All right, keep your place there in Exodus 32. Keep your place there in Exodus 32. Before we start the sermon today, I want to have a safety moment because of what's been going on in the world lately, especially in the news with the Komodo virus going on. I just want to let you know that there's going to be some changes around here for me personally anyway. I won't be shaking any hands today. I just want to let you know. And as a matter of fact, I would like it if everyone could keep like a five foot radius away from me. I've instructed the ushers that if anyone gets near me to just sacrifice themselves and keep people away from me. I mean, look, stop. This is serious. I'm the one that does the preaching here.  So you hear that? I'm the one that does the preaching here. If I go down, it's bad. OK? So look, that's the rule. So don't be offended. I'm telling you these things so you may not be offended. Second of all, if anyone coughs or sneezes, we're just going to have to drag you out of here. Just like that guy a couple of weeks ago, we're going to have to just drag you out of here. So just don't be offended. It's for the safety of everybody. All right. So I'm just kidding, of course. But this morning, we're going to preach on pestilence. I want to tell you, let's get some perspective on pestilence this morning and see if the Bible actually has anything to say about it. And maybe we can get some clarity on what's going on around us. So you see in Exodus 32, the Bible actually talks a lot about pestilence. It talks a lot about pestilence. So let's get a biblical perspective on what could possibly be going on in our world today, because the Bible applies to every day and age and to every person that's ever lived. So pestilence. Pestilence in the Bible. We see here in Exodus 32, this plague, this pestilence came upon the people. If you look at the last verse of Exodus 32, the Bible says, and the Lord plagued the people because they made the calf which Aaron made. If you go back to verse number 26, let's just reread a section of this story and kind of get, I want to show you a trend in the Bible. I want to show you a few examples in the Bible of pestilence and of plagues in the Bible. And let's see if we can recognize a pattern or why these things happen or what's going on and how we should react to it. Okay, so that's the whole point of the sermon this morning is so we can look at what's going on in our world and we can know how we should react to what's going on. All right, look at Exodus 32 in verse number 26, where the Bible says, then Moses stood in the gate of the camp and said, who is on the Lord's side? Let him come unto me. And all the sons of Levi gathered themselves together unto him and he said unto them, thus saith the Lord God of Israel, put every man his sword by his side and go in and out from the gate to gate, from gate to gate throughout the camp and slay every man his brother and every man his companion and every man his neighbor. So of course, Moses was up on the mountain getting the law from God and God told him, hey, go down there because the people have gone, you know, they've gone crazy. They're doing, they're sinning, right? Verse number 28, and the children of Levi did according to the word of Moses and their fellow the people that day about 3,000 men. So we see that people died from the sword because of this sin, that was a judgment. Verse number 29, for Moses had said, consecrate yourselves today to the Lord, every man upon his son and upon his brother that he may bestow upon you a blessing this day. And it came to pass on the moral that Moses said unto the people, ye have sinned a great sin and now I will go up to the Lord, pair adventure, I shall make an atonement for your sin. And Moses returned unto the Lord and said, oh, this people have sinned a great sin and have made them gods of gold. Now don't miss verse number 32. Moses says, yet now, if thou wilt forgive their sin, and if not, blot me, I pray thee, out of thy book which thou hast written. And the Lord said unto Moses, whosoever hath sinned against me, him will I blot out of my book. Therefore now go, lead the people unto the place which I have spoken unto thee, behold, my angel shall go before thee, nevertheless in the day when I visit, I will visit their sin upon them. And the Lord plagued the people. So the Lord sent, not only did 3,000 men die of the sword, that God also sent to plague upon the children of Israel because of this sin. All right, if you go back, there's two interesting points that I wanna point out here. First of all, we see in this plague, we see that it was God's judgment, this plague upon Israel. But one thing that we see here is that we see the man of God here in Exodus chapter 32. And the second point I wanna show you is that we see that the man of God is advocating for the people. Throughout the whole chapter of Exodus 32, if you go back to verse 11, right at the beginning before Moses even comes down from the mountain, it says in verse 11, it says, and Moses be soft the Lord his God, and said, Lord, why does thou wax hot against thy people? He's already advocating for them. Moses was a great advocate in the Bible. He said, okay, that's Moses. Let's look at another example. Let's look at another example of the children of Israel. So we see the man of God turned to Numbers 25. We see that there's a man of God amongst the plague. And we see that what is that man of God doing? He is advocating for the people. He is advocating for the people. Go to Numbers 25. We'll see another example with the children of Israel. Numbers 25. Numbers 25, look at verse number one. And Israel abode in Shittim and the people began to commit Hortom with the daughters of Moab. So here the people were intermingling and they were committing fornication with the people of these heathen lands that they were going into and they called the people onto the sacrifices of their gods and the people did eat and bowed down to their gods. And once again, whenever God told you not to mix with the heathen people, it's always because he knew that they would adopt their religion and start worshiping false gods. It's no different here. In verse number three. And Israel joined himself unto Baal Pior and the anger of the Lord was kindled against Israel. Skip down to verse number eight for sake of time. And he went after the man of Israel into the tent and thrust both of them through. This was Phineas, okay? The man of Israel, the woman through her belly, so the plague was stayed from the children of Israel. And those that died in the plague were 24,000. So God sent a plague against this and the Lord spoke unto Moses saying, Phineas, the son of Eliezer, the son of Aaron the priest, had turned my wrath away from the children of Israel while he was zealous for my sake among them that I consume not the children of Israel in my jealousy. So basically you had these people, they were intermingling, they were fornicating with these heathen people and they started worshiping their gods. And there were some people that were unrepentant about it. And here you had Moses there, but you had Phineas the priest who saw two of these people in the temple that were unrepentant and he kills them with a spear. He kills them. And God says that he basically, it stayed God's wrath because the man of God was advocating for the people. So you say that this was another example of the judgment of God with a plague, okay? Let's look at another example that doesn't have to do with Moses and the children of Israel in the Promised Land or before the Promised Land. Turn to 1 Chronicles chapter 21. 1 Chronicles chapter 21. I just wanna show you a pattern here that God is judging people and when God is judging people with a plague, there's a man of God there or man of God in this last case and they are doing what? They're trying to stay God's wrath from the people. They're trying to stop God's wrath. And God literally said in our last example in number 25 that because of what Phineas did, I consume not the children of Israel. He's saying I stopped because he saw the man of God advocating because he saw the right thing starting to happen, okay? Look at 1 Chronicles chapter 21. 1 Chronicles chapter 21. This is King David. We see King David here and he makes a terrible mistake, all right? King David. And the Bible says in verse number one of 1 Chronicles 21, and Satan stood up against Israel and provoked David to number Israel. And David said to Joab and to the rulers of the people, go number Israel from Beersheba even to Dan and bring the number of them to me that I may know it. And Joab answered, see Joab knew that this wasn't the right thing to do. This was a common knowledge that this was not the right thing to do and I'll explain that in a minute. Joab answered, the Lord make his people in hundred times so many more as they be but my Lord the King, are they not all my Lord's servants? Why then doth my Lord require this thing? Why will he be a cause of trespass to Israel? Nevertheless the king's word prevailed against Joab therefore Joab departed and went throughout all Israel and came to Jerusalem. So David decides to number the people. You say what's wrong with numbering the people? Well we just talked about last week that basically God promised the children of Israel as he promises you that God will fight your battles for you. That one man will chase how many? One man will chase a thousand. So to go out and number the men of war and number the people of Israel to know how powerful you, it's a simple lack of faith in God. It's the reason that David was in trouble here. Okay, skip down to verse number nine. And the Bible says, in the Lord spake unto Gad David see your saying, go and tell David saying, thus saith the Lord I offer thee three things, choose thee one of them that I may do it unto thee. He says I'm gonna offer you three judgments. So Gad came to David and said unto him, thus saith the Lord choose thee, either three years famine or three months to be destroyed before thy foes, while that the sword of thine enemies overtake thee, or else three days of the sword of the Lord, even the pestilence in the land and the angel of the Lord destroying throughout all the coasts of Israel. Now therefore advise thyself, what word I shall bring again to him that sent me. And David said unto Gad, I am in a great strait. Let me now fall into the hand of the Lord for very great are his mercies, but let me not fall into the hand of man. So the Lord sent pestilence upon Israel and there fell of Israel 70,000 men. And God sent an angel unto Jerusalem to destroy it. And as he was destroying the Lord beheld and he repented him of the evil. So here we, who repented here by the way? The Lord repented here. Proving once again that repented, repent in the Bible means to simply change your mind. God did not repent from his sins here. You know, this is a modern invention, a modern redefinition of a simple Bible word here. And he repented him of the evil and said to the angel that destroyed, it is enough, stay thou nine hand. And the angel of the Lord stood by the threshing floor of Orn and the Jebusite. And David lifted up his eyes and saw the angel of the Lord stand between the earth and the heaven having a drawn sword in his hand stretched out over Jerusalem. So imagine this, the angel had already gone and spread the pestilence everywhere throughout Israel and now he's over Jerusalem. And he's about to, you know, smite Jerusalem with the same pestilence. Then David and the elders of Israel who were clothed in sackcloth fell upon their faces and said unto God, is it not I that commanded the people to be numbered? Even I it is that have sinned and done evil indeed. But as for these sheep, what have they done? Let thine hand I pray thee, oh Lord my God, be on me and on my father's house, but not on thy people that they should be plagued. So what do we have here? We have David, we have the man of God and the elders of Israel pleading for the people, pleading for God to, it's enough, that's enough God. They're just pleading.  They were not proud. They were not, oh, you know, we don't deserve this. We haven't done this. David said it was me that did it. Leave the people alone. You know, let them, let the sheep, it's not their fault, I pray thee. He's begging God to stop the plague. Okay, so we see the man of God once again, advocating for the people. Do you notice a trend here? Do you notice a trend of number one, God using pestilence as a judgment? I mean, for sure there's a trend. God's using this pestilence as a judgment. But also there is this recognizable trend of the man of God that is intervening, that is advocating for the people. So the coronavirus, the application for coronavirus. You know, what does that mean for us, right? So as of this writing this morning, I checked there's 104,000 confirmed cases of coronaviruses and there's about 3,400 confirmed deaths of the virus. I mean, that's 3.4% or so. I mean, that's fairly serious. Okay, so what should, I mean the question is, what should our response be? Turn to Ezekiel chapter 25. Turn to Ezekiel chapter 25. You know, people are generally panicking about it. We'll get to that later. Turn to Ezekiel chapter 25. Ezekiel chapter 25. So Ezekiel is talking about, he's lived through the Babylonian captivity when the people of Judah have been taken into captivity by Babylon and he's seen the whole thing unfold. Ezekiel has. He's seen, you know, the three carrying away of Babylon, the three times he's in Babylon and he's writing the word of God from captivity. In Ezekiel 25 and verse number one, the Bible says, And the word of the Lord came again unto me saying, Son of man, set thy face against the Ammonites and prophesy against them and say unto the Ammonites, Hear the word of the Lord God, thus saith the Lord God, because thou had said, Aha, against my sanctuary when it was profaned and against the land of Israel when it was desolate and against the house of Judah when they went into captivity. So here he's talking about these Ammonites who basically when Judah got taken into, the Ammonites were enemies of Judah. They were the heathen enemies and when Judah got taken into captivity by the Babylonians, the Ammonites gloried in that captivity. When the temple was profaned, they said, Aha, ha, ha on you, you're getting taken over. But now Ezekiel is proclaiming judgment on them, which is interesting. Well, verse number four, Behold therefore I will deliver thee to the men of the east for a possession that they shall set their palaces in thee and make their dwellings in thee, they shall eat thy fruit and they shall drink thy milk. And I will make Raba a stable for camels and in the Ammonites a couching place for flocks and ye shall know that I am the Lord. For thus saith the Lord God, because thou hast clapped thine hands and stamped with the feet and rejoiced in heart with all thine, despite against the land of Israel, behold therefore I will stretch out my hand upon thee and I will deliver thee for a spoil to the heathen and I will cut thee off from thy people and I will cause thee to perish out of the countries.  Now Ezekiel 25 goes on, he goes on. It's not just the Ammonites. He goes on and he talks about the Moabites. He talks about the Edomites. He talks about all these people that gloried in the judgment of Judah. And he says, so it's really interesting how God operates because he basically used this heathen nation Babylon to judge Judah and Judah deserved it. And then you had all these other countries around, their enemies, who took advantage of, it says the Edomites, they took revenge on them, took vengeance on them, when they were going through this hard time of being carried away. The Ammonites, they clapped, they said, aha, they're glorying in the judgment of Judah and then God judges them for that. That's interesting. And even Babylon, even Babylon itself is judged by Persia later on in the Bible. Babylon is overthrown by Persia. So look, God is the perfect judge here, folks. Nobody's getting away with anything. So we look at China, we look at China.  The sick map is completely red in China. I mean, it's just like red, right?  I mean, they're under this pestilence right now worse than anybody else, for sure, all right? So look, and let me give a disclaimer here. I'm not one to come out and declare God's judgment on anybody, okay? I'm not one to say, oh, this is God's judgment on China, but let's take for a moment and just look at the spiritual state of China, okay? From a 2019 article in The Guardian, I didn't have, you don't have to dig too deep on this stuff. There's a growing popularity in China against Christianity. All right, and as a matter of fact, a quote from an article in The Guardian just last year says this, China's Communist Party is intensifying religious persecution as Christianity's popularity, you know, is still popping up there. A new state translation of the Bible will establish a correct understanding of the text. As of 2018, the government has implemented sweeping rules on religious practices, adding more requirements for religious groups and barring unapproved organizations from engaging in any religious activity. But the campaign is not just about managing behavior. One of the goals of a government work plan for promoting Chinese Christianity between 2018 and 2022 is thought reform. The plan calls for re-translating and annotating the Bible to find commonalities with socialism and establish a correct understanding of the text. So not only is it illegal in China to have, look, you could not start a Baptist church in China. You could not do it, it's against the law. I would be immediately thrown in prison. You cannot go soul winning in China. You would be put in jail immediately. But not only that, but they are trying to establish a state type common understanding of Christianity by changing the Bible itself, okay? So look, China is an extremely spiritually dark place. I mean, everyone knows this. Like I said, I'm not here to declare God's judgment, but personally, I don't think it's a coincidence that a lot of these things in the last many years are coming out of China, all right? But that being said, we should not glory in their judgment, all right? If it is the judgment of God, it is just. Number one, Ezekiel teaches us, if he teaches us anything, it's that we should not glory in the judgment of others, especially the United States, by the way. Because I got news for you, ours is coming. Ours is coming, okay? Turn to Matthew chapter 24. Matthew chapter 24. Matthew chapter 24. Let's look at the pragmatism of the pestilence. What does it mean for us and how should we actually react to it in our lives? What does it mean? Matthew chapter 24. Look at verse number three. And the Bible says, And as he sat upon the Mount of Olives, the disciples came unto him privately, saying, tell us, when shall these things be? And what shall be the sign of the coming and of the end of the world? And Jesus answered and said unto them, take heed that no man deceive you. For many shall come in my name saying I am Christ and shall deceive many. And he shall hear of wars and rumors of wars, see that ye be not troubled. For all these things must come to pass, but the end is not yet. For nations shall rise against nation and kingdom against kingdom, and there shall be famines and pestilences and earthquakes in diverse places. All these are the what? They're the beginning of sorrows. So you notice he lists here, Jesus lists as a sign of the end times, famines, pestilences, earthquakes. This is just the start of things. So coronavirus is not going to be the last one. Guaranteed. You say, how do you know? Well, because the Bible says so. Turn to second Thessalonians chapter two. Here's how I know. And here's how you know that it's not the last one. Second Thessalonians in chapter number two. So number one, we don't have to think that this is it. This is the end. It's over in a couple of months. We don't have to think that. I can guarantee it. And here's how. Second Thessalonians chapter two. Look at verse number one, where the Bible says, Now we beseech you brethren by the coming of our Lord Jesus Christ and by our gathering together unto him. Talking about when Jesus comes back to gather us together, that ye be not soon shaken in mind. Okay, so don't be shaken up in mind or be troubled, neither by spirit, nor by word, nor by letter as from us, as the day of Christ is at hand. Excuse me.  Okay, well, I mean that could be today, right? Because there's not too many people that want to hear Bible preaching today, all right? Oh, but look at the verse. And the man of sin be revealed, the son of perdition, who opposeth and exalted himself above all that is God or that is worshiped, so that he is God, sitteth in the temple of God, showing himself that he is God. Go back to Matthew 24 and look at verse number 15. This is talking about the abomination of desolation. This is talking about the antichrist of the end times. This is talking about the antichrist sitting in the temple of God, declaring himself to be God. Look at Matthew 24 and verse number 15. When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, whoso readeth, let him understand. So what do we know about coronavirus? We know that God uses pestilence as judgment. We know that. But we know that the end is not yet. Now look, if there had been a third temple built already and there was some world leader standing in that temple, declaring himself to be God a month ago or whatever, and then this was going on, this would be a very different sermon if we had already seen those things happen. But we also see that there's a danger in glorying in the judgment of others, okay? And then we also see that there's a pattern of times of pestilence, of times of God's plaguing the people, of a pattern of men of God advocating for the people in God's judgment, okay? So we see a recognizable pattern here and we know that this is not the end, right? We know that this is not gonna be it. So the conclusion of the whole matter is this. Turn to Mark 13 and verse number 37. Turn to Mark 13 and verse number 37. Mark 13 and verse number 37. Now look, it's not that we're to have blinders on. It's not that we're not to notice things. I mean, Jesus told us over and over and over again and look at Mark 13 and verse number 37.  You're saying pay attention. You're saying pay attention when you start to see these things happen. That's why he gave those details. That's why he gave those details of, you know, hey, there's gonna be wars and rumors of wars. There's gonna be famines. I mean, you know, there was like a whole thing of grasshoppers going across Africa for the last month, ate everything. I mean, we should just notice these things. We should notice these things happen. We should not be the ones with our heads buried in the sand. I mean, these things are gonna get worse and worse as the end approaches. But I probably have it. No, I'm just kidding. But some perspective, okay? Some perspective. This is not the first thing that has happened even in the last 10 or 15 years, folks. I mean, do you remember SARS from 2003?  Then you had the bird flu in 2013. I remember we had, I worked at a power plant in North Dakota in 2013 and we had these turkey farmers come through and they would take tours of, I mean, big turkey farmers. They had like barns of like half a million turkeys. And they were all losing their businesses and they would come through because they were major customers of the power utility, right? So they would get free tours of the plant. And I remember sitting at lunch with one of these turkey farmers and it's just a matter of time because basically what would happen, and I don't think it really came to humans in 2013, but basically what would happen is one turkey would get sick and within 24 hours, like all their turkeys would die. Like every turkey would die. So he said they're washing the trucks with bleach that come onto the farm and they're trying to, you know, bio-hazard, keep everything, you know, clean and clear. He's like, but it just takes one goose flying over and, you know, dropping something on the feedlot or whatever and he's like, it's over. He's like, it's just a matter of time. I guess that's what insurance is for, he said. He's just stressed out about it because a lot of people had that happen.  I mean, so there was a major economic impact, okay? Now look, do you remember the swine flu from 2009? Let me give you some perspective here. Like 500,000 people died in the world from the swine flu in 2009. Like 60, 70 million people. So where are we at with coronavirus? We're at 100,000 people have it, 3,400 people died. 500,000 people died. You know who got the swine flu? I did. I actually got it. Look, there's no hiding from this stuff. I'm telling you, I can't even explain the type of middle of nowhere that I lived in to a normal California person. I lived 40 miles from the nearest 30,000 person town. The nearest doctor that I went to was 20 miles away. And look, I never call in sick, but I called in sick because I had the flu and I actually went to the doctor. And here's what they did by the way. They're like, they did some tests and they're like, hey, you know, you have the H1N1. You got the swine flu. And I'm like, do I get a shirt or something? They're gonna give me, you know what they gave me? Nothing. They said, go home and you're gonna feel better in a day and a half or whatever. And I mean, thank God I got better. I mean, it wasn't fun, but there's no hiding from this stuff.  The swine flu was actually the same type of flu that the Spanish flu of 1918 was, which is interesting. Because the Spanish flu in 1918 killed 50 million people in the world. They say that a third of people on the planet got it. Got the Spanish flu of 1918. So look, what I'm trying to get you to understand is that this is really nothing new that we're seeing. Okay, and it's nothing that isn't going to continue. Look back at Matthew chapter 24. Look at our, it's our verse of the week. Look at your bulletin. Well, here's what's interesting about Matthew 24-7. The Bible says this. It says, for nations shall rise against nation and kingdom against kingdom. And there shall be famines and pestilences and earthquakes where? In diverse places. Go to Daniel chapter 12. This matches perfectly with Daniel chapter 12. Go to Daniel chapter 12. In diverse places. That means it's going to be everywhere. Look, I lived in a diverse place. I was in the middle of the country, in the middle of nowhere, where there was no people. And it got me there. The swine flu, it found me there. But it will be in diverse places, these pestilences. Look at Daniel chapter 12, verse number four.  Even to the time of the end, many shall run to and fro and knowledge shall be increased. Now I've already talked to you about if this isn't talking about our time as far as knowledge shall be increased with the internet and the amount of actual information available to the common man, I mean, we must be at least beginning this point. And I don't know, maybe it goes on for another 1,000 years. What do I know? But knowledge shall be greatly increased. But look at the phrase before that, many shall run to and fro. There's never been a time in the history of mankind where people can just travel the world faster, cheaper, and easier than they can today. That's why there's no containing this. You watch the little red dots, it's just there's dots everywhere. Because people are going, you can get anywhere in the world in like 15 hours, anywhere. I mean, we're gonna go to the Philippines next year. It's like 12 hours and you're there on the other side of the planet. And you think about how everybody's interconnected, there's many that are running to and fro. So people have never traveled more than they have today. So you say, what's your point? Well, my point is turn to 2 Timothy chapter 1. This is my whole point right here. How should we take this? We see the perspective that it's not new that there's been these things in just recent history. 2009, the swine flu killed 500,000 people. That was 11 years ago, just over a decade ago. Turn to 2 Timothy chapter 1 and look at verse number 7, where the Bible says this. It says, for God hath not given us the spirit of fear, but of power and of love and of a what? A sound mind. Be not therefore ashamed of the testimony of our Lord. I find it very interesting that after he says that, he starts talking about, you know, having a testimony for the Lord. Nor of me in this prisoner, but be thou partaker of the afflictions of the gospel according to the power of God. And I wish we could read the rest of the chapter because it's just a great chapter. But look, the public today, the public has a spirit of fear. That's what they have. That's what you're seeing is a spirit of fear. If people are afraid of their own shadows, I'll tell you what does scare me is the general public scares me. Because the general public is generally dumb. They're panicking.  There's no water left. There's no water left. There's no hand sanitizer, but a little thing like this on Amazon is like 20 bucks now.    They move in herds. That's what you're seeing happen here. They panic easily. I mean, medical masks. I mean, I had this mask. Look, I've been hoarding emergency supplies for years. I'm well ahead of this. I had this in my garage. You probably can't even buy one now, for all I know. Toilet paper at Costco, gone. People are like, oh yeah, that's gonna save us, right? So, look, I mean, don't freak out because we don't have to have the spirit of fear. All right, the public has the spirit of fear. The Bible says we don't have to have the spirit of fear. I mean, it might be a decent idea after this passes to have more than five minutes of food in your house, just so when the public does freak out, you know, and then they clean out all the shelves in town in like five seconds, that you'll actually have something to eat. But I mean, don't freak out now.  We were in Dallas when Hurricane Katrina hit, and most of those people came from, that came from Louisiana, came to either Houston or Dallas. We've seen people freak out. We had first hand accounts of what was going on in, you know, Louisiana when the hurricane happened. I mean, it wasn't good, but it was because of the public and what they did to each other and how they reacted in situations like that. So look, from there, here's what we need to do. Okay, from there to know that we don't have the spirit of fear, here's what we need to do. We need to pray for the people. We need to advocate for the people.  Lord, Lord, give us more time to reach more people. Look, guess what? Many run to and fro, and that's why you're not gonna contain these things, right? But guess what can be spread by people running to and fro other than coronavirus? The gospel can be spread. We can run to and fro. We can go to the Philippines. We can go to Mexico. We can go wherever we want and we can spread the gospel. That's what we can do. But not if you have a spirit of fear. Not if you fear that you're gonna get on an airplane and look, we can pray that God would keep countries from passing laws like China so we can run to and fro. So we can go freely to countries and we can spread the gospel. Look, the people of China need the gospel. Whether or not their government will allow it or not, the people of China still need to be saved. I mean, how can we get it there with all these restrictions, right? With all these government restrictions, how can we get the gospel to China? We should pray that more countries don't go in that direction. We should pray for time that we can get to and fro to people. Like, thank God it's not like that everywhere. You know, thank God. So we need to watch.  And then another one after that. And then, you know, at some point, we will see the other things happening that we saw in the Bible. Maybe we will see it, maybe we won't. I don't know. But as for me and my house, we will serve the Lord. It is what I'm trying to get you to understand. We will go soul-winning, I will get on an airplane as long as the airplane flight is still available. And look, safeties of the Lord. We go out in these neighborhoods, safeties of the Lord, period. I wanna get killed soul-winning. I mean, what a great way to go out. Hopefully not today. But I mean, look, so we need to advocate and we need to spread the gospel is what we need to spread. And we don't have to have this panicked attitude. Look, if you use, I was wondering, you know, daylight savings time plus coronavirus, is anyone gonna come to church today? You know, but look, if you really do believe that coronavirus is a judgment from God, don't you think that you would wanna be as right with God as possible? I mean, don't you think that you would wanna be coming to church and, you know, going soul-winning as much as possible and just living for the Lord? And then, you know, God will advocate for you as you advocate for the people. All right, so it just kinda, I just wanted to give you a little bit of perspective from the Bible this morning, okay? We don't have a spirit of fear. We don't have to be afraid of anything.  That's part of being around people, you know what I mean? And crawling in a hole and living in the middle of nowhere is not gonna help you anyway, all right? But it's just part of being around people.  But look, there's always a man of God in these stories in the Bible and he's always advocating for the people. And that's what we need to do. We need to be out there advocating for the people. We need to be spreading the gospel and we don't have a spirit of fear here, right? Let's bow our heads and have a word of prayer. Dear Heavenly Father, we thank you for the safety in you Lord, we thank you that we don't have to be these panicked people just running around and not knowing what to do. Or we thank you that, you know, safety is of the Lord and we know that you will take care of us and that you will help us advocate for the people, Lord. I just thank you for this church and I thank you for the people that in this church that actually go out and advocate for the people in this community and in our Judah, in our Samaria and to the uttermost parts of the world, Lord. We love you, we thank you for today and we ask that you bless the soul winning today and church tonight. In Jesus' name we pray. Amen.


Thank you very much. On behalf of Paul Spellman and myself and the rest of the members of the papillary renal cell carcinoma working group, analysis working group, we want to really thank the NCI and NHGRI for putting this together. As on a personal note, as a urologic surgeon who's worked on the genetic basis of kidney cancer for 31 years now, I would say this project and the previous project we worked on, the TCGA clear cell and the TCGA chromophobe kidney cancer really are sort of the dream of a lifetime. So what we're going to talk about is the comprehensive molecular characterization of papillary kidney cancer. Just for background, kidney cancer is not kidney cancer. It's a number of different types of cancer that happen to occur in this organ, different histologies, different clinical courses. We'll talk a little bit about the genetic basis of them, obviously. What we're talking about today is papillary kidney cancer which makes up 15% of kidney cancer and what we knew when we started this project, what has been a given for a long time, about 25 years now, is that papillary kidney cancer roughly is divided into two types. Type one and type two papillary kidney cancer. Type one, from a clinical point of view, is a relatively homogeneous disease. Appears clinically to be more indolent than type two kidney cancer. At this point in May of 2015, by the way, we have no effective forms of therapy for any type of papillary kidney cancer, the NCCN guidelines. If a patient comes to someone like me with advanced papillary kidney cancer is to put them on an experimental trial. We have seven drugs approved for kidney cancer, primarily targeting the DHL pathway in clear cell kidney cancer. We have no drugs for this. What we know or the field has known most about the genetic basis of papillary kidney cancer really comes from a couple hereditary types of kidney cancer. The first one being this hereditary papillary carcinoma, HBRC, which is the inherited form of type one papillary kidney cancer. The gene for this, of course, is met. In all of those families you find mutations in the activating mutations in the tyrosine kinase domain, and a few met mutations have been found in sporadic papillary kidney cancer prior to the starting of the study.  At the NCI we even refer to them sometimes as non-type one to tell ourselves we really don't understand these cancers very well. You could say clinically and phenotypically that these must be about three or four different types of cancer, and we'll talk about that. Again what's been known a little bit has been found from studying hereditary types of this of type two papillary kidney cancer, a disorder called hereditary Lyomaomatosis renal cell cancer, a very aggressive form of type two papillary kidney cancer caused by mutation of the Krebs cycle enzyme fumarate hydratase. So, in this analysis, of course, 161 samples looked at copy numbers, somatic mutation analysis, methylation, mRNA, microRNA, and protein expression analysis. We will not talk about whole genome sequencing in this talk. So initially then we had a lot of discussion about this, I must say a little controversy about it, whether we should actually have our pathologists look at these and characterize them. We decided as a group that it was the thing to do because that's what we do clinically and that's what we think about these, and we think they're very different. So we put together a group of expert pathologists, really are expert pathologists. I would say the five best kidney cancer pathologists I would say in the world, but we'll say in the U.S., and they looked at an incredible job, looked at these, had a single slide to look at, off of frozen, which is not perfect, but they did a great job, characterized 75 of them as type one papillary kidney cancer, 60 as type two papillary kidney cancer, and 26, they really couldn't call, they called them unclassified. And I think it was their sense and our sense that most likely most of the unclassifieds were actually type two. Now, in this analysis looking at copy numbers, so when you looked at copy numbers, there were basically three different clusters. Cluster one was a relatively stable, genomically, a few numbers of gains and losses. If you looked at cluster two, very different. You most notably, big time, increased copies, chromosome seven, also some 16 and 17. But the big thing here in cluster two is increased copy number seven. For cluster three, a lot of deletions, very genomically, you might say unstable type of kidney cancer, and most notably we would say would be deletions of chromosome nine, and we'll come back to that. Now, if you look at the clusters for survival, cluster one and cluster two, clustered for survival pretty close. Cluster one was more type two papillaries, cluster two was almost exclusively type two, and cluster three had the poorest survival that was mostly type two papillary and high stage, stage three and four. Now, when you looked at mutations, and this was done by looking at Mutsig 2.0, and then also we evaluated genes that were identified in Pancan 21, and a number of notable genes were identified, met, of course, fat one, set D2, which we'd seen, of course, in clear cell, NF2, KDM6A, BAP1, PBRM1, SMARC B1, NERF2, STAG2, P53, the chromosome three, chromatin remodeling gene mutations that we had seen in clear cell kidney cancer, that being set D2, BAP1, and PBRM1, chromosome three, chromatin remodelers, were mutated mostly in type two papillary kidney cancer. We then looked at a number of pathways, pathway analysis looked at mutations and pathways, found a number of pathways that were notable, we thought, one of course being met, other pathways such as hippo pathway and a number of chromatin modifier pathways. The SWE SNF complex was mutated in genes in that pathway in about 20, 27% of type one and type two, chromatin modifiers in 35 and 38%, both in one and two, and the hippo pathway mutations were primarily in type two papillary kidney cancer. Now the MET mutations that were found, 14 MET mutations were somatic, three were germline, most of them were in the tyrosine kinase domain, had a couple outside the tyrosine kinase domain, one in the gesticular domain and one in the semidomain, and they were all except one type one papillary, well, either type one papillary or unclassified, also found a specific MET splice variant in eight samples, resulting in loss of the first two exons and the gain of the novel exon of MET, not unexpectedly, but when you look at MET mRNA significantly higher in type one versus type two, same thing for phospho MET. We find amplification of seven, mutation, splicing, an increased copy number of chromosome seven, primarily in type one papillary kidney cancer, we'll come back to that. Also, gestic analysis revealed a specific region deleted on chromosome nine containing the CDK-N2A P16 gene. CDK-N2A hypermethylation was identified in 10 tumors, each of these, both the mutation and methylation correlated with low expression of P16, and when you looked at the 21 altered cases of either silencing, loss, or mutation, they were almost all either type two papillary, 71% or unclassified. When we looked at survival of all the tumors, all the type twos, the ones with CDK-N2A mutation had a significantly decreased survival versus those that were wild type. This was all of the papillary tumors. We also found TFE3 and TFEB fusions in 12% of type two papillary renal carcinoma, which was surprising. This is a surprisingly high number of TFE3 and TFEB fusions. Traditionally we would think of it as being more like 1%, including patients in their seventh and eighth decade, which is also surprising. Usually we think this was originally TFE3, we originally described in kidney cancer in 1996, and we traditionally think of it as tumor in children and young adults, but it turns out that's not the case. The TFE3 fusions also included four known fusion partners as well as two novel fusion partners, and both of the TFEB fusion partners that we identified were also novel. Now, when we did methylation analysis, we saw a number of things. We saw three different clusters. One of them which demonstrated a CPGiolin methylated phenotype, the SMP phenotype, and eight of the nine SMP phenotype papillary renal carcinomas were type two papillary renal carcinoma, and the SMP phenotype strongly associated with somatic or germline fumarate hydratase mutation or decrease levels of FH. That's the Krebs cycle enzyme. Again, when we looked at the SMP papillary renal cell carcinoma phenotype, we found that it was, it characterized early onset papillary renal cell carcinoma and low survival. So it's a very aggressive early onset phenotype. Now, when we looked at a number of metabolic genes, what we found was we think pretty remarkable. When we looked at glycolysis, fatty acid synthesis, AMPK, and TCA cycle, what we found was in the SMP phenotype, so here we have the SMP phenotype, here we have type two, and here we have type one papillary kidney cancer. In the SMP phenotype, this was very, very characteristic. Increased glycolysis, increased pentosephosphate chunt, decreased TCA cycle. This is like your classic Warburg metabolic shift. Increased glycolysis, decreased TCA cycle. That, if you look then at the type two papillary kidney cancers, what you see is a shift toward increased glycolysis and pentosephosphate chunt, but decreased, but normal oxfoss activity, looking at gene expression patterns. So this would be consistent with what we see clinically, either patients with papillary kidney cancer, very high PET scans. So what this would suggest then would be that those tumors are doing, have shifted to, made a significant shift to aerobic glycolysis. Now when you think about that, then you could also imagine that those tumors also would be characterized by increased oxidative stress, increased reactive oxygen. So we're going to come back to that in just a minute. So think about these type two papillary kidney cancers, the poster child being the SMP tumors, but the other papillaries as being very metabolically active. So how do you put this together? Well this was the model, very similar model that we saw in clear cell kidney cancer in the, in the Kirk paper and the clear cell TCGA paper, in which we saw with high grade, high stage, low survival, aggressive clear cell kidney cancers, we saw a metabolic shift toward aerobic glycolysis and decreased oxfoss. We're seeing the same thing here, exact same thing here in the SMP phenotype, increased glycolysis, increased pentose phosphate shunt, and decreased TCA cycle activity. Now when we did look at cluster of cluster analysis, the COCA analysis, we saw four different, four different, four different clusters basically, and this was Chad Creighton and Katie Hundley, did a beautiful job putting all this together. And the first cluster, C1, you can see here, is primarily type one papillary renal carcinoma. And the cluster, cluster 2A, 2B and 2C are type two papillary. And the cluster 2C is, went completely with the SMP phenotype. Cluster 2B, which I'll show you is the very aggressive type of type two papillary, was also characterized by a significant increase in the number of set V2 mutations. So then if you look at survival, if you just look at type one versus type two, type two papillary kidney cancer has decreased survival over type one, which is what our clinical experience would fit with. Then when you look at the cluster of cluster analysis and look at survivals, the C1, which was type one papillary predominantly, and C2A, which was one of the clusters in the type two papillary kidney cancer cluster, they did very relatively well to each other relative to survival. The cluster 2B, T2B, is significantly worse survival than C1 and C2.  Now finally, we looked at a number of pathways, including this one, which were our most prominent pathways when you did pathway analysis. And we talked a minute ago about the type two papillary kidney cancers being characterized by potentially by increased reactive oxygen, increased metabolic stress, and a more metabolic shift aerobic glycolysis. Now a very pretty study by Ben Tay had shown looking at array patterns in type two papillary kidney cancers that this fit with this pathway, which is the NIRF 2 pathway. And NIRF 2 is the turns on NQ01 and the antioxidant response pathway, which is essentially a defense against reactive oxygen, oxidative stress. This is also something that many of us are working very, very hard to target. And we are very hopeful that this will be a targetable pathway. So because we're so desperate to find therapy for this, we're hoping this may lead us down the right path. But when you look at the NIRF 2 pathway and the surrogate here is NQ01, which is kind of a perfect readout for NIRF 2, as you see with the C1, which is predominantly papillary renal carcinoma, and then the 2A2B and SMP, you see that the NIRF pathway is increasing in those versus the type 1 papillaries. And you can see that also correlates with mutations in this pathway, which is NIRF 2, C3, and keep 1. And when you look at survival, we see significant decrease in survival in the tumors that have increased expression of NQ01. So what we show in this study is that type 1 and type 2 papillary renal carcinoma are genetically distinctly different tumors with different clinical outcomes. The type 1 papillary renal carcinoma is associated with MET mutations, MET splice variants, and gain of chromosome 7. The type 2 papillary renal carcinoma is made up of at least three distinct subtypes with differing survival. The CDK and 2A alterations are associated with type 2 papillary renal carcinoma and with poor survival. The TFE3 and TFEB gene fusions are found in 12% of type 2 papillary renal cell carcinoma and are found also in older patients versus just in younger patients. That the SMP type 2 PRCC phenotype tumors are early onset, poor survival tumors characterized by metabolic shift to aerobic glycolysis and decreased oxidative phosphorylation. And finally, that the NIRF 2 pathway is upregulated in type 2 PRCC and is associated with high grade, low survival papillary renal carcinoma. Thank you very much. For one or two questions, if you want to come to the microphone. For your presentation, could you give more details on what you saw about the unknown subset with respect to the genomic alterations you saw? You started your talk by talking about the fact that those are unknown subsets. Do you understand that? You have a non-type 1, non-type 2, a third other category. Where did they fit in? That's the question. I'll classify. You're unclassified. Oh, I'm sorry. Oh, so sorry. The unclassifieds, I'm sorry. Sorry. Great question. The unclassifieds really, okay, so the unclassifieds, that was by pathology. And that was by looking, all we could do was take the frozen, make an H&E, PCJ did a great job on this, getting into those slides, but really hard for pathologists to make a call on that. Anyway, so the 26 unclassifieds we had, most of those fit with type 2. Okay, so our presumption is those were really type 2 papillaries. Yeah, but are related to one of the subsets of type 2 or not? You know, that's a very good question. I don't know the answer. That's a very good question. It was where would they fit in with the TFE3 or the others? That's a good question and I don't have that in my head right now. We'll have to look that up and I'll get back with you on that. That's a good question. We didn't analyze that specifically, other than we should have. So I wanted to ask about the non-MET mutated type 1 tumors. Any ideas as to what the drivers are in those that sort of make up for MET? That is a very good question and that is something we are desperate to know and I hope you recognize that we said chromosome 7 increased copy number. We didn't say that MET was the target there because there's a lot of stuff. It is incredibly characteristic of type 1 papillary. But what the driver genes are, we don't know. That's a very good question. So we would assume, and we've got the whole chromosome 7 to think about including EGF, HGF, all sorts of things. We have increased copy number. We have increased, we have increased phosphoment. We have increased MET. But is that the target? That remains to be determined. That's a very good question. We also have 16, 17, but we don't know. Thank you so much. Sure, thank you. Our next talk is Dr. Angela Books, who will be telling us about the high throughput somatic variant impact phenotyping using gene expression signatures.


that the nation can bring to bear, and you're gonna get a firsthand opportunity to mix it up with them. So you are here at the Deployment Control Center on Golden Hill. So I'm Allison Black, commander of the First Special Operations Wing. I have two hats. I run the installation to make sure that the lights on and the bills are paid, our child development center folks are taken care of, our facilities are taken care of, then I also have the mission hat. And the mission hat is for the First Special Operations Wing, which you'll see a lot of our aircraft and our aviators and our special tactics airmen. We come together when the nation calls to get out there and get after it, and it starts here. So in this room, these walls and these hallways could talk. They would tell you stories. As a lieutenant, I sat in this room. I walked the hallways, I spent many hours at those stations, receiving my gear, getting the mission briefs. They will come in here, we'll look at the kinds of people we need to send, the equipment we need to send, the iron that we need to send, now we'll all get hashed out, and then they'll move through our processing line. Many of our men and women spent thousands and thousands of hours here. Our families come here to say their goodbyes. In fact, zero 200 this morning, tomorrow morning, I'll be back here pushing out our next group of deployers for six months. So it is a continuous cycle, and the nation is always calling us to build partnerships, to impose costs and create the lenders for the enemies and adversaries around the world. But it's not just about the sad detergent, it's about the homecoming. We have homecoming here. Homecoming's here. We'll bring our families in, the kiddos in. So as sad as it is to see them go, it's pretty darn great to bring them back and see that joy. Whether it's the pets that are here to greet them, whether it's mom, dad, brother, sister, kiddos, it is phenomenal. Again, thousands and thousands of hours, laughs, tears, jokes. So I ask you to just think about that as you get to process the OR station. We are gonna do it in record speed today, but you're gonna get a chance to hear our professionals talk to you about what our people will go through to get out the door. From an initial in processing to medical, to our religious, of course, our top one is there, our legal piece. And then we're gonna get you to the back of the building, another holding room, where we'll talk about our mission brief and what we're gonna show you today. We're gonna kind of tee up a scenario that would be very likely our folks would be called to be a part of. So ask the questions, they're excited to share it with you. Again, thank you for your time. Like Janice, I'll be with you most of the day today. Pepper me with questions and I will put you to the right professionals to give you the answers if I can't answer it myself. Again, thank you. And I think Bobby, the first group, is going to be. I'm sorry, Davis. Okay. Last name is Boyle. B-S-M-B-O-Y-L-E-Y-E. These are five. The first group is your group. Check this out. All the separation. We'll verify it to make sure everything is in place. Go to the center. All the way. We'll send it to go. I'm sorry to be in there. Stress things, parking checkers. Stress things, appreciate it. And we're also here for any type of spiritual support you might need before you head out the door. Yeah. You guys are mine. You guys are mine. I guess not me. I guess not me. We're waiting for that 30 seconds. My name is Dean Larger. I'm a professor of white lab. I'll go with him. I'm so proud of him. I'm a professor of scholarship. Yes. So all we need to do is make a message. So, like, you have an impact on your anxiety, anxiety, and anxiety. Oh, this is your group. I'm good. Ikita, you need to go. Correct. Okay, I'm sorry. Run and blood and don't... Oh, there are, like, a lot of things I need to do. Thank you. Thank you. Thank you. So I'm going to start the grade on the Section Chief for Individual Protective Equipment. These are some of the items that we issue out to our employers. They protect them from chemical. Yes, they do. Just grab one of these. Then you can proceed. These items are issued out to our employers when they get ready to go downrange and they protect them from chemical, biological, radioactual, and nerve agents that might be in the air. So these are some of the items. I would suggest that the helicopters don't blow up dust so we'll switch over to those.  Yes, thank you. And you want to end this as well? Yes, that one too. Any size or year for the big heads? No, it all comes in the same size. Okay, I got a big head. So, I am one of your guys's niece. So if you have any questions, I've got 14 years. Good morning to all of you. Thank you. Are you filling in the fourth row? Absolutely. Good morning.


Come to the next session on homomorphic encryption. And our first speaker is Nathan Manohar. He's telling us about science series approximation of the mod function for bootstrapping of approximate efficiency. Hi. I'm Nathan Manohar. And I'll be presenting science series approximation of the mod function for bootstrapping of approximate HE. This is joint work with Charangy Jutla. I hope you enjoy this presentation. In this work, we focus on the CKKS homomorphic encryption scheme. The CKKS HE scheme is unique among FHE schemes, since it natively supports approximate arithmetic over real numbers. The upshot of CKKS is that it is ideal for applications, such as privacy-preserving machine learning, that naturally lend themselves to computation over real numbers. For these kind of applications, using CKKS is much more efficient, because one doesn't have to first try to represent computation over real numbers via monpy arithmetic or Boolean circuit over bits. CKKS homomorphic encryption inherits many of the properties of BGV, but has the clever idea of mimicking fixed-point arithmetic directly. Since fixed-point arithmetic is inherently noisy, the LWE error present in FHE schemes can be added to the approximate arithmetic error and only affects the least significant bits of the message. It can be shown that CKKS can perform approximate arithmetic homomorphically with only one additional bit of precision loss over plain text fixed-point arithmetic. Let's review the structure of a CKKS ciphertext. A CKKS ciphertext consists of a ciphertext modulus q over here, and as you'll notice, the message and its associated error lie at the bottom, and there are many excess ciphertext modulus bits that are 0 at the top. And what happens in the CKKS scheme is after you perform a homomorphic multiplication and rescaling, some of these excess ciphertext modulus bits at the top get consumed, and the ciphertext modulus decreases. What this means is that after several multiplications, all the excess ciphertext modulus bits have been consumed, and no more homomorphic computation can be performed. So what happens if we want to perform high-depth computation? Well, a natural question is, can we simply increase q to support the depth of the computation? Now, unfortunately, we can't because not only would increasing parameters decrease concrete efficiency, it's actually worse than that because increasing q decreases security, and we would need to increase the ring dimension, which corresponds to the degree of the ring polynomials to compensate. So it becomes completely impractical very quickly for large-depth computation. So what we need if we want to be able to perform large-depth computation is a method of taking a ciphertext where all the ciphertext modulus bits have been consumed and bringing it back to something close to a fresh ciphertext so that homomorphic computation can continue. And this is where bootstrapping comes in, and CKKS bootstrapping refreshes the ciphertext as desired. Now, because of the nature of approximate arithmetic, the data loses precision every multiplication, and bootstrapping will not be able to bring back this precision, so for large-depth circuits, it is necessary to operate at a high precision, including bootstrapping at a high precision. This has proven to be challenging, as we will see, and it's the focus of this work. Right, so in this work, we ask, can we support high-precision bootstrapping? And we show yes up to arbitrary precision, and in fact, our implementation achieves 100 bits precision. Let's review the CKKS bootstrapping procedure. Bootstrapping begins with a ciphertext with no more excess ciphertext modulus bits, and the first step is to simply view this ciphertext as a ciphertext with respect to the largest modulus Q. Now, what you'll notice is that this ciphertext now encrypts a different message, namely little Q times I plus M in the error. And now the goal of bootstrapping is to homomorphically compute upon the ciphertext to recover a new ciphertext that encrypts an approximation of M, but where there are a lot of excess ciphertext modulus bits left over so that homomorphic computation can continue. So bootstrapping for CKKS essentially comes down to performing coefficient rounding modulo Q. Now, there are two challenges here. The first is that the CKKS scheme operates on the ciphertext slots and not on the coefficients of the ring polynomial. However, this can be handled by applying homomorphic linear transforms. The second challenge is that the mod function is not easily represented by a polynomial, and this is the focus of this work. So in this work, we're gonna be focusing on approximating the mod function by some polynomial. We need to approximate it by a polynomial because that is what CKKS can compute homomorphically. And our first observation is that we can assume that M is significantly smaller than Q so that we only care about approximating the mod function in these red approximation regions. Now, why can we assume this? Well, we can simply begin bootstrapping when there's still a few excess ciphertext modulus bits at the top. However, there are several challenges and not any old polynomial approximation will do. The most obvious challenge is that the polynomial better be a good approximation because if it's not, then the error of approximation will be large and most of the precision bits of the message will be destroyed. The second challenge has to do with polynomial degree. Because we have to evaluate this polynomial homomorphically, if the polynomial degree is too high, we may either not be able to compute it homomorphically at all, or after we compute it homomorphically, we'll have consumed so many ciphertext modulus bits that we'll basically have to bootstrap again immediately. And the final challenge has to do with coefficient magnitude. You see when we evaluate this polynomial homomorphically, we have to treat this qi plus m as the message. And if the coefficients are small, we can operate it essentially this evaluation precision. However, if the coefficients of the polynomial are large, we have to operate at this larger evaluation precision and this corresponds to losing more ciphertext modulus bits per depth of the computation. So we need to find polynomial approximation of the mod function that simultaneously has small approximation error, has a low degree and has small coefficients. So what were some of the prior approaches to approximating the mod function? Well, there were several works that used a scaled sine approximation of the mod function. However, this had the downside that it can only achieve low precision since the sine approximation has a fundamental cubic error from the mod function. There are also a couple other recent approaches. The work of LLL plus 21 approximated the mod function by performing algorithmic search on a composition of functions. And the work of JM 20 gave explicit formulas for direct polynomial approximation of the mod function using a technique called modular grunge interpolation. However, one of the issues with these works is that the coefficients of the polynomials can be too large, which as we saw before causes more ciphertext modulus bits to be consumed when the polynomial is evaluated homomorphically. So how do we go about approximating the mod function? Well, our first observation is that there's a well-known technique to approximate periodic functions called the Fourier series. However, if you zoom in on the red approximation region we care about, you'll notice that the Fourier series performs quite poorly. In fact, it performs even worse than sine at approximating the mod function in the red approximation region. Now, why is this? Well, in essence, it's because the Fourier series is attempting to approximate the mod function everywhere instead of only focusing on the red approximation region. So a takeaway from considering the Fourier series, right, is that it performs poorly in the approximation region and thus cannot be used for bootstrapping. So what do we learn by considering the Fourier series? For simplicity, suppose that we want to approximate modding down by 2 pi so we don't have to worry about any scaling factors. Now, the Fourier series was a linear combination of sine x, sine 2x, sine 3x, et cetera. Now, observe that all these sine terms all have periods that divide 2 pi. This means that any linear combination will automatically mod down by 2 pi as desired and perform the same in all the approximation regions. So in this work, right, we ask the question, can we use a different linear combination to approximate the mod function, specifically one that only focuses on the approximation region? So just to quickly recap, right, in this example, right, we want to approximate modding down by 2 pi on inputs of the form 2 pi i plus x for small x. And since all the sine kx terms have periods that divide 2 pi, this equation holds and thus it's enough to consider behavior for small x because how the sine series performs around zero, it'll mimic the same behavior in all the other approximation regions. So in particular, we want to find some linear combination of the sine kx terms that's approximately equal to x for small x. Now it turns out it's easy to find such a linear combination however it is harder to prove that such a linear combination gives an exponentially good approximation to the mod function. So now just as an example, consider the following order 2 approximation, right? So a linear combination of sine x and sine 2x. So consider the following, 4 third sine x minus 1 6 sine 2x. Now what happens if we plot this approximation? So going back to our picture, right, at the red approximation region we care about and in purple we have sine for comparison, we plot our sine series approximation of order 2. You see it already does much better than sine and it's very close to the red approximation region already. So why was this? Why did this work? Well, just quickly reviewing why was sine a good approximation, right? Well sine was a good approximation because if you look at the Taylor series of sine to analyze its behavior near the origin you'll see that you get the x term as desired, right? That's the mod function. And then you have this alternating series just gives a cubic error. And now if we take our approximation of order 2, right? You just look at the Taylor series expansions of sine x and sine 2x. We add the coefficients and then add these two terms. What you'll notice is that we get the x term as desired and now we get a quintic error as opposed to a cubic error. Right, and this worked because we could sum the linear terms, they summed up one which gave us x and the cubic terms canceled. And thus we got this approximation with a quintic error. Right, and so our natural question is can we cancel higher order terms by introducing additional sine terms? And the answer is yes. And so going back to our picture, right? This was the sine series approximation of order 2. If you add an additional sine term, a sine 3x term, you see the approximation gets even better.  The approximation region is completely covered by our sine series approximation. And now zooming out, what you'll notice is that as expected our sine series approximation to the mod function is a very good approximation in the approximation regions we care about but as expected is not a good approximation to the mod function outside these approximation regions. So what are some of the challenges to formally proving strong error bounds for our sine series approximation of the mod function? A first attempt would be to simply use the Lagrange remainder term of the Taylor series expansion of our approximation to bound the error. Unfortunately, this gives a poor error bound. We are able to exponentially improve on this error bound using more sophisticated techniques. We show a stronger error bound using Leibniz's alternating series test. However, proving that our approximation satisfies the alternating series test is not immediate. And in order to do so, we have to calculate the determinants of generalized Van der Maan matrices. These are Van der Maan matrices where the last column is replaced with much higher powers. And to calculate the determinants of these generalized Van der Maan matrices, we use the well-known generating series of the complete homogeneous symmetric polynomials. Now what error bound are we able to show? Well, we're able to show that our sine series approximation with n terms has an error of approximation of order epsilon to the two n plus one. And thus, by adding additional terms to the series can be made arbitrarily small. This also matches our intuition, right? Because each additional sine term we add in the sine series has an additional free variable and it's coefficient. And thus, essentially is canceling an additional term in the Taylor series expansion of sine and reducing the error further. Now in contrast, approximating the mod function by just sine had this inherent cubic error and could not be made arbitrarily small. Furthermore, we also prove that the coefficients, these beta k's of the sine series, all are small. In particular, the first one is less than two and all the others are less than one and they alternate sine. And now recall that one of the things we wanted was for our polynomial to have small coefficients. And now, because the beta k's are small and the Taylor series approximation of sine kx has small coefficients, the resulting polynomial that we obtained from our sine series approximation also has small coefficients as desired. Now how do we go about homomorphically computing our sine series? Recall that ckks is only capable of homomorphically computing polynomials, so it can't compute the sine series directly. But here, we use the fact that ckks actually supports computation over complex numbers. So the first thing we can do is we can use a Taylor series approximation of e to the ix and then by extracting the imaginary part using this standard identity, we can obtain an approximation to sine x. And now, having computed an approximation of e to the ix, this has this really nice property that by simply squaring, we can obtain e to the two ix and by extracting the imaginary part, we can compute an approximation to sine two x and we can proceed in this manner by repeated squaring to compute in general e to the kix, an approximation to that and then extract the imaginary term to obtain an approximation to sine kx. And in particular, we can compute our sine series approximation to the mod function via a low degree polynomial. So what do we do? We wanted to approximate the mod function by a polynomial that simultaneously had small approximation error. We saw that by adding additional sine terms, we can obtain arbitrarily small approximation error. And our polynomial would have low degree, which it also does because it doesn't have very many terms in the sine series to obtain a good approximation. And we also wanted to add a small coefficients, which it does because the coefficients of the sine series are small, as well as the coefficients of the Taylor series expansion of sine kx. So to evaluate our sine series approximation to the mod function in practice, we implemented this approximation on top of the Heon library and we were able to obtain 100-bit precision bootstrapping using a sine series of order six. And thus, high precision computation is supported. Thank you. Questions? Oh, questions. If you have a question, can you use the microphone? Thank you. What? Does it work? Yes. So thank you for your talk. My question is the FHE schemes are well known to be kind of slow. So how long does it take to actually compute your methods? Oh, yes, yes. Okay, cool. Yeah, so it is a bit slow and this is just because, well, first of all, the Heon implementation library that we used is not the most advanced. But it's a good, we used it for like just to compare to prior work because a lot of them use this library. And so if we wanted say 45-bit precision bootstrapping it would take about 30 seconds to run. But for higher precision it takes, so it starts to take around two minutes. And the reason for this big jump is because around this point, when you increase the input precision you need to increase the, so you know how I mentioned that if you increase the modulus Q you have to increase the ring dimension to compensate for security. And this was sort of the jump point where we needed to increase the ring dimension from two to the 16 to two to the 17 in order to maintain security, right?  It's of the side modulus. So you need a bigger modulus to evaluate the same function when you're operating at higher precision. Okay, you finished it? Yeah. Hi, thank you for the really great talk. I'm wondering how this technique compares to the double angle formula method, which seems to try to just like shrink the range that you're trying to approximate as opposed to your technique which like improves the accuracy over at the larger range. Yes, well, so, I mean, so I mentioned that we first have to approximate sine, right? Like, and then from sine we get approximations of sine two X and et cetera. And we do sort of do this like double angle electric because we take e to the ix and like I mentioned, we approximate e to the ix. And the way we actually do that is we divide e to the ix by this variable capital K which represents like the number of intervals we need to approximate. And so in that sense, we are like shrinking the region and then like we're doing these squareings. So I didn't mention in the talk what we are doing this internally. This is what was some of the prior work did also. I see, I see. So you're like doing both at this, okay, yeah. Yeah, we're doing that to get a good approximation e to the ix. From that, we get, we can use e to the ix to easily get approximations of the other terms. Now, of course, like how much you have to do this depends on how many intervals you need to approximate with. That depends on all sorts of things like the, you know, the hamming way to the C or T. And also if we wanna operate like, so if you take an approximation sine X, then from that you get approximations say sine two X, sine three X, right? The error is gonna blow up a little bit. So you need a little bit of a better approximation of e to the ix to begin with, then you would have needed if you were only computing sine. I see. Thank you. Yeah. Thank Nathan. I don't know if we're supposed to clap if they can hear us clapping, but I think we should clap anyway. Thank you.


This is stock number 10474. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used. Heavy-duty truck and Ram headquarters. Today we are checking out this extremely clean 2019 Ram 2500 crew cab, short box, big horn black package. This truck has the 6.7 liter Cummins diesel and has been fully safety and inspected by our service shop. Has a fresh oil and filter change. All the fluids have been checked and topped off. The truck has been gone through mechanically 100% and is 100% ready to go. Diamond black pearl coat is the color. We shoot all of our videos in 1080p 60 frames per second. So if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is like you were right here looking at the truck with me and definitely your best way to check out the vehicle quality and condition wise before seeing it in person.  If you want to check out more photos of this truck in the upper right hand part of your screen as they link right to our website click that and check us out there. Has Firestone Transforce LT28560R20 tires and the front tires have probably about I'd say 60 to 70% of the tread on them. Frame and underbody is a really nice shape which you'd expect on a 2019. You get the blacked out hood bezels right there and the 2500 logo. The LED lighting group so you get the LED running lights, LED headlamps and the LED fog lamps, front bumper parking sensors. You get the blacked out grille and RAM logo on the front here. Lower valance is in excellent shape as well. And down this side just clean as that driver's side fender no dents or dings on that and the passenger side rim no scuffs or scrapes. As far as I can tell this truck's entirely stock and as you go down this side of the truck just as clean as the rest. Didn't see any dents or dings in the box. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down but you're still interested in purchasing the truck you can see the truck here the truck and have confidence in the vehicle that you're looking at before you even get here. So then when you do get here there's absolutely no surprises. And down this side very very clean as you'd expect. In fact we offer a Summit Auto Fastpass option in the upper right hand part of your screen a link right to our website where you can apply for financing get pre-approved see a payment quote even appraise the trade all from the comfort of your own home. Has all the remaining factory exhausts and all the little rockers look to be in great shape as the plastic wheel well liners which keeps your frame and under body looking good. Speaking of that frame and under body very clean back here and the back tires have right around half the tread left. Back rim no scuffs or scrapes on that and as we come around to the back of the vehicle rear bumper really nice shape no major dents or dings on that it does have the backup parking sensors. Full towing package which includes a receiver hitch four pin and seven pin wiring get the LED license plate lights the blacked out ram logo big horn and four by four logo on the back of the tailgate here does have a backup camera that tailgate comes down nice has the spring and bed liner LED bed lighting I got the cargo lamp on right now so you can see those lights in action and you do get some side box tie-downs as far as the box goes very clean in the bed I didn't see any major dents or dings and the spring and bed liner is in nice shape you get the LED tail lamps as well with the LED lighting group and on this side of the truck just as clean as that passenger side no dents or dings on this box here very nice and clean and for full disclosure this back rim no scuffs or scrapes on that guy down the rest of the side of the truck no dents no dings no scuffs no scrapes it does have the heated fold-out tow mirrors they also have built-in directional signals and they also power fold it you do get LED side lights that are blinkers as well inside the big horn black package gives you the dark charcoal and black cloth interior there are no rips there are no tears on the seats you do get power driver seat with lumbar factory all-weather formats throughout auto headlamps power pedals and a tilt steering wheel our windows power locks power mirrors these mirrors do power fold in always like showing that both sides are in working order even though this truck has all the remaining factory warranty you have the woodgrain door trim with the dark cloth inserts and as we hop inside the truck here you can see that this one has 9,170 miles you get the digital speedometer and compass display as well as range to empty you get the leather wrap steering wheel cruise controls and gear selector on the right and bluetooth and information center controls on the left you get the push button four-wheel drive you do get in two USBs two USB C's and an AUG's hookup there comes with the 8.4 4C radio really cool radio has AM FM and series XM radio capabilities as well as Android Auto and Apple CarPlay capabilities so if you have like Waze or Google Maps on your phone you can project those right to the screen and it's like you have navigation right on the screen you can control everything on the screen it's really cool in fact we're going to be doing a video very soon here on how that works but anyways that's the cool thing about this radio you also this is also where your backup camera shows up and you can see just how HD that backup camera is they really improve the backup cameras on these trucks in the past couple years climate controls down here you got your factory brake controller factory exhaust brake tow-haul mode front and rear parking sensors you can turn those off and on passenger side all-weather floor mat and seat are an excellent condition I don't think this truck's ever been smoked in smells very very clean headliner is an excellent condition you do have map lights up there and you do get home link buttons for your garage door security systems and lighting systems has an auto dimming and we'll take a quick look at the back seats and then we will check out under the hood 40 20 40 split bench seating the back seats are just as clean as the front seats no rips no tears back here you do get the latch child safety system for all your child car seat needs fixed glass rear window with built-in rear to frost and what I like on the new Rams is they kept the load floor so that's a really nice item for you if you got pets you got a nice flat place for them to lay if you put both sides down or if you got muddy boots or tools you put them on there and you're not going to wreck or get your nice seat sturdy storage underneath and then you do get to in-floor storage units in the back here with removable containers for easy cleaning and you can put ice and drinks in there it's like you have too many coolers wherever you go wood grain trim on the back doors you also get the child safety locks back here and we will take a quick look under the hood I would personally like to thank you for checking out the video today and my hopes is that you were able to tell just how clean this truck is all the way around inside now I would highly recommend it for make quality and condition standpoint under the hood we have the 6.7 liter Cummins diesel engine base very clean runs very smooth this truck has been fully safety and inspected by a service shop has a fresh oil and filter change all the fluids have been checked and topped off truck has been gone through mechanically 100% and is 100% ready to go to see more pictures of this truck or one of our other 450 new and used cars trucks SUVs minivans Wranglers half tons three quarter tons one tons you name it we got to go to our website www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summit auto.com and if you like to check out more HD videos you can go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos that you see there in fact in a second you will see links to subscribe to our YouTube channel on your left it links more ram 2500 videos like this one on your right if you've not been on our website on the bottom link to this vehicle on our website click those checks out and we really look forward to helping you with this extremely clean 2019 ram 2500 crew cab short box big horn black Cummins diesel thanks again


My name is Chris Jacobs, I'm the creator of Vallejo Historic Home Support. Today we're talking about backup power supply or backup power sources You could use if for example PG news to turn your power off during wildfire season Next up on the list is a power inverter What a power inverter does it takes DC current it turns it into AC current This one's designed specifically to hook up to your car So you put these guys on your car battery. We're going to talk about the exact order of how to do that And then it turns the car batteries DC power into AC you can plug into it with it on and And you'll have basically powered and maybe charge your phone or some other purpose This one here happens to be a 750 watt power inverter In the links for the video, we're gonna have I'll put two on there I'll put a 300 and something around a 500 I'll select 750 is a lot for a car Even with the engine running you're probably gonna kill that battery. It's not gonna. It's not gonna make it I mean I use this on my car, but I don't pull 750 off and I pull a lot a lot a lot less so Okay on the back Anytime when we're dealing with DC or really even if we're dealing with electricity at all We want to make sure we have really good connections.  So that's what we're trying to do Just slightly safe.  So take take a look at what you're trying to run You're trying to run a coffee maker. That's 800 watts. This is 750 it can serve There's two things. There's continuous power and surge power. This can surge up to 1500 But it can't maintain it for long and more importantly your car is not going to maintain This is really ideal again for charging cell phones for charging laptops charging your electronics Interesting enough. I just talked about this one in the last video. I Put this on my counter. I plug my stove into it because my stove doesn't work without a little bit of electricity This is where we charge our cell phones and charge our laptops and about you know Every three days I hook this to my car run an extension cord under my kitchen door and I charge this and That's on a power strip. We charge kind of all the electronics at once and this gets all charged up And we go on another couple days Right next up. We're going to talk about a power inverter one of a larger size something a bit bigger Something that's a bit more like the kind of power inverter you'd see in a small cabin with running solar So stay tuned to that video


Vatic Ventures, you've just joined the Critical Minerals arena, or you tell me you joined in 2018. Is that correct Peter? Yes, I joined Vatic in 2018. I only recently stepped into my role as CFO. But yes, we are very excited about our Critical Minerals Rare Earth project in Southern New Brunswick. So you have a Critical Mineral project in Southern New Brunswick and you told me you have tin, tungsten, rare earth, molybdenum and platinum group elements.  Yes, this is our Gold project in Quebec. We call it Hansen and it's located in the Chippukamu area of Northern Quebec. And when I asked you earlier which project you're more excited about you said you're excited about them both? I am, yes. But I think our immediate target is our Gold project first. So your immediate project is your Gold project. You most recently put out a news release about your geophysical survey set to commence. You want to tell us a little bit more about your timeline for that, please? Yes, so we're in the middle of getting our contractors and our program set up and we'll be moving mobilizing crews in the summer. And we have two areas that we're focused on at our Hansen Gold project, a northwest grid and a southeast grid. Those areas have seen previous drilling surface work very promising and we're excited about it. Well actually I was reading here that your CEO said the previous surface sampling and diamond drilling done on the Hansen project have shown exceptional Gold values. Can you tell us what you define as exceptional please? Well previous work has shown the samples of 12.8 grams per ton over a meter, almost 8 grams per ton over another couple meters and there are some outliers such as 75 grams per ton over smaller intersects. But it's according to the Quebec Geological Survey, it's the most promising area for Gold exploration. So what are you planning on doing this quarter and next? We're looking forward to finding out a lot more about bad adventures. So because the area has shown so much promise from surface sampling and previous diamond drilling, we're initiating our IP survey and that will hopefully lead to drilling later on in the year. Well Peter it's so nice to meet you and for everyone interested in more information on bad adventures please go to their website and or send us an email and we'll get you right over to bad adventures. Thank you Peter. Thanks Jason.


What's good Josh your boy Ross back out again with another video. So the long-awaited much anticipated fight of the year some would say Floyd Mayweather versus Logan Paul man a retired Boxer versus a YouTube Boxer Now I'm not gonna discredit Logan. I'm sure he has been training. I've seen some of the clips Yeah, they were Inspirational some would say but at the end of the day when it's all said and done, let's be real here Logan should not even come close to winning this fight. This should be literally a landslide He had a tough time dealing with KSI What do you think is gonna happen against a actual boxer granny?  They will always be stuck with you Floyd is still in pretty good shape For his age. I'm sure this will be nothing for him. But at the end of day, this is a payday This is a major major payday They're gonna walk out millions of dollars richer, bro Floyd is literally Pretty much just sparring with someone and getting paid multi-millions and Logan Paul a YouTuber Getting into the boxing ring and one of the greatest fighters of all time. Like I I Wicking is a this is this is a smart play. This is a smart money move Would I say it's worth buying to watch? No, am I going to buy the fight to watch the fight? No, I'm not uh, I have my methods and ways of seeing this fight And I'm going to use those methods to see this fight, but I'm not paying for this fight But hey to anyone that feels like they need to pay for it. Go ahead Hey, this is up to you. I mean, it's your money, but to me. I feel like it's not worth The full price they're probably asking for The only amount of money I could ever say That I would pay for for this fight. It had to be like $10, bro I'm being serious. I'm being dead ass Like I would pay $10 for this fight for pay review no more no more Because honestly, I'm just here for the memes I think a lot of people just want to see Logan Paul get knocked out so we can get some spicy delicious memes That's it. That's it The fight I think more people would definitely be more interested in Mayweather versus Jake Paul Because Jake thinks he's just a boxing God now and I would actually pay a little bit more to see them go at it. I would pay $20 I wouldn't pay the full $60 for a pay-per-view. I would pay $20 just to see Jake get knocked out, but Let's let's let's just say for whatever reason for whatever ungodly reason Logan wins this fight tonight, bro I'm not even gonna lie to you, man. I don't even know if the internet can handle that I don't know if I can handle that. I don't know boxing as a whole to handle that. No No No, no, no, no, no Just know and I'm sure there's someone betting on Logan I'm pretty sure they are there betting on Logan and if they were to win The money from betting on Logan, they would probably be a static I'm sorry, man. I just know This is this is just one of those type of things where it's like I'm all for people making no money, but At some point it's like come on, bro.  That's more of a UFC guy He didn't give two f's. He was walking out smiling after he got knocked out to the canvas He was smiling because he know he was millions of dollars richer. He didn't give a damn. I'm just like I Don't know man. I don't know but I am gonna watch For the free so comment down below Let me know if you guys are actually going to spend money on this fight Or are you gonna find other means to watch this fight for free and who do you think is gonna win? Do you think Floyd is gonna win or do you think by some miracle that? Logan Paul will get the W and literally change the boxing world and Change the internet culture YouTube culture as a whole because the headlines will read a youtuber Beat a professional boxer a world-class professional boxer that has never lost the fight. Oh Man comment down below. Let me know who do you guys think will win? I appreciate all the love and support roll to 50k. Appreciate y'all kicking in with me And I'll see y'all on the next one peace