Hey guys, what's up? In this video, what I'm doing is I'm cold calling dealers with some live sales calls. You don't want to miss us.  Yeah, I was going to see if I could check on the availability of a vehicle. I'm seeing it here on your website. 2016 Ford Fusion white one. I was just going to see if it's still available. Are you on start number? It's GR215848. Now listen guys, I'm going to hit this guy with an objection here in just a minute. Obviously, he's already picked up the phone. He hasn't asked me my name. Yeah, well number one, so it is still available. Okay, awesome. And let me ask you, where are you located? He never asked my name. He didn't ask me how my name was going or anything like that. Now watch. Okay, I appreciate it, man. I didn't realize you were so far. I'm actually a couple hours away from you. I'm just going to look for one more local. I appreciate you. If I don't find one local, I'll definitely give you a call back. Thank you so much. Thank you. Okay, listen, I'm going to say this real fast, right? And by the way, I'm not making up a difficult phone call. This is pretty simple. Guy calls. I said, Hey, I was calling about the 2018 Ford Fusion I saw on the internet. Guys like, Hey, I got it, right? Never asked me my name. He said, Okay, hold on, let me look it up. And I said, Would it be better if I gave you the start number? He said, Sure, I gave it to me. He said, Yeah, we still got it. What time can you make it? Boom went straight for the appointment. You wonder why you're getting fake appointments? Because nobody's going to show. Did we build a relationship? Look, how about when he answered the phone? He's like, Hey, hope you have a wonderful day. This is Andy. How can I help you? I'm calling about the Ford Fusion beautiful. We've got a lot of vehicles in stock. While I'm looking that up, who do I have the pleasure of speaking with? Okay, my name is Tom. Tom. It's phenomenal meeting you. Look, do me a favor and reboot my computer. It's going to take me about 30 seconds while I get you all the information on the vehicle you called about. Where you calling from today? You know what I mean? Look, the cell can't be closed until it's open. You wonder why your sales teams aren't winning? It's because of this. Let's make another call. All right, guys. Yeah, I was going to check the availability of a vehicle. I'm looking at 2019 Mitsubishi Outlander. Listen, what's my name? How's your day? Nothing. These are your people. Just watch. Yes, sir. Yeah, you got it. When would you like to come take a look at it? Yeah. So number one, I saw that the price on it is $18.995. Is that right? Okay, cool. What's your best price? Okay, so you can't get me a better deal at all. Okay, I appreciate it, man. All right, I'll get back with you. Thank you so much. All right. Can you just see that? Now, listen, let me ask you this. Did that salesperson have a rapport with me? Did he even have my name? No. Let me ask you this. When you tell somebody you're not going to miss a business over a couple hundred dollars and that's your best price, do you need to have a relationship to do that? Can I ask you a question? Are your salespeople and your internet department and your people answering your phone, do they work at McDonald's? Do they work at McDonald's? Can I take your order? How can I help you? Or your people's job actually to make connections with the customers who call? Make the decision. Look, I'm going to tell you this, right? Those that are ready to win, those that are going to be the best in the world right now will make relationships on the phone. Let me explain how they'll do it. Number one, hope you have a wonderful day. This is Andy. How can I help you today? You're going to tell me what you need. I'm going to say, hey, thank you so much for calling. By the way, who do I have the pleasure of speaking with? We're going to get their name. He didn't get my name. I'm about to make another call. I'm going to call two people back to back right after this. You're not going to believe what they're going to say. I promise you, you're going to be blown away. Now watch, once I call, once I call and they get their name and they're like, hey, I hope you have a wonderful day. You say, hey, give me about 30 seconds. I'm rebooting my computer. I'm going to give you all the information on the vehicle you inquired about. By the way, where are you calling from today? Dude, start building some relationship with me and start building some rapport with me. This guy didn't do anything. And then you know what happened? It was really simple. What happened? He said, that's my best price. I just asked him, hey, what's your best price? He said, that's my best price. And I said, you're saying I can't get a better deal? And he's like, no, that's our best deal. And I said, okay. And he's like, I won't miss you over a couple hundred dollars. But if you think I got thousands to mark it up, I don't. Let me ask you a question. Is it just a question that someone can ask? Yeah, people ask all the time, can I get a better deal? What does salespeople say? Salespeople always say, we don't put our second best price up front, we put our first best price. We're an internet based price store. So the price you see is the price you pay, you don't have to haggle with us. Well, are you saying I can't get a better deal? And at that point, they say, well, that is my best price, or we won't miss your business over a couple hundred dollars, or it motivates my manager to have you here. And if he knows you're serious about the car, he'll work for a better deal while you're here. You know, if there was a better way to do it, would you want to know? There's five different ways to handle price suggestions to ensure that you get every single customer in every time. Let's make two more calls. You're going to be blowing away about what these people say. Yeah, I was going to check the availability of a vehicle. It's going to be a 2019 Chevy Colorado, a gray one. Sure. I'm on my wife's phone right now, so I'm about to have my phone back. Can you just check on the stock number? 212-376A. One second, one second. Okay guys, listen, time out. Did this guy ask me my name? No. Hey, I hope you're having a wonderful day. My name's Andy. How can I help you today? What do you look for? I told him what I wanted and he said, okay, hey, do you have the stock number? He's talking to me like I'm an employee there. Okay, think about it. Do we talk to our people like there are customers and we're serving them at the highest level and giving them world-class customer service, or how do we speak to them? And then the guy's like, hey, what's the best number I can call you back at? I like that trick. But notice when I told him I'm on my wife's phone, he's like, any number of workers are yours. It doesn't matter just in case we get disconnected. He stopped. But let's just say I'm not training on that here. When I was done, I gave him the stock number and he immediately said, oh yeah, I got it. What time can you make it in? He didn't even tell me how was the nicest one in the country or anything like that. Okay. Dude, are we salespeople? Watch. I'm going to ask him what his best price is. Okay, cool. Sorry about that. I was talking to my wife. Okay, so you have the truck. Awesome. And I see it's online for $32,887. What's going to be your best price? What is your best price? Okay, so yeah, I've never paid what somebody was asking before. So could you find out what your best price would be real quick for me while I put a saddle hole? You're going to lose all your business. Tell people your own last price is it. Stick it or leave it. I promise you, there's a better way. So you're saying there's not a better deal. Now it's $500 better. No wonder people don't trust salesmen. Okay, cool. Well, what I'm going to do is I'm going to continue to look around just a little bit and I appreciate you. Listen, I didn't say I wanted to look at another one. Do you feel me? Do you see what I'm saying guys? This is why salespeople have such a horrible job right now because they've never had any change. Never.  Okay, this is your team. This is teams up there. Okay, awesome. No, I'm really interested in this truck. I didn't even say I was interested in anything else. I just, I'm going to think on this one and then I'll get back with you. Okay, never got my name, not one damn time. Look, I'm going to tell you this.  I'm not. I'm actually moving fast. Okay, this guy picked up the phone, didn't get my name. I asked him for the best price. He went in and started talking about hard ads. Do you think your customers know what hard ads are? Sir, I don't have any of those hard ads and this and that and this. Do you think they understand your language? No, they don't. So why are we talking to them that way? Because you haven't been trained. Look, we're going to make another call. If you want to train your sales team, shoot me a text<PHONE_NUMBER>.  Look, dude, your sales team sounds like this. I can assure you go back, listen to their calls. This is you.  You want to be the best and your dealer doesn't give you training. Reach out to me. I'll help you with it.<PHONE_NUMBER> in the air of the worst salesman in the history of time. Let me show you how to be the best in the world. We're going to make one more call. Stick with me. Yeah, buddy. I was going to check the availability of a vehicle. Oh, sounds like I got a veteran. See what happens. Hey, by the way, hey, my name is Vince. Who am I speaking with? Yes, a used one. Yeah, I do. It's GH172639. Yep. Now listen, he hasn't asked me my name and that just bothers me. Yes. Okay. Listen to me. Are we order takers? Are we information givers? Are we doing our job? Our job is to make a connection. He's already asking for the appointment. Well, okay. So you do still have it available. Is that right? Okay. Awesome. And what is your best price? So are you saying you can't give me a better deal on it? Watch. I'm going to hit him with another one. Watch this. I'm going to double up this guy. Okay. Yeah. So another deal. I think the miles are a little bit too high. Okay. Well, I appreciate you. Thank you so much. All right. Guys, I'm telling you if I freaking see this, this right here, this is why it's so easy to be great right now. It's so easy. Go back and slow down. Go into the beginning of the call. This guy said his name was Vince. He said his name is Vince. Okay. He said, how can I help you? This is Vince. I said, Hey, Vince, I was checking the available bit of the vehicle. He should have said, Awesome. May I ask about the pleasure of speaking with? No. All he said is, do you have a stock number? Boom. I give it to him. He's like, looks like no deals are working on it. What time can you make it? That fast. You guys are wanting free money. This is embarrassing. I sit here every day and I call 20, 30 dealers. We train 200,000 salespeople at this time. My guys don't sound this way. This right here, this is embarrassing. This is why it's never been easier to be great, but you got to train.  This is what your sales team sounds like. Reach out to me.<PHONE_NUMBER>. If you're a sales pro, you want to know what to say? A lot of times people reluctant to say something because they don't know what to say. Let me teach you how to close every single deal in the world and be like Alcatraz. No one escapes guys. All right, guys. So what I did is I just took a couple minutes, called a couple dealers, right? And you can tell people are really frantic on the phone. They don't have great dad attitudes. They don't have good energy. And guess what? When someone is asking like, what's your best price? The miles are too high. You know, I'm a little bit too far away from you or anything along those lines. People get very defensive. Think about it. How are we making it on our customers? Are we making a better buying experience or a horrible buying experience?  People aren't training. Sales pros. Reach out to me.<PHONE_NUMBER>. Look, my last year selling cars, I made 716 grand. How? It was too easy. No one out there is doing the training. Our people that are training are crushing and killing the competition. If you have a dealer, reach out to me. I'll train your team overnight. Have a great day.<PHONE_NUMBER>. See you in the next video.


Hey, Mr. Cameron, this is Mark over at Good Doors. Uh, listen, we got the door done for the scene at the end of Titanic. I am a little concerned with the size, sir. You said it's only for one person. This door looks like it could fit three or four.  We can make adjustments. I'd appreciate it. Jim, I just saw the dailies for the end of Titanic. It's looking great, sir. Uh, quick note, could we get the door a little shorter? I'm concerned people are gonna think Kate Winslet's character is a total bitch, and that Leonardo DiCaprio could fit on that thing. James, we gotta do something about this door. It is driving me up a wall. You could land a jumbo jet on that thing. Hey, Jim, I got a joke for you. Knock, knock. Who's there? Leo cut. Leo cut who? Leo cut DiCaprio and fix the door. I fear people will only talk about this scene.


Hey everyone, welcome to alchemy stars. So we have here smooth mechanic Roy's or red diesel wrench We have here his skill preview for a five star. So he is a thunder I was actually thinking he was a fire element, but definitely thunder support class Kind of decent attack for support. So let's check out his Skills or active skill lightening resupply. So uses two supply points to choose one traversable tile From three surrounding clusters convert that tile into a yellow tile So it's kind of bit more of a hybrid a Converter some sorts and someone one mechanical be so one for the tile one for the mechanical be or Use one supply point to convert any one tile in the battlefield with a mechanical be on it Into a yellow tile. Okay supply points gain one point at the beginning of the battles Automatically as soon as we start he gains one and one point per round. So definitely he can He cannot spam this because Um Well, he can as long as there is a be ready. He can use one supply point for that one but more or less this is Generating every beginning of the battle and one per round if a mechanical be disappears from a yellow tile Gains another point up to seven points. So you can stack this and Actually just hold on to it Until you really need to place them. So you don't need to to what they call this This is similar to ami morris. Um mechanic wherein she can store Um, also her katanas. This one is a point This a supply point as well. So up to seven points for him Okay, so up to four mechanical beasts can exist in the battlefield at the same time Mechanical beasts disappear when they are touched by an enemy. Okay, so that's the He is a converter. He summons a b for his active skill and up to seven points Next is his chain combo. You have gyro blast at fourth chain deals 160 to three enemies with two surrounding clusters At eight chain deals 160 again to three enemies within three Surrounding clusters and at 12 chain deals 160 damage to all enemies within three surrounding clusters Okay, this is kind of useful, but also kind of limited but again, he's a support This is just additional or probably your supplementary damage for The aurorian m the last one is equipment skill honey healers if a mechanical b is within the area of effect of Roy's chain combo recover 40 percent of Roy's maximum health Sad to say it's not for the team, but only for himself Each mechanical b will ray within range increases the recovery factor by 10 percent Okay, um again, I just want to point out that the skill This should have been at least Not only himself, but partly some of the team members that he has because again Um This is kind of frustrating that you heal only Roy's max HP so He's kind of a part converter part damage dealer part healer for himself So well, he's five stars. So what what do you expect? But definitely Um, if I want to rate him he's gonna be at around between six to seven out of 10 His cut is his his his kit is actually average and no really synergy At this point with anybody but himself But he does have he does convert more. He can actually burst convert like for example If he if he stacks enough points, he can pick and choose conversions the mechanical b Um, that is actually what he is going to do for you. So he's kind of your supplementary converter with also the ability to do damage or decent damage for that matter Okay, so let's go to our new six star So we have azure's over finished with Roy azure most of you guys have been Waiting for her especially me. I need a detonator for water. Definitely gonna be summoning for her Not only is she is she good looking but I think her kit is good so water attribute detonator class and um kind of Kind of if I want to rate her her combat power This is kind of around a not a plus, but it's okay We can make do with that. So for her attack skill, I'm sorry active skill Cyrilian mirage. So cooldown is one preemptive strike So she can spam this Every turn definitely choose any traversable tile to project a Cyrilian image Which can be used to perform mirage strikes and mirage transformation. So mirage strikes Mirage Um, immediately immediately triggers a mirage strike that deals 2.5 damage if there is already a mirage on the selected tile. So again similar to a mimora skill She has to project a mirage before she can do a mirage strike. So first turn mirage second turn mirage strike Mirage strike deals 200 damage to enemies within 12 tiles in a diamond shape So nice damage for 200 range is increased to two surrounding clusters if the mirage is on a blue tile so definitely You have to place this one on a blue tile and to add to this one a mirage transformation converts the tile It's on to blue. So definitely the mirage will also convert the tile to blue Actually, this is a nice skill to have. So you have here tile conversion You also have here damage as well similar to roy But this one I like this more because this you can respam this every turn not not the damage, but you can place That place Explode place explode Also tile convert as well. So for her chain combo nitro storm Two chain deals 130 to 12 tiles in a diamond shape and Cyril mirage cost tier one Uh Chain combo once nine chain deals 165 damage to 16 tiles in a radial shape and Cyril mirage costs casts tier one combo Combo chain combo once what's the matter with me? Okay for 12 chain deals 175 damage to two surrounding clusters in Cyril Cyril and mirage casts Tier one chain combo once Cyril Cyril and Mirage is like a tongue twister Anyway, um, I think I think you need to you know, you need to have at least nine chain to maximize her damage up to 12 chain because um This is the usual average for damage for chain combo around 165 to 175 to 180 So for two chain, it's good to activate this but definitely go with nine and 12 and last is her equipment skill balsam accuracy Azur's attack is increased by 20 percent if so two surrounding clusters If within two surrounding clusters of a cirulia and mirage So both of them actually have um Have identical kits, but definitely azure is ahead of Roy because mainly of Uh, what do you call this? Bigger damage definitely Also tile conversion to blue and she can spam this every turn She has to actually For her to be more effective. So and she's also a detonator um chain chain combo Um, I think it's going to be good Especially with the cirulia mirage casts Uh eight here one combo chain combo once. Okay Again, sorry. So It casts a serial mirage serial mirage So additional mirages definitely I think Once she triggers her chain combo So there's a chance that she can detonate as because she can create additional mirages for your chain combo This is kind of good Another another way to clear mobs for this one And again increase attack by 20 percent if you're near serial mirage So definitely you have to trigger her chain combo You have to have her chain combo as frequently as possible It would help if she is a captain Because uh, even if it's not her own um tile color, she can still do a chain combo Well, I think this actually fits her kit really so definitely, um, I would you know, I would Like to rate her Definitely, I'm gonna rate her kit with a nine out of 10 as of the moment. I think she has promise in terms of um usability Um content and also aside from regal, um, if you need another I think we need I think blue needs another detonator which Which right now I think is more versatile than any other detonator that we have except for Some for example for kovacs. Um, he has um, he has teleport but for her I like her kit Because it you know, it it has a lot more mechanics anyway. So that is it. So, um My recommendation someone for azure for roy. Um, I'm not sure at this point for roy. Um, if you want his kit Definitely could you could summon um as as you remember my rating for him is around a 6 to 7 out of 10 Azure definitely a 9 probably in 8.5. So That is it guys. Um someone for azure Um for roy. It's really really up to you. So anyway guys, thank you very much for staying this far So hopefully this review and first impressions of the new units dropping soon Has helped you decide who you'll pull for but I'm sure you already decided to pull for azure So thank you guys for being here. Stay safe. Take care. This is the warden and I'm out of here


This study found that nursing students have a high level of knowledge and positive attitudes towards needle stick injuries, but a low level of practice. Female students and seniors scored higher on all needle stick injury domains than males and juniors. Those who had been injured more than three times in the past year reported lower levels of knowledge, attitude and practice compared to those who had experienced fewer injuries. To improve safety practices, it is important to raise awareness among nursing students and conduct continuing education related to sharp devices and safety.


Greetings and welcome to the Introduction to Astronomy. In this lecture, we will talk about ancient astronomy and that is astronomy of ancient time. So we will start off with some of the very earliest, even the prehistoric astronomy and what astronomy was used for at the time. Astronomy is really one of the oldest sciences and has been considered since people have looked up at the sky thousands and thousands and millions of years ago. So it is something that has been around for a long time, not a new science, but a very old one, in fact probably the oldest science. So let's start off here with the very ancient, what do we mean by it being an ancient science? So we see astronomy as an ancient science because it has been around forever, ever since people could look up at the sky. And why was it useful to these people? Well, for a number of reasons and one was that this was their calendar. Because as you recall, perhaps we use things like the motion of the sun to measure our day. We use the phases of the moon to measure our month. And we use the motions of the sun relative to the stars to measure our year. So our calendar is based on astronomical events. So they are used to be able to determine the calendar where we are in the year. And some of the other things, such as the Nile flooding, was actually predicted as well. It came at a certain time of year. But how to know when that was thousands of years ago? And one of the things the astronomers noted was that the rising of Sirius would correspond to about the time of the Nile flooding. So when Sirius was first visible, when they were first able to see that in the sky in that time of the year, that meant that the Nile flooding was not far off. And that was very important for agriculture in Egypt at that time because the Nile flooding would then bring water to the desert areas and actually give some water as a way for to be able to grow crops. The sky, ancient sky, was also used for navigation. And the Polynesians used that. One example is Polaris, the pole star, which happens to be located near the North Celestial Pole. Its position changes depending on where you are. The further north you go, the higher up it gets in the sky. The further south you go, the lower it gets in the sky. And that gives you a way to be able to determine your location. So navigation was something else that was very important and used for, used astronomy was used for. Now one of the very ancient monuments and one of the best known ones is probably Stonehenge. Stonehenge is the, in England and you see the great stone structures here that are pictured. That is the ancient monument from thousands of years ago and built over the course of thousands of years. There's actually more to the monument than just what is shown in the image here. Further out, there are holes that remain that were probably other wooden, earlier wooden monuments that have since decayed and gone. But we do see the remnants of even older structures. And what we see on the right hand side here are some of the alignments that we see. So the altar stone here, if you look out from that direction, out on what we call the main axis of it, if we look over the heel stone here, which would be out at this direction, on the first day of summer, the sun would rise over the heel stone. So if you were standing in the center of this monument, you would be able to watch the sun rise on over the heel stone only on the first day of summer. Any other day, it would rise further to the south of that and would not appear to rise directly over the stone only on that one day. Now, there are other alignments shown here. And one of the difficulties with Stonehenge and other monuments like this is that there is no manual. So we do not know how this was supposed to work. We don't know if all of these alignments were planned or if some of them are just coincidental that you happened to line it up to match for the summer solstice sunrise. And maybe some of these others just happened to work as well. But we don't have any instruction manuals for Stonehenge or any of the other great monuments scattered around the world. So there are monuments, not just similar monuments that have alignments with various astronomical events, not only in Europe, but in Australia, in the Americas, all over the world, we see various different monuments that show that probably these were used as a calendar early on and a way of being able to predict the time of year. So let's go a little further forward into the ancient Greek astronomy. So this is really the basis of what we use and this is, we're going to look here at some of the early astronomers and we'll talk about a few more of these in detail later on, but Eudoxus is one who gave us a very early model of the universe and it was what we call a geocentric universe, meaning that the Earth was at the center. He used nested spheres to explain the motions of the planets, so by having spheres, multiple spheres for each planet to be able to explain the various motions. So you would need a sphere to explain the rising in the setting of that object, of that planet, for example, but you'd also need to be able to have other spheres that would explain how it moved through the stars. So it would take multiple spheres to be able to explain that. Aristotle took and built on this, built in this geocentric universe and also knew that the Earth was round and there were a number of different proofs of this. One big astronomical one is the shadow of the Earth. How do we see the shadow of the Earth? Well, during a lunar eclipse, we can see the shadow of the Earth on the moon and it was noted that it was always circular. The only object that always casts a circular shadow, no matter how it is oriented, is a sphere. So they knew very early on that the Earth had to be spherical and in fact, Eritostanese actually measured the circumference of the Earth so they knew that it was spherical and not only that, but they were able to measure how big it was. Aristarchus was one early astronomer who suggested that the Sun might be the center of the universe. That would be a heliocentric universe. So a heliocentric universe would be another possibility. At the time this was discarded, how could the Earth possibly be moving? We would know that the Earth is moving and one of the things that was missing is that they could not detect parallax. Parallax is the apparent shifting of a nearby star relative to a more distant one and if the Earth were moving around the Sun, it should be something that was detected and the Greeks were unable to detect it so that meant that the Earth could not be moving. Of course, we now know that the parallax is just so small that it would not have been possible to measure it. Hipparchus will talk about in more detail. He gave us the magnitudes, measuring the brightness of stars and discovered procession and how the pole is moving over the course of time. And then Ptolemy kind of put everything together in his great work, the Almagest, which gave us a formal mathematical model explaining how the universe works and our understanding of it at the time. So let's look at some of these in more detail. First, we'll look at Aristotle. Aristotle gave us two things here. He gave us the concept of circular orbits and uniform speeds that everything in the heavens moves in a circular orbit. That's the perfect shape and everything moves at a uniform speed that there's no variations in speed. Everything in the heavens was perfect and that was very important there and really led to the basis of our understanding of planetary motion for over a thousand years. This was the basis of it. Now these are what we call postulates or assumptions. We did not know that they were true but they were assumed to be true because they made sense. We use postulates today and in fact Einstein did in his special theory of relativity saying that the speed of light in the vacuum is the maximum speed that anything can attain. So if that turns out not to be true, there's no proof of it other than that it has held up to experimentation over time but it is something that Einstein's theory was based on. If we ever find something that can travel faster than light that throws out Einstein's theory of relativity just like when we found that things did not follow circular orbits and did not follow uniform speeds, it threw out Aristotle's model of the universe but for over a thousand years this was our understanding of how things worked. Now we did not only do we know the earth was spherical but Eratosthenes actually measured the size of the universe. So Eratosthenes was able to do this by making some measurements and actually making note of the fact that at Syene in Egypt on the first day of summer that the well cast no shadow meaning that the sun was straight overhead. So that's this image right here. This object would actually cast no shadow. If you look down a well you'd be able to see straight down it because the sun is shining straight overhead. A little further north of this at Alexandria on the same day the sun was not quite overhead but was at an angle of seven degrees. So you'd have that slight angle shown here and the difference between those allowed him to determine the circumference of the earth. You could measure the linear distance between the two cities here and you knew this angle this was seven degrees. You know that the entire circle is 360 degrees and you can set up a ratio that you have now measured. You know that this is seven degrees out of 360. Well then this distance if you can measure that is the same proportion of the entire circumference of the earth and he got a very accurate measurement based on the numbers of the time. If our understanding of their units of measurement is correct they may have gotten this correct to within a few percent or so. So it could have gotten a very good measurement of the size of the earth thousands of years ago. Now one of the other astronomers we mentioned was Hipparchus. Hipparchus gave us a couple of things here. He told us about magnitudes. He developed the magnitude system that we use today and procession. First looking at magnitudes he divided the stars into six bins. This was based on their apparent brightness how bright they appeared in the sky and his first magnitude stars were the brightest. So that was the brightest groups those were stars of the first magnitude and then down to the sixth magnitude stars that were the faintest. That was just barely what you could see. That was barely what you could see with your naked eye those were just visible. Now that led us to the fact that magnitude system is backwards because as we've used it today a star with a magnitude 1.5 and a star with a magnitude 3.5 this is the brighter one and this is the fainter one. So there's a difference in that but the bigger number means a fainter star whereas the smaller number means a brighter star and that's the opposite of what we usually do in terms of measurements. But everything is still based on what Hipparchus gave us thousands of years ago. Now procession is another example and that is how the earth spins. The earth spins much like a top. If you've ever watched a top spin you notice that it spins very quickly on its axis just like the earth spins once a day on its axis but that the direction of that axis changes at a much slower rate. The earth axis does the same thing so where the North Pole is pointing in the star in the sky is changing over time. Right now it's pointing towards the direction of Polaris. Over time that changes and thousands of years from now, 2,000 years it'll be closer to another star here and thousands of years after that it'll be closer to other stars and there will be times when it is not close to any star. So a couple thousand years ago there was no star near the North Celestial Pole. The fact that we have one now is just a coincidence and this changes over a 26,000 year cycle. So Polaris is now near the star near the North Celestial Pole and it will be again in 26,000 years. In between that we'll take turns with other stars and times when there is no star near the North Celestial Pole. Now let's look a little bit about how this works. So here's kind of a diagram that shows how that pole changes over time. It's near Polaris right now but later on as this moves it will actually go around and we'll watch it here again in 12,000 years or so. Vega, an even brighter star will be somewhat close to the North Pole. Won't be near as close as Polaris is but it will actually be a very bright star near the North Celestial Pole. And that change will change consistently over time due to procession and that ends up changing the entire astronomical coordinate system over time. So how we measure where the positions of stars are is constantly changing because we measure them relative to the North Celestial Pole. Now this was all put together by Claudius Ptomey and what he did was give us really a formulation of the geocentric universe. So looking at things as a geocentric universe and some of the terminology that we use here is he gave us the epicycle, which epicycle is A in this image. So the epicycle is this small circle. The deferent is C, that's the orbit that the center of the epicycle takes and the equant is B. I'll come back to that in a minute. Let's first look at how this worked. The epicycle, here's the Earth, very close to the center and the center of the epicycle moved around the Earth and while it did that, the planet moved around on the epicycle. So the planet was actually orbiting empty space here and while it did that, this moved. Now this was important because this accounted for retrograde motion and this was important because the planets would appear to move backwards relative to the stars from time to time and we had to be able to make that prediction to be able to have our model explain why that happened and this was one way to explain how retrograde motion occurred. We'll later see with the heliocentric universe that there was another simpler way to be able to explain this. However, in this case, it does explain retrograde motion and Ptolemy was able to make predictions of the positions of planets that were about as accurate as the observations of the time. So very relatively accurate and worked for the predictions and was able to give us pretty good predictions of how things worked. So the epicycle, this part, the deference, the big circle here, the equant is actually point B here and that is directly opposite the central object. So the center of the universe is actually here offset from the Earth a little bit and the equant is the point on the other side. So the object, not actually going around the center of everything or around the Earth, but actually around the equant, a pretty nice on the opposite side of the center from the Earth. And that accounted for things getting a little bit closer to and a little bit further from the Earth and changes in their apparent speed. So it was able to account for some of the observations that occurred. And as I said, this lasted for a thousand years, well over a thousand years as our way of explaining how the universe moved, how objects moved within the universe. Now, what happened after Ptolemy? Well, we had the fall of the Roman Empire and that led to a decline in Western science. The great library at Alexandria was burned and a lot of the information that was lost, a lot of the information from some of the astronomers that we talked about ended up being lost. So there's probably a lot more that they knew and that they did that simply has not been recorded. However, not everything was lost at that time. Much of the work was advanced through Indian and Arab astronomers who had copies of some of these works and continued to build on them. So they translated them and then refined these Greek works and developed the mathematics, especially of algebra that was needed to be able to do these calculations. The Greeks did everything with geometry. So they built everything geometrically. Algebra was then needed to be able to do some of the calculations to explain these motions. So their refined works then eventually ended up returning to Europe at the time of the Renaissance and then were continued and expanded and we'll see eventually led us with more accurate observations to a heliocentric universe that we have today that the sun is at the center of the solar system and not the earth. So let's summarize what we've looked at in this lecture and we started off, we talked about how this guy was important for timekeeping and navigational purposes, being able to know what time of year it was and how to be able to travel was very important and the stars were an important way to do that. We used Stonehenge that we talked about and other ancient monuments that were used for the timekeeping process to be able to tell us when summer was starting or when winter was starting. We knew when those seasons were. We looked at the Greek astronomers and kind of went through how they developed a geocentric model of the universe that lasted for over a thousand years and during the Middle Ages, not much was going on in Europe but Indian and Arab astronomers preserved and improved upon this work that later returned to Europe and helped lead to the Renaissance and our updated understanding of the universe. So that concludes this lecture on ancient astronomy. We'll be backing in next time to discuss another aspect of astronomy. So until then, have a great day everyone and I will see you in class.


Tease Australia, major multi-site renewable energy development and wastewater upgrade. Tease Australia, the country's second largest red meat processor, is working to dramatically reduce its carbon footprint with two new state-of-the-art wastewater treatment systems. The company's beanlea and rockhampton facilities upgrades will reduce annual carbon dioxide emissions by 72,000 tons. That's equal to taking 24,000 cars of Queensland roads each year. These wastewater systems will deliver a combined reduction in natural gas and coal that is equal to the natural gas used by about 900 Australian homes each year.


arms and legs are our appendages. So the arm and the leg, these are appendages. So the bones that make up these appendages is called appendicular skeleton. So all of these bones, the arms, the legs and the bones that connect them with the rest of the skeleton is called the appendicular skeleton. So in this video that's what we are going to look at. You and I together we will explore how the different bones make up the appendicular skeleton and what they are called. So these are the arm bones and these are the leg bones and there are quite a few parallels between these two. So that's why I've kept them side by side and we will make comparisons as we go along.  You might remember from our previous video that the axial skeleton consists of all the bones that is close to the long axis of our body. So these bones include the rib cage, the vertebrae, the skull etc. So this part here it's called the pectoral girdle. So this is the pectoral girdle. The pectoral girdle consists of two bones. This one, the long one right here it's the collar bone and the scientific name for it is the clavicle. And the triangular bone over here this is present on the back on the dorsal side and is called the scapula. The English term for it, the common English term for it is the shoulder blade. The parallel of the pectoral girdle for the leg is the pelvic girdle. So this right here is the pelvic girdle. The word pelvic refers to a basin. It originally means a basin. So the pelvic girdle on both sides the right and the left they form a basin like hollow space inside our body and hence the name pelvic. Whereas pectoral means chest and this is very close to the chest hence the name. So just as the pectoral girdle connects the arm with the axial skeleton similarly the pelvic girdle connects the leg with the axial skeleton. And what is the bone that the pelvic girdle is made of? It's called the hip bone or the coxial bone. The hip bone is made up of three bones which are fused from the hip bone. We will see shortly the more details of that. Now let's come to the arm. So this is the bone of the upper arm and is called the humerus and similar to that our leg has the femur. So that's the thigh bone. Then in the forearm we have these two bones radius and ulna. So this is radius and this is ulna. Now you can ask me how can you tell between radius and ulna? So remember the radius bone always is on the side where the thumb is whereas ulna is on the opposite side. Similar to radius and ulna the portion below the knee has two bones so this is tibia and this is the fibula. Again the same question how do you know which is the tibia and which is the fibula? So I remember when I was in 11th grade my teacher told me that the bone that looks more feeble so this is thin and feeble compared to this bone. That feeble bone is fibula. Now there is an extra bone over here in the leg which is not there in the arm which is this rounded bone over here and it's the kneecap called the patella. There is no such bone in the arm. Now let's come to the hand and the foot. Again the bones that are there are very similar so the bones that are there in the wrist are called carpals and there are eight of them and the bones that are there in the heel they are called tarsals. Sound very similar carpals and tarsals. Tarsals are seven though one less than the carpals. Then the palm. The palm is made up of these bones which are the metacarpals. So the bones right next to the carpals are the metacarpals and there are five of them five four for each finger and then one for the thumb so five metacarpals and then corresponding to metacarpals we have metatarsals in the foot so metatarsals again there are five of them so in the hand after the palm we have the fingers right. So the fingers are made up of these little bones called phalanges so each of these bones are phalanges. How many of them are there? So each finger has three phalanges and the thumb has two phalanges so four fingers times three twelve plus two fourteen so there are fourteen phalanges and the corresponding bones in the foot are called the same phalanges again and once again there are fourteen of them. So these were all the bones in the arms and the legs. Now let's look more closely at the pectoral girdle and the pelvic girdle. So first the pectoral girdle so this is the collar bone or the capicle so this is the collar bone and the collar bone is connected to the scapula the triangular bone and this part of the scapula is the one that connects through a joint to the collar bone as you can see and this is called the acromion. Then you see this curved edge of the scapula this is called the glenoid cavity. This is where the end of the humerus the upper arm bone fits. Now let's move on to the pelvic girdle the details of it. So as I told you earlier the pelvic girdle has only one bone on each side so this whole bone this is called the hip bone or the coxal bone. The hip bone originally had three bones which got fused it has three parts to it which are actually fused to each other so this part here this is called the ilium then this part here the second part is the ischium and the smallest one right here at the end is the pubis. The two hip bones on either side they join over here through a cartilage and this cartilage is called pubic symphysis. Just like the glenoid cavity in the pectoral girdle there is a depression in the pelvic girdle into which the head of the femur fits. So this depression is called the acetabulum. To summarize the appendicular skeleton consists of the arm bones the leg bones the pectoral girdle and the pelvic girdle. The pectoral girdle has the collar bone or the clavicle the scapula then the scapula has this part called the acromion which connects to the collar bone. There is this glenoid cavity at the end of the scapula which connects to the top of the humerus this is the humerus the upper arm bone then there is the radius on the forearm on the side of the thumb the ulna the other bone on the forearm then the wrist bones are the carpals the palm bones are the metacarpals the finger bones are the phalanges then in the pelvic girdle we have the hip bone and two hip bones are joined by the pubic symphysis then in the leg we have the femur the thigh bone the kneecap the patella the tibia the stronger bone in the lower leg and fibula the weaker bone then the ankle has tarsals the sole has metatarsals and the fingers of the feet have phalanges


Impartation has the power to accelerate your spiritual growth and to help lay a foundation for the future of your ministry. Impartation is the spiritual transfer that takes place through relationship. When I open myself to the teachings of or relationship with an anointed individual, I become a recipient of impartation.  So here are the three kinds of biblical impartation and how to experience them in fullness. Number one, given impartation. Number two, shared impartation. Number three, received impartation. Given impartation is when I reach down. Shared impartation is when I reach across. Received impartation is when I reach up. Given impartation takes place when I act as a mentor. Shared impartation takes place when I act as a fellow laborer or friend. Received impartation takes place when I act as a student. Number one, given impartation. You may think yourself too spiritually undeveloped to teach anybody anything about the Lord or spiritual truths, but this is simply not the case. For example, let's take the new convert. Now, the new convert typically knows little to nothing about what the Bible says about various truths and life applications. However, even the new convert can share their testimony. In sharing their testimony with a non-believer, the new convert is sharing the gospel. And in sharing the gospel, the new convert is evangelizing. Therefore, go and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit. Teach these new disciples to obey all the commands I have given you and be sure of this. I am with you always even to the end of the age. That's Matthew chapter 28 verses 19 and 20. Evangelism fundamentally is a form of impartation. So no matter where you are in your spiritual growth, there's something that you can impart to someone who is coming along the path after you. Number two, shared impartation. The scripture tells us that iron sharpens iron that's in Proverbs chapter 27 verse 17. It also tells us that bad company corrupts good character. That's 1 Corinthians chapter 15 verse 33. Impartation doesn't just take place between a mentor and a disciple. It can occur between two spiritual peers.  Number three, received impartation. Now it's important to note that all power comes from the Holy Spirit within you and that power works in proportion to your time spent in fellowship with the Holy Spirit. The more time you spend in the presence of the Holy Spirit, the greater the manifestation of power on your life. But God has given to us gifts in the form of anointed individuals. For example, this is what the word says in Ephesians chapter four. Now these are the gifts Christ gave to the church. The apostles, the prophets, the evangelists and the pastors and teachers, their responsibility is to equip God's people to do his work and build up the church, the body of Christ. Ephesians chapter four verses 11 and 12. Well, receiving from anointed men and women of God, it's important to keep this in mind. There is a big difference between impartation and imitation. You're not the next anyone. You're the first you. In fact, impartation makes you a unique expression of God's power. As you glean from various servants of the Lord, you become a unique and uncommon blend of the anointing. Impartation doesn't just help to make you unique. It also accelerates your spiritual growth as you learn by the spirit from those with decades of experience. Growth from impartation should be a reality experienced by every single believer. I'm David Diga Hernandez and that is your Moment of Truth. Thank you for watching Encounter TV. Don't forget to subscribe and click the notification bell. Also, help us spread the gospel of Jesus Christ in the power of the Holy Spirit. Make a one-time donation or become a monthly supporter by clicking on the donate link now.


The Cube at EMC World 2014 is brought to you by EMC. Redefine, VCE, innovating the world's first converged infrastructure solution for private cloud computing. Brocade, say goodbye to the status quo and hello to Brocade. Hey, welcome back everyone. We're here for the wrap up for day two on the Cube, our flagship program. SiliconANGLE and MugiBond, we go out to the event and track the signal from the noise. I'm John with Dave, Dave here for the wrap up. Got Dave, long day, how you feeling? We got a hold on the day tomorrow. I just want to say that today was a fun day because yesterday was very high energy. Today, high energy again. Pat Gelsinger giving the keynote. Big fan of Pat Gelsinger. He's really spends the time to come on the Cube. We had two other Cube alumni come on that are very notable and we've gotten to know over the past four years. Now going on our fifth season, Jeremy Burton and David Goulden. And we've had other folks come on. We just had the advanced software division. We're getting to know the groups, Dave. So I mean, it's exciting for me personally to get to know these tech athletes, these tech musicians, if you want to call it, whatever analogy you want to use, get to know them because they are serious players and EMC is under a lot of pressure. I mean, they've transformed their business. You know, Tutsi at the top, we've talked about the Federation. They've now branched out. They are executing this Federation strategy which is, in essence, a holding company across multiple portfolio of companies and products and executing well. And it's fun to get to know them and hear their insights. And what I've learned is, the master plan is coming together, Dave. Now, you could argue how much is coming from M&A and pure organic innovation. We'll see. I don't think the meat is on the bone on the R&D at that point, at this point. I think more M&A has certainly led the field in terms of activity. I want to get your take on that, specifically around the excitement around the, quote, third platform, the bridge to the third platform, execution of the Federation, and do they have organic R&D? Is there meat on the bone? Well, so let's take the third platform first. I mean, it's sort of a, to me, the third platform is kind of a euphemism for all new stuff. You know, I'm not really sure what the third platform is. I mean, I think it's, you know, IDC's defined it, but I don't really, I don't know when I see it. But I do think that there's a convergence of obviously cloud, big data, mobile, social. And I'm not sure the industry knows what that third platform looks like yet. I think they're trying to figure it out. I think it's a combination of, we have glimpses of what Amazon is doing in the public cloud. You talk a lot about DevOps. We spent a lot of time in Hadoop. Those worlds are slowly coming together. So anyway, let's assume that is, okay, the third platform. The big challenge for EMC is obviously, we had Jeffrey Moran last week at Service Now Knowledge. How do they cross the chasm? And the formula that they've chosen to cross the chasm is I think very innovative. They've selected this federation model. So you got Pivotal, which is, I guess a couple hundred million now because they've moved some assets out of there, growing at 40% per year. Has to grow faster, by the way. You got Amazon at three billion, growing at 60 to 70% a year. Not that Amazon and Pivotal are directly comparable, but they are in the sense that Amazon is the new, Pivotal is supposed to represent the new. You got VMware now, $5 billion software company, growing at 15 to 20% a year. That's a nice business with a lot of legs. But you see people trying to nip at their heels, whether it's Amazon, whether it's OpenStack, et cetera. HP, even, with its cloud. And then you've got EMC Classic, which is basically flat, right? The install base, you mean? No, the revenues are flat. And now, some of that was math, we heard from David Goulden, but the naysayers are going to point to that and say, aha, now it was, I called it accounting. I thought it was the way in which they accounted. He said it's math in terms of the way in which they deal with end of quarter builds. But nonetheless, they are on track to throw off $5.8 billion in cash, free cash flow this year.  It gives you options to pay down debt. It gives you options to pay dividends, which EMC just increases dividends by 15%, keeping shareholders happy. When its stock is up, it has more flexibility to do things. It finance things like AirWatch. So the federation model, to me, is a really savvy way for Tucci and company to navigate through this turmoil.  And this is their angle on not getting disrupted. And you see the making investments. And yeah, I've always said, John, EMC is one of those companies that will always survive, they'll always find a way to win. They'll always gain share. They just, it's in their culture. I think to me, Dave, the big thing is Viper 2.0 has legs. It looks like it's going to have some meat there. I like that direction. I think that's a good bet. I honestly, last year, I thought it was great slideware. I think they didn't have much there. Clearly, they shipped. We heard Goulden pretty proud of that. Being a product manager on Nile, that was a good inside base. Well, we kid in fun, but apparently that's true. Supported by the Advanced Software Division president. I like what Viper's doing with OpenStack. I think EMC could actually be a bigger player in OpenStack than I thought. Certainly, I think the Cloud Foundry is a lot of hype right now. I think Cloud Foundry is a strategic asset, as Jeremy Burton pointed out. But I just see that as a lot of Barney action going on. I love you. A lot of deals getting done by Paul Moritz. I think Paul Moritz is going out and doing the deal, sitting down with people saying, I'm Paul Moritz, you're going to do a deal with us. And kind of making people feel good about it. But ultimately, that's good news for them, but they have to execute on that. They still have no community. That has to get stitched together. And they're basically betting out, the bet in the farm, that the methodology of the open source approach will work. Will an open governance model work? That's still unproven, right? So with Red Hat coming into the ring, other forces, that is not a sure thing. So I think the federations can certainly help that. So Cloud Foundry has a wind at their back with the federation support of Cloud Foundry. Yeah, so, you know, Viper's interesting. I mean, I still got a lot of questions about it. I think it looks good. I think it's solving a problem for EMC customers and that EMC customers have all these disparate systems and they need a way to bring them together and Viper does that. What I don't understand is whether or not, the world wants an open source object store. Viper's not that. And Viper, we heard from Jeremy, probably won't be that. EMC's going to keep that. They're going to have a, be able to get right to the API, but they're not going to open source it. So that's going to be kind of interesting. To me, open source is the wild card for this company, John. I think open source is a mega trend and I think EMC, VMware, they're dipping their toe in the water. They're not leading open stack by any means. I can't see any substantive contributions of ongoing development resources. They could provide, we heard some of the key things from the Advanced Software Division, separating this application from the hardware. If EMC can be a nice little lightweight glue layer, Dave, between rapid growing cloud development frameworks, whether it's agile development and or some data fabric layer, like what Pivotal's approaching, EMC could basically jury lock the whole thing. So that's Pivotal, right? I mean, that's what Pivotal's trying to do, but Pivotal and other people, the EMC could be independent and basically jury rig the whole thing for themselves to win the whole game. So again, to me, open source is the wild card for companies like EMC. I would say open source is a wild card for Amazon, too. It's a potential blind spot and it's disrupted so many industries. I mean, it essentially neutralized Microsoft Monopoly. We've seen the ascendancy of Red Hat. Now there aren't a lot of open source software companies, but open source as a phenomenon can create some incredible innovation. I think the moves that Red Hat is making in storage are very interesting, so those are things to watch. So we had the Vatican library on today that was exciting to hear that little Italiano, little accent there. We had Guy Church, who had always dynamic, Amitabh just recently on software. I mean, literally the stuff we talked about last year was what we talked about, what was on the keynote this week. David Goulden was superb, other notable guests we had, a lot of the Brocade guys on. You know, Brocade is one of those stories that a couple of years ago, people were like, oh, Brocade, you know, I'm going to go on there, I'm going to upload, actually the investments that they made back then, Clayco and company really made good calls and the wind was at their back now and they had a good spot around software to find networking, et cetera. And tomorrow, another blockbuster schedule. I mean, we're wall to wall. Tomorrow, we're setting a record here, the most CUBE interviews we've ever done at an event. I think we're going to be over 70. Brian Gallagher's coming on tomorrow. Brian Gallagher, John, he is a great perspective on the future. You know, here's his business, everybody's all under fire, everybody says it's dying, but you'll see tomorrow, he is so confident and has such a great perspective on the future. Stella Lowe is coming on, she's the new head of Com, she's the one who's organized all the AR and PR stuff. Jason Mendenhall from Switch is coming on, based in Vegas. Switch is a really interesting company and Jason is a guy who can really talk to how organizations like EMC are going to compete in VMware with the public cloud. Jonathan Martin's coming on, we're going to ask them to play the guitar, I hope. And of course, Howard Elias is coming on, the head of EMC Global Services, big time exec at EMC. So really excited about being here with you, John. Stay with us tomorrow, wall to wall day three here at Live in Las Vegas. This is the CUBE, we're out for day two, we'll see you tomorrow.


All right, thank you for the introduction. Hi everyone, welcome to the last talk of the conference. And thanks for sticking around. My name is Mohamed Hajjiobadi, and I want to tell you about a joint piece of work with Sanjom Gart on a construction of chapter function from the competition of the Fee-Holman assumption. OK, so chapter functions, you have heard about them probably a lot during this conference.  They were first introduced in a landmark paper by Defi and Helman in 1976, which developed the foundations of what we now call public crypto. So another fundamental primitive in cryptography is a public encryption that was first designed in the famous RSA paper in 1970s. And they were later rigorously defined by Goldwasser and Mickley in 1982. So in order for me to set up the stage and notation for this talk, let me quickly go over these two notions. I'm sure that all of you are familiar with, but just to set up the notation. Public encryption, as you all know, is given by three algorithms, G, E, and D, the key generation, the encryption, and the decryption algorithm, where the key generation algorithm gives us a public key and secret key. And you can use the encryption algorithm to encrypt a plaintake message M to a public key Pk using some randomness R to get a ciphertext C. And you can use the decryption algorithm to decrypt the ciphertext if you have the right secret key. In terms of security, we have the basic notion of semantic security, which says that encryptions of any tool on plaintext should be computationally indistinguishable. Now, trapdoor functions are defined exactly like public encryption, with the only difference that the encryption algorithm that we now call the evaluation algorithm does not take as input any randomness. So this means that the decryption algorithm that we now call the inversion algorithm can recover the entire input to the trapdoor function evaluation algorithm. And since we make use of no randomness, we cannot achieve semantic security, but we should settle for something weaker. In particular, the one-ray notion says that a randomly chosen function from the family should be one-ray. OK, so as I mentioned earlier, a main distinctive feature of trapdoor functions is that no randomness is used in the evaluation algorithm. In terms of the relationship between these two notions, we know by classical results that trapdoor functions imply the existence of public encryption. As for the other direction, we know that it's impossible with respect to black box reductions. So in particular, what this impossibility result says is that techniques that generically give us public encryption may not be sufficient for trapdoor functions if we are working with black box reductions, which are most of the techniques in crypto. So I want you to remember this point because I want to come back to it later. All right. So you might ask that we have public encryption. It's pretty useful. Why do we care about trapdoor functions? Are they a theoretical object that people want to build out of curiosity? Or do we have any applications of this notion? So let me motivate this notion a little bit. Suppose we have a trapdoor function. And imagine we have two users, Alice and Bob, where Alice has two index keys, IK1 and IK2. And suppose that Bob has both these keys plus a trapdoor key for IK1. What is happening is that Alice is sending two image points Y1 and Y2 to Bob, which were made with respect to index keys IK1 and IK2. And she wants to convince Bob that these two image points correspond to the same inputs. So the question is how Alice can do this. Does she need to provide some kind of proof for Bob in order for Bob to check for this? Or can Bob do it by himself? So it turns out since we deal with trapdoor functions, which make use of no randomness, this is easy for Bob to check himself. Namely, Bob can make use of his knowledge of TK1 to recover X1. And then he can check whether F of IK2 comma X1 gives us Y2 or not. This is not a toy example. In fact, this is the main reason behind the success of building CCA to secure public encryption schemes in a black box way from various forms of trapdoor functions. In contrast, when you think about the same situation, but when we use public encryption, this is difficult to do. Because in general, it is difficult to check whether two ciphertexts are encrypting the same plaintext. You need non-interactive zero-knowledge tools to do this. And when you use NISC in a protocol, the protocol will be non-black box and will not be efficient. So this is one important property of trapdoor functions. So far, we knew how to build trapdoor functions from a very small set of assumptions, which are limited to factoring DDH and LWE. And in fact, there's a very big gap from the set of assumptions that give us public encryption. In our work, we showed how to build TDFs from the computational Diffy-Hillman assumption. And this question has been open for more than 30 years. OK, so let me review the notion of CDH and the related notion of DDH. Both these assumptions are defined with respect to a group G. The CDH assumption says that from G, G to the x, and G to the y, it is hard to compute G to the power of x times y, where G is the random generator of the group, and x and y are random exponents. And the DDH assumption says that the joint distribution of G to the x, G to the y, and G to the x times y is pseudo-random. OK, so you might ask that, why do we care about building TDFs from the computational Diffy-Hillman assumption? The answer is very simple, because CDH is a weaker and more trustable assumption. In fact, we have examples of groups which are plausibly CDH hard, but are provably not DDH hard. OK, so let me tell you a little bit about the challenges that one would face when wanting to build chapter functions from Diffy-Hillman related assumptions. In general, this is not a trivial task, and the short answer for this is that all these Diffy-Hillman related assumptions rely on the discrete log problem, and we don't have a generic chapter for the discrete log function. So to see how this makes things more difficult, let's try to solve an easier problem. Let's try to build a chapter function from DDH. So from DDH, we know how to build public encryption, so let's try to d-randomize L-Gamal encryption, which is a CPH secure public encryption based on DDH. So remember that L-Gamal works as follows. The secret key is a random exponent alpha, and the public key is g to the alpha, where g is a generator. And if you want to encrypt a group element m, you raise g to the power of r, and you also raise the public key to the power of r and multiply it with m. Now you can see that if you have the secret key alpha, you can easily recover m, which is the plaintext, but you cannot recover r. And we cannot recover r is not because we are not smart enough to recover r. We have a very good reason that why we cannot recover r? Why we cannot recover r? Because recovering r is as hard as solving the discrete log problem. So the take-home message that I want you to take from this slide is that if you want to design a trapdoor function based on Diffie-Hulman related assumptions, you should not perform exponentiations in the evaluation algorithm. Because for the exponentiation function, we don't know a trapdoor. So with this intuition in mind, let's let me review how the previous work managed to build a trapdoor function from the DDF assumption. So this was first built by Piper and Waters, and it was simplified by some other paper. I just realized that they don't have the most updated version of my slides. OK. So the trapdoor function works as follow. The injective key of the TDF is g to the m, where m is the random invertible matrix of exponents. And the g to the m means g to the first element, g to the second element, and so on. And the trapdoor key is m inverse. Now we can see that for the evaluation algorithm, if you have g to the m and if you have an input x, which is given to you as a row vector, you can perform linear algebra in the exponent to compute g to the power of m times x transpose. Now if you have the trapdoor key, which is m inverse from the image input y, you can very easily compute x bit by bit, where the is bit is given at g to the xi. So when we want to prove that this trapdoor function is one way, we need to rely on this rank indistinguishability property, which is implied by DDH, which says that the distribution of g to the m is computationally indistinguishable from g to the m prime, where m is a random invertible matrix, and m prime is a low rank random matrix. This property can be proved based on DDH, but it cannot be proved based on CDH. The main reason is that when you want to prove this property one way or another, we should reason about a homomorphic property of the underlying hardcore function. And we don't have such a property based on CDH. So we do not really have any techniques that give us trapdoor functions based on CDH. So this is what we do in our work. We give the first construction of trapdoor functions from the computational Diffie-Hillman assumption. Our methodology in a very high level involves de-randomizing a specific class of public encryption schemes. So what I'm going to do is that I will first tell you what this notion is, which is the class of public encryption schemes that we de-randomize. We call it recyclable targeted key encapsulation schemes. We actually called it something else in the paper. I'm calling it this way in the stock. This notion combines properties from some previous work, from a piece of work of Sanjom and Deutling last year and from a paper of Bilor Adol from 2003. So I will tell you what this notion is. And then I will show you how we can build trapdoor functions from this notion. And I will refer you to the paper on how we can build this notion from CDH. OK. So let me tell you what recyclable targeted Kim is. So it's a kind of key encapsulation mechanism enhanced with some properties. So let's review the notion of Kim. A Kim scheme is defined exactly like a public encryption scheme with the only difference that the encapsulation algorithm does not take as input any plain text message m. It takes as input a public key pk and some random sr. And it gives us a cypher txc, which is encapsulating in some sense a key e. So it is encapsulating in the sense that if you have the right secret key, you can derive the value of e from c. So in my talk, I'm always going to assume that e is the single bits. So this is the notion of Kim. Now let me tell you what these two properties mean. Let's start with the targeting property. What it says is that the input to the encapsulation algorithm contains two new values, a target index i and a target bit b. So the output is the same as before. It's a cypher tx and a key value e. Now what is going to happen is that in order for you to be able to decrypt, not only should you come up with the valid secret key for pk, but that secret key should have the property that its ith bit is b. So i and b were specified in the encapsulation phase. So you might ask that, what will happen if I have a secret key that is valid relative to pk, but its ith bit is not b? This brings me to the security notion that even if you have the secret key, but if you are given an inconsistently formed cypher txc t, you cannot distinguish the true value of e from a totally random bit. OK. Now the recyclability property in a very high level says that the cypher txc output part of the encapsulation algorithm does not depend on the given public key. It only depends on a public parameter, which is the same across all public keys. Now you can see that I have specified the outputs of e as e1 and e2, and I didn't put pk as an input to e1 because e1 is independent of pk. OK. So these are the two properties, and this concludes the notion of recyclable targeted chem. Now, this picture summarizes the two properties that I just told you about. Whenever we want to build a chapter function from any assumption, one way or another, we should show two different deterministic ways of reaching the same output. OK. The way that this is enabled in our study is that you can drive the value of e in two different ways, either by applying the algorithm e2 to a public key pk and a randomness value r, or by applying the algorithm d to a cypher txc, which uses that randomness value r, and with secret key, which is consistent with this cypher text. So with this intuition in mind, let me give you a version of our chapter function, of our chapter functions, which allows us to recover the first bit of the input. All right. So what we are going to do is that the index key of my chapter function consists of two chem cypher texts, and the chapter key contains the underlying randomness values. The input to the chapter function is the secret key sk of the chem scheme. And what we are going to do is that we are going to first compute the corresponding public key. And then, depending on the value of the first bits of sk, I'm going to apply the algorithm d to either ct1 or ct prime 1. Remember that I told you that we can apply the algorithm d to a cypher text, which is consistent with the secret key. The part that I've marked with orange comes from the property that I told you in the previous slide. Now, if you want to invert, you have all the randomness values. You can form both these e2 values, and you can check for a match. So this allows us to recover the first bits of sk with probability 1 half. But this is not a problem because you can repeat this process in parallel to amplify correctness. So this is not a problem, but we have a problem. When we want to prove security, we will not be able to prove security. The main reason is that the security property of the chem that I told you about does not guarantee that we can hide the value of the target bits b. This is the main challenge that we'll have. The fix that we give to this problem is very easy. And that is based on this idea that we put a random bit in the input of the trapdoor function. And that random bit is going to be placed in the output in the place where we cannot apply the algorithm D. Now, in a little bit more detail, in a much more detail. So the key generation algorithm is exactly like before. Now, the only difference is that in the evaluation algorithm, I have a new bit b1. And the way that I'm going to form the output is that I will apply the algorithm D to one of the two ciphertexts. I can apply it to only one ciphertext. And for the position that I cannot apply D, I will put the bit b1, which is coming from the input. This magically solves the problem. And if you want to know how it solves the problem, I will refer you to the paper. OK, so I gave you a construction that allows us to recover the first bits of the input. You can do the same idea to recover all the bits of the inputs in a secure manner. So let me conclude. We gave a construction of trapdoor functions from the computational Diffie-Hillman assumption. As a couple of open problems, we would like to know whether we can build more advanced forms of TDFs from the CDH assumption, like lossy trapdoor functions. And as a second open problem, which I think is very interesting, it is whether we can build or separate trapdoor permutations from a CDH or DDH. Thank you very much.