shop but Digikey also has them. Nothing beats having a resistor capacitor kit. You never know, you need some weird value. Sure, you're all here. And a crystal kit also really useful because sometimes you don't realize you're laying at your board, you get all the parts, you don't realize, oh shoot, like the crystal I need is the wrong size or I need a slightly different frequency. I misread it. I thought it was 20, it's 24. Crystals are using everything, right?  Great. Want to show this book? Yes. All right, I'll show this book and then we'll... Okay, so design kits for crystal resonators. Thank you. So there's all instructions on how to use it and then basically this is how it works. So you see that there's these clear pages and they're used for like baseball cards or whatever. And then underneath it, there is for each one a description. So these are like super tiny 1.2 by 1 millimeter, 32 kilohertz crystals. And then moving up there is 3.2 by 1.5 and then they've got 32 megahertz. They've got 25 megahertz, 27.12, 27, not the one too, 32, 37, 0.4, 30, 0.4, 40, 48, 16, 20, 24, 25. They have a couple different frequencies in different sizes, but they kind of cover them all. These are all the kind of the most common frequencies I've seen. And of course, once you've used these in your production and you're happy with the package and the size and the stability, you can of course use that part number type indigiki and then purchase it by the real, your heart's content. So you got 66 different values and then 55, sorry, five pieces of each value. So multiply that out. Okay, and that is this week's IonMPI. Tick tock. IonMPI.


There but let's start with the Mount Pleasant line up the shape of like this Daniel Russell between the sticks Of course the captain Suley McCullough Fitzroy Cummins the big centre back who was the captain of very united for quite a while Jamoy Tope in the national centre back Shaqeel da Kimoni Bailey Ramon Howell Shaqeel Bradford gets his first start for Mount Pleasant Nathaniel James the talented TNT midfielder Demario Phillips and Daniel Green fresh from his exploits in Vietnam Daniel Green and two seasons ago He was a joint leading goal scorer has three goals so far in the season. He's been in good form and A good-looking line up Let's see how the chemistry between Bradford and company go Dwight they shape up with water for three three Yeah, normally they're formation They have a world of talent and they play that formation because for them it gets their better players on the park Treasure Beach they will shape up like this homes between the sticks Anderson comes into the line up stone Nemha the captain court and right who already has a goal this season They need goals Hall Herrera Taffar Thompson Lamont knew into this line up their number 17 Tedla parchment and Romario Brian Brian of course it Experience officiating team led by O'Shea nation the man with a whistle and Mount Pleasant Started the game the best way they could by scoring They're 22nd goal of the season and Suley Makala had his third Daniel Green picking up the assist and Makala with a smart flick with the right boot the captain Pass home pass home who could do nothing about it Mount Pleasant With a beautiful start and Setting the pace early had other opportunities Shaquille Bradford had quite a few of them half chances as he always does Bradford What was unable to add to his eight goals that was a strike with the left foot wide of the target Then green putting that one in and I came Bradford as you could see half chance heading over the top always willing to try Then treasure beach they were reduced to 10 men a Silly fall from Romario Brian in the second half and he saw yellow for the second time Her smile on his face, but yeah a bit irresponsible from him Treasure Beach had to do it with ten and that they did in terms of staying in the game Daniel Green did hit the crossbar from a glancing header And that's the closest they came then this was a moment for treasure beach to draw level and just couldn't take it Comfortably wide in the end from Carlton salmon and Daniel Russell a lot to see quite annoyed with his defense line Luckily for him someone was inaccurate and treasure beach the chance was gone Of course a charm came on as a substitute so to a tough boy by Grave and they combined on a couple occasions But couldn't find in it As treasure beach continued to be stubborn to try coming the man of the match with the head over the top He was solid right throughout the game was coming and then Chong again combining grocery and Locked again treasure beach standing firm but yet Unable to create any real opportunities of their going in Aubrey had this strike which was up target and saved from home And that was all she wrote Matrix 15 for these two teams Mount Pleasant one treasure beach nil Three on target from ten attempts for Mount Pleasant They weren't at their best in terms of finishing but they got the job done nothing on target recording for treasure beach over Ninety minutes that was disappointing for my weatherman and company There were some 27 falls between the two and six yellow cards shown from a Shane nation Treasure beach the more in disciplined of the two and losing a player as well two saves were made By Carlisle Holmes between the sticks But he couldn't stop the important goal for Mount Pleasant to a majority of the possession at 60% and the lone goal in this contest Three big points for Mount Pleasant. They win this one by a goal to nil Dwight Jeremiah's with our man of the match None other than Fitzroy Simpson Cummins you had a decent game today The rest of your team up front door, what do you make of their performance? I mean we go back to the training ground again, you know, we take it from there You know, we just have to kind of go by the top and put our chances away It seems like it's you don't get flustered I see other defenders around you and they have arguments with the players above that are in front of them Not doing what they're supposed to do maybe tracking back or finishing off a chance You just go about your business is that a nature of how you play normally just not bothered You just deal with what you have to do. I mean not necessarily, but again, we have to go again I mean they put the work up there after those stay behind and different for them as well So I didn't have a day. I mean they have to go and have to come back and different as well It would appear that it wasn't Treasure Beach that made the game difficult for Mount Pleasant today It was more Mount Pleasant making it difficult for themselves I mean again, we just go back to the training ground and take it from there and go back to the join board and Good performance from you today. Thank you so much. I hope it continues Yeah, I think it would work. So Mount Pleasant walking away with all three points Cummins with the man at a match performance really good performance from