Honestly, that's the worst thing about going on vacation. So, I wanted to tell you guys that I grew up and drunk in the morning. Hey, what kind of dad? This is the sequel. Hey guys, what is up? Welcome to a new video. Cheers to that. So, I just got back from the cabin with my boyfriend and his family and we had such a great, relaxing time and I took the week almost completely off. I just did like a couple of things for YouTube because I just had to like upload some thumbnails and finish editing something. But other than that, I wasn't really focused on filming or anything like that. I filmed one which was like the road trip in a tiny bit. It's probably like the last vlog that I posted. But yeah, I'm officially back now. So, I just wanted to come on here and just like talk to you guys because I put out a little community like post saying that I'm not going to be posting at all this week which is last week when you're watching this video. But it was like my first time not posting for a week straight in like six months which is crazy.  And I'm like, you know, I think it's a healthy break and that's totally fine and we're coming back better and stronger. I was thinking a lot and I decided to follow my intuition and my gut and I decided on posting two times a week now instead of three times a week. The reason why is because so two out of the three videos was the vlogs and then the one video was a sit-down video. And as much as I love doing the sit-down videos and everything it's like I don't want them to start to feel forced because there's some weeks where I have to like think of a topic and kind of force it because I need that video if that makes sense and it was feeling a bit forced and I don't want things to get too repetitive. I felt like they were getting a little repetitive and so I'm going to incorporate more moments with Michaela in my vlogs. I'm going to make sure to try to do one every single vlog that I post. But in terms of like my sit-down videos I'm still going to do them just not every single week. It's just going to depend the week and it's just going to depend if I am fired up about a topic that one week. But as for now I'm just going to be posting my two vlogs a week and then whenever I feel very inspired and I really want to talk to the camera and just make a huge sit-down video like a full sit-down video then that's what I'm going to be posting them. So that's just making sure that nothing is forced and that I'm staying true to myself and true to my content and like doing what makes me happy. But yeah, I just think that a huge part in my journey is just learning along the way, learning what works for me. And right now this is just what I'm feeling and this is what I'm going to do because I want my videos to be have my 100% effort and be 100% authentic. I never really want to fake anything. I don't want anything to be forced.  I'm more about quality content rather than quantity. So yeah, I know you guys will understand and still love and support me. Yeah, just always make sure to stay true to what you're feeling in the moment and some people might think that going from posting three videos to two videos a week is taking a step back. But I think that for myself and my journey it's actually taking two steps forward because I'm listening to my intuition and I'm making sure that I'm going to be putting quality videos out there that are meaningful to me and that are not forced and that I truly want to put out. So I think that this is a step in the right direction. Okay, guys, I got my iced coffee. It's currently $257.  Honestly, that's the worst thing about going on vacation is the unpacking. I literally dread it so much, but I'm just going to do it so that I don't delay it because we just got back yesterday. If I don't do it now, I'm not going to ever do it. Like, this luggage is going to be sitting in my room for months. So I just got to tackle it. A lot of the stuff needs to go to the wash anyway, so it's going to be pretty easy. So we're good. Let's do this. I changed because I just wanted to wear sweatpants and I also finished unpacking. It's currently $3.30. I did that in half an hour and I thought it was going to take me so much longer for some reason, but it didn't even take me that long. So I'm so happy this is done.  It just feels so accomplished doing that because I usually procrastinate unpacking. I could procrastinate that for like literally like weeks. It gets bad. So I'm so happy I just got this done and I'm probably going to do my laundry in a couple of days just because I just want to fill my bin before. I was just listening to Emma Chamberlain's podcast. It's the episode called Rock Bottom and you guys should give it a listen. It is so good. She talks about like finding your passions and your hobbies and how important that is to put your energy into things that you get excited about waking up about. And she was saying how like, if you don't have something to focus on and put your energy towards that you love, then you're going to start, it's going to start with spiraling inside. And she was saying that like humans are problem solvers and when you don't have problems to solve, you're going to make problems for yourself like on the inside and it just makes so much sense. And it was such a good, such a good episode. So while we were away, we ate so unhealthy, like literally Pillsbury Doughboy was me. Like I was Pillsbury Doughboy. We ate that unhealthy and it just motivated me to get back on my health kick for real this time. So I'm meal prepped. I have a few recipes on here that I'm going to do for the rest of the week. Tomorrow we're going to go grocery shopping to get everything for them. Stock the fridge so that I can make some nice dinners. I'm excited. It gets me excited to eat healthy and get my body the nutrition that it needs because it hasn't been getting literally any nutrition this past week. So I'm really excited to get back on my health kick. It has to happen.  Obviously it's okay to indulge sometimes everything in moderation. But for the most part, I do need to start really eating healthy and getting good dinners in nutritional dinners, nutritional meals. So this starts tomorrow not now tomorrow because we're going to go grocery shopping tomorrow. So starts tomorrow. So what I also did is I filled one of these like vitamin things up with vitamins for the PM and AM so that I remember to get all my vitamins in because I find that if I don't have something like this then I'm going to neglect vitamins and forget to take them. So this is going to hold me accountable. And I know this is like a really granny thing to have but honestly, it's how to stay on track with all your vitamins. Like it's actually so beneficial like I feel like granny with this but it really works. Hey guys. So it's currently 6.50 and I'm current and I'm currently on the way to the gym. Joel's just driving because he needs the car to do some errands. Well, I'm at the gym. I'm going to meet Julia there. So we're going to do a good workout together. I haven't gone to the gym in over a week because we were like on vacation. So this is going to be a rough go but it'll be fine. I just got back home from the gym. I totally forgot to vlog at the gym. Like usually I show like my little montage of my workout but I like totally forgot to. But anyways, I'm just out enjoying the night right now. The moon is so freaking cool. Joel dropped off our camp. Me and Julia's disposable cameras to get developed. So we're going to get the photos and I'm so excited to see them. It's like such a cool surprise. I don't know. It's just so exciting. So I'm so excited. So I wanted to tell you guys that I have quit TikTok and what I mean by quit TikTok is like I quit watching TikToks because it feels like a waste of my time and the more I go on my phone and watch TikTok or just on my phone in general during the day the more that I like feel the about it and less productive and I have decided I've made the decision to stop watching TikTok and even before bed I would scroll through TikTok but now I'm just going to make a rule that I want to do more reading. I'm going to read before bed and not even touch my phone and I feel like it'll just be a lot healthier and I'll go to bed earlier. I just got some new books. So I'll show you guys when I get inside and I'm so excited to read them. But yeah, because I found that TikTok was kind of like it sounds dumb but it was kind of like a roadblock and it was just like distracting me and it's like I can't be always looking at my freaking phone and scrolling like I need to be looking elsewhere and if the time wasn't dedicated to TikTok like what else could I be doing and that has been like resonating with me like if I wasn't scrolling through TikTok for an hour I could have been doing something more productive and that like gets me kind of angry because it doesn't make me feel fulfilled and I feel so much better not going on it. Yeah, I'm still gonna maybe post a video now and then if I want to but I'm not it's not gonna be something that I'm gonna do like look through constantly and be addicted to. The sensor light just went off so that's what the lighting changed. But yeah, so I just wanted to come on here and tell you guys that focus on what makes you feel the best and if you need to make changes in your life make sure you're listening to yourself your body and make the changes necessary. Don't make excuses.   That's the secret is you control everything. You control your thoughts. You control whether you want to be happy. It's all in your control and in your thoughts, in your mind. Anyways, I'm gonna go inside now, eat, shower and watch The Bachelor in Paradise but I'll talk to you guys later. Oh, that was such a good freaking workout. Like I feel so good. Hey guys, so me and Joel are just about to go grocery shopping. We're going to like this big grocery store that's kind of like 15, 20 minutes away from my house. We're venturing out because they have like way better prices. It's so much bigger. They have literally everything. So we're going there instead of my local grocery store because it's going to be like literally probably triple the price for everything. So we're going to super store if you guys know what that is. But anyways, this morning, okay? We're at Starbucks right now and I'm going to explain why. This morning I went to go make myself a smoothie and I found pineapple in the fridge and I was like, I was going to use a frozen pineapple but Joel had just finished it. So I look in the fridge and I was like, oh, there's pineapple in here. And it was like in the container. So I was like, oh, might as well just use this. I opened it and I'm like, the color was fine and I didn't smell it. So I didn't expect it to be old.   So then I go to the pineapple and I smell it and it literally smells like wine. It smells like fermented pineapple. And I'm like, are you kidding me? Because it wasn't like moldy or brown. Like it didn't look bad. You could have gotten drunk from it. I know, I could have gotten drunk. It's not a bad thing. That's what they do in prison. I know, that's what I was telling Lucas. Yeah, that's exactly what Lucas said. He's like, you could have gotten drunk in the morning. Accidentally, like imagine that got me drunk.  Well, it probably doesn't taste good. It was disgusting. Yeah. And anyway, so I wasted it.  And I had a piece of bread instead because I didn't want to make another smoothie. I'm like, I'm done. But now we're at Starbucks and I'm gonna get a Starbucks because that was a bit of a shitty start to my morning. So we're gonna, I'm gonna treat myself to Starbucks because when something happens like that, you got to treat yourself to make yourself feel better. And it sounds like weird, but Starbucks will make me feel better. So that's what we're doing anyways. But we're gonna get an iced caramel macchiato. Are you gonna get anything? I might get a regular coffee.  If anybody knows how these air fresheners work, let me know because this has been in my car for like months now and I haven't smelt it at all. Like, is it supposed to like, how is it supposed to dispense the, am I supposed to pour it in something?  Hold on, let me see something. I think what you're literally supposed to do is this thing is just to hang it and you're supposed to just keep it open. It doesn't spill. But that's kind of a shitty car air freshener then. It's like, this is supposed to hang on my thing. Where else am I supposed to put this on the drive? Well, I think maybe it's supposed to slowly leak out of this thing but it just... Yeah, whatever. But if you guys know, if you guys have one of those and you probably don't, but if you do, let me know. Let help a girl out. See, this is why I hate these things in the middle. Like, I literally have a rosy that my mom... No. No, I just have put it perfectly up Joel. It's broken. Oh my God, it's broken. My mom got this rosary blessed. That's gotta be padlocked. My mom got this rosary blessed and she put it in my car and I didn't even know it broke. Maybe I did, but then I just like wrapped it around a long time ago but I don't remember. Anyways, let's go get Starbucks because... We deserve it. Yes, especially after my smoothie incident. See, it always makes me so mad. I'm sorry if you guys have never noticed this and are just noticing it because I'm pointing it out but this always makes me so freaking mad in the videos. Why don't we just take it off? Yeah, I don't even know. It's because this was there and anyways, let's go. Okay, Starbucks review. Got the ice caramel macchiato. This is like my go-to without milk because this only has two espresso shots in it and I never knew this but I used to order the brown chicken espresso and that has three espresso shots in it and I always wondered why I felt so jittery after that one. It's because it has three espresso shots in it. So I like to stick to the one that has two and this is just literally just always hits the spot. Cheers. Joel, how's yours? Good. Just coffee though. Boring. Actually, that was like half the price of this, so. All right, let's go to superstore. Okay, let's rock and roll. Hey guys, so it's a lot later. It's currently 7.37 and I just finished making dinner. I made butternut squash risotto. I'll insert some pictures right here. It was so good. Immediately I want to go to the gym but Joel has my car right now because he's mountain biking. So I'm kind of just waiting on him to come back and then hopefully we can make it to the gym if he gets home on time. But yeah, I was just working today and then I cooked so nothing really special. But I'm excited to get back on eating healthy and just nutritious, good dinners and meals. And I love like making different things, experimenting, it's fun making different things. I think right now what I'm going to do is I'm going to watch some YouTube because I haven't watched YouTube in so long. One of my favorite YouTubers is Hitomi Majizuki. Sorry if I botched that but she's like a spiritual YouTuber I would call her and she just like has really wholesome content. Has a calming persona. Okay, I'll talk to you guys later though because I'm going to binge a little bit right now. Hey, we're kind of done. We're going to go anywhere. What a great girlfriend I am. What is it? I have to be promoted. We need too much of that. This is enough for maybe a ladybug. What? Is it good? Maybe the biggest one. Okay, so I'm aware that I look like a hermit right now but I told you guys that I would show you the books that I got so I'm going to do that before I end this vlog off. So, this is a sequel. It's called The Summer I Turn Pretty. I got the full three books and then the second one is It's Not Summer Without You and the third one is We'll Always Have Summer and it's by Jenny Han. I got three books. I just started this one. It's good so far but I'll keep you guys updated when I finish. But yeah, like I said, I really just want to get into rooting more instead of being on my phone because it just feels more productive. It makes me feel better and it's all around. Your brain is working rather than scrolling your social media. It's just kind of like almost could be toxic sometimes. So, I'm becoming a reader. Next thing I want to show you guys, a sweet subscriber of mine has her own little business and so she sent me a little package and I wanted to shout it out. So, her website is called Novel Wix and she sells candles. So, go check her out, you guys. She's on Etsy and look at how freaking cute it is. Do you guys literally see that shimmer? It's unbelievable. I haven't burned it yet because it looks too pretty to burn. Almost like I don't even want to touch it. So, thank you so much, Murphy, for sending me this. This was so sweet of you. I cannot wait to burn it and use it. Go check out her site. She gave me a coupon code. That is Mikaela10 and you guys can get 10% off if you shop her site. So, I'll link it down below. So, go check her out. I love supporting small businesses. If you guys have a small business or anything, just let me know and I would love to promote it for you guys. But anyways, thank you guys so much for watching this vlog. Stay tuned for my next one. Give it a thumbs up. Subscribe. Yeah, I love you guys as always and I'm always sending you guys positive vibes. See you guys in my next one. Bye.


Thanks to you all for joining me today as I discuss product market fit from a FinTech perspective, looking back in time. I'm Leo Hurwitz, Senior Product Manager at Microsoft. This presentation is given in my personal capacity and is not related to work I currently perform at Microsoft. Let's start with an intro. In about 2007, I joined a company who worked on FinTech in South Africa. They revolutionized the ATM, credit card, and prepaid card space in South Africa. It was a gutsy company, often at the front of innovation, from self-cached ATMs to prepaid gift cards and independent credit card services. Little did I know that this FinTech journey would go from South Africa all the way to the Middle East where I am today. The anecdotes provided in the next 15 minutes or so will give a view to products that fit certain markets yet failed in others. I will also provide some evidence that products which you think may have started in one place may have actually had their seeds elsewhere. This journey will take us through South Africa, Israel, Kenya, the USA, and beyond. I hope you enjoy the ride. In South Africa, due to the median salary being particularly low, airtime or contracts for airtime and contracts for data are not accessible for the majority of the population. The Gini coefficient, which is a measure of income inequality in South Africa is one of the worst in the world. This is due in large part to historical reasons where the vast majority of the population were excluded from the broader economy based on their skin color. Due to this low median salary, instead, what they have are vouchers that can be purchased with provide prepaid airtime. This eliminates the need to budget on a contract and prove financial means to qualify for a contract. Airtime can be purchased by cash or card at a certain number of outlets. This airtime is printed on slips or receipts with a code and by using USSD prompts, the user is able to load airtime to their account for immediate use. For those unfamiliar with USSD, USSD is a method for communicating with the telecoms provider servers without needing a smartphone. In South Africa, this mode of use is common due to the relative expense of smartphones. Back in 2008, more or less, I was working at a credit card company and we decided to diversify into the airtime space. We thought it was a logical step as we had the credit card machine in place which could print receipts and we could easily develop a system to store vouchers and then pull them down to the terminal for printing a time of purchase. We developed the system with gusto and rolled out the feature at incredible pace. We engaged marketing teams, legal teams, formed partnerships to supply the vouchers to us wholesale and created new menu options on old school credit card machines. We made sure that our voucher store was fully stocked and that our devices were able to quickly and efficiently pull a voucher down on demand. The benefits to the merchants were clear too. They could sell airtime for additional revenue and increase foot traffic in the store which would invariably lead to other sales as well. We were ready to go. And at first, the results were promising. But we couldn't keep up with the pace of signups where the captive audience with people who owned our credit card machines and so sales came easily. In addition, sales of airtime were going up, orders for our machines were increasing and stores that had one machine suddenly started requiring a second to keep up with demand. But then, unforeseen issues started to arise. As word spread that our stores were selling airtime, people started buying. The issue was that people were coming to buy just airtime. Hues formed for the airtime, but people trying to buy large ticket items were stuck behind people buying a few dollars worth of airtime at a time. Eventually, after waiting in line, people gave up and went elsewhere or complained to management about the wait. Imagine the scene.  Slowly, the voucher distribution system started fading as cancellations began trickling in. This wasn't sustainable. We tried to pivot going to other types of merchants on the lower income brackets spectrum and in other areas, but in the end, this failed dismally. The lesson we learned from this is that often, although product market fit can seem to be perfect, there are external factors which could impact an otherwise sound plan. Our next case study is the peer to peer money transfer markets. I'm sure most of you have heard of Zell and Venmo. These are apps used for transferring funds between users with the use of cell phone apps in the USA. What many people don't know is that a forerunner to this existed in Africa that started as far back as 2007. Impeza, the M stands for mobile and Impeza Impeza is so healing for money is a mobile phone based money transfer service payments and microfinancing service. It was launched in 2007 by the photo phone group and Safari come the largest mobile group network operator in Kenya. Impeza allows users to deposit, withdraw, transfer money, pay for goods and services and access credit and savings, all with a simple mobile device. There's no need for fancy apps or even a smartphone. The service allows users to deposit money into an account stored on their cell phones to send balances using pin secured SMS text messages to other users, including sellers of goods and services and to redeem deposits for regular money. Users are charged a small fee for sending and withdrawing money using the service. Impeza is a branchless banking service and customers can deposit and withdraw money from a network of agents that includes airtime resellers and retail outlets acting as banking agents. Impeza spread quickly and by 2010 have become the most successful mobile phone based financial service in the developing world. By 2012, a stock of about 17 million Impeza accounts had been registered in Kenya. By June 2016, a total of about 7 million Impeza accounts had been opened in Tanzania by Vodacom. The service has been lauded for giving millions of people across access to the formal financial system and for reducing crime and otherwise largely based cash based society. So how did it work in South Africa? In September 2010, Vodacom and Nedbank announced the launch of the service in South Africa where they were estimated to be more than 13 million economically active people without a bank account. Impeza was slow to gain a foothold into South African market compared to Vodacom's projections that it would sign up 10 million users in the following three years. By May 2011, it had only registered approximately 100,000 customers. The gap between expectations for Impeza's performance and its actual performance can be partly attributed to differences between the Kenyan and South African markets, including the banking regulations at the time of Impeza's launch in each country. Despite efforts as of March 2015, Impeza still struggled to grow its customer base. South Africa's lag behind Tanzania and Kenya with only about 1 million subscribers. On further investigation, this came as no surprise as South Africa is well known for being a head of financial institutions globally in terms of maturity and technological innovation. This may be interesting to hear considering the low means of the vast majority of the population, but as an anecdote, checks have not been accepted in South Africa for years and bank to bank transfers are common across all banks. According to Genesis analytics, 70% of South Africans are banks, meaning that they have at least one bank account with an established financial institution which have their own banking products which directly compete with the Impeza offering. This is in contrast to Kenya and other African countries which have much lower penetration. Taking this all into account, even though there were a number of similarities between the markets in Kenya and South Africa, the product market was not right in South Africa. Now a little about impulse. Square was founded in 2009 by Jack Dorsey and Jim McKelvie. The Square Reader was the firm's first product. It accepted credit card payments by connecting to mobile phones, device audio jack. The original version consisted of a simple read head directly wired to standard three and a half millimeter audio jack through which unencrypted analog card information was fed to smartphones for amplification and digitization. Even though it wasn't secure at the time, this innovation started a revolution. Small merchants throughout the USA were able for the first time to accept credit cards as a form of payment. This reverberated around the world and we in South Africa at the time followed suit and introduced an impulse offering. While the concept was the same, due to the fact that South Africa had already started planning for the EMV shift, our devices connected via Bluetooth and accepted EMV or chip and pin cards through a different card reader. Following our release, the banks were quick to follow as well as a major competitor called the Open. Today, South Africa has hundreds of thousands of micro merchants for whom this is a great solution to accepting their card payments. The merchant in impulse in South Africa was a game changer. Everywhere you went, you could now pay with card and everyone everywhere was able to accept card payments. Even buying a newspaper on the side of the road or apples in a market, the merchant was now accepting this form of payment. The demand for this product kept growing and some banks had been caught flat footed, even approached us to white label the product for them. We had struck oil. We were offering in an in demand service with reports fraud prevention and portals with easy access and viewing of transactions. It was about this time that I decided to relocate my family and I packed up our bags, our house and our lives and we relocated to Israel in the Middle East. Here, impulse was also taking off and it made sense. There were plenty of micro merchants with stalls at markets or similar schools or smaller schools. Due to my experience in the market in South Africa, I was hired by a company here to help with their credit card business and the impulse offering. After a few months of working on the product, it was clear there was something that wasn't working. The market was stagnating. Why? Well, I'm not 100% certain, but I can only surmises due to the following. In Israel, the population size and addressable market are too small. Israel has about 10 million citizens in total. Two, the cost of owning a traditional credit card machine is low. So the cost of saving on an impulse terminal is limited. Three, unlike in South Africa, the vast majority of Israel is banks and have access to smartphones, so people pay with P2P applications with ease. And four, Israel's fraud cases are very low, meaning there's a high trust factor in payments, reducing the need for a secure payment mechanism with the card. People again fall back on P2P applications for their businesses. We then pivoted to offer gift cards, gateway services and other financial services while keeping the impulse offering as a value add. As can be seen, what worked well in the USA due to demand and share population size and South Africa due to informal sector being so large was not a fit for the market in Israel. So, as we close out, there are three takeaways from our presentation today. One, innovation is everywhere, as can be seen with EMPESA. A startup in Africa, which is not often seen as the hotbed of innovation, revolutionized payments in 10 countries. It is still going strong and is a great fit for the market where smartphone penetration is low and banking access is limited. Two, innovation doesn't work everywhere, as we saw with EMPESA and EMPOS. What seems to work in one place won't work elsewhere necessarily. EMPESA failed in South Africa and EMPOS is struggling along in Israel, even though at first glance, the market seemed perfect fits for these products. And three, product market fit has an element of art, as can be seen with the EVD. Even the best research solutions may fall at the unseen hurdle, like foot traffic for low cost items being higher than the demand for higher value ticket items. Thanks so much for joining today. It's been a pleasure presenting to you. And should you want to reach out, these are my contact details. I look forward to hearing from you.


So here at the Sony and who are you? My name is Mark Weir. I'm the senior technology manager for digital imaging here at Sony Electronics We're here at CES 2016 We're going to talk to you today about the new a7r mark 2 and a7s mark 2 cameras, which shoot 4k video internally these models are in the market already a7r mark 2 was introduced last summer and gained a lot of interest along the photography and videography community because it's a 42 megapixel camera that can capture 4k video and can do it very very cleanly and without any artifacts which is common with high-res when you're trying to shoot video with high-resolution cameras With 42 megapixels we can operate in both the full frame 4k recording mode for 3840 by 2160 at 24p or 30p We also have an option to crop for super 35 and shoot at 24p or 30p And when we've cropped at super 35 we can have two times over sampling for an amazingly well graded and sharp image in 4k So these cameras using a full frame sensor. It's one of only two cameras Available today that can shoot 4k video on the full width of the image sensor. This is the a7r mark 2 It's in the market today at about $3,200 for the body the second camera that we're going to talk about today Is the a7s mark 2? So the a7s mark 2 is physically the same as an a7r mark 2 We're showing it here with a video lens a 28 to 135 servo zoom video lens But the difference with the a7s mark 2 is in the image sensor instead of using a high resolution Sensor which is great for both stills and video the a7s mark 2 uses a low megapixel sensor This is just 12 megapixels and the purpose here is to get maximum Sensitivity and dynamic range we're using a full frame sensor with just 12 megapixels the individual pixels are very large Have tremendous light gathering capability that couldn't be possible with a higher resolution sensor And also they have very high saturation levels So this camera can deliver Sensitivity and dynamic range that allows it to see beyond human vision you can shoot video and stills up to 409,000 ISO And the camera can shoot clean 4k video in light that is lower than what you can see in So the real advantage here for both photographers and videographers is the ability to capture in light So low that other cameras would very much struggle this camera can shoot cleanly easily At a hundred thousand ISO which is well above the limits of any other camera available today in its class So this camera can shoot 4k video across the full frame sensor It's one of only two cameras that can do that and record internally in the XAVCS codec 100 megabits per second or 60 megabits per second 24p or 30p So this is the a7s mark 2 and this is in the market We reached the market in October and November of 2015 and this is positioned at about three thousand dollars And so the video enthusiasts are very excited about these full frame Cameras for 4k. Yeah, the reason why is that? There really are no cameras that are shooting 4k video across the full width of the image sensor That's very very challenging to do and by using a very large image sensor like that Videographers can control the plane of focus to use depth of field as a As a part of dramatic storytelling they can shift the plane of focus from an actor in the foreground to an actor in the background And that becomes part of the storytelling of the video so full frame and what full frame brings to video Production is a tremendous advantage, and that's one of the things that's been very attractive for videographers Of course on top of that you have the advantage of interchangeable lenses and lenses that can match the requirements of video This is very special one right yeah This particularly is well suited for video because in addition to having a zoom. It's also a servo zoom There's a motorized zoom, which is something that you can't find in lenses for SLRs It's also a par focal lens, so there's no focus ramping There's no focus breathing which again is not something that you find in lenses designed for SLRs But only lenses that you are designed for video So some videographers are probably saying that this is the best camera in the world Well, some have said that there's no doubt, but there's room for both of these models The a7s mark 2 is particularly well suited to those who are shooting in low or no light and not in control of their lighting situation a7r mark 2 is Again a tremendous advantage for videographers But this is more suited for those that want to be able to have high-resolution performance for stills and video and Perhaps don't need quite as much capability in low or no light But the two of them are really a pair and they appeal to videographers and photographers alike Just slightly different applications depending upon their work, but when it has a great performance for low or low light Does I mean it has great performance for all kinds of light to also for a lot of light? Absolutely It's not just a question of low light It's a question of wide dynamic range And that's really where the the very very large pixels of the a7s mark to come into the benefit


Good morning, and thank you for showing up this early. What I'm going to talk about is an application of ideas of course-grainning and the Wilsonian approach to the realization group to a problem to which, as far as I know, these ideas have not been used. It's recently the discussion started along those lines. And the talk was prepared for a longer... The talk is longer, the transparencies are for a longer talk. That's why I'll skip through some pages. I just left them there for completeness. I'll just point out the main points. Now the problem that concerns us is this. So this is the distribution of matter in the universe. This is the large-scale structure as measured through galaxy surveys. And the homework is to understand how this thing comes about in the context of the cosmological evolution, in the context of the cosmological model. And this is today's picture of the universe. You can go back at higher redshift, which means back in time, and you can see how the thing evolves. And basically the idea is that structures form at later times, starting from some initial perturbations which were generated during inflation. So the problem is how to predict what we should see today, starting from some scaling variant spectrum, probably generated by inflation, and how this can constrain the parameters of the cosmological model. Now this is a difficult problem to solve analytically. The best results are obtained through numerical simulations. That's the best understanding today. But lots of work has gone into analytical approaches to this problem. And this is what I would like to describe, an approach to an analytical understanding of this problem. Now, basics of cosmology, we assume homogeneity and isotropy of the background. So on large scales, we approximate the universe through the FRW metric. We get Friedman equations for the time evolution of this structure. The matter content of the universe our best understanding now assumes two main elements. One is a pressure less fluid characterized as dark matter. It's modeled as a perfect fluid with zero pressure. It accounts for 25% of the budget of the universe today. The usual assumption is that it's composed of weakly interacting particles. Basically, you can even assume that they're completely non-interacting. And then there's another component characterized as dark energy or cosmological constant if it's time-independent, which accounts for 70% of the time. It results in negative pressure, and it gives a current acceleration observed for the expansion of the universe. Now, what we're interested in are in homogeneities on top of this background, which are treated as perturbations, which grow under gravitational collapse, and eventually they result in the structure that we observe today. Now, the relevant field is what's called the density field is the local variation of the energy density. Over the average density of the universe, in Fourier space, these are the Fourier components of this field here. And these correlators give what's called the spectrum of these cosmological perturbations. And this is what we would like to compute. Now, there are measurements, as I said, from galaxy surveys. And one thing that's plotted here is the galaxy correlation function. The Fourier transform of that is the spectrum. And you can see a bump here, which is characterized as the bump of the barrier and acoustic oscillations. You can see that the distance of approximately 150 megaparsec, the distance between the typical distance between two galaxies is over the one megaparsec, just to give you an idea of the scales. The size of a galaxy is 10, 20, 30 kiloparsec, depending on how far you assume the dark matter extends, typical clusters of galaxies are of the order of one megaparsec again. Above 10 megaparsecs, you assume that homogeneity sets in in the distribution of matter in the universe. This is just to give you an idea of scales. So this is a particular feature that's of interest because it has been observed and can be measured with precision, as you can see here, from more recent surveys. This is the form of the spectrum over a large range of wave numbers. What I would like you to keep from this is that it falls off at a large scale, roughly a scale to the minus three, and this is important for what I'll say in the following. Now, in this region here, which is around 0.05, 0., sorry, yes, 0.05 to 0.1, 0.2, in these units, if you magnify the spectrum, you see here it's normalized with respect to a smooth spectrum. And you can see oscillations in the spectrum, which are the result of that particular feature that I showed you before, this bump in the correlation function of galaxies. And these oscillations are of particular interest. This is what we'd like to understand precisely. Now, they are characterized by a scale which comes from the alien universe, and it's actually a scale of acoustic oscillations during the recombination era. When photons and barions were coupled to each other, and then they decoupled, this feature was generated around that time. And it's also imprinted on the cosmic microwave background, where it's measured very precisely. As you can see here, these points here have error bars. And you can see how precisely this feature is measured in the CMB. Now, the task is to predict this feature in the context of the cosmological model, what it would look like in the distribution of matter, and combine the two in order to get precisely the parameters of the cosmological model. This is the task. Galaxy surveys, ongoing and future surveys will measure the distribution of galaxies very precisely. The aim is a precision of the order of 1%. The task is to obtain something similar through analytical or numerical calculations. And this is a hard task. And that's where all this work comes in. Now, standard cosmological perturbation theory is used to study this problem. Perturbation theory, it means that you write down some hydrodynamic equations for a pressureless ideal fluid, and you solve them. There are interactions. There are nonlinear terms in these equations, which you view as interactions. And you set up some kind of perturbation theory to solve the system of equations. But at a linearized level, these hydrodynamic equations, each Fourier mode evolves independently. But at a nonlinear level, higher order corrections to this perturbation theory take into account mode coupling. And this is a difficult part to take into account. Now, the current interest in this subject started from the work of these two people, even though the original works go back to the mid-80s. As I said, the Baryon acoustic oscillations is a feature that's viewed in the spectrum at this range of 0.05 to 0.2 inverse megaparsec. This is a mildly nonlinear regime of perturbation theory. That's why the attempts were made to compute it analytically by resumming orders, higher orders of perturbation theory, using techniques from field theory. Now, the problem is that if you go to even higher case, smaller length scales, these higher order corrections dominate, and the system becomes completely nonlinear. And this is a problem that you cannot predict analytically what happens at small scales. It's a range where things collapse to form virialized structures, galaxies, clusters of galaxies. And there, this perturbation theory doesn't work. And the theory becomes strongly coupled for k larger than one inverse megaparsec. Actually, the whole hydrodynamic description fails at those scales, slightly higher k. So this deep UV region is out of the region of perturbation theory. And the inspiration for what I'll describe comes from the suggestion of these people here that since you cannot really describe this microphysics of galaxies, well, what you could try to do is to use some effective description on large scales in which you introduce effective couplings to take into account the coarse-graining of the short distances, of the galaxy-level distances. And this goes under the name of effective field theory of large-scale structure. It was instigated by these people here. And what I'll describe is a variation of this theme in the context of the Wilsonian energy. And let me remind you a couple of, very briefly, a couple of very basic points that will appear in what I'll show in the following. So what's the coarse-graining about integrate out all the modes above a certain mode, I'll call it KM. And replace them with effective couplings in the low-energy theory. This is the Wilson's idea. Now, in the context of the effective average action and the veterinary equation, let's take the simple example of a scalar theory with bare action S of chi. You add a regulator, you do the Lausanne transform and remove the regulator, and then you gain a coarse-grained effective action which satisfies an exact equation. Now, in the approximation that you just take a standard, the local potential approximation and they even neglect the wave functionalization, you just have the potential. And if you solve at one loop, what you find is that your potential at the scale KM is the bare potential plus something like a one-loop integral, but with the momentum integration constrained between the scale KM, this coarse-graining scale, and the fundamental scale of the theory. So basically what this says is integrate out the UV and put it into effective couplings and then study the low-energy theory, but now you have to remember that the low-energy theory contains these new couplings that correspond to these contributions, but you have to compute everything on the low-energy theory with the UV cutoff because everything above KM, you've already put into the effective couplings. So this is the basic framework. Now, one question that I'll mention briefly is why is all this relevant for this problem which seems to be classical physics, so why bother with these techniques? The problem is that the reason is that this problem has, you know, the early universe is a stochastic medium. Okay, these fluctuations, the fields that fluctuate, the density and the velocity fields to a very good approximation of Gaussian random variables with an almost scale invariant spectrum that comes from inflation. Okay, so it's this stochasticity of the medium that forces you to use field theoretical techniques in the spirit of what's done in condensed matter, for example, in systems with knowledge. Now, the coarse-graining that we want to introduce it will be formally implemented on the initial condition for the spectrum at recombination. After this era in which variance and photons are coupled, you have initial condition which describes a stochastic medium, okay? Now, within this context, what I will argue is that dark matter, contrary to the standard assumption, is not a perfect, pressure-less fluid, but you have to include these higher-order couplings and in this case, they amount to effective viscosity at speed of sound. These are tiny variables that contribute. They're not big, the viscosity and the speed of sound are not large, but still they're important in order to get a consistent description and convergence of whatever perturbation theory you do in the low-energy theory. This is what I would like to show. Okay, now the scales, just to remind you again of the scales, what would be the fundamental cutoff is something of the order one to three inverse megaparsec. This H is around 0.7 is the Hubble constant in units of 100 kilometers per second per megaparsec. So length scales are three to 10 megaparsec. This is a scale of clusters of galaxies or higher. So at these scales, a fluid description becomes feasible and I'm allowed to use hydrodynamic equations. Then, at even larger scales, this fluid description becomes simpler so I can describe it within the first-order formalism by just introducing viscosity and speed of sound in the, for the fluid. Now, for viscosity, I can include, you know, I can have two types, what I would call effective viscosity, which is a result of the coarse-graining or fundamental viscosity, which comes about if I include interactions between dark matter particles, I won't have the time to discuss this. I'll focus more on the effective viscosity because this is what's related to the notion of coarse-graining. Now, one important point now because first of all, I want to, you know, to see what kind of, what are the relevant scales for the viscosity that I expect for this fluid. And one particular amount, which is not very well known, it's known and realized by the people working in the field, but the description of dark matter as a fluid is not obvious. I mean, it's a non-interacting gas of particles in the most common, that's the most common assumption. So it's the don't interact, how can they form a fluid? I mean, that's the question. And the reason why you can describe dark matter as a fluid is because dark matter is non-relativistic, it has a finite velocity, maximum velocity, and the age of the universe is finite. So, here's the reasoning. Now, you can take the phase space density for dark matter, you know, for the dark matter particles, factor out the homogeneous density, and these are the perturbations. Okay, and you can expand those in the lasagna polynomials and these coefficients here are what generate higher moments of the distribution function, which will give you the density, the pressure, the shear tensor and so on, it will be generated by moments of this related to these coefficients here. Now, if you write down the time evolution of these coefficients, starting from the Boltzmann equation, or if you neglect the interaction, what's called the Vlasov equation, what you find is that the time variation of these coefficients is given by expression like that, it's proportional to higher and lower coefficients, but there's a factor here which is the scale of that perturbation that you're looking at, this is what this k stands for, and the typical velocity of the particle. So it's this coefficient here that is small for dark matter and which tells you that if this time variation given like that, which is given like that, and the time that you have your disposal is finite, it's one over h where h is the Hubble parameter, so this is the age of the universe or the magnitude, then how much can these things grow from zero because initially the system is in equilibrium at very early times, so the higher moments are negligible so you can neglect them. So you need these coefficients to grow in order to have a substantial form that forbids a fluid description. If this coefficient is small enough and the age of the universe is not too long, so basically if this times one over h, this combination here, which is a dimensionless parameter, if it's smaller than one, then these coefficients don't have the time to grow. So basically this means that you can describe your system only with the first two coefficients or the first two, the lower moments of the distribution function, which means that you can have a fluid description. This is the reason why dark matter is described as a fluid, not because it's an interacting medium close to thermal equilibrium with small deviations from equilibrium, it's because the particles have small velocity and there's a finite age of the universe. So you can estimate what the typical, with the maximal velocity of these particles is, I won't go into the details, you can ask me if you want for the justification, but basically what you find out is that the typical velocity is the velocity of dark matter particles at scales of order of a few megaparsecs. So these are the typical rotation of velocities in galaxies, okay, which actually you can estimate that they're related to this scale Km, which I took to be around one megaparsec, times h, the couple parameter, and today times a function which is a linear growth factor, this is a function that tells you how perturbations grow with time. So it's this combination that gives you the typical maximal velocity of dark matter. Actually, here I'm neglecting any velocity that comes from early times, from the primordial times, I assume that after freeze out of the dark matter particles when the velocity red shifts to almost zero and then they pick up velocity again when structure starts forming and then things start moving around because of the potentials that develop at late times. And then the typical velocity is given by something like this. So if you put this into this expression here, what you find is that a hydrodynamic description is possible for K, which is larger than this scale Km, sorry, if K is larger than Km over this growth factor, which is one today and it's smaller than one at early times, for K larger than this combination, you cannot neglect this higher coefficients in this expansion, I showed you before, higher moments of the distribution function have to be included. So you need the whole Boltzmann hierarchy to describe the system. So a fluid description is impossible. This tells you that short scales don't have a hydrodynamic description. At some point, this breaks down. But still, long scales do have a hydrodynamic description. And this is what's of interest. So basically that pushes you to the idea, integrate out the part you don't really understand very well and use an effective description at low energies or large length scales. Now, so this is a justification for using a fluid description for dark matter. Now, one consequence of this is since there is typical velocity, maximal velocity, and there's a typical time scale as well, which is the age of the universe, you can estimate the typical shear viscosity or viscosity that you could expect for the system.  And since the mean free path is the velocity of this particles times the time, one over age, you can estimate what's the typical kinematic velocity you expect for this fluid now. And you find something which looks like this. It's a squared over Km squared times this growth factor squared. Now, this ratio H over K is awarded 10 to the minus three. So squared is around 10 to the minus six. And this growth factor is one today and smaller than one as you go back in time. So basically this means that this viscosity that you have to attribute to this fluid is tiny and it's time dependent. On the other hand, as you will see, it's important that you include it in order to get a consistent description. Okay, now I will not discuss fundamental viscosity for a lot of time. So I will just move on with... How much time do I have? Because we didn't start the time. 10 minutes only. Okay, so basically, okay. So I just want to give you the basic elements of this. Now, what you do in practice is you take the energy momentum tensor and you go beyond the perfect fluid description. You include shear viscosity and speed of sound, okay? So here's the shear tensor. You write down Einstein equations for the conservation of the energy momentum tensor. These are the fundamental equations. Your answer for the metric is the Friedman metric, the F and W metric with additional gravitational potentials. At the end of the day, what you find is evolution equations for the fields of the theory, the density perturbation of the velocity. Now, this graph here, what shows you is the linear spectrum and one and two loop corrections computed with standard perturbation theory. You can see that low K, at large length scales perturbation theory works, but as you go to large scales, these higher order corrections perturbation theory become comparable to linear, to the linear contribution and then dominate. So that's why perturbation theory breaks down completely. Now, okay, the essence of what I'm going to say is contained in this expression here. Basically, what you end up doing is the following. Here, you can see the one loop correction to the spectrum if you start with your dark matter being a perfect fluid. So this is the linear spectrum and this is the one loop correction. This goes like K squared with multiplied by a coefficient which is given by this parameter here. This is an integral over the linear spectrum, okay? And what you find then is that the one loop correction to the spectrum is something that goes like K squared and at large length scales is small, smaller than the linear spectrum. So this tells you that the effective description should include something that generates contributions which have a K squared in them. For example, if you look at the spectrum, what you find is that the one loop correction that you would compute instead of perturbation theory would have a coefficient, would have a factor K squared times this integral here, a parameter with this integral here, okay? Times the linear spectrum, times a matrix. Well, this is just details. So basically what this teaches you is that what you, this integrate, see now what it will generate for the low energy theory is something that will have a K squared in it. Now, if you want to translate that into an effective coupling for the low energy theory, this would correspond to terms in the energy momentum tensor which have two derivatives because two derivatives will give you a K squared. These are exactly speed of sound and viscosity terms that you have to include into your energy momentum tensor. And what you have to do is to map this one loop correction to an effective coupling related to shear viscosity and speed of sound. Now, the details of how to do that, okay? First of all, since you want to integrate only the UV, starting from the lesson from the Wilsonian approach to the RG, what you know is that you have to integrate out only modes above the scale Km, above which you do the coarse-graining up to infinity and this is what will go into an effective coupling of the low energy theory into some shear viscosity for the low energy theory. So basically it's this kind of combination that determines the shear viscosity. Now, I don't have the time to go through all the details. You assume that you have a speed of sound which goes like this factor H squared of K squared that we said before. This is the typical scale that you expect times a coefficient which is time dependent. Same thing for the kinematic viscosity and then you want to determine these coefficients here by doing this exercise. Computing one loop corrections and mapping them onto three level contributions from a low energy description that includes shear viscosity and speed of sound. Now, okay, there are lots of details that I mean just to give you an idea of what the general setup looks like. You know, these are the equations for a fluid with speed of sound and non-zero shear viscosity in a cosmological context. You can make them prettier by defining, where is it? Okay, here, you're going to free a space so you have this. So these terms are the linear contribution but then you can see non-linear terms which you can treat as interactions, these bit as here and so on which include products of the fields. You can make it even prettier by defining a doublet of fields. This is a density field and this is the velocity field and this is the evolution equation that takes this form here and you can see the linear part and you can see the interacting part. The linear part includes a contribution proportional to k squared from the viscosity so this is the most general description and the question is how you compute this couplings here. The first naive thing that you can do is by doing this matching that I showed you before. Compute some physical quantity. For example, I showed you the spectrum but let's look at the propagator. The propagator is the derivative of some field at time eta with respect to the value of the field at time eta prime. You can compute that within perturbation theory for a perfect fluid and you find the linear propagator here plus a one look correction that goes like k squared. Here in this coefficient sigma d that I told you before, this integral that I showed you before. Now you can do something else. You can compute the propagator for a viscous theory. So here is viscosity. It also allows speed of sound. With a viscosity and speed of sound that go like k squared over k m squared. This is the relevant ratio that I expect times a coefficient which goes this alpha that I wrote before. Now this alpha was time dependent. Here I make an answer that it depends as e to the two eta is time, let's say, very roughly. And this effective three level or linear description here results in a propagator which is the linear propagator of the perfect fluid theory plus corrections which come from these terms here and now because the fluid is imperfect. And I can calculate the correction to the propagator now which depends on viscosity and speed of sound has some time dependence and some matrix. And then what I want to do is to map this one loop contribution for the perfect fluid theory with the momentum integral starting from k m to infinity with the three level contribution arising from these new couplings that I'm including the low energy theory. So this is the trick. And this fixes these couplings. Actually I can express, you can see these betas which are the velocity and speed of sound with respect to the sigma square, this integral that I showed you before that I can compute from perturbation theory. So this is the trick. And these are the results. Basically what you want to compute is this spectrum that I showed you before that has these little waves on it. These are the baryon acoustic oscillations. Now what the red line here is the result of the end body simulation of a Monte Carlo simulation. And this is the prediction of this core screen in business where this is a linear contribution in the effect of low energy theory when on zero viscosity determined through the recipe that I described before. This is a one loop correction. Now I'm doing a loop expansion, a perturbative expansion in the low energy theory. So basically here's a linear correction. Here is the one loop and this is the two loop result. All these are computed now with a cutoff of, UV cutoff of order KM because this is what I have to require for consistency. And you can see that I get very good agreement up to some K's of order 0.2. And I can go to earlier times higher edges, the persistence, the agreement gets better because the system is more linear as I go back in time. And here I put everything together and you can see that even this KM that I've introduced to do the calculation, which is an artificial scaling. I've chosen it arbitrarily. I can vary it within a certain range and the results of the two loop calculation do not vary very much up to 0.2. So basically this says that there is a independence on the choice of that scale, which is exactly what I want because this is not a real physical scale that I want in the system. And I get good agreement within body simulations and scheme independence if you want. The independence on this cutoff scale is the intermediate cutoff scale that I want to use. So this works as opposed to what you would find in perturbation theory, in standard perturbation theory in which I wouldn't do this course gradient business. And there I would find that higher orders fell miserably. Here what is the spectrum normalized to the end body spectrum. And this would be the linear spectrum. This would be the one loop. And these lines here would be the two loop. Now I'm imposing artificial UV cutoffs in perturbation theory in order to cut off the region where I know that it fails completely. And then what I find is very strong dependence on this artificial cutoff that I put in. And higher orders which deviate a lot and dominate the lower order. So basically standard perturbation theory fails. So this is a well-known problem with cosmological perturbation theory for the system. And you can see that what I showed you before corrects this, you know, there's good convergence. Okay. Now, okay. Why am I giving this talk in energy conference? The reason is that there is a way you can give a functional representation of this problem and improve it by using energy techniques very briefly just to mention what you do. Yeah, the questions we're trying to solve I put them in this form here with this five in the field, the two component field with density perturbations and velocity perturbations. This was the linear thing and these were the interactions, right?  You know, the spectrum that came from inflation is the stochastic spectrum and you have to put this into your calculation and then calculate correlation, spectrum, whatever you want. Now, the way to do that, it's standard in contest matter, you know, and you can describe something very similar to this. Basically, what you do is you introduce an auxiliary field, chi, and you can see that this couples to the initial spectrum. So this is what carries information about the stochastic nature of the initial conditions. And then the equation of motion, okay? You can sandwich it between chi and phi. You'll feel this new field that you introduce in phi. You can introduce sources and define a partition function like this. And this partition function describes your system from this. You can extract all the information you want about correlations in the system. Now, you can define the generating function of the connected Grinch functions. You can take derivatives with respect to the sources and this gives you back the spectra. This is what you want. And the propagators, this G is the propagator in this theory. You can do a Lausanne transform and define effective action again, now functional derivatives with respect to the fields again give you the inverse retarded propagator or another object which is related to the spectrum. You can derive renormalized field equations by very, by extremizing this effective action. And this give you, for vanishing sources, this give you improved effective equations. So it's not just the standard hydrodynamic equations you started with, this give you extra corrections.  So you only allow the high scales. Then your effective action now becomes scale dependent. It's described by an exacter G equation of the verteric type. You can do exactly what you do in standard FRG, you can use an ansatz, and you can try to solve this functional differential equation for the objects that appear now in this ansatz, for example, this H here, or the inverse propagator, and so on. Basically, I don't have the type because I've run out of time, so I'll just leave it here. Basically what happens is that this procedure here, this RG improvement of this intuitive calculation that I showed you in the beginning, it justifies what I showed you before. At one loop, what it tells you is that these parameters which I estimated very coarsely in the beginning by just matching the one loop corrections coming from the UV to the effective couplings of the low energy theory can be reproduced through this technique. I can even enlarge my ansatz and allow for a more general form of the viscosity and speed of sound, it's time dependence and scale dependence, and what I find is things like that, so basically these are various functions that appear in the parametrization of the effective terms. You can ask later if you want about exactly what they are, we can look back or look at the transparencies. Basically, this dotted thing is the one loop reumization group calculation in this truncated, with this truncated ansatz and with certain projection prescriptions in order to get the scale evolution of this parameter. So for example, just to give you an idea, this kappa here is something that determines the time evolution of the viscosity and so on. The viscosity of asunda, it goes like e to the kappa eta before I took kappa to b2 and you can see that the RG calculation gives me something which as I integrate things down, it converges to k equals two. There is a focus in behavior, so initial conditions at the high scale don't seem to matter much. I get something like an infrared fixed point. It's not really an infrared fixed point, but I get focus in behavior at low scales. So this gives you a description which is not very sensitive to the UV, to the details of the part that I integrate out. And the more important thing is that it matches pretty well results from n body simulations, from completely independent calculations. So I'll just flash the conclusions and I'll just leave them for you. As I said, you have to introduce bulk and shear viscosities in the effective description of dark matter, which come from the integration of the UV. Now this I didn't discuss at all, so let's skip it. Standard basal theory cannot describe reliably the short distance cosmological perturbations. It is possible to integrate out the short distance modes in order to obtain an effective description of the long distance modes. So in this effective description, you have to allow for non-zero speed of sound and discuss it in dark matter, even though this is not conventional. You know exactly, you can predict exactly the form, they're tiny, time dependent, but they're crucial for doing the calculation in the non-linear spectrum computed through this effective theory, is in good agreement with the results from n body simulation. While perturbation theory fails standard perturbation theory, but perturbation theory within this scheme seems to converge quickly for the effective theory if this UV cutoff is taken in this range here. These are the results that I showed you before. Okay, thank you. Stop here.