Hey there Virgo, this is Kelly. Welcome back to another episode of Your Love Life. This is House of Virgo. If you're new, please do hit like, share, and subscribe to my channel. I would greatly appreciate that. Please be mindful that these messages are general. So every day there is a message. Some days they will resonate. Some days they will not. Okay, so take it with a grain of salt. If it fits, great. If it doesn't, just leave it way for the next reading. Okay, so this is a channel for Virgos only, but you can also be Virgo, not only Virgo's son, but also Virgo Moon rising Venus. Okay, personal reading links are also below this video in the description box. Okay, so Virgo, let's see what's going on. This is going to be now going into the month of June. I cannot even believe that we are in that position already. We're already going into June. So yes, from this point forward into the month of June. Let's see what Virgo's love messages are going forward. Virgo Sun, Moon, Rising, or Venus. Virgo Sun, Moon, Rising, or Venus. Hmm. All right. The chaser. Okay, chaser in a codependent relationship, fear of abandonment issue. Okay, fear of abandonment. Somebody here is a chaser. Somebody here is codependent. Somebody here is chasing after love, chasing to get back into some type of a relationship, chasing another person to reconnect. Okay, you have the axe and the golden mirror. Great. Okay, looks like we're back to that other reading similar as today. The axe. There's a breakup, separation, stopping the pattern, silent treatment and abandonment. Okay, and the golden mirror, self-absorbed narcissist. One-sided relationship, love bombing. Okay. There we go. So we've got obviously a chaser and a runner. We obviously have someone who is probably possessing narcissistic traits, someone who is controlling, manipulative, codependent across the board, someone who is trying to reclaim a relationship because somebody axed it. Somebody broke something off, said no more. Done with this. Moving on. Point blank period. Alright, let's get into the rest of this reading, Virgo. Oh my goodness. It's crazy. You just said the golden mirror. So, alright, you just had that what? Not yesterday's reading? The day before? Okay. Somebody's chasing after you, Virgo. Okay, now, please know that these roles can be reversed. So if you're recognizing this in yourself, pay attention to that. I'm not here to judge or tell anybody how to live your lives. I'm just here to give guidance through the messages. Okay. So let's take a look. There's obviously someone here who doesn't want to let go of a relationship. And this is a person who I feel somebody might have given you the silent treatment or ended something. Okay. Now, some of you accepted that and just said, alright, that's it. Fine. Goodbye.  And now there's a love bombing situation occurring in the month of June. Okay.  It's like, okay, somebody doesn't want to let go but gives the silent treatment. And then when the person receiving the silent treatment just accepts it and says, okay, this is done. The person giving the silent treatment is like, wait a minute. Now, no, I gave you the silent treatment so that you would try to reach out and chase me. But the person receiving it's like, no, that's not going to happen. So the one giving the silent treatment is now the chaser. This is what I feel like is happening here. Okay. Let's take a look and see what these other messages are. These, these types of relationships are game playing, and they're territorial and they're controlling. And they're just like, not even that's it's such a waste of time. There's no way to cultivate a healthy loving relationship when games are being played. Okay, when somebody's using manipulative tactics of control, or manipulate, you know, codependent behaviors very manipulative. Let me see here. It's just very immature energy. Okay, boom, the tower, somebody got their ego struck. Okay, this axe came in like a lightning bolt to the ego to the crown. Okay. Yep, whoever this person is for go, I feel like for the majority of you, somebody was behaving in this way. To what extent to how far in the spectrum, I don't know. But somebody was behaving in a way where it feels like you Virgo, without intending to harm, just didn't play into the games, it may look like you were acting like the one who was the abuser, but I don't feel like you were I feel like you were just more or less protecting yourself from someone who may have been very manipulative. Okay. And now that person, I don't feel like this person expected you to strike them down to, you know, and something I feel like something backfired on another person who was very codependent, who has fear of abandonment, has issues, who's chased after you. And then when they got you right where they want to do, then they would give you the silent treatment or discard or that kind of energy.  So that's causing a huge injury here with the tower nine of swords.  Okay, so I don't feel like this person wanted you to do that. I don't feel like that was their intention. Their silent treatment has backfired on them. Their intention with the silent treatment was to get you into a state of panic and to get you in a state of reaching out trying to find out what's going on. It was all purported. It was all planned. It was a strategic move. It was done on purpose. Okay, and I feel like the person that you're going to see here, who I feel like is going to be chasing after you coming up in the month of June, you're going to hear from them. This is someone I feel like who love bombs, and then give silent treatment advantage, and then love bombs, and then silent treatment. This is like a pattern. If you haven't noticed, see, listen, it's not in and of itself. Somebody's actions, right? It's it's the pattern that you have to look at. Is there a pattern? Was there a pattern in past relationship with someone? Or if this is somebody new coming in, who has similar patterns to someone you dealt with before, what that's why you have to take your time. You can't get rushed in, right?  Okay, so whoever this person is, extreme anxiety, because they didn't expect you to not respond. This person, okay, so yeah, King of Pentacles, okay, I feel like they're looking at you and you're in, you're silent. You're in quiet mode with the high priestess. Yeah, your, your energy is pulled out, pulled back.  It's like, you know, and this person is knows that you know. That's what I feel like is going on here. They, they really, they're coming to realize here in the month of June, that you caught on to them or that you're aware of this pattern and this game, and you're not playing anymore. So you've gone into stealth mode. Okay, you're, you're kind of like, or at least that's how they're viewing you.  You, you catch on. You finally realize, okay, that this person was acting out of ego, acting out of abandonment issues, fear of abandonment, acting out of codependency. This person was being manipulative. And I feel like you are, you know, now I see you stopping this pattern because it is a pattern of abuse. Okay. And I feel like this person is looking at you and they, they know that you know. And without calling anybody out because I don't feel like you're calling anybody out here. I don't see this. Your, this person views you as gone. This silent treatment thing, you're just like, okay, right back at you. That's what I feel like your energy is here. Wow. The devil card, crazy, extreme anxiety. This person's mindset is so toxic. Look at the tower, nine of swords, and the devil. I mean, this is craziness. This is, the devil card is very minute. This person is, they know that you know they're aware that you know that their behavior, like I said in the other reading a couple of days ago, that this person's like living with these demons. Okay. And I'm not going to go too, too deep into this, but this person is obsessed with the fact that you've axed this connection with them. Okay. Because of, and you know, the card says narcissism, I like to just say spiritual disordermy. Is that a word? I just made it up. There you go. Spiritual, spiritually disordered. Okay. So, let's get on with this story here. This, let me get on with this story. I'm going to take a look at this tower. The two major arcanas falling on this person's side is the devil and the tower. Okay. Oh, King of Wands. Okay. So, this very well could be, for some it could be Virgo Taurus Capricorn for others. It's a fire, energy, Aries Leo Sagittarius. Okay.  Really, really big. Also, I want to tell you with the high priestess, it could be a cancer and with the devil card, it could be a Capricorn and with the tower card, it could be a Scorpio. Okay. Just to bring some clarity. So, yeah, this person's ego completely shot. I hate to say this. This is going to sound vulgar and crude, but hey, we're all Virgos here, right? You get it.  They were getting off on the fact that you were staying in the game with them and you were duking it out with them. Okay. But you've destroyed that. You've left the stadium. I just see here, you've gone quiet. If you haven't actually left the actual stadium or the arena that you both were in, you've definitely gone into silent mode here because you're giving the silent treatment right back to this person. But I don't feel, some of you, it might be intentional, but I feel it's more like your gut is telling you to stop engaging with this person because of these behaviors. Okay. And here you go. Six cups. This person's definitely going to try. They're stuck in the past, but they're also going to try to bring the past back to the forefront here with you and try to reconcile. Have some kind of a reunion with you. Definitely. Oh, definitely. The devil, it's sitting on the devil card which I clarified and so it's basically like the demon or the devil on their shoulder is telling them approach Virgo very cautiously, carefully and childlike. Innocent. Approach them as approach Virgo with an innocence. Okay.  I had a problem with my kids or something to do with my kids. This is for their excuse for why giving you the silent treatment in order to play on your pity to try to come back in. I was busy with family members like siblings or, you know, I was, I had to take care of some past issues. These are all excuses. Okay. They're all excuses for why someone would give you the silent treatment if they're trying to come back in with this love bombing energy. This person is coming back in with, it was out of my hands. It wasn't my fault. And I had to leave because I had to do this and I had to do that. Whatever. Okay. Or I was dealing with some past trauma childhood problems and things like that. Okay. How do you know Virgo that this person is not telling the truth? Well, I know because it's sitting here on the devil card. This is a tactic and it's a pattern. Okay. Now look at this. Just flipped out. All of a sudden, 10 of sorts, seven of cups, three of sorts. So I'm hearing, gosh, this is awful.  It's placing blame. Okay. It's placing blame. I couldn't commit to you because you know or there was a third party situation that I had to put an end to and I had to deal with. It's just all excuses, right? Because there's really, if you're in a relationship with someone, people talk to each other. When they're going through trouble, we don't dip out on each other. When we're having problems in a relationship, when we're in a relationship and we're having external problems, we rely on each other. We talk to each other. We let each other know what's going on in each other's lives. We don't disappear or ghost or give the silent treatment unless we're in a freaking coma. Okay. That is indicative of manipulation and someone who's got some serious issues. Okay. Just running away or not talking to your partner about a problem that you're having external or even internal. What is that? That's not healthy. Okay. So anybody who's coming back, you know, it's like being on the job, right? And you're employed and then you just disappear. You don't show up for work for like weeks or months or whatever, days, whatever. And then all of a sudden, you just show up with, oh, well, I had this like, you know, you're supposed to be accountable in your relationships with people, whether it's career or in intimate relationships, personal relationships, people that, you know, this is the way life works. And so if we're needing to leave or, you know, I mean, short of just saying I was kidnapped against my own will, I mean, yeah, okay, that's valid. And if, you know, there's proof that's valid or this person's in a coma, that's valid. I mean, I'm sure you guys can think of other reasons that valid excusable reasons for not being able to let somebody else know what's going on.  So anything other than that is just an excuse. And that's what I feel like is happening here.  And somebody here needs to know it and hear it and see some stuff. So it feels to me like this person is looking at you in the month of June. You've gone quiet. They don't know where you are. They don't know what you're doing. And that's rattling them up. That's shaking them up. Where's my contender? Where's Virgo? Where's the person that Virgo's not letting me abuse them anymore? Virgo's not letting me control them anymore? Virgo's like, oh, I'm on the new love. Holla, I'm looking for something healthy. This is you right here.   No, because that's not even right. Virgo, you're, you're preparing yourself, you're opening yourself up to receiving new blessings, new love, new developments in love. Some of you may be a new spiritual path that's having a deep emotional effect on you. You're looking for that love elixir that's healthy and you're cup overflowing. That's what you want. You're not looking for these games, right? You're done with the past, Virgo, or this particular person, whoever it is. And again, as I say in my readings, you know, these are love readings, but love's an umbrella term. Love can cover intimate partners. Love can cover relationships with friends and siblings and things like that. So whoever this person is, okay, in the month of June, they're definitely going to be reaching out, but I do feel like they're going to be coming in with a bunch of bogus excuses for where they've been or why, you know, whatever, okay? They had to finish something. There's no excuse for that. There's no, it's so easy to text. It's so easy to talk to somebody and just say, hey, I got this going on, you know, busy right now, but I'm going to try my best to keep in touch with you each day in a healthy relationship, you know? 24 hours, no response from someone. It's so discourteous, you know? And it's not like you're in this anxiety state where I feel like somebody groomed or conditioned you to be in some kind of anxiety state. And now your silence here, your, and how they perceive you as not coming back into the stadium with them, is causing them great anxiety because you were, you were a good contender. You might have been number one supply. You were a good contender. You played the game with this person for some time and no one played it better than you. You served this person pretty well until you just got to a point where you're like, you know why I'm serving myself now.  I'm not serving anybody anymore. I'm serving, this is self-serve over here. There we go. Okay, look at you. I love it. That's your card right there. See other nine of pentacles. You're all up in your own business. You're doing fine. And if you're not doing fine right now, you will be. Okay? This is, this is going into June.  You are shining bright, self-sufficient, working on your solo gains and the things that you are trying to achieve for yourself at this time. Oh, sorry about that. You're doing your own thing. That's a Virgo card right now. You're, I feel like there's an old saying that I heard once. The egg does not chase the sperm. It's the sperm who chases the egg and that's for the females. Okay? We're different sexes here. And don't argue with me about that. And men operate differently than females. Majority of my viewers are females. So this is specifically a message for the ladies. Okay? But you are in a position where you, I see you working on or will be working on or positioning yourself to attract love into your life, to attract it. Why isn't this, hold on. I don't know what's going on. Positioning yourself to attract new, healthy love. That's what you're doing. I don't feel like you're out there seeking. Look, she's static. She's just showing up and showing up at the door in her best threads, shining like a star. She's not out under the spotlight. She's, she's underneath like an archway. You know, she's just very casual standing there and just looking her best to attract that love. Okay? So I like your energy here, Virgo. I don't really see that you are going to be too bothered because some of you just kind of, it just feels like maybe in the past, if this is someone from your past, you didn't understand what was going on. A lot of you probably just didn't understand what you were in. I, you know, there's an old saying, a fish doesn't know it's in a fishbowl til it's out of the fishbowl. And then that's when that fish can take a broad view and say that's what I was in. That's what I was living in. That murky water, I thought that's what life was like because I was stuck in it. And I see like a lot of you have stepped out of it and said this had nothing to do with me. There wasn't anything going on with me. This was this person because their issues they projected on to you. That's what I see here. And a lot of you are just, just the knowledge, knowledge is power. And a lot of you having that knowledge that the high priestess has that intuitive knowledge. This is like the aha moment, like, oh, I know what's going on here.  They don't like that you're on to, even if it's not, you know, NPD or anything like that. You know, and I'm not a doctor. I don't know enough about that. I don't make diagnosis, believe me. I just, whatever messages are coming to me, whatever this person had, whether it's just extreme selfishness, whatever. Yeah, it doesn't matter because I feel like even if this person is just spiritually disordered, you know, I see you knowing and I see you positioning yourself in a much better, you know, this darn emperor keeps showing up here. I'm sorry. Oh, the king of swords. I just saw the emperor, but the king of swords is here. So let's take a look and see what this is all about. You might have someone on your mind at this time, a king of swords. Now, some of you, it could be a king of swords from the past. Gemini Aquarius, uh, almost said Leo, Gemini Aquarius Libra. That could be this person.  In spite of yourself, okay? You're positioning yourself to be, not to show offy, but to show that, yes, you're a contender, but I don't get in the ring with people who cheat and bite their way to win, right? It's almost like this all-knowing, like, yeah, you're going to look at me and you're going to see that I don't need you. So a lot of you, um, I don't really feel like you're hiding, but I feel like you are kind of giving that silent treatment and just showing up, like, unaffected. You're showing up in a way where it's kind of like a little, a little, I don't want to say boastful, but it's kind of like, how you like me now? Look, no marks on me, no bruises, I'm fine. I'm doing well. I'm perfectly fine. Look, I've actually matured, I've grown, I've changed. I'm, I'm not unaffected. So some of you might be showing your, trying to show that, present yourself to this person in a way, and I do feel like if you're doing that, that's causing them great anxiety.   At least that's how they're viewing you. Okay?  It's just not your natural way here, Virgo, and this person knows that. And yet at the same time, you know that, you know that about yourself.  And, um, you might also have somebody else that you're interested in that you might be trying to attract into your life at this time, specifically an air sign. Okay? Maybe, but let's see. You might not be right now, okay, but they might show up. Now, here's the thing. I was clarifying this, King of Swords, and the Five of Swords is here, and that is always a card of a bully, of an abuser, and so I, my main message here for you is that you're trying to show up to somebody here that you, um, your light's going to shine no matter what they do.   And, um, if this was the person, maybe possibly an air sign, or show, is showing up here, or you view them as being an air sign of someone who's quite strategic and intentional with their words, or is a verbal abuser, um, you're definitely showing up that your heart is still fresh and clean and new, and just like you're, just like you, like you're just unscathed. I feel like you're showing this person, and some of you, that's what your intention is, like, mm-hmm. Well, for everything that was done, everything that was said, everything that wasn't said, the silent treatment, the breakup, um, you're stopping the pattern, and you are in recovery mode here, even, not even so much. It's more like I'm not a victim, I'm a survivor, and I'm going to show you how I survived this. You know, it's like showing up, like not boasting, but you're showing up here, and welcoming new love. Okay, the wheel of the year and the nine of cups, beautiful. Virgo, you're just, you're moving on, going after your wishes, your things that bring you emotional happiness, okay, and making those wishes come true. You're in good health, it could be something that you're, I don't know, maybe you're working on a, working out on a spin bike or something, taking classes, um, moving, having moving, there's a turning point happening here for you, Virgo, and I love it. I just love it, it's so inspiring.  You've, you've put yourself in a position to be above because knowledge, the knowledge that you're gaining or that you've been gaining, you're able to see what was what, and this, you've detached yourself or you're detaching yourself in going through the month of June, um, from any kind of trauma or anything like that. You're, you're seeing it for what it is. You're calling a spade a spade, and this is, this is the, the card of, these are the cards of spades. You're calling a spade a spade. I don't feel like you're, um, you're not claiming somebody's words or things that they've done. You're not claiming that. You're kind of like, that has nothing to do with me. Somebody came in this way and they're going to go out that way too and you're staying more true to yourself, more in your authenticity about who you are, getting back to self, focusing on self.  I was just going to say, this person's going to try to, um, reach out to you and they're going to start their love bombing kind of thing, right? You've got the eight of wands and the ten of wands. So, you know, their exhaustion, the effort and the work they're going to put in to, um, be reaching out to you. I want to come see you.  I want to connect with you. I'm just finishing up this thing. I'm totally exhausted. I'm stressed out but, um, I'm coming your way. That eight of wands, I always feel like that's, that's Cupid's arrows. That's like speed. That's like, um, that's like machine gun love right there. Shoot, just love bombing. Message after message, communication, news, bringing you news. This is supposed to be good news, okay? Quick change, um, and is this person trying to get back into your, your life? Uh, yeah, because they have a fear of abandonment that you're going to be gone for good, okay? That you're, you're moving on. Let me see here. Oh yeah, look at them. Nine of wands charging in fast.  Um, they're stacking them up. Look, they're, they've gone out to the forest. They're getting all their love darts or stacking them up. This is their arsenal. They're bringing it to you.  That's not a warning, okay? Um, but this is more like charging in, okay? Um, this could be somebody who's at a distance. So, uh, this eight of wands can have something to do with travel as well. Coming in on there as a knight, okay? Oh yeah, the star wanting to heal this. Want to be the, the shooting star, the number one, um, the all star in your life. They're going, oh man, Virgo. I can't even with this reading. I can't. I want to heal this. I want to try to fix this, you know? I've, or I've healed. I've been healing. I've been making changes in my life. Oh yeah, look at this. Nurturing energy. This is water element here. Um, Cancer Scorpio Pisces. You know, um, I've been healing. I've been doing a lot of thinking. Um, I've been getting a lot of support. I want to bring in, I want to support us. Aquarius energy here. So, look at this. I'm going to be more consistent. Um, I don't know, just with that devil card and everything just coming off of that. Yeah, I don't know.  Calling it spade is spade. I know what it is. Um, I am going to do an extended reading to see, um, what this person is going to do, what their actions are going to be going forward throughout the rest of the summer to see how things are going to change. The Queen of Pentacles is here. Um, this feels like a mirroring image here with the Eight of Pentacles and the Queen of Pentacles, because I feel like this person sees you working really hard, um, being in your abundance. This is all about the, the coin. Um, you're very down to earth. You study. Some of you study. Uh, you're very well versed on facts of things. You understand things, data, looking at data. Some of you have been looking at like data. Um, you understand how things work. You understand how to make money. You understand about consistency and perseverance. Um, and I feel like this person is going to, they want to, I don't know if they're going to do this. They're going to tell you. They're, they want to, they admire you.  Um, it's kind of like projecting, right? Um, this person comes in with this, um, projection. Um, it's kind of, uh, how can I say this? Um, all the things that you do, that they think that you are better than them, they're going to tell you that's what they're doing. Right? Um, king of cups and the ace of sorts. Okay. So again, with the water element here, cancer, sclerpio, Pisces energy. And also as, as I said, we have, yeah, see there's a lot of mirroring. So the king of cups and the queen of cups, and then we have the king of pentacles and the queen of pentacles. And then the oddball out is the king of wands. So I see things differently. Okay. This is going to segue into this, um, this is going to segue into this extended reading right here. And I'm going to use these three cards to segue into that because there's a perspective here. And I want to find out if this person is coming through, um, with absolute truth, okay, about what they're going to be saying to you if they've really seen, if they have clarity, if they've really seen the light, if they're coming in and saying to you, um, uh, maybe I did have this problem. Maybe I do have this problem. Maybe I am a big N word. Maybe I am spiritually disordered. Um, I think maybe I am or I might be, um, or I might have like these extreme selfish, I have trauma, I have things, um, you know, maybe I should, you know, I gotta go see Jesus or I gotta go see the man on the cross or I gotta go get some counseling or something like that. You know, um, I've been stuck. Um, I've been stuck in this way of life for a long time. So we're going to take a look in the extended to see if there's going to be any changes. Okay. If this person's really coming in with the truth because the Ace of Swords is a card of truth and clarity. All right. Let's look a little bit more into you and your energy going forward. Okay. And then I'm going to cut it short because I really want to get to this extended. All right. Let me see. What other messages are there here for Virgo? This is crazy. Oh, Virgo, Virgo, Virgo. All right. Water. Emotions are at their peak. Medusa. Jealousy leads to a downfall and the caduceus. You will receive news from afar. Okay. Right. So you're definitely going to be getting some connection, some news, the caduceus. That's a two of cups energy. That's healing. Um, but it's also a meeting of the minds. Emotions at their peak, jealousy leads to downfall. So this message you're going to get, this news, also is going to come from someone who, um, says they were very jealous that, hmm, you might be moving on to somebody else. I don't like it.  Um, okay. Let me get, let's do some signs and then let's get into the numbers and some charms and see what's going on here. You're definitely going to be getting a message from this person. Go over to the extended reading when it's over here. Um, click on the link that's below the video to get to the extended reading and that will tell, that there'll be more information in there about you know how, how the rest of this is going to play out and if this person is really coming in with truth and or if they're, if they're feigning. All right. We just had a charm fall out here. Oh, we have like, it's like a capital. It's a building here. Somebody's from Washington maybe or Italy. Sorry if you can't see it. Um, it's a domed, a domed building. Maybe it's Russia or somewhere in Europe where there's dome topped buildings. Okay. All right. So somebody is 40. Okay. We also have Pisces. Taurus, double Taurus, triple Taurus. Again, triple Taurus. Okay. So somebody might have triple Taurus in their chart somewhere. I can't believe it's amazing to me how Taurus falls out all the time. Okay. So the numbers they're giving me are 83. They're giving me 510. They're giving me 1016. They're giving me 23. Um, and they're giving me the number 4. Okay. Now these could be years. These could be ages. These could be, um, you know, birth dates. We have area codes 416-237-510-310-835. Okay. See what else you have here. It's dark. All right. We have Sagittarius, Aries, Leo, and Gemini. Okay. Um, numbers 715-909-22, 59, 32, and 12. Okay. Um, we also have, so September, September 1990, um, and 1992, um, we also have the 25th. Did I say that? I can't remember if I said that. Okay. Oh, and then I just saw cancer real quick. All right. Let's see. One more shuffle. One more roll. Okay. Double Gemini, Leo. We have Virgo. Okay. 45. We have, huh, October 2nd, 2010. We have 88. We have 19, 24, 28, and 54. Okay. And 51. Okay. Double Gemini. Interesting. Now, let me get a couple of charms. Okay. Don't forget about the extended reading if you're interested to find out how this is going to turn out or what this person's energy is going to be. Okay. So, we've got a web, Spiders Web, Caught in the Web, Caught in a Web of Lies, Surfing the Web. There's a spider on here as well. Maybe you just see a spider's web somewhere. Okay. And we've got a little birdie here and that looks like the Twitter bird. So, maybe something on Twitter or you're browsing Twitter or posting something on Twitter. Maybe you're posting something about the Amber Heard situation. We've also got a rose. Okay. So, are you preening your roses? You could be getting a rose or receiving roses. You just got some. Put them in a vase somewhere in your house. It's very pretty. Also, somebody's name might have rose in it. Okay. Or a street name or a city. There's two keys. Again, you guys and just like I said in one of the last readings, those two keys represent the fifth element, the unseen, the spiritual forces. Okay. So, there's something unseen here in regard to unlocking the gates. That's the Harfa and the high priestess here. Okay. Working in tandem, each with their own key, opening up spiritual truths, unlocking that fifth door that nobody knows and that's the forbidden door. Some of you are trading in your keys or you're looking for your keys. We also have a moon, a black moon with a star. Okay. This feels to me like, I don't know. It's weird. I just saw somebody, did it get dark all of a sudden? I just saw somebody eating, taking a bite of a cookie, a chocolate cookie. Okay. And there's a Christmas candle here with some holly. Okay. So, something to do with the holidays, with Christmas, is very significant to someone here. And also, don't forget, there is, looks like a state building or some kind of very important building that has domes on it. Okay. It could be, I don't really feel like it's a castle. It's somewhere in Europe though. It could be here in the US too or somewhere else in the world. I'm picking up strong Europe but it doesn't have to be. It's just somewhere in the world. Wherever you, you may see one, maybe just saw one. Wherever there's a dome. Okay. A building or several buildings that have archways and domes. Okay. So, I'm going to leave this reading here for you and it was a little shorter than normal but leave this here for you and go over to the extended link will be below and we'll take a look at the energies right here. What this truth is, this person is really seeing things differently or are they just telling more fibs? Okay. And we'll see how things turn out with this particular relationship going forward throughout the rest of the summer. All right guys. Thanks for being in the chat. Hello to the mods. Thanks everybody for being here and I will see you in the extended. All right. Take care. Bye.


John, just looking at the box score, and what did you, what's it all to you for what happened tonight? I think just the very first possession of the game, that sequence of them getting offensive rebounds was the tone-setter for the night. And we were reactive instead of dictating across the course of the night. They were the more aggressive team, give them an extreme amount of credit. But it's a good challenge for us to see how we regroup. What was your message to the guys who won't come off the court? Yeah, that was it. It was give them credit. They basically kicked our butts. We all were a part of it. I'm a part of it. And we got another game on this trip. How will we respond with this last game on the trip? From the point where you have the game tied, 40-all, to give up a run like that, 29-4, whatever. How disappointing was the effort during that spin? It was kind of, it was interesting, the plays that happened, whether it was offensive rebound, whether it was us missing a three, them getting an offensive rebound, kicking out, making a three, giving up a transition after we missed a three. So the sequence of it was a little, I don't know, shattering to our confidence a little bit. And that run kind of propelled them to hold on to the rest of the game. There are going to be runs like that. The thing I did like is our group, we stayed together in the huddle, and we were trying to figure it out. So that part's great. But we got to eliminate those runs. Jeff, why do you think the effort was so lacking? I don't know if our minds, our bodies, and souls are still in L.A. L.A., I do that to you sometimes. And so we definitely gave maximum effort against the Clippers, and we've been reeling since. So a great time to get a good night's sleep and be ready to go in Portland. If you look at a positive on this, Ben Simmons, it looked like he was attacking to the rim, just kind of a different mindset. What did you see from him tonight? Yeah, I agree, Megan. I think early on his first attack to the rim was great. I thought he pushed the pace, a lot of pain attacks. I think the game was at his speed. He was able to get the ball to his teammates, so a lot of good from tonight. So good thing is we'll have a lot of minutes left in Portland to play everybody, and everybody should be fresh. And let's see if we can get a win there.


Tyon just said a few minutes ago that you're fearless on the mound. He doesn't think he's seen somebody attack Ramirez the way that you did Do you do you feel like that out there? I feel like you have to have that confidence on the mound if you don't a lot of hitters can sense the lack of confidence But that's nice of him and he's a good buddy of mine. So thanks for hyping me up What's the feeling like when you're in the zone like you were tonight striking out eight guys in a very good lineup It was actually weird. I felt terrible in my pregame bullpen I was talking to Barney the bullpen catcher and it was literally terrible I could not throw a strike and then I go out there and it was 3-0 and I was like, oh, here we go and then I Don't know it just clicked and I felt good after that. So maybe I got to have more bad bullpence I was talking to Nester about it too because he said that some of his best performances have been that because it Almost locks you in and in my pregame bullpen. Normally. I'm just throwing getting my pitches in getting warm For the last five ten pitches of my pregame bullpen I was like lock it in dude. Like let's go. We're about to get in this game So it totally could have but yeah, I'm not going to intentionally do that anymore But yeah, it felt pretty good to actually execute when I got out there I mean just kind of build off the confidence build off of Locate my fastball pretty well staying ahead of the count This is one of those where I had both off speed pitches Commanded pretty well, and yeah, so I just got to kind of build in and stay confident Does that play differently where you know, I think later in things guys are probably focusing on one or two pitches Yeah, I Thank you for that. I I felt like I was I was able to command it today And that obviously doesn't happen often I actually had a text from Sam Breened our minor league pitching director and he said like you had all four working today Because I've always talked about if I have four Hopefully plus pitches and only two of them are working out of the bullpen I can easily get through a lineup not easily but at least be confident getting through lineup And when I have all four it allows me to kind of do some fun stuff and and toy around with players and really keep Them off balance and so yeah, it's been a weapon for me And I feel like that was the first time I had my change up That I was able to locate and then was able to really have sinker and foreseam That I could put Kind of wherever I wanted and I was able to get ahead of counts that way I had no idea that I had seven in a row I knew I struck out the side in the second And then when I went out there for the third I realized I struck out the side of the third But I wasn't paying attention that it was seven in a row. No The franchise company's eight and you wish you had a chance to Boney, come on. No. I had no idea But yeah, I mean I'll take my three innings and bounce


seems like it should, right? It seems like if you do a better job at doing very careful work that it should increase the impact of your paper. And I would think that no matter what else is going on, careful work should be something that we all strive for. Because we can all do better in terms of being very careful in doing our science and reporting on our science. And that should be its own reward. But that being said, I think that this is something that we need to measure. We need to look at journals where you know the same kind of paper is published with and without an RRID or a set of RRIDs and really try to figure out you know are people able to now find these reagents more easily? And I think that again this is something that will start to come out over the next few years. This initiative is still relatively young. We now have a lot of uptake in some of the big journals, but we're going to have to really understand, okay so there's a cell paper without an RRID and there's a cell paper with an RRID. Maybe they're only a few months apart. Hopefully in a few years would we know what the impact of those papers with and without R. We'll be able to take a look and say okay here is the increase in impact factor based on the RRID. That would be great. I don't quite think that we have enough data at this time. We don't it's really a little bit too new. But one way or the other there's no reason to be sloppy. There's reason to be a little bit better in reporting these materials. Because that can only help you. It can help your colleagues. It can help the people reading your article. And if we can help them read more easily I would think that they would cite you more frequently than they would if they had to really go and track down and call you up and try to figure out where that antibody is that you used.


Welcome back to another video. So this is now the third video in our Power BI series and we're gonna continue on from where we left off in the last video. So if you haven't seen the last previous videos, then you can find the link to the playlist below this video. So yeah, you can go check those out if you haven't seen them and you need to get started with installing the application. Else we'll continue this video from where we left off. So we've got our data set here. So this is now put together our three data tables from our base Excel file. But as you can see, it's kind of a bit boring information that it gives us the name and it gives us the setting. But it's not really giving us any meaning information. So you can see all it does is gives us everything by name. If we wanted to keep this table, what we wanted about the summarized by the city level, all we need to do is remove name from our base table and you can see it gives us a summary basically by city. So what we could do if we wanted is leave this table here and let's just do a copy. So let's go to control C, click off our table control V. So copy and paste works in Power BI as it does with any other Microsoft application. I couldn't even make it then. And let's say we've got our city over here in this table. So we can see city and the total sales and the total units. Then this one we want about to give it at the individual level. So what we could do here is just bring our employee name but remove city. So all I did here is drag employee name into the new table. I'm going to delete city like so and let's just make this one a bit bigger and let's just drag up as well. Just so in multiple pairs, why not? And let's just do the same of our city table as well. And as you can see as I'm navigating around, it's really useful because it gives us these red dotted lines. And what those are is it just allows us to make sure that the two tables are either aligned at the top, aligned perfectly in the center. As you can see if I have it down here, all aligned perfectly at the bottom as well. So that's just no great feature available to us just to make sure that everything is aligned if you're particularly fussy about making sure everything is perfect. But having said that, we want people to be able to see and work as well. So we do want it to be as perfect as possible. So now that we've got the two tables, we've got the flexibility. We can now see the summary at the city level and we can also see the summary at the individual level. So let's say we wanted to look at Brighton. All we need to do is select Brighton and what will happen is our second table will now automatically be filtered so that we only see the individuals and the sales available in Brighton. And we can see that total sales in Brighton was 224,400. And if we then look in our people table, so by individual, we can also see that again, yet we can validate that yes, this is just Brighton sales because our total is 24,400 and there was a total of 133 units sold in Brighton. So this is another really easy way to obviously manipulate our data or not manipulate, but break it down so we have a better understanding of what is happening and where the sales are coming from. Again, I keep going back to example of Excel, but this is a real benefit of Power BI. If we wanted to have both two steps as data and the flexibility to dynamically update for us, you can obviously probably already know by now that would be a bit of a, should we say a bit of a pain to have it produce and do exactly that functionality as easy and simple as it is doing here. So let's just move our tables down here because they're all good, they're working fine. So let's move that one there and let's just move this person one down as well. So what we're gonna do is now, as the title of the video is, is we're gonna bring in our very first chart. So what we'll do is we'll just use a chart to summarize the sales per city rather or we'll keep it in the table, but just as an addition to that, it's nice to see it in an actual visual. So when it comes to using any of our visualizations, all we simply need to do is just decide what one we wish to use and select that chart. So I'm just gonna go for a stacked column chart and you see it's added in there. And exactly the same way we populated our table, you can see that we've got now the ability to drag our relevant fields into our visualization. The only thing we need to do is just be clear on obviously where we're putting our information. So the first thing we wanna do is populate our access. So this is the value that's obviously gonna be along the base and measure our timeline for each of our sales. So you can either drag data in here, but for us, we're gonna simply just bring the city into the access. So we can literally just see, okay, for each city, there'll be a specific file chart for each city and in the total sales for that city. So in order to do that, we usually go into locations and drag city into our access. And you can see it's populated city at the top here, so we know information's been captured. And then all we're gonna do is go into total sales and drag total sales into our values. And there we go. As simple as that, we have now got total sales by city available in our visualization. So as you can see at the moment by default, it just sorts all the data by the largest to the smallest. So we can see that London is the largest there with just sort of 16,000. If you don't want to have it filtered or demonstrated or sorted, that's what I'm looking for, in this manner, all you need to do is having selected the graph. If you click the three dots on the left here or the right, sorry, you can see you could even have it at the moment it's selected by sort descending. You can have it sort ascending. So obviously it goes smallest to largest or my personal preference, or well again, depends what you're actually trying to filter on. You can change it so rather than being sorted by sales, you can have it by city. And then by that way, you can see we've now got an alphabetical order, what's quite nice on the eye to look at. So it goes from bright and through to path and you can see each of those total sales. If you want to make any changes to this graph, you know, in changing the appearance of it, all we need to do is go again, having selected the graph itself, is if you navigate to the right hand side, you can see at the moment where we've got our fields, we have this option selected here for fields. If we go into the next one, so the little paintbrush or the paint roller, you can see we're now got the flexibility to make some updates. So let's just go and add some data labels. So to all do that, all we need to do is select this toggle button, so go on to on and you can see that our values have now been added to that graph for us. We can then select our dropdown and this is where we can now change the year. So we can change if we want to be in millions, thousands on them or leave it on auto, what I tend to do. And we can also change the color or obviously what their values are showing in. So if you want to have it maybe in a purple color, then you can see it's purple. Or if you want to have it in white, you can have it in white. Obviously it's not really gonna show up on the graph, but the color I think most of the users will probably be gray like that. So like so. And then we can obviously, you can play around with the text sizes and anything else that you wish to play on there. So that's the color. And then let's go and compare that. And let's say you know wanted to change titles. So you can see we've got the title option available to us. So we've got total sales by city. If you didn't want to have a title, toggle button to remove that. Or you can obviously just change in here the text that you wish to show if that doesn't show you the correct words that you're looking for. And you can obviously go through and play around with all these different options to get the chart to suit how you prefer. And the benefit again with charts is if you want we can obviously move them around and obviously everything is dynamic. So we'll move around and move forward as required. But let's say we again wanted to look at just Brighton. So when we're in this table, we just click Brighton and it filters out a table for us. Likewise with our charts, if you just want to select Brighton for my chart all you need to do is select the relevant column and everything else will be filtered. And it goes both ways. So again, if you wanted to select Brighton from the table or from a chart, everything else on your page will be filtered to match that selection. And again, if we go into, I don't know if I've got any options like this, but let's select the name, let's say Amber. Okay, so then all we see is Manchester. But again, the reverse of that is if we select a name, so the most lowest level in our current data you can even see or update our charts so we can see exactly where that sales from Amber came from. At the moment all 4,000 of her sales are literally just in Manchester, but if she had appeared multiple times and she had other sales in other cities, then again, this chart would be a great way or a table to display where all those sales were. One last thing when it comes to charts, let's say we've suddenly changed our mind and we no longer want to have the stacked bar chart and we wanted to instead have a stacked bar or bar chart rather than column chart, sorry. All we need to do having selected the chart itself is then literally navigate to our visualizations, select another chart and you can see it's updated for us and it's maintained the ascending order, filtering or sorting that we've put on here as well. So hopefully by the end of this video, again, you've got more understanding of how to bring the data into Power BI and being able to start playing around with the different graphs and the tables available to us. So as we step forward in the series we'll be getting gradually a bit more technical with the ability or the information that we have available to us and obviously displaying that in Power BI. If you did enjoy this video, please don't forget to give the video a like and also if it's your first video or if you haven't already, do subscribe to the channel and make sure you hit that bell notification button that way you'll be notified of all of our future videos. And if you've got any questions at all, please drop me a comment below this video and I will get back to you as soon as I can. So thank you very much and I'll see you in the next video.


Forgive me. I feel it again. I call to the light. I know now what I must do, but I'm afraid I don't have the strength. Will you help me? Yeah, those are both dark side editions. Oh, you don't say. Only things. I've been wanting to try out some more white. Well, the black one is Darth Vader inspired. Oh. Oh, so it is. Bring this up. Press this.


On NVIDIA, NVIDIA is up another, what, $3 after the close, Intel continues to go higher. Microsoft, not that far away, by the way, Microsoft, not far away from the top of the channel either. We should definitely keep an eye on that as well. So yeah, there's a lot of good actions.


Hi, my name is Arcadia Rakhmovich and today I want to tell you about our work entitled some more of the merrier reducing the cost of large-scale MPC. This is joint work with Dove Gordon from George Mason University and Daniel Stern from Peraton Labs. So as the title suggests, this paper is going to be about optimizing the performance of a secure multi-party computation or MPC and in particular we're going to look at the setting where we want to run a secure computation between very large numbers of parties. But unfortunately, even though MPC has been a research topic in the crypto community for over 30 years, most of the truly practical protocols are really specialized for small numbers of parties, think two, three or four parties. And the reason for that is that in most of the protocols today, as the number of parties grows, per-party costs actually increases as well. So we're not getting sort of savings by increased number of parties, instead the costs increase and so in general we don't look at the case of main parties. And this brings us to our goal, which is how do we build large-scale MPC such that a per-party cost diminishes as the number of parties grows?  We achieve the following result. Our main theorem says that assuming a secure pseudo-random generator as there exists an MPC protocol that's secure against a static malicious adversary corrupting at most a third of the parties as it has both communication and computation that decreases as it grows. And in particular, the communication sort of behaves as a circuit size over the number of parties, while the computation grows as s log n over n times the circuit size, where s is a statistical security parameter. So today I'm going to present to you how this construction works. But before I do that, I want to quickly say that we're of course not the first ones to achieve, you know, MPC whose costs decrease as number of parties increase. And in particular, traditionally such MPC protocols fall under the title of sublinear MPC. And the reason is that when you look at the total cost of protocol, if it grows sublinearly as the number of parties increases, then the average per-party cost is decreasing. There are two general approaches for achieving sublinear MPC. The first one of these introduced by Dan Gardel back in 2010 is to use SIMD computation and the basic idea behind SIMD computation is that instead of operating at individual inputs, we'll instead operate on vectors of inputs component-wise. So instead of adding two integers, for example, we'll add component-wise two vectors of integers. And we can set up such a way that the cost of doing this in MPC is essentially the same for adding two vectors as it is for adding two individual elements. Because that's of course, if you pack in enough values into these vectors, then this achieves significant savings in our MPC and allows us to get costs that grow sublinearly and end. But there is an important thing to remember, which is that there is an overhead. Because we want to operate on vectors, that means that we need our circuit to sort of be nicely aligned, what's called a SIMD circuit. And to convert a general circuit to the SIMD circuit, we have to pay some overhead. That's going to be a big bottleneck for this approach. On the other hand, another way of getting sublinear MPC is something called committee-based MPC. And here's the idea is instead of running our MPC protocol in all-end parties, let's first elect a small committee, in particular, say a committee of size of polylog N to preserve the honest party threshold. And just have those committee members run an MPC protocol for us, where everybody else just provides input and then kind of sits idle. And the point is, of course, because all of these non-committee members are doing nothing, the total amount of work, and hence also the average amount of work, does decrease. But there's also the drawbacks of the committee members still do a good amount of work. So the non-committee members do nothing, but the committee members do a lot of work. And both of these approaches sort of have some drawbacks. Our solution really is going to take these and combine them to sort of get the best out of each one in order to achieve a solution that beats all prior ones. In particular, let's quickly compare our solution to the best prior available solutions. So if you look at the best committee-based solution by Denver et al, you will actually see that our solution is, or their solution is O of log C times worse than ours. And this, of course, comes from having to convert a general circuit into a CMD circuit. Now, I should say that a subsequent to our work, very recently at Crypto 2021, are going out, I showed how to reduce this overhead from O of log C to O of 1. But unfortunately, their protocol does not have an implementation. And so it's very hard to judge how it concretely compares to our protocols and relieves that for future work. Then looking at sort of committee-based approaches, the best solution there seems to be a full-core solution where you kind of elect a large number of committees and then have them execute the whole protocol together. And sort of the way we estimate the cost of such a committee-based solution, it turns out that O of S times worse than our solution. And finally, the best implemented solution is actually not at all a sublinear solution. It's actually a variant of the SPEEDS protocol by Demgard et al, which has communication cost as O of N times worse than our protocol here. So as you can see, we essentially beat out all the previously available examples by more or less combining them in a more efficient way. So now, before I jump into our protocols, I want to give some preliminaries that will help you build up the basic tools our protocol uses. But before I do that, I want to talk a little bit about how we measure complexity of large scale MPC. The traditional measure in this setting is something called average complexity, which makes sense. Its idea is here is we just count essentially as a total cost, let's say communication cost across all parties and then divide by a number of parties, and that gives you the average cost. But this has some weird behavior. For example, it benefits from having many parties that do nothing, because they all show up in the denominator, but not in the numerator, hence reducing the average. So for example, if you think of the case of committee-based MPC, the average complexity will decline, even if the committee members do exactly as much work as they did before. So even though they're doing just as much work, because all these other parties are now sitting idle, the average complexity actually goes down. And for this reason, we feel that a more natural complexity notion to really consider in this setting is something called bottleneck complexity, which was proposed by Boyle et al in 2018. And bottleneck complexity rather than averaging complexity across all parties looks at the maximum cost for a single party. And this way, of course, the parties that do nothing no longer help, because if the party don't do anything, they obviously aren't going to help reduce the bottleneck complexity of the party that does the most work. And additionally, if you consider synchronous protocols as our protocol is, then the bottleneck party will actually determine the time it takes the protocol to complete, right? Because the protocol is likely going out to wait until the last party completes whatever it's doing, and this party will form the bottleneck. And so because of this observation, our goal and hopefully you will see how we achieve this is to distribute the work as evenly as possible among all the NPC parties. So we want all NPC parties to be equally involved in every stage of our protocol. Now let me quickly cover a few of the basic tools that we use. The first tool that we use is a standard shimmy and secret sharing. I wish to share the secret, just fix the random polynomial degree D. And the shares happen to be poisonous polynomial. And the point is that if you have D plus one points, you can recover the secret, but if you have less than D points, then you can't. But for this talk, what's going to be important is that you can actually compute in these values. So you can add semi-secret shared values by just adding your shares locally. And you can actually also multiply semi-secret values by multiplying your shares locally. But of course, this causes your degree to double. And so you have to do a little extra work to drive the degree back down. So that's true for semi-secret sharing. We're also going to consider an extension semi-secret sharing called packed secret sharing. And here the basic idea is that there's no reason why you have to store only one secret. In particular, before we store the secret, the value is zero. But you could have also designated the values as a negative one and negative two, or really any points that aren't given out of shares as secrets. And the point again is that if you have a polynomial degree D that stores some number of L of secrets, if you have D plus one shares in that polynomial, you can recover all L secrets. But if you have less than D shares, or less than D minus L shares, then you actually can't recover those secrets. And again, we can compute on these shares, but now in exactly in a pairwise fashion. So the point is that by adding my local shares, I actually add all of the secrets to the pairwise value. And by multiplying my shares, what I can do is I can multiply as a pair of secrets, but again, the degree doubles. And so again, I'm going to have to work to reduce that degree back down. Another standard tool that we're going to use is called out of the secret sharing. So for those who don't remember, out of the secret sharing is the basic idea where to share a secret, I just pick and random values that sum up to that secret in say a field. And each party sort of gets one of these shares. And then we have an extension about the secret sharing that we also use called authenticated secret sharing. And here's the idea is in addition to that out of the secret sharing of a secret S, we also add a MAC key alpha and we secret share alpha as well as alpha times S. And you can think of this as essentially an authentication of secrets that there's no way for you to modify what the secret is and successfully open it unless you know alpha. And the nice properties that both these former secret sharing still allow non-interactive linear operations. For example, you can still add secret shared values by just adding your shares. So that's all the basic tools that we need. You know, hopefully if you remember those work. And now let's dive into our protocol. And I want to start with a very high level overview of protocol. So we're going to follow sort of by now a very standard way of building MPC protocols, which is by using Beaver multiplication triples, which means that we're going to have an offline phase in which we generate multiplication triples. And then an online phase that uses those triples to actually evaluate an arbitrary circuit C. So we're going to start by having all parties prepare these triples. But because we want to be communication efficient and sublinear, we're going to do it using Pax secret sharing. So we're going to have each part of the party essentially choose values AI and BI and then pack them in into Pax secret sharing and produce the Pax secret sharing of triples. Then we're going to take those Pax secret shared triples and somehow unpack them because remember we want to compute general circuits. So we can't want unpack triple standard out of the triples, which we then pass into online committees that then syndicate them and then run some online MPC protocol and we'll cover all these steps in a little more detail now. So let's start with the triple generation step. So our goal here is to produce Pax multiplication triples, AI, BI and CI, such that CI is a point wise product of AI times BI. And what we're going to do is we're going to use a Pax version of the well-known Damgard Nielsen protocol. So the idea here is that each party is going to produce a Pax secret shared vector of random values A, another Pax secret shared vector of random values B and what's known as a doubly shared vector of value random values R. What that means is we're going to have a Pax sharing of R of degree D and another Pax sharing of R of degree 2D and we're going to have the same values. And the way that's nice thing here is that this requires a per-party communication of all of that, right, just to sort of send out these shares to everybody else. Now what we need to do now is of course the problem is that these AIs, you know, parties know these AIs. And now we want to produce random values that nobody knows. One way of doing this of course would be just to sum up all the AIs, but that's very inefficient because that requires essentially N AIs to produce one secret value A prime. Fortunately, the Damgard Nielsen protocol preserves that if you use some random subtraction, particularly by multiplying these AIs by a Vandermonde matrix, then you can actually get all of N secret values such as an adversary controlling a small number of parties, doesn't actually know any of them. And you can also do the same thing for the Bs and the Rs. So you can get essentially all of N Pax shares of A, all of N Pax shares of B, and all of N Pax shares of these Rs. And the important thing is that now you've packed in all of N squared values, you know, with only all of N communication. And now we do the following. And this is again still following Damgard Nielsen protocol. So what we do is we have each party locally multiply their packed vector A, you know, this A prime they produce times the vector B prime and add to it this two G C to sharing of R prime. So the problem is when you multiply A times B, the polynomial degree went up to 2D, but you can still blind this with this 2D secret sharing of R. And then you open that value to a designated party, let's say P0. P0 can now reconstruct all of these secrets, so you can reconstruct this vector AI, BI plus RI. And he's going to again reshare it as a packed secret sharing, but now our degree D. Now all the parties receive their shares of this packed secret sharing. They also have shares of the packed secret sharing of degree D of RI. And so they can subtract this out and actually get a packed secret sharing of CI, which is AI times BI. And so it seems great because now we have N squared packed values and it took us only over then for party communication, but not so fast. Unfortunately, this is a problem. And the problem comes from something that was observed by the Jenkins et al. that showed that actually this packed version of Demger Nielsen is vulnerable to something known as a linear attack. So the idea here is that these inputs of the AI or the BI, if one of them is not now deformed, meaning that they're not actually degree D secret shares, then the adversary can cause correlation between the packed slots. So for example, here, we see that the second slot of the product vector has a term that depends on the first slot of the input vectors. And this is very problematic. In particular, if you work through the online phase of protocol later, you'll see that having such correlated products and such correlated triples actually completely breaks security. But fortunately, there's an easy fix in this setting. Basically, we just need to check that all the original sharings of AI, BI and RI are actually valid sharing in the sense that there are a line of degree D polynomial. And the reason we can get away with this is that we only need to do one layer of multiplication. We never have a case where we have to take it out for that multiplication and multiply it by something else because we will do it differently. So because all the triples are generated in one layer, we just need to check them all. And in particular, because they're all done in parallel, we can actually batch this check and just do all the checks all those shares at once. And so this ends up being really cheap. And so just adding this really does not impact the cost of our communication. And we still get all of n of all of n squared communication to get all of n squared packed values. So this is great. Now we have these packed triples. So what do we do is I'm so let's think about that. So what can we do with these packed triples? Oh, here we go. So the first thing we can do, of course, is we can just perform the online computation and the packed values. We already talked about this, you know, we can do SIMD computation. But unfortunately, this means that you pay an O of log C overhead to convert your circuit into a SIMD circuit. Of course, you combine this with a committee based approach by, say, sending those packed triples to a large online committee, say, of science by log n. And you still have this log C overhead. So this is still not great. A third approach that is going in some different directions to say, okay, let's actually unpack these triples first. So we have these packed triples. Let's just unpack them. And then we can send them to a small online committee. In particular, once we unpack them, we can convert them into additive secret shared triples. And then we can use a dishonest majority committee. Right. The nice thing is this avoids the log C overhead. But the problem is that once you unpack the triples, you actually have O of n squared triples, right? Because that's what you had. And now you'd actually send all those O of n squared triples and then, unfortunately, it causes all of n squared communications. So what we do is something a little different. So what we do is we actually send packed triples to many small unpacking committees. Now, this is a little bit counterintuitive because the whole point was that when these triples are packed, you know, we pack them optimally. So it requires all n parties to actually reconstruct such a triple. And so how can we get away with sending these packed secret shares to a small committee which can't even reconstruct them? And here we sort of use a very useful trick, which is the following. We observe that what we can do is we can have each party take their packed secret share. So their share of this packed secret sharing and add only share that to what we call an unpacking committee. Let's suppose that this committee exercise O of s, then, you know, this requires essentially O of s times n communication per party. So if we want to have these n of z packed triples, then it takes O of s n to send them all to this unpacking committee. And this still is now holding, you know, O of n squared triple values in there. But now the question is, okay, so now that we have this, how does this online committee deal with this? How does it unpack this? And fortunately, it turns out that, oh, sorry, I forgot to mention that we actually improve this to O of n by using a PRG. But it turns out that unpacking, you know, packed triples is actually a linear operation. And so we can do this unpacking step entirely inside of the additive sharing. So now that we've additively shared our packed shares, we can actually unpack them inside of the online committee by just doing linear operations with no additional communication. And so again, we now have O of n per party communication to extract O of n squared triples, right? And now these are actually additively shared triples. So I do want to sort of talk about some advantages of this committee-based approach. So the one thing is that by using many committees, we have to split all of these triples to unpack across the many chosen committees. In particular, if you have committees of size O of s, we can choose, you know, O of n over s, such committees without having the overlap of parties. And each of these committees is now responsible for just a s over n fraction of, you know, the circuit of that number of triples. And this allows us to reduce the, make it a computation cost of unpacking triples by just splitting the work equally across all of these unpacking committees. And other benefits, as we've said, is we sort of switch now to dishonest majority committees by using the added secret sharing. And the observation here is that if we think of concrete values, you know, if we wanted to use even honest majority committees to achieve, say, two to the negative 40th probability of failure of selecting a good committee, you need to check, remember, we started with a T lesson anniversary overall population, you would actually have to select about 430 parties in your committee. Whereas just to guarantee, you know, at least one honest party in each committee, you only need to select a committee of size approximately 25. So as you can see, even concretely, you know, this is saving a factor of almost 20 by electing, you know, many, many more committees and keeping them as small as possible. So now moving on, of course, now we know that we unpacked these things into these out of the secret shared secret shared triples. Now we should finalize how do we actually compute on this. And for this, we just follow the details of the speech protocol. So essentially, what we do is we have these unpacked out of the secret shared triples. The first thing we do is authenticate them. For this, we just kind of use a standard technique that originates from the speech paper, as it requires us using eight unauthenticated triples to produce one authenticated triple. We also use the same approach of speech to do the inputs and also just end up using the speech protocol in each of our committees to actually evaluate the circuit. So now let's think about how well does our protocol perform. So again, you know, what we've done is we use an initial pack secret sharing step to produce our triples. And then we use a, you know, committee based approach to unpack and run online pages of protocol. So how well does this work? Well, so for the first comparison, we actually came up with a folklore solution that most resembled our approach, which is as follows, basically you take committees, either honest majority committees or dishonest majority committees, and you use as many of them as possible to compute the offline phase and online phase of protocol, you know, also transferring triples in the meantime, and we, you know, figured out what the cost of that would be. And if you look at these, the communication, you know, across the board, our protocol beats the best possible sort of folklore committee based approach directly because we're using these pack secret sharing combined with committee based approach. And just a comment, we use the protocol of cheat at all for honest majority and we use speeds for dishonest majority.  Now I do have to say that we didn't have, you know, millions of parties to run this on special communications, the communication is estimated and simulated, but the computation costs are actually measured using the Lib IOP library. And you can see the results here shows that for, you know, and say up to two to 20, you can clearly see is that, you know, performance is improving as an increasing in particular for n equals to the 20, we're able to produce, you know, a million authenticated triples in about 10 milliseconds. So hopefully you see that as n grows, clearly the, you know, amount of work is decreasing and the efficiency of our protocols growing as well. Or as we would like to say, the more the merrier. Thank you very much for listening.